JPRS ID: 9756 WORLDWIDE REPORT NARCOTICS AND DANGEROUS DRUGS

• Document Type: CREST
• Collection: JPRS
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00850R000400050052-5
• Release Decision: RIF
• Original Classification: U
• Document Page Count: 147
• Document Creation Date: November 1, 2016
• Sequence Number: 52
• Content Type: REPORTS

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
FOR OFFICIAL USE ONLY
JPRS L/ 10002
22 September 1981
USSR Re ort
p
PHYSICS AND MATHEMATICS
(FOUO 8/81)
i]
FSIS FOREIGN BROADCAST INFORMATION SERV~CE
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
NOTE
- JPRS publications contain information primarily from foreign
newspapers, periodicals and books, but also from news agency
transmissions and broadcasts. Materials from foreign-language
sources are translated; those from English-language sources
are transcribed nr reprinted, with the original phrasing and
other characteristics retained.
Headlines, editorial reports, and material enclosed in brackets
[J are supplied by JPRS. Processing indicators such as [Text]
or [Excerpt] in the fir~t line of each item, or following the
Iast line of a brief, indicate how the original information was
proc~essed. Where no processing indicator is given, the infor-
mation was summarized or extracted.
- Unfaa~iliar names rendered phonetically or transliterated are
enclosed in parentheses. Words or names preceded by a ques-
tion mark and enclosed in parentheses were not clear in the
original out have been supplied as appropriate in context.
Other unattributed parenthetical r.otes within the body of an
item originate with the source. Times within items are as
given by source.
The contents of this publication in no way represent the poli-
_ cies, views or attitudes of the U.S. Government.
COPYRIGHT LAWS AND REGULATIONS GOVERNING OWNERSHIP OF
MATERIALS REPRODUCED HEREIN REQUIRE THAT DISSEMINATION
OF THIS PUBLICATION BE RESTR~ICTED FOR OFFICIAL USE O~ILY.
J
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICI.4L USE ONLY
JPRS L/10002
22 September 1981
USSR REPORT
PHYSICS AND MATHEMATICS
(FOUO 8/81)
CONTENTS
~ CRYSTALS AND SEMICONDUCTORS
- Lithium Todate: Crystal Growing, Properties and Applications..... 1
- LASERS AND MASERS
Electron Beam-Controlled Copper Vapor Laser 4
Physical Processes in Generators of Coherent Optical Radiation.... 7
Optical Resonators and the Problem of Laser Emission Divergence... 15
NUCLEAR PI~iYSICS
Linear Induction Accelerator s....~ 116
Intense Steady-State Electron Beams: Extraction Into the
Atmosphere and Investigation 124
OPTOELECTRONICS
Radio Holography and Optical Data Processing in Microwave
Technology 1'36
Three Channel Electro-Optical Waveguide Commutator 142
- a- [III - USSR - 21.H S&T FOUO]
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
FOR OFFICIAL USE ONLY
CRYSTALS AND SEMICONDUCTORS
UDC 548.5+537.311.33
- LITHIUM IODATE: CRYSTAI~ GROWING, PROPERTIES AND APPLICATIONS
Novosibirsk IODAT LITIYA: VYRASHCHIVANIYE KRISTALLOV, IKH SVOYSTVA I PRIMENENIYE
in Russian,1980 (signed to press 23 Oct 80) pp 2-5
[Annotation, preface and table of contents from book "Lithium Niobate: Crystal
Growin~, Properties and Applications" by Klavdiya I1'inichna Avdiyenko, Sergey
Vasil'yevich Bogdanov (general editor), Stanislav Mikhaylovich Arkhipov, Boris
Ivanovich Kidyarov, Viictor Vasil`yevich Lebedev, Yuriy Yevgenevich i~levskiy, Vladimir
Ivanovich Trunov, I?mitriy Vasil'yevich Sheloput and Rozaliya Mikhaylovna Shklonskaya,
' Institute ~f Physics of Semiconductors, Siberian Department of the USSR Academy of
S~~iences, Izdatel'stvo "Nauka", 1200 copies, 125+ pages]
[Text] Data are given on the physicochemical properties of lithium iodate, and
the technique for growin~ crystals in the hexagonal modification. Results are
given from studies of t:he actual strticture and defects of crystals, the inf luence
of various factors on Lheir optical, giezoelectric and other physical properties,
gen~ration of the seconrl harmonic of laser emission and parametric contrersion of
- infrared images to the visible range. An examination is made of the application
a of lithium iodate crystals in devices of nonlinear optics, acousto-optic~ and
acousto-electronics.
For scientists and engineers engaged in growing and using crystals in applied
physics, and also for undergraduate and graduate students. Figures 61, tables 28,
references 190.
Preface
Among the large number of piezoelectric and nonlinear optics crystals of halogenate ~
compoun.ds with physical properties under intense study in recent years, the most
widely used in applied physics have been crystals of hexagonal modification of
lithium iodate (a-LiI03).
The properties of lithium iodate crystals were first described in 1969 by (Nat) and
(Hauszyul'). Practical interest in these crystals stems from the fact that their
effective nonlinear optical coefficients are comparable to those of lithium niobate,
and at the same time, lithium iodate presents no problems involving optically in- '
duced inhomogeneities, which are a severe restriction in the ~.:~e of lithium niobate.
Therefore, lithium iodate crystals are used as effective laser radiation frequency
doublers in intracavity generation of the second harmonic. In particular, the
1
� FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
second harmonic of the yttrium-aluminum garnet laser used to pump the first indus-
trial light generator was stimulated in a lithium iodate crystal. This material
was chosen because of its resistance to optical radiation. In subsequent years
a great deal of research was done on detailed investigation of different physical
properties of lithium iodate crystals, and their extensive possibilities were noted
f.or practical application in laser physics, acousto-electronics and acousto-optics
as a piezoel.ectric and nonlinear optical material.
The use of such materials, that have a high conversion efficiency and a wide relative
transmission passband, considerably improves the working characteristics and ap-
preciably expands the frequency range of various optical, acousto-electronic and
acousto-optical devices, for example for delaying and processing radio signals,
- modulators, laser emission deflectors.
This book attempts a systematic exposition of the set of problems relating to crys-
tal growing, investigation of physical properties and the use of lithium iodate
crystals in devices of nonlinear optics, acot~sto-optics and acoustoelectronics.
In the description of physicochemical properties, and primarily optical and piezo-
electric properties, attention is turned to their connection with production tech-
niques, purity of the initial materials, specially introduced dopants and structural
perfection. In addition to analysis of Soviet and non-Soviet research dealing
with lithium iodate, the main part of the book presents mater~als of original re-
search done by the authors from 1970 through 1978.
We hope that th.is publication will stimulate the investigation of other interesting
properties of lithium iodate crystals, and will promote more extensive use and
development of new technical devices in applied physics and their introduction
in the national economy.
The book was written by researchers at the Institute of Physics of Semiconductors
of the Siberian Department of the USSR Academy of Scie~ces K. I. Avdiyenko., (chapters
I and IV), S. V. Bogdanov (chapter III), B. I. Kidyarov (preface, conclusi.on, chap-
ter II), V. V. Lebedev (chaprpr V), Yu. Ye. Nevskiy (chapter VI), V. I. Trunov
(chapter V), D. V. Sheloput (preface, chapter VI), and researchers at Novosibirsk
Rare Metals Plant S. M. Arkhipov and R. M. Shklovskaya (chapter I). The authors
thank their calleagues in the work for useful advice and technical assistance in
_ preparatior~ of the manuscript. Critical comments should be addressed to: 630090,
Novosibirsk, 90, pr. Nauki, 13, Institut fiziki polu~rovodnikcv SO AN SSSR, kand.
fiz.-mat. nauk K. I. Avdiyenk~.
Contents p~ge
Preface 4
Chapter I. Physicochemical properties of lithium iodate 6
l. Crystalline structure
2. Phase diagrams and thermodynamic properties 12 . .
3. Production of lithium iodate 17
Chapter II. Growing lithium iodate crystals 20
1. Crystallization of lithiun~ iodate from melts, and phase trans- _
- formations a- S - y-LiI03
2. Investigation of principles governing crystallization and growth
of lithium iodate crystals from an aqueous solution 24
~
~
~OR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAI. USE ONLY
Chapter III. Electric, dielectric, piezoelectric and acoustic properties
of lithium iodate crystals 34
1. Description of physical properties of hexagonal crystals -
2. Specif ic electrical conductivity 39
3. Permittivity 42
4. Piezoelectric properties of a-LiI03 ~ 48
- 5. Acoustic properties of a-LiI03 crystals 53
- Chapter IV. Defects in lithium iodate crystals and their effect on physical
properties 62
1. Inhomogeneities in a-LiI03 crystals -
2. Optical properties of a-LiI03 crystals and their dependence on con-
ditions of growth 76
3. Piezoelectric properties of lithium iodate crystals as dependent on
- growing conditions 76
Chapter V. Nonlinear-optics properties of lithium iodate 80
. 1. General concepts -
_ 2. Nonlinear-cptics susceptibi.lities in an a-LiI03 crystal 81
3. Stimulated emission of second optical harmonics in an a-LiI03 crystal 84
4. Parametric conversion of infrared radiation to the visib band 89
5. Angular and spectral characteristics of parametric conversion of
infrared images 91
6. Infrared image conversion in a critical vector synchronism (CVS)
system 96
Chapter VI. Use of lithium iodate crystals in acousto-optics and acousto-.
electronics devices 101
1. Ultrasonic converter based on lithium iodate plates 102
2. Ultrasonic delay lines based on a-LiI03 plates 115
3. Acousto-optical devices based on a-LiI03 single crystals 117
Conclusion 121
References 123
COPYRIGHT: Izdatel'stvo "Nauka", 1980.
6610
CSG: 1862/186
- 3
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
LASERS AND MASERS
i
ELECTRON BEAM-CUNTROLL~D COPPER VAPOR LASEK
Leningrad FIS'MA V ZHURNAL TEKHNICHESKOY FIZIKI in Russian Vol 7, No 7, 12 Apr 81
(signed to press 18 Mar 81) pp 427-430
[Article by I. M. Isakov, A. G. Leonov and A. N. Starostin, Moscow Physicotechnical
Institute]
[Text] The independent var~_ation of field strength and electron concentration
required for optimum conditions of gas laser operation is impossible in a self-
maintained discharge. The use of an electron beam-controlled discharge is more
convenient in this sense. In this case, the field strength will now be determined
by the electron concentration set up by the time the discharge is activated by
the electron beam (or more precisely by the ratio between the resistance of the
3ischarge gap and the internal resistance of the excitation oscillator) racher
than by the conditions of breakdown. Such experiments have been extensively done
for example in the init~ation of excimer lasers. We have been the first to use
a method of this kind for excitation of a laser based on dense copper vapor.
g ~ Fig. 1. Diagram of the in-
stallation: 1--electric
- discharge generator; 2--ex-
ploding wire generator; 3--
2 5 ~ voltage pulse generator; 4--
- laser chamber; 5--exploding
conductor; 6--vacuum diode;
8 6 y 7--grid electrode; 8--sepa-
3 rative film; 9--output window
Copper vapor with density of (1-3)�1018 cm 3 was produced in our experiments by
the method of electrical explosion of conductors [Ref. 3]. A diagram of the in-
stallation is shown in Fig. 1. The electron source in our experiments was a vacuum
diode with cold cathode fed by a 12-stage Marx generator with output capacitance
of 0.83 nF. The generator was based on K15-10 ceraniic capacitors, and was placed
together with the divider and dischargers in a cylindrical jacket filled with nitro-
gen under a pressure of 4-8 atmospheres.
A beam of electrons with energy of 100-300 keV and current density of 10-20 A/cm'`
was coupled into the chamber through a window measuring 4 x 21 cm covered with Mylar
4
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400054452-5
_ FOR OFFICiAL USE ONLY
" film 25 um thick. The absence of any part subject to heating in the installation
enables the use of ordinary sealing of the separative film. Beam current duration
was 100 r.s. The current density and pulse shape were measured by using an elec-
tron collector with signal recorded by the I2-7 nanosecond meter. The beam energy
beyond the output window was measured by the method of foils. Beam homogeneity
and divergence were monitored from the glow of a UFD-89 luminescent x-ray screen.
The discharge was excited by a Blumlein generator based on ~triplines with total
capacity of 13.5 nF inade from foil-covered glass Textolite 1 mm thick. Interelec-
trode distance was 10 cm.
Excitation by electron beam, electric discharge and a combined method were studied
separately in our work. In all cases the delay between explosion of the condu%:tor
and the excitation pulse was 600 us.
In the first version, the cavity used in the research was formed by flat dielectric
mirrors with ref:iectivities R~ 99% and 67% on a wavelength of 5105 A. Lasing energy
was 11 ~;J for copper vapor density of 3�1018 cm 3. The reason for such low lasing
energy was due to the fact that the laser in all probability was working in near-
threshold conditions. This is clearly evident from the dependence of lasing energy
on vapor density and reflectivity of the output mirror (Fig. 2a). A situation
of this kind is due to the small energy contribution of the beam to the active
medium. According to estimates [see for example Ref. 2], the amount of~this contri-
bution is ~400 uJ/cm3 at a yapor density of 3�lO1e cm 3.
- 90
2 a b
~
~ 5 j ~ 15
90 I
~ 5 Il
ZO 60 900 ~0 20 30 40
R, % t, ns
Fig. 2. Lasing energy as a function of output mirror re-
flectivity: 1--N = 1018 cm 3; 2--N = 3�101B cm 3; b--
~ oscillograms of voltage across the discharge without beam
action (I), and with the beam (II)
Upon excitation by an electric discharge the maximum lasing energy was considerably
higher and amounted to E= S mJ at a charging voltage of 25 kV. The output mirror
was a quartz plate without any coating. Increasing the reflectivity in this case
only reduced the lasing energy. Laser pulse duration was 20 ns.
Upon a transition to combined excitationthe energy of the laser pulse increased
to 10 mJ despite the fact that the beam energy absorbed by the copper vapor was
much less than the energy contribution from the discharge (~2 Lasing duration
also increased to 30 ns. Let us note that the discharge pulse was delayed relative
to the beam current by T= 60-80 ns.
5
FOR OFF[CIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2407/02/09: CIA-RDP82-00850R000400450052-5
a FOR OFFICIAL USE ONLY
An investigation of the current-voltage characteristics of the discharge shara+ed
that the pulse shape of the discharge current and of the voltage across the dis-
r_harge Z;ap changes with a transition to the combined method (Fig. 2b). Just as
was assumed, there was a considerable reduction in the amplitude of the voitage
across the discharge sinc:e the medium already had considerable conductivity by
the time of arrival of the exciting pulse. According to estimates [Ref. 2] the
electron concentration at beam parameters of Ub = 200 keV and jb = 20 A/~m~' may reach
3�1013 cm 3 at N= 1018 cm 3. It has been pointed out previously [Ref. 3,1 that
in the case of short-pulse excitation of copper vapor lasers using a Blumlein line,
the high voltage across the discharge o~p at the instant of the main energy contri-
bution reduces lasing efficiency. On the other hand, a reduction in the voltage
across the discharge makes for more optimum conditio~ns of inversion fo~mation.
Let us note that although laser efficiency was doubled over the case ~of pure dis-
charge excitat:ion, the actual gain is even greater since lasing eff~cienry with
- respect to the energy investment in copper vapor was tripled due to a reduction
in efficiency of energy transfer to the discharge by a factor of 1.'~. Based on
measurement results we can conclude that ~he proposed excitation arrangement may
be quite useful for large volumes of copper vapor or high-density vapor. The vapor
density in our experiments was limited by the energy s~orage of th~ explosive capaci-
tor bank.
~ In conclusion, the authors express their sincere gratitu~de to I. ~Brchka and
" A. N. Steklov for assisting with the experiments.
REFERENCES
1. I. M. Isakov, A. G. Leonov, ZHURNAL TEKHNICHESKOY FIZIKI, Vol 50, 1980, p 126.
2. V. A. Danilychev, 0. M. Kerimov, I. B. Kovsh, TRUDY FIAN, Vol 83, p 147.
3. I. M. Isakov, A. G. Leonov, "Tezisy dokladov na Vtorom Vses,oyuznom seminare
po fizike gazovykh lazerov" [Abstracts of Papers to t~e Second All-Union
Seminar on Physics of Gas Lasers], Uzhgorod, 1978, p 65.
COPYRIGHT: Izdatel'stvo "Nauka", "Pis'ma v Zhurnal tekhnicheskoy fiziki", 1981
6610
CSO: 1862/196
6
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
FOR OFFICIAL USE ONLY
UDC 621.378.001
PHYSICAL PROCES~:ES IN GENERATOR~ OF COHERENT OPTICAL RADIATION
Moscow FIZIKA PROTSESSOV V GENERATORAKH KOGERENTNOGO OPTICHESKOGO IZLUCHENIYA in
Russian 1981 (signed to ~ress 12 Aug 80) pp 2-5, 434-439
[Annotation, preface and table of contents from book "Physics of Processes in Gener-
ators of Coherent Optical Radiation: Lasers, Resonators, Dynamics of Processes",
by Candidate of Physical and Mathematical Sciences Lev Vasil'yevich Tarasov, docent,
Moscow Institute of Electronic Machine Building, Izdatel'stvo "Radio i svyaz
4000 copies, 440 pagesJ
~Text] The book deals with the physics of processes in lasers. Three groups of
problems are considered: methods of producing inverted active media, formation
of the radiation field in the resonator, and the dyna~ics of processes in lasers.
The choice of material reflects the current level of development of laser tech-
nology. A systematic examination is made of inethods used in the theory of lasers,
various approaches and approximations.
The book is intended for scientists and engineers working in the field of laser
technology, and also for instruc`ors and students in institutions of higher edu-
cation. Figures 224, Tables 14, References 295.
Preface
Generators of coherent optical radiation include two groups of devices. The ma.in
_ group is lasers. The second group includes generators of optical harmonics, para-
metric light generators and so on. Thi~ book is devoted to the physics of processes
in lasers.*
The writing of a book that reflects the current level of laser technology from
a physical standpoint is topical in view of the fact that lasers are being more
and more extensively used both in research and in different areas of the national
economy. There is a continuous rise in the number of engineers and researchers
engaged in the field of laser technology and related areas.
It has been the author's intention for this book to handle two jobs: first, to
systematize and expand the reader's notions of the physics of processes in lasers,
*Generators of optical harmonics and parametric light generators will be the
subject of another book by this author.
7
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
FOR OFFICIAL USE ONLY
to acquaint the reader with the latest advances and directions; secondly, ~o pr~-
vide the reader with. information that might be of help in improuing the facility
for future use of the special literature. The author has tried to relEl~ect the
cu~~ent level of development of laser technology, and at the same time to proviele
- a systematized examination of inethods used in the the~ry of lasers, ta discuss
different approaches and approximations. In doing so, the authar ha,s atten~te-d
to produce a book that would be not only of definite interest to sci~n~ists and
engineers, but might also serve as a scientific and procedural basis for ~deueloping
special academic courses and textbooks.
The book examines three groups of problems: methods of producing im~erted active
media, formation of the radiation field in the optical cavity, and the dynamics
of processes.
~ In examining methods of producing inversion in active media, t~e first chapter
discusses the principles and peculiarities of operation of laser~ uf eiifferent
types� solid-state, dye, photodissociation, gas-discharge, e~.~c~ron~beam controlled,
gasdyramic, chemical and plasma lasers.
The second chapter analyzes the role of the resonator ~xi f~ormatimn of the radia-
tion field of the laser, gives the fundamentals of the tk?eorx ot onen resonators.
The author uses the geometric optics approximation, tk?e FGx-Li iteratton method, ~
the gaussian beam model, the ABCD law. Consideraticati ~s taken of the apertures j
of mirrors, the presence of a lens or diaphragm witlain t~e ca~vity, misalignment
of components in the resonator. Cavities of different geom~tries--both stable
and unstable--are examined. In the case of active resonators the author discusses
effects of the heat lens, frequency pulling and "hole burning." Consideration
is given to problems of longitudinal mode selection and a~lso to the physics of
waveguide resonators and film ~asers with distrib~?ted feedback.
The third chapter begins with a survey of different modes of stimulated emission
of the laser, including modes of active and pass~ve Q-switching of the cavity,
longitudinal and transverse mode locking, load modulation. Balance equations
(Statz-de Mars equations and their modifi~ations) are intro~iuced, analyzed and
put to extensive use. These euqations are used as a basis for examining different
aspects of the dynamics of single-mode lasers: transient processes,that lead to
damped emission power pulsations; undamped power pulsations that show up in the
presence of weak modulation of losses, generation of giant pulses with instantaneous
Q-switching. The electro-optic and acousto-optic methods of active Q-switching
are compared. A detailed analysis is made of processes in lasers with phatotr~pic
filters. Longi.tudinal mode locking is discussed with the use of both spectral
and temporal approaches. A temporal description based on fluctuational concepts
is used in consider~.ng self-mode locking in a laser with phototropic filter. The
temporal approach is also used to describe acousto-optic mode locking in a laser
with uniformly broadened amplification line. Methods of studying ultrashort light
pulses are discussed separately. The appendices examine Hermite polynomials, Jones
matrices, singular points of a two-dimenional dynamic system and other questions.
This book is a logical continuation of the author's previous work "Fizicheskiye
osnovy kvantovoy elektroniki" [Physical Principles of Quantum Electronics] (Moscow,
Sovetskoye radio, 1976), giving the general physical picture of the interaction
of optical radiation with matter.
8
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
_ The author is sincerely grateful to V. G. Dmitriyev, V. R. K:ushnir, V. K. Novo-
kreshchenov, Ye. A. Shalayev, V. N. Morozov, V. A. D'yaico:~, V. V. Nikitin, Yu. N.
Pchel'nikov, A. M. Amel'yants, A. A. Solov'yev and V. F. Trukhin, who read the
manuscript of the book and offered constructive comments and wishes. The author
thanks A. N. Tarasova for assistance in preparing the manuscript for nrinting.
Contents page
Preface 3
Chapter 1: METHOBS OF OBTAINING INVERTED ACTIVE MEDIA
1.1. Some General Problems ~
Inversion of the active medium as a necessary condition of lasing (7). Quantum
yield and efficiency of the laser (8). Condition of inversion for the four-level
model (10). ~eneral nrinciples of creating inversion (11). Mechanisms of popu-
lation of levels (12). Mechanisms of dzpopulation of levels (13). Classification
of lasers with regard to pumping methods (15). Some problems that arise in cor.-
tinuous lasing; collisional lasers (15). Advantages of pulse pumping; lasing on
self-limited transitions (18). Lasers based on dissociating molecules (20).
T.2. Optical Pu~r,ping. Solid-State Lasers 21
- Specific properties of optical pumping (21). Conditions uf realization of steady-
state inversion in optical pumping (23). Solid-state lasers; problems of realiza-
tion of optical pumping, working laser designs (26). The ruby laser (28). YAG:Nd
laser (30). Optical pumping by semiconductor laser or LED (33).
1.3. Organic Dye Lasers 34
" Organic dyes (~4). ~Dptical pumping of dye lasers (36). Scheme of levels and main
transitions (37). Tuning lasing wavelength; selective cavities (38). The problem
of expanding the tuning range of lasing wavelength (40).
1.4. Gas Lasers with Wide-Band Optical Pumping 41
The problem of optica? pumping of gaseous active media (41). Photolysis lasers
(42). The iodine photolysis laser (43). The problem of direct conversion of solar
- energy to laser emission (44).
1.5. Pumping by Self-Maintained Electric Discharge in Rarefied Gases 44
Types oF gas-discharge lasers (44). Electric discharges used in gas-discharge
= lasers (46). The argon laser (47). Mechanism of inversion in the argon laser
(48). The helium-neon laser (51). The copper-vapor laser (52). Carbon dioxide
molecular laser (53). Inversion mechanism in the C02 laser (54).
1.6. Electron-Beam Controlled Lasers S~
- The problem of increasing pressure in the gas laser (57). The electroionization
pumping method (58). Electron-beam controlled C02 laser (6Q). Use of different
active media (60). Ionization methods (61).
1.7. Gas-Dynamic Lasers (Thermal Pumping) 62
Thermal methods of creating inversion (62). Gas-dynamic GG2 laser (64). Inversion
mechanism in the gas-dynamic C02 laser (64). Ways to improve the efficiency of
_ gas-dynamic lasers (67).
- 9
FOR OFFICIAL USE OP4LY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
FOR OFFICIAL USE ONLY
- 1.8. Chemical Lasers 68
Chemical reactions; initiation and accelerat_un of reactions (68). Chemical and
laser length of a chain (70). Lasers with :?irect and indirect formation of in-
version (72). ChemicaJ. laser based on a fluorine-hydrogen mixture (73). Hydrogen
sulfide chemical lasers (74). Chemical lasers based on electronic transitions of
molecules (75).
~ 1.9. Plasma Lasers (Recombination Pumping) 75
Recombining plasma as an active laser medium (75). Fundamental problems of creat-
ing a recombining plasma laser (77). The "open" two-level model of a plasma laser
(78). The problem uf depopulating the lower working level (79). Pulsed plasma lasers
(81). Plasma lasers using rigid ionizers; the reactor-laser (82). Plasmadynamic
lasers (83). Plasmachemical lasers (84).
References 85
Chapter 2: FORMATION OF THE RADIATION FIELD IN THE LASER CAVITY
2.1. Condition of Stimulated Emi;~ion 90
Necessity of increasing the initial gain over the coeff icient of losses (90).
Initial gain for optically allowed and forbidden transitions (93). Dependence of ,
initial gain on pumping rate (94). Frequency dependence (96). '
_ 2.2. The Optical Cavity and Laser Radiation 97 ~
Optimum coefficient of useful losses (97). Resonant frequencies (99). Modes of
the optical cavity (101). The role of the optical cavity in the laser (103).
Passive and active cavities (109).
2.3. General Remarks on Open Resonators 109
Impossibility of using volumetric resonators in the optical range (109). The open
resonator (111). Cavity Q(112). Q due to transmission of the output mirror (114).
Q and modes of the open resonator (116). Diffraction losses; Fresnel number (116).
Major parameters of a passive resonator formed by two mirrors (119). The geometric
appro:cimation (120) .
2.4. Lens Waveguides and Open Resonators (Geometric Optics Approximation) 123
� The lens waveguide and the open re.onator (123). Condition of stability for the
lens waveguide (125). Stable and un~table open resonators; stability diagram (127).
Light beam transmission matrix (130). Light beam transmission matrix for a round
_ trip of the cavity (135) .
2.5. Detuning of the Open Resonator ~37
- Misalignment of optical component (137). Resonator with misaligned optical com-
ponent (139).
2.6. Analysais of Open Resonators Based on the Fox-Li Iteration Method.
Equivalent Resonators 141
Kirchhoff-Huygens diffraction integral (141). The Fox-Li integral equation (143).
Transverse modes of the open resonator (144). Resonator formed by two spherical
mirrors (145). Confocal resonator (149). Accounting for the aperture of cavity
mirrors (151). Equivalent resonators (154). Resonator equivalent to a cavity with
_ internal lens (155). Irised Cavity (159). .
10
FOR OFFIC[AL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02109: CIA-RDP82-00850R000400054052-5
FOR OFFICIAL L1SE ONI,Y
2.7. Gaussian Beams 162
Spatial form of the gaussian beam (162). Propagation of gaussian beam in free
space (164). Radius of curvature of a surface of constant phase (166). Principal
relations (169). Complex parameters of gaussian beam (168). Gaussian beam as a
solution of a parabolic equation (169). Generalization to modes of higher oz�ders
(170).
2.8. Transformation and Matching of Gaussian Beams ~ 171
Transformation of gaussian beam in free space (172). Lens as a phase corrector
(172). Transformation of gaussian beam in lens (173). Transformation in a lens
- system (175). ABCD law (175). Transformation of gaussian beam in square-law medium
- (178). Matching of gaussian beams (180j.
2.9. Gaussian Beams in Stable Resonators 182
Self-reproduction of gaussian beam upon reflection from a spherical mirror (182).
Gaussian beam in resonator (large mirror apertures) (183). Remarks on considera-
tion of the mirror aperture (186). Phase shift for the gaussian beam, and resonant
frequency spectrum (189). Application of the ABCD law to examination of the field
in the cavity (190). Indefiniteness of the caustic of a confocal resonator with
unbounded mirror apertures (192). Confocal resonator with finite mirror apertures
(194). Irised conf ocal resonator (195).
2.10. Unstable Resonators 197
Homocentricity of beam coupled out of an unstable resonator (197). Losses in an
_ unstable resonator according to the geometric optics theory (199). Application
of the ABCD law to unstable resonators (203). Accounting for diffraction on the
edge of a mirror (208). Advantages of unstable resonators (210).
2.11. Principles of r'requency Selection 212
Different types of f requency selection (213). Use of wide-band absorbing filters
and dispersion elements (214). General comments on longitudinal mode selection
(216). Interference methodsofselection (217). Resonators with anisotropic elements
_ (219). Nonlinear-optics method of frequency selection (221).
2.12. Effects of "Hole Burning" and Frequency Pulling 222
Homogeneous and inhomogeneous broadening of spectral lines (222). Saturation of
amplification in homogeneous and inhomogeneous broadening of lines; the "hole
burning" effect (224). Specifics of analysis of gain saturation with inhomogeneous
broadening of a transition line (227). Frequency pulling effect for cases of
homogeneous and inhomogeneous broadening (228).
2.13. Heat Lens 230
- Heat lens effect (230). Thermoelastic stresses; thermal distortions of a cavity
(232). Focal length and principal planes of the heat lens (234). Accounting for
the heat lens in laser systems (236).
2.14. Waveguide Resonators 238
Waveguide resonator; waveguide modes (238). Number of waveguide modes in a reso-
nator (240). Half-waveguide cavity (241). Advantages of waveguide resonators (242).
11
FOR OFF[CIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
FOR OFFICIAL USE ONLY
- 2.15. Optical Radiation in a Thin-Film Waveguide. Distribuced Feedback 244
~ Waveguide modes in a thin film (245). Number of waveguide modes in film (249).
Field distributioin in waveguide modes (249). Method of input and extracti~n oC
radiation for a thin-film waveguide (252). Operating principle of prism-film couplin~;
element (254). Distributed feedback (256). Distributed-feedback film lasers (257).
Film lasers with periodic structure as a cavity reflector (259).
References 259
Chapter 3: DYNAMICS OF PROCESSES IN THE LASER
3.1. General Information on Modes of Laser Operation 2h6
Causes of unsteady lasing (266). Free lasing mode (268). Mode of stimulated emis-
sion of ~iant pulses in active Q-switching of the cavity (270). Mode of stimulated
- emission of giant pulses in passive Q-switching of the cavity (273). Longitudinal
mode locking (275). Transverse mode locking (277). Cavity-dumped operation (279).
Generation of a pulse sequence in lasers with continuous pumping (281). Using
- negative feedback to produce microsecond pulses (283).
3.2. Approximate Equations for Describing the Dynamics of Processes in
Lasers (Balance Equations) 286
' Differential equation for luminous flux density (286). Differential equations for
inverse population density (287). Complete system of partial differential balance
equations (290). Averaged balance equations (rate equations) (291). Statz-de Mars
equations (293). Comparison of Statz-de Mars equations and the system of averaged
balance equations (295). Inverse population threshold density and the lasing con-
dition (297). Dimensionless form of recording Statz-de Mars equations (298).
Accouriting for the contribution of spontaneous emission to field intensity (299).
General remarks on the method of balance equations (300). The laser as a dis-
tributed self-oscillatory system (302).
3.3. The Free Lasing Mode. Regular Damped Pulsations of Radiation Power 304
Pre-l.asing stage (304). Transient processes that accompany the onset of lasing
(306). Phase portrait of a free-lasing solid-state laser (310). Determination of
the structure of the laser phase portrait (313). Analysis of pulsation pattern
based on balance equations (314). Remarks on free lasing in the multimode laser
(316) .
3.4. Laser with Unsteady Resonator. Undamped Pulsations of Radiation
Power 317
Balance equations for a laser with periodically varying Q of the cavity (317).
Low-amplitude pulsations (319). Comments on the feasibility of realization of un-
damped high-amplitude pulsations (321). Periodic Q-switching with uniform motion
of a reflecting plane (322). Periodic Q-switching upon heating of the active ele-
ment (323). Nature of undamped pulsations in the free lasing mode (324).
3.5. Active Q-Switching of the Cavity 325
Opticomechanical Q-switching (325). Electro-optical Q-switching (326). Acousto-
optical Q-switching (330). Acousto-optical and electro-optical Q-switching (com-
parison) (333). Modulation of useful losses (335).
12
FOR OFFIC[AL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFI('IAI. USE ONLY
3.6. Mode of Emission of Giant Pulses with Active Q-Switching 335
Principal time stages (335). Balance equations; instantaneous Q-switching (338).
Phase portrait of the laser in instantaneous Q-switching (339). Analysis of the
stage of linear development of lasing (342). Energy characteristics of the giant
pulse (343). Duration and shape of the gi.ant pulse (345). Mode of stimulated
emission of giant pulses for different Q-switching times (346). Comments on the
development of a pulse in the direction transverse to the cavity axis (349).
3.7. Lasers with Phototropic Filter 350
The phototropic filter (350). Differential equation for averaged luminous flux
density (353). Complete system of balance equations for laser with phototropic
filter (355). Steady-state solutions of the system of balance equations (357).
Instability of the initial steady state, and the condition of self-excitaticn of
generation in a laser with phot~tropic filte?� (359). Soft and hard excitation of
lasing (360). Stability (instability) of steady states in the case of soft excita-
.tion of lasing (362). Modes of stimulated emission of a laser with ~hototropic
filter (364).
3.8. Mode of Stimulated Emission of Giant Pulses with Passive Q-Switching 365
Conditions of stimulated emission of giant pulses in a laser with phototropic
filter (365). Development of the giant pulse (367). Balance equations; analogy
with the case of instantaneous Q-switching (369). Comparison of modes of [stimu-
lated emission of giant pulses in active and passive Q-switching;] combined Q-
switching (371). Natural selection of transv~:r~e modes in passive Q-switching (374).
3.9. Longitudinal Mode Locking (Gerieration of Ultrashort Light Pulses) 375
Essence of the idea of longitudinal mode locking (376). The non-selective cavity
(378). Active mode locking (380). Passive mode locking (self-mode locking) (381).
The combined method of mode locking (383). Methods of reducing the relaxation time
of phototropic filters (384). Influence of the effect of self-focusing of light (3$5).
3.10. Measuring the Duration of Ultrashort Pulses 387
Major directions in the development of inethods of studying pulse structure (387).
Method using generation of the second harmonic (388). The two-photon technique
(389). Complete and incomplete mode locking and the problem of time measurements
(391). Method based on measuring the structure of the signal spectrum (393).
3.11. Analysis of Longitudinal Sel.f-Mode Locking in a Laser with Photo-
tropic Filter Based on Fluctuational Concepts 394
Qualitative description of the physical picture (394). Spectral and temporal de-
scription of mode-locking (397). Initial profile of the radiation field (399).
- Index of nonlinearity (402). Transformation of the profile of the field when
radiation acts with the filter on the stage of pilototropism (402). Feasibility
of mode locking in the case of stimulated emission of the second harmonic (404).
Conditions ot complete self-mode locking (405).
3.12. Time Description of Active Longitudinal Mode Locking in a Laser with
Uniformly Broadened Amplification Line 406
Formulation of the problem; principal assumptions (406). Change in the light pulse
as it passes through the active element and the modulator (408). System of
13
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFiCIAL iJSE ONI.Y
differential equations describing the process of establishment of mode locking
(409). Comments on phase (electro-optic) and amnlitude (acousto-optic) mode syn-
chranizers (411).
References 413
_ Appendi.x 1. Hermite polynomials 42~
Appendix 2. Gaussian bea:~ in free space 426
Appendix 3. Stable an~ unstable spherical waves in the unstable cavity 427
Appendix 4. Jones matrices 4`$
Appendix 5. Singular points of a two-dimensional dynamic system 430
Subject index 432
- COPYRIGk'T: Izdatel'stvo "Radio i svyaz 1981
6610
CSO: 1862/216
14
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
FOIt OI~FICi:11. i.'�SF: O`I.1'
UDC 539.1
OPTICAL RESONATORS AND THE PROBLEM OF LASER EMISSION DIVERGENCE
Moscow OPTICHESKIYE REZONATORY I PROBLEMA RASKHODIMOSTI LAZERNOGO IZLUCHENIYA in
Russian 1979 (signed to press 29 Oct 79) pp 135-154, 172-188, 220-301
[Excerpts from book "Optical Resonators and the Problem of Laser Emission Diver-
_ gence" by Yuriy Alekseyevich Anan'yev, Izdatel'stvo "Nauka", 4,000 copies, 328
pages]
[Excerpts] Section 2.6. Angular Radiation Selection Procedures ~
~ In this section an analysis will be made of the efforts to decrease the diver-
_ gence of laser radiation with planar or stable resonators (or resonators simi-
lar to them; see below) which have been made at different times and with varying
degrees of success. The majority of these methods are now only of historic in-
terest; however, some of them are used even today.
Efforts To Solve the Divergence Problem on the Basis of Resonators With Small
Diffraction Losses. In a number of papers a study has been made of the possi-
bility of creating resonators from mirrors with aspherical surface, the shape of
which is selected in such a way that the diffraction losses in the lowest mode
are just as small as for stable resonators, but they increase with the trans-
verse index faster than for stable resonators. This theoretically facilitates
the achievement of unimodal oscillation. Some systems of this type are
presented in Figure 2.1'L.
The resonators depicted in Figure 2.22, a, b, were made from dihedral reflec-
tors, the angle between the flat faces of which is ~r - a in the former case, and
~r/2 - a in.the latter case (a � 1). The effect of the first type cf reflector
on a narrow light beam to a certain extent is similar to the effect of a concave
mirror; some "fine focusing" of the beam is realized. The reflector of the sec-
ond type only adds "inversion" of the beam cross section to this effect; there-
fore resonators of these two types are equivalent to each other in the absence
of aberrations. It is possible to see that the transverse dimensions of the
light beams corresponding to individual transverse modes increase in them with
the transverse index faster than in stable resonators, which ensures greater se-
lectivity �or reflectors of finite dimensions. The properties of these resona-
tors are described in more detail in [120, 121].
- 15
_ FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400054452-5
FOR 0[~ FICIAI. USE: Oti1.1'
a c
;
.90'- rc ,
b = ~ ~ . _ _ . - d - : ; - - -
Figure 2.22. Some types of resonators with aspherical mirror.s~: a, b--resona-
tors with dihedral reflectors [120, 121J; c--resonator with cen-
tral "indentation" [122]; d--resonator proposed in [123].
Figure 2.22, c, depicts a resonator in which the eigenvalue spectrum is still
more radically rarefied. The dimensi~ns of the central section of the left-hand
reflector--the "indentation~~--can be taken so that they will be equal to the di-
mensions of the~basic mode spot formed by thi~ section and the right-hand mirror
of a stable resonator. Then the losses of this mode will be small; broader
beams corresponding to other modes will go beyond the limits of the central sec-
- tion and scatter quickly in the peripheral part of the resonator. This must
lead to significant increase in the losses.
At first glance it may seem that an analogous effect is achieved by simple irising
of the stable resonator, However, in the latter case as we have seen in
Sections 2.1, 2.2, the high-order mode field begins to be confined inside the
resonator by edge diffraction (the edge of the dia~ragm has the same effect on the
light beam as the edge of a mirror); in the resonator depicted in Figure 2.22, c,
the diffraction on the edge of the "indentation" turns out to be significantly
attenuated as a result of the presence of halation. Vaynshteyn [3] indicated
_ the possibility of using a similar procedure; the effort at practical implemen-
tation in the optical range (in the example of a helium-neon laser) is described
in [122).
Sometimes proposals for a different plan are encountered in the literature.
Thus, in [123] the properties of the resonator. depicted in Figure 2.22, d, were
analyzed. With a strictly defined form of the components of its reflectors, the
equation for finding the natural oscillations has only one solution. However,
in [123] a study was made only of the equation of an empty resonator made up of
infinite mirrors; consideration of the edge effects and the introduction of an
active medium should change the situation sharply--nothing may remain of "uni-
modality." In addition to everything else it is unclear how such reflectors
would be made with the precision required in the optical range.
In contrast to the last-mentioned version, the possibility of using the resona-
tors depicted in Figure 2.22, a-c, is unquestioned. However, they are all char-
acterized by the same deficiency as the ordinary stable resonator itself: under
16
FOR OFF[C[AL USE Ol~'LY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
FoR ot~ ~~ic~:~~. ~ ~s?~ ovi.~~
conditions of unimodal oscillation it is possible to make effactive use of
only a very small volume of the optically uniform medium (it is sufficient to
point out *hat in the mentioned experimental work [122J the depth of the "inden-
tation" was ~aj10). Therefore the devices with aspherical reflectors are not
able to compete with the stable resonators which are simple to make and align.
It must be noted that for cross section dimensions of the active medium not ex-
ceeding several millimeters, unimodal oscillation can be achieved using
both stable and planar resonators. ln particular, it is appropriate to note the
successful method of empirical selection of the optimal parameters of the reso-
? nator near the "stability" boundary used for the first time in [124] and also
used successfully in a number of subsequent experiments. The method is based on
the application of a combination of plane and concave spherical mirrors, the
distance between which L varies near a value equal to the radius of curvature of
the concave mirror R. For L= R(or in the case of the presence of an active
element of length Q with an index of refraction n~, for Lequiv - L- k(1 -
i/no) = R) a so-called semiconcentric resonator is realized wi~ich is equivalent
to the planar resonator and thus is at the "stability" limit (Section 1.2). For
shorter lengths, the resonator is stable; it is important that for L~ R small
variations in the distance between the mirrors lead, as it is easy to see, to
significant simultaneous variation of the diffraction losses and spot dimensions
of the fundamental and other transverse modes. This makes it easy to select the
optimal combination of them from the point of vieca of the output characteristics
of the laser. Obviously~ when this choice is made empirically, the "Lenticular-
_ ness" of the sample is automatically taken into account if it exists, and so on.
_ p~mm~.r TfA~an - -
CN - - ~ _ _
, , ~
Q/' _ - ~
0,4 - - - ~
n, ~ - - _ _ _
o - - - -
a,R~r 0,96 ~n i/~~
Figure 2.23. Results of experi.ments in oscillation selecti.on in a resonator
- close to a semiconcentric resonator [128~.
Figure 2.23 shows a standard graph for use of the indicated method borrowed from
(28], where this method is discussed in great detail. The graph was obtained in
experiments with a helium-neon laser; the ratio L/R is plotted along the x-axis,
the line L/R = 1 is the "stability" limit. On approaching it from the left, the
diffraction losses increase, the total oscillation power P decreases slowly,
then the number of transverse modes present in the oscillations are reduced. At
the point noted by the arrow, only the lowest mode TEM~~ remains. The resonator
length corresponding to this point can also be considered optimal: further
movement Coward the stability limit and transition to the region of instability
17
FOR OFFIC[AL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
(~OR OPl~ICIAL [itif~: Ovl.l
located to the right causes only a sharp dec.rease in power and then cessation of
oscillation.
All of this is good, however, oniy in the case of lasers with small cross sec-
tions of the active medium for which the problem of rzdiation divergence [n };en-
cral is not acuCe. As for the lasers oL primary lnterest to us wl?ich hav~ s
large exit aperture, for them the application of stable resonators leads, as has
already been noted more than once, to oscillation on higher-order modes with a
broad radiation pattern. Nevertheless, efforts have been renewed many times to
solve the problem of divergence even in this case. In Chapter S there is a
brief discussion of the conversion of light beams corresponding to the high-
order modes to narrowly directional light beams by the methods of holographic
correction. A search was also conducted for simpler methods; from the work in
this direction there are some interesting papers (for example, [125]), but their
practical significance is low. Therefore hereafter we shall limit ourselves to
the investigation of the methods of angular selection (decreasing the angular
divergence of the radiation) in planar resonators which has received signifi-
cant development in its time.
Lasers With Planar Resonators and Angular Selectors. For constriction of the
radiation pattern of a laser with planar resonator it is necessary in the gen-
eral case also to decrease the number of modes in which oscillation is realized
and, what is usually even more important, the deformations of these modes. The
number of modes is determined primarily by the ratio between the diffraction and
nonselective losses. Therefore for angular selection in the hypothetical case
- of an ideally uniform medium where the mode deformations are small, it is neces-
sary to try to increase the differences of the diffraction losses.
In the presence of aberrations of any type, the most important problem turns out
to be decreasing the mode deformations; in accordance with perturbation theory
(Section 2.5), for this purpose ^t is necessary to increase the differences of
the eigenvalues of the operator P, including the phase corrections.
riaking this remark of a general nature, let us proceed with investigation of the
specific methods of angular selection.
In order to obtain the desired effect usually addi.r.ional elements called angle
selectors are introduced into the resonator. They are essentially filters, the
transmission of which depends sharply on the direction of propagation of the
radiation. Historically, the first type of angle selector was a ~ystem of
two confocal lenses and a diaphragm with a small opening placed at their common
focal point [126, 127]. A concentric resonator with a diaphragm in the central
plane [128, 129] (Figure 2.24, b) is entirely identical to a planar resonator
with such a selector (Figure 2.24, a). The operating principle of such a selec-
tor is obvious. Instead of a diaphragm a passive shutter can be used: part that
cle~rs first then acts as an iris aperture [130].
The effect of the selector based on the Fabry and Perot etalon [131, 132] is
based on the fact that the transmission of the etalon depends not only on the
18
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR Of~l~IC1:11. i!SF' O~~LI'
wavelength, but also the direction of propagation of the radiation. Inasmuch as
for inclined incidence of the beam, this relation becomes sharper, the etalon is
installed at an angle to the resonator axis (Figure 2.24, c). ror realization
- of angular selection in both directions it is necessary to use two etalons.
Probably the method of selection based on using the dependence of the reflection
~ coefficient at the interface of two media on the angle of incidence had the
greatest popularity. Near the critical angle of total internal reflection, the
indicated relation is especially sharp; therefore these angles of incidence are
used. In order to eliminate the selective effect it is possible to make the
light undergo multiple reflections (Figure 2.24, d). In the 1960's a large num-
ber of versions of selectors of this type [133-140] grouped under the general head-
' ing of total internal reflection selectors were proposed.
Let us consider the mechanism of the effect of the selectors on the angular di-
vergence. From very general arguments it is clear that the presence of a fil-
ter, tbe transmission of which depends on the direction of propagation of thQ
radiatioa is primarily felt in the magnitude of the losses of individual trans-
. verse modes. The phase corrections are determined for fixed configuration of
the resonator in practice only by the number of angles of distribution of the
amplitude with respe~t to cross section (that is, the transverse mode index),
and in the presence of a selector, they must vary insignificantly (see Section
2.2 for the similarity of phase corrections in open and closed resonators). The
results of strict calculations [141J confirm this obvious conclusion.
Let us present the data for the idealized case of a Gaussian selector, the shape
of the passband of which is intermediate between the shapes of the b ands of real
selectors presented in Figure 2.24, and it is described by the formula g2(~) _
exp[-(~/0~)2] (Figure 2.25; see [141]); ~ is the angle between the direction of
propagation af the radiation and the resonator axis; is the passband width,
g2 is the transmission with respect to intensity. If we consider that the
transverse modes with the index m correspond to values of ~~�(m + 1)ediff~2
(see Sections 2.2, 1.1; Adiff -~~2a), the ma~nitude of the losses introduced by
the selector follow directly ~(2dm) _(m + 1) (ediff~2a~~2 ~this same result was
obtaiiied in [141J by a stricter procedure).
Let us now trace how the magnitude of the angular divergence of the radiation
must vary with the passband width of the selector.
In the absence of aberrations the role of the selector reduces to variation of
the conditions of competition of the modes (Section 2.4) by increasing the loss
differences. The losses introduced by the Gaussian selector turn out to be
greater than the diffraction losses in an ideal empty resonator on satisfaction
of the condition 2~~/0diff ~~a2/~L)3~4. Inasmuch as for lasers with large
cross section a2/aL = N � l, the angular divergence in the given idealized case
can decrease sharply even for comparatively greater width of the selector pass-
band. Estimation shows that to achieve the unimodal conditions with an ideal
active medium it is surficient to use a selector with 0~ several times greater
than ~diff/2�
19
~OR OFFtC[AL USE Oh'LY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
FOR 0[~FICIAL [~SH: O`Ll'
! - 5 I I _ ~r
,
a - ~ - - -
- ; _ ,
t '
~
,T I --~-J
b _ ~ -
. I
Z ~ ~ T.
C ~
, ; ,
T. ~
d i 7
~
- T.
~y .
Figure 2.24. Diagrams of lasers with angle selectors: 1--active sample;
2--plane mirror; 3--spherical mirror; 4--diaphragm with hole; 5--
lens; 6--Fabry and Perot etalon; 7--plane-parallel plate.
:n
~
, ~
~ ~a,s
, \ C~
~ o~
_?.1.. - L~`-=-i -
- 4 0 1 7. J~
_ ?'~JA'
Figure 2.25. Shape of the passband of different angle selectors; Gaussian
selector (dash-dot line), the selector based on the Fabry and
Perot etalon (dotted line) and the ideal selector (solid line).
This possibility is based on the fact that the losses introduced by the given
type of selector are even noticeable for p~ (see Figure 2.25). Among real
selectors, only the selector based on the Fabry and Perot etalon (see Figure
2.24, c) has this (quadratic) form of the function g(~). The selectors with an
opening (Figure 2.24, a, b) and the total internal reflection selectors (Figure
~ 20
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
rou or~ic~,af_ L~sF ov~.~~
2.24, d) have a passban~ with shape approaching a rectangle ("ideal" selectors
_ according to the terminology of [141, 142]). In this case, just as should be
expected, the presence of a selector is felt noticeably in the value of tlie
losses only for the modes, the indices of which are close to the value of
2a$~ediff ~141]; therefore the selectors of the given type can decrease the
amount of angular divergence only to a value approximately equal to
In the presence of noticeable aberrations the basic function of the selector
must be tc decrease the deformations of the oscillation with the highest Q. Let
us remember that the mode deformations themselves can be interpreted as the re-
sult of the presence of induced oscillations in the modes of an ideal resonator
(see the preceding section). Beginning with this fact, it is easy to see that
in order to decrease the mode deformations the losses introduced by the selector
must turn out to be larger in magnitude not only than the diffraction losses,
but also the phase corrections in the empty resonator. Hence, it follows that
for noticeable aberrations (that is, in pr�actice always) only selectors with
sufficiently narrow passband, independently of its shape, can turn out to be
useful. ,
When using angular selectors, just as in the case of angular selection by in-
creasing the length of the resonator which will be considered a little later,
not or.ly the angular radiation characteristics are of interest, but also the en-
ergy characteristics of the radiation. The possibility of decreasing the widtli
of the radiation pattern without significant gain in radiation power is con-
nected with the magnitude and the nature of the aberrations. This relation is
exhibited most clearly when investigating the shape of the scattering index of a
coherent light beam.
I, relative units I. relative units
~ ~ ~~Bdiff ~ ~~~diff
a l ~y')
_ Figure 2.26. Radiation patterns after single passage of the light through the
active medium: a--light dispersion on microinhomogeneities; b,-low-
order wave aberrations as a result of the presence of macroinhomo-
geneities.
Figur~ 2.26 contains a schematic representation of two radiation patterns of a
ligtit beam after single transmission through an active sample (at the entrance
to ttie sample the wave tront is planar). These pstterns directly characterize
the angular divergence of the beam at the exit from the laser system using the
given sample as the final amplifier (of course, if a well-collimated beam is fed
to its input).
21
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OGFtCIAL L'Sl: O~ii_l'
The first of them (Figure 2.26, a) pertains to the case of weak light dispersion
on microinhomogeneities. The greater part of the energy of the light passing
through the sample (on the order of 1- Pdis~ the presence of secondary diffrac-
tion peaks is neglected) is concentrated in the central core having diffraction
width. The remainder of the radiation is distributed in a comparatively wide
range of angles.
Figure 2.26, b, corresponds to the presence of low-order wave aberrations (refraction
on macroinhomogeneities). Primarily the most central core of the pattern
expands, the axial luminous intensity decreases significantly. From the Rayleigh
number it follows that the core width begins to exceed the diffraction limit ne-
ticeably when the aberrations exceed a/4.
It is obvious that the effort to realize angular selection will lead to essen-
tially different results in the cases of Figures 2.26, a, and 2.26, b. The ligl~t
dispersion on the microinhomogeneities does not prevent achievement of the
diffraction limit; the power of the generated radiation in this case, if the
pumping intensity is sufficiently high, decreases insignificantly (the effective
losses increase by approximately pdis ~26]). In the case of Figure 2.26, b, an
effort to constrict the angular divergence to less than the width of the central
core of the scattered light indicatrix is coupled with unavoidable significant
energy losses.
The experimental data correspond quite well to the above-discussed arguments.
First of all, it must be noted that when using all types of angle selectors a
decrease in angular divergence and an increase in the axial luminous intensity were
actually observed. Nevertheless, the angle selectors have not found broad ap-
plication. The reason for this lies hoth with the high requirements on the pre-
cision of their manufacture and alignment and a number of specific deficiencies
characteristic of_ each type of selector.
The basic deficiency of systems with a diap~ragm (see Figure 2.24, a, b) is un-
desirable concentration of the radiation in a small section of the cross section.
In lasers of comparatively low power this leads to rupture of the diaphragm or
electric breakdown near its surface (see, for example, [129]). Angular selec-
tion using the Fabry and Perot etalons is greatly complicated as a result of the
presence of a large number of transmission peaks; therefore no one has followed
the example of the authors of [131, 132] who were able to realize it in low-
power ruby lasers. Only total internal reflection selectors have found some ap-
plication in powerful pulsed lasers, but even they in the final analysis disap-
peared from the scene as a result of the extraordinary requirements on the pre-
cision of manufacture and alignment and also the degree of finish of the working
surfaces.
Angular Selection of Laser Radiation With Planar Resonators by Decreasing the
Number of Fresnel Zones. If we do away with angle selectors, it remains only
to increase the selective properties of the planar resonator itself by decreas-
ing the number of Fresnel zones N. This can be achieved by reducing the cross
section or by increasing the length of the resonator.
22
FOR OFF'iC[AL U5E Ol\LY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
FOR OFF[CIAL USE ONLY
A significant decrease in the active cross section by irising the resonator, of
course, must lead to a corresponding drop in the output power, and therefore
cannot be considered among the efticient selection procedures. Some movement in
this direction is still possibleo The f~ct is that a light beam always broadens
somewhat on passage through a planar resonator (as a result, diffraction losses
appear). If we use an exit mirror with cross section only somewhat less than the
cross section of the active element, the latter will still be completely filled
by the irised beam. It only remains to use the radiation exiting from the laser
through a narrow circular zone around the mirror as the useful signal along with
the radiation passing through the semitransparent exit mirror. Thus, it is pos-
sible to decrease N somewhat, almost without relinquishing output power. This
procedure was described for the first time in j143]; the name of diffraction yield
of radiation was attached to it. The same method was used with slight modifica-
tions in j144]; the given direction reached a logical conclusion in the laser de-
scribed by Kalinin et al., the reflection coefficient of the exit mirror of which
decreased smoothly from the center to the periphery j145]. In all of the enumera-
ted cases, ~ust as should be expected, an increase in the degree of directionality
and a decrease in the sensitivity to the misalignment of the mirrors were observed
(as a result of a decrease in the total or effective size of the exit mirror),
- but with intense pumping the angular divergence significantly exceeded the dif-
fraction limit.
Let us note that lasers with mirror transmission that is variable with respect to
cross section ar~ a clear example of systems having extraordinary dependence of the
mode structure on the excitation conditior.s. In the case of uniform distribution
of pumping slightly exceeding the lasing threshold, the field configuration of the
individual types of oscillations will be close to the configuration predicted by
= the theory of the corresponding empty resonators j146]. If the amount the threshold
is exceeded is large, then as a result of the competition of the transverse modes
the distribution of the gain with respect to cross section approaches the loss
distribution, and the structure of the individual modes will become similar to the
structure in lasers with ordinary mirrors.
A much more radical decrease in N without reduction of the working volume can be
achieved by a simple increase in the distance between mirrors. This method of
angular selection is the most natural and, in addition, very effective: here, in
contrast to the case of the application of angular selectors~ not only the losses
increase~ but also the phase corrections~ which leads to a rapid decrease in the
mode deformation, In addition~ it is simpler by far to vary the length of the
resonator than to introduce a selector and change the pa;;sband width; therefore
the given method of constricttng the radiation pattern has been studied most
systematically.
The most important result of numerous studies was solid establishment of the fact
- that on variation of L within very broad limits the angular divergence of the
radiation varies with a high degree of accuracy proportionally to L-1~2--indeed
the theoretical estimates based on any models pertaining to mode deformations and
to multimode oscillations (Sections 2.4, 2.5) lead to the same relation: This
relation has been exemplified by lasers of the most varied types: a ruby laser
(the resonator length was varied by approximately 15 times) [147],
23
~ FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400054452-5
f I OR Of~l~[('1:1l. i'tif~. l)~1.1'

~

~
~
a neodymium glass laser (-15 times)~ a fluorite laser with sam~rium (~103
~ times) [26], and an c+lkylio~iid~ molecule photodissociation laser (~30 times)
[].48]. The Eollowing is characteristic. IE Clie meclium has a comparatively high
~ amount oL optical L1JI11111iIOC!I11CV, increasin~; the lenfith of tlie resonator abov~
some limit is accompani~~d by quite rapid decrease in power to complete cessation
of oscillation, although it may still be Ear to diffraction divergence. As a
result, the axial luminous intensity~initially increasing with resonator length,
goes through a peak, the P09itLOt1 and height of which depend on the degree of
optical nonuniformity of the medium. This fact was noted for the first tim~ by
= Sventsitskaya and Y.hazov in j147] (in this paper, the method of representing data
on the angular distribution of radiation in the form of the dependence of the
proportion oE the beam ene.rgy included inside the axial cone on the angle at the
apex of this cone, see Figure 4.4, 4.7, which has acquired deserved popularity
was introduced). It is oE interest that wtien the sharp lasi~ig power drop
begins, the angular diver~;ence begins to decrease with an increase in L even
faster than L-1~2 [14~]. 'rhis is explained by the fact that as a result of a
sharp increase in ttie ttireshold, the 1 a s i n~; b e~; i n s to be local ized in indi-
vidual sections of ttie cross section with tlie largest gradient of the index of
refraction [147, 148J--the "et�ective" value oE c1n decreases.
r1s the optical uniformity of. tlie medium increases, it is possible to come closer
and closer to diELraction diver~ence without noticeable loss of power (it is
- true in this case the requirements on the necessary precision of ali.gnment of
- the resonator increase). Finally, when the raedium is so uniform that ~L < a/4,
the diffraction limit can be reaclied. For ttiis purpose tlie distance between the
mirrors must be usually so large that N exceeds 1 somewhat. Herein lies the ba-
- sic deficiency of the given selection method: for lasers in the visible range
even with diameters of the active elements only 5-8 mm, the required
r.esonator length is several meters. If we consider that for maintenance of the
same N the length must incr.ease proportionately to the square of the linear di-
mensions of the working cross section, it becomes clear that in the case of
~ powerful lasers it is entirely unreasonable to solve the problem by a simple in-
crease in distance between the mirrors. It is also necessary to consider that
- for short lasing pulses long length of the resonator is in general unacceptable
inasmuch as the pulse development time increases together with the length.
The way out of the indicated difficulty consists in using resonators tliat have
short actual length, but equivalent to the planar resonator with small N. This
method oF an~ular selection is of definite interest not only from the practical
point of view, but also from tr~e procedural point of view; t!:erefore let us
discuss it in somewhat more detail.
Plane Resonators of Long EfFective Length. Ln Figure 2.27 several versions of
devices of tliis type are presented. The first oE them was used to decrease the
angular divergence in 1963 [149], but correct notions of its properties
were still not developed at that time. Using the mPthods discussed in Section
- 1.2, the corresponding analysis will be performed without special difficulty.
However, we shall not consider the beam matrices of these resonators as a whole,
but we shall use a more obvious procedure which will also be useful hereafter to
cons ider unsi.~ble resonators.
24
FOR OFFiCIAL US~ O!~LY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2047/02/09: CIA-RDP82-00850R000404050052-5
r�o~ oi~~Er 0, ri < 0, Nequiv ~(these include, in particular, the
confocal resonator depicted in Figure 3.3, c). On making the transition from
(13) to the comple:c conjugate equation, replacing X' under the integral sign by
-X' and using pl(-X') = pl(X') and M=-~MI we obtain
~'-*;(*(.X)=)~~ f ('~~X')r~xplinN~At~I~~-~~i/~)Zlx*~-.C')d1"
-ro
� (the ~ indicates, just as everywhere, complex conjugation).
It is known that the eigenfunctions of such resonators are symmetric (XS) or
antisymmetric (ka). Substituting the expression Xs,a~-X~~ -�Xs,a~X') in the
latter we obtained equations distinguished only by the factor for Y and for the
rest coinciding entirely with the equation of the resonator having the parame-
ters N, IMI. In the final analysis we have
Ys,a (1~, - ~ llf i~~r �(N, ~ 1~!
X~.a (N, - ~ n~ x) - X~,n tN, ~ nt .Y).
For resonators with N< 0, ri > 0, Nequiv ~ 0(as an example we can use the sym-
metric resonator made of two sharply concave mirrors)
'Y~-~N~,Af)--'y*(~N~,M), X~-INI~A7,.X)=x''(~N~,M,X).
Finally, for N< 0, ri < 0, Nequiv ' 0(for example, the confocal resonator made
of concave mirrors in which a mirror with large R is used as the exit mirror)
~.,�!-~N~, --~MI) _ ~Y~.�(INI. I~~I),
x(--In~~, _~,~rl, x(In~~, ~~~r~,
From the presented formulas it is obvious that for all types of unstable resona-
_ tors with identical N, Tf and Nequiv With respect to absolute magnitude, the
eigenvalues are distinguished by phase factors, but they coincide with respect
_ to modulus; thus, al_1 of them have identical diffraction losses. The eigenfunc-
tions recorded on the ec~uiphasal surface of the diverging wave of the geometric
appro:iimation turn out to be complex-conjugate for resonators with Nequiv ~ ~
33
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
with respect to the eigenfunctions of resonators with Nequiv ' 0. Inasmuch as
the transition from the indicated reference surface to the surface of the mir-
rors is realized by multiplication by exp(i~NequivX2), the distributions on the
mirror surface are also complex-conjugate.
All of this permits us hereafter to limit ourselves to :he investigation of any
one type of resonator. We shall illustrate everything in the example of a reso-
nator made up of two identical convex mirrors (Figure 3.3, e; N> 0, M> 0,
Nequiv ~ limiting ourselves, as a rule, to the investigation of the two-
dimensional case and departing from this rule only when the transition to three
dimensional leads to a qualitative change in the oscillation spectrum.
Unstable Resonators With Completely "S~noothed" Edge. Initially, following [151,
154), let us consider the properties of such unstable resonators for which the
~ edge diffraction effects are insignificant. From the general arguments it is
� clear that this occurs in the case where the reflection coefficient of the mir-
rors, and with.it also the field amplitude, smoothly decrease toward the edge of
the system. From the materials presented in Section 3.2, it also follows that
the f ield distribution of the fundamental mode in such resonators must be described
well by the formula for the opticogeometric approximation (S) which satisfies
equation (9). The relation between the equations of the diffraction approxima-
tion (13) and the opticogeometric approximation (9) is quite obvious. Actually,
the factor exp[i~r1~f(X' - X/M)2J for large values of X` - X/M oscillates rapidly.
Therefore if the product plx iG a slo~oly variable function of X' the magnitude
of the integral in (13) is in practice determined only by the behavior of this
function in the vicinity of the point X/M (see also Section 1.1). Expanding it
near this point in a Taylor series
~X~) x ~X~~ _ ~t ( jN ) X ( A1 ) (.l~ ~ ) ~dX x) `x'-,x/et . . .
and limiting ourselves to the terms written out, after integration we immedi-
ately obtain (9) with the aberration function F(X) = pl(X/M)/pl(0) (in the case
of an empty resonator K- 1).
_ In order to discover what the mode spectrum of unstable resonators with smoothed
edge is, let us consider their properties in the diffraction approximation in
the exatnple of a resonator with Gaussian distribution of the mirror reflection
_ coeffic:ient:
P~x) = exp(-7.x~la~)? Di~X) oxp(-2X~),
This case is especially interesting in that the mirrors with Gaussian distribu-
tion p can b e considered to have an ideally smoothed edge: As a result of re-.
flection of the light beams from them with an amplitude having Gaussian or uni-
form distribution, the Gaussian beams are generated, the far-field pattern of
which does not have additional peaks. In addition, for resonators with such
mirrors there is an exact analytical solution [3]. When the transverse di.men-
sions of the mirrors and the diffraction losses are not too small (more
- 34
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400054452-5
FOR OFFICIAL US~ ONLY
- nreci5ely, on satist~ziction oL the condition ~rNequiv~M - 1/M) � 1), after tran-
sition to the normal coordinates this solution acquires the form [151]*
u,~(x)Nu,(x)IIm(2~-inN.,,,, Q), m=0~~~2,..., t= equiv (14)
N / ~ t- ' ~ 15 ~
YM lA'f ~ ,
where up(x) = exp(-[2/(M2 - 1)][x2/a2)), H~(t) _(-1)mexp(t2/2) x(dm/dtm) x
exp(-[t2/2J) are Hermite polynomials. Inasmuch as H~(t) = 1, the function u
directly describes the field distribution of the lowest mode; it is easy to see
that it satisfies the opticogeometric equation (9) and can be found using for-
mula (5):
, .
~.r> Tl (?l 1~\~l _Zx2 Lr.z _ p~~~ - 2 s
~ (A4/ \h~Zl l n1`~~ A/~nz . . .l . . ( A12 ~ nt)~
/
idow let us consider the Hermite polynomials. All of them contain the term tm; in the
first two polynomials it is unique (HD(t) = 1, H1(t) = t); the rest, in addition
to it, also contain the terms of lower orders (H2(t) = t2 - 1, H3(t) = t3 - 3t,
and so on). These additional terms play a significant role only for small val-
ues of the argument Hm; from (14) it is obvious that this occurs in the investi-
gated case of large Nequiv only on the small central section of the resonator
cross section. Thus, the first two modes on the entire resonator cross section,
and the subsequent ones, on the larger part of it are described by the functions
up(x)(x/a)m which are solutions of the opticogeometric equation (9) (see the end
of Section 3.2). The exponents on x/a actually turn out to be integral, except,
in spite of the proposition of Sigmen and Arratun, this does not follow from any
conditions on the resonator axis (where the geometric approximation ceases to be
valid), but from the requirement of the bounding of um(x) at infinity [151].
~1n example of the field distribution of several lowest modes for M= 2 and
~Neq~iiv - 50 is presented in Figure 3.10. The field amplitude of the fundamental
mode (m = 0) decreases on going away from the center of the mirrors by a Gaussian
law, the characteristic size of the "spot" in the plane of the mirror is
2a The fields of the other modes fill the central region of the reso-
natox less uniformly. With an increase in the transverse index m the zone of
larger amplitude shifts away from the center. The equiphasal surfaces of the
_ modes with m= 0, 1 naturally coincide with the surface of the spherical wave of
the geometric approximation (Figure 3.10, b). In the wave fronts of the higher-
order modes near the center of the mirrors noticeable deviations from the spher-
~ ical shape are observed--it turns out that the Hermite polynomials contain, in
addition to tm, also other terms.
* On comparison with the published data it is necessary to consider that in a
number of papers, including [151, 154], the dependence of the field on time
exp(iwt) was used and not exp(-iwt) as in the present publication (as a result,
the sign on i changes everywhere).
35
FOR OFF[CIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
FOR OFFICIAL USE ONLY
Nevertheless, the most interesting for us now is not the specific form of the
solutions in the resonator witti Gaussian mirrors, but the Fact that in expres-
sions (14), (15) the form of the distribution p(x) essentially determines only
the f actor u~(x) common to all eigenfunctions (inasmuch as Nequiv ` a2, the
value of the argument Hm does not depend on a). It is also remarkable that the
eigenvalues in accordance with (15) do not depend on the sizes of the mirrors
and coincide with the eigenvalues which were obtained by formal methods in ref-
erences [158, 159] for resonators with mirrors of infinite dimensions.
We have already seen ttiat within the framework of the opticogeometric approxi-
mation the isolation of the factor describing the field distribution oF the funda-
mental mode for any form of aberration function F(x) reduces the corresponding
equation to the equation of an ideal resonator (see the transition from (9) to
(9a)). By analogy it is possible to propose that in the diffraction approxima-
tion the eigenfunctions have the for.m (14) not only for Gaussian mirrors, but
also in the general case of many unstable resonators with well-smoothed edge.
The field distribution of the fundamental mode u~ which figures in (14) here must be
considered using (S); the eigenvalues must be eq~xal to the following (see (11))
1'm - K~~)P~~)~~l~lf)n'~ uz
(15a)
1,0 . . . - - - - - . .
~ 0. ~7
G
_ 41 ~ Uh ,i
'd 41
~ ~ 0, 4
a, �
- ~ ro
~ ~O.i >
--1 ~ ~ ~ ~ ~
0 /1,5 >,0 1,,6 Z,0 r./a
a)
~ ~ .
~ ~ 'm-0,m-f
cNd ~U ~
.C ~1 i
a ,z
- a --._...i_
� 0 l1,.f lU I,; Z.0 ,xyn
li)
_ Figure 3.10. I~'ielcl distr.ibutions of the lowest modes in a resonator with
_ Gaussian mirrors (M = 2, ~Ne uiv - 50): a--amplitude distribu-
tion; b--phase distribution ~the origin is the spherical wave of
the ~;eometric approximation).
Then it will be obvious that these arguments formulated in [151] are basically
true; however, it is still necessary to become familiar with the properties of
resonators, the mirrors of which have regular geometric shape with sharply out-
lined edge.
36
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAI. USE ONLY
Unstable Resonators With Sharp Edge. As we have already mentioned in Section
3.1, in Sigmen's first paper [4] he stated the argument that in unstable reso-
nators with large losses the edge diffraction must influence only the peripheral
part of the~beam immediately exiting from the resonator. Hence, it follows that
the field distribution on the mirrors (or with one-sided output, on the output
mirror) and the magnitude of the losses must not noticeably dep~nd on the edge
. eftects; the analogous conclusion regarding the properties ef unstable resona-
tors with large losses can also be found in Vaynshteyn ([3], problem No 8 for
Chapter 4). However, precise machine calculations performed by Sigmen and Ar-
ratun [157] by the iterative method demonstratecl ttiat the picture of the prop- �
erties of unstable resonators with totally reflecting mirrors of finite dimen-
sions is far from simple. It was discovered that the Field distribution for
oscillations with the least losses does not differ too strongly, but neverthe-
less, noticeably, from the predictions oF the geometric approximation (Figure
3.11). It turned out that the nature of this distribution and the magnitude of
the losses depend in a complex way on the transverse dimensions of the mirrors,
revealing explicit periodic dependence with variation of Nequiv for fixed M.
- The typical form of the relation calculated in [157] for the losses as a func-
" tion of N~quiv is presented in Figure 3.12, a(the ~~rocediire used made it pos-
sible simultaneously to find the losses of the two highest Q modes).
~,n
L I
1,S ,
~ ~
- v
~ >>n - . _
~ �r.,
~ ~
~ v a�s
� ~
'
i r~:,�~~~ P~' P-)~ i ~1)
(a)
Key: a. amplification
where p+ and p are the flux densities to the exit mirror and in the opposite di-
rection, respectively (Figure 4.1).
- ~ _
1
~
.:r_ ~.r~Za/AI
I r' - _ _T-
1
- ~
Figure 4.1. Radiation fluxes in a laser
with telescopic resonator.
It is easy to see that inside the region I which is f illed by the fluxes in both
directions, the inverse population and the flux density itself var.y only along the
length z(0 < z< L), and these values are constant with respect to cross sectiori.
'lhen for p+ and p in the indicated region the obvi.ous relations are valid:
. z �
p+ (z) p+ (0) ezp [ky~(z') - R,1 dZ~ ,
0
z a
p' (Z) = p- (0) exp - [kyc ~z')- vo] dz' � ~ ~ � z ) ?
o � ~2)
where 6~ is the coefficient of inactive losses; the factor [z~/(z~ - z)]2 describes
the decrease in the density of the diverging spherical wave on going away from an
imaginary center z~ coinciding with the common focal point of the mirrors.
Equations (1) and (2) must be solved jointly with respect to p+(z) and p(z) con-
sidering the boundary conditions p+(0) = p(0) and p+(L) = p-(L). Finding the
exact solution in analytical form is impossible. For a roximate solution it is
convenient to use the fact that according to (2) ?p (z)p-(z) = p(0)zp/(z0 - z).
Inasnuch as the sum p+ + p is with an accuracy to several percentages equal to
2?p~- up to values of p~" and p differing by two or three times (larger differ-
ences in practice do not exist) it is possible by the cori-esponding substitution
to convert equation (1) as follows:
49
FOR OFFIC[AL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
FOR ~OFFICIAL USE ONLY
kyo = kyc ~ 1-}- ZP zo/(zo - z)J'1. (la)
The substitution of (la) in (2) with subsequent integration leads to the equation
f or determination of p(0) :
~f I ZP I~) -I- i] M_. 1 n M-}- rtoL
2~f - 1 P~~~ ~n 2P (0)11f i i kyoL '
where M= z~/(z~ - L), as always, is the magnification of the zesonator.
Finding p(0), it is possible by using (2) to calculate the distribution p+(z) in the
region I. W'hen the part of the radiation flux remote from the axis (r > a/M, 2a is
the diameter of the active element) intersects the boundary between the regions and
goes into zone II where p= 0, further amplification of the flux is easily consi-
dered by the corresponding formula for the amplifying mode [186], which is a direct
consequence of the radation transport equation:
(b>
ln ,P~ : (ko ~ l ~'v,; ~1? lkY~~~e~ - 1- Pea: '
t P = l - o~ R ~k�yc~�o~ - i- p r
0
Key: a. out b. amplif ication
where p is the flux density at the entrance to ragion II; pout is the flux density
at the exit from the resonator as a function of the distance k traveled by the flux
in this region (see Figure 4.1). It is obvious that the value of Q, and with it
also Pout' increase with an increase in r.
Figure 4.2 shows the graphs of the density distributions of the radiation leaving
the resonator calculated in this way. As is obvious from Figure 4.2, with an in-
crease in M the radiation density at the laser exit decreases, but the width of the
radiating zone (a - a/M) naturally increases. For some value MoPt the power of the
outgoing radiation will be maximal.
p ; niny. e~~
~a~ ,N=1,~
~0 15 ~
3d Z
~ I
r,
-
U O,Z 0,4 0,6 UAiya
Figure 4.2. Density distribution of outgoing radiati~n with respect
~ to cross section of the active element for the case k L= 3.0,
6~L = 0.12 and different values of Ma~p
Key: a. relative units
50
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
- FOR OFFIL'IAL USE ONLY
The effectiveness of the energy conversion and the resonator X introduced in ~3 1.4
can be calculated as the ratio of the number of lasir.g photons ~eaving the resona-
or I I dS (integration is performed over the area of the exit aperture) to the
(S)
total number of acts of filling out the inverse populatian in the volume of the
_ oscillator ; PPumPdv. Inasmuch as in the case of a four-level medium with uniformly
(V)
_ broadened line and unpopulated lower level of the operating transition Ppu~p = kamP/oc
(see ~ 1. 4) , we obtain X= ( I P+~sllr f h�y� dvl. In garticular, for the case of a
~cs~ J l tv> J
circular cylindrical element with unifor~ pumping ~
a
ko ~az I(~ny~x (r) r ~Ir.
(b) `a)
Key: a. out b. amplifica~ion ~
_ Figure 4.3 shows the efficiency of the resonator X calculated using the last
formula as a function of the value of M for a number of values of 6~L and kam L(let
P
~ us remember that in the case of a four-level mediu~ the ratio kamp/6Q is the amount
= the lasing threshold is exceeded in the absence of losses to radiation, tha.t is,
for M= 1). The data for a telescopic resonator are compared with the data pertain-
ing to a planar resonator with the same total losses and l~.sing threshold (the
reflection coefficient of the output mirror R' is 1/M2).
- Fron Figure 4.3 it follows that the efficiency of the energy conversion in a tele-
sCopic resonator ~xi the given ~~ase is somewhat less, but it is very close to the
, efficien.cy in the correspondin~ planar resonator. Thus, for a laser with a tele-
scopic resonator, the formulas of ~ 1.4~ can be used unde~ the condition of replace-
ment of R' in them by 1/M2. Iii particular, for o'oL that is not too large, the value
of Y can he determined usin~; the expression
= ,Y,,~; ln1~t (1 _ 1nM-}-aaLl
_ ln M-}- aal, t kpcL J' (3)
the optimal magnif ication of the resanator, by the formula
ln l~'Io~a~~ QoL~~~~iclQo - 1~e ~4)
Key: a. opt
tinally, the maxi.mum value of X, just as in the ca~~e of a plane resonator is
approximately equal to
:
a
.Y~:,: ~ 1 - ~Rp~1,�y~~ � ~5)
The above-discussed analysis was performed in reference j1~37], being the f irst
. example of calculation of the energy characteristics of lasers with unstable reson-
ators. Later, more compleY cases were investigated whtch :~equire very awkward
machine calculations (we shall touch on the ~nethods of performing these calculations
- 51
F!)R OFFICIAL ~1SE ON~.1'
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
6'OR OFFICIAL UtiH: ONLY
in ~ 4.2). Thus, in [188] ~alculations were made of the eFficiency for nonuniform
distribut.ian of the pumping with respect to cross section and large excesses
over the threshold; it turned ouc that tt1P form~las (3)-~5) remain in force under
the consition of substit.ution of the value of k averaged over the cross section
amp
i.c~ triem. Analogous laws occur, as is known, also in the case of planar r�eson-
ators.

~ i~ (~aj (ti~}~,t
0% - ~ lI, ; - ~Gol.=0,06
,
- Q~,' ~~,L ~D,~'F , '
- ; _ o~~ .
~ ~ c..- ; c ~s
~ /r~, ~ ~
~ .
Y! ` n/ ~
/ 7 ~
~ ~
~ ~
~ 'J, /6
U.~ / ~ 0,~
~``Q,-f
Q ~ . L_-.~ II,' _ ~
U 1,~:' ~:'r' Ql' !1B lj~/;b" ~0 Q~, 0,4 r'.~ 1;4/; K'
Figure 4.3. Efficiency of the resonator with telescopic (solid curves)
' and planar (dotted curves) resonators as a function of the values of
1/r12 and R' , re ,pectively, for kam L= 2 and 3.
P
Key: a. amplification
This similarity of behavior of ttie telescopic and planar resonators of course is no
accident. Its causes consist in the fact that the nature of filling of the cylin-
- drical active elenent with lasing radiation in these two types of resonators with
identical losses to radiation is not so strongly distingu ished as it appears at
first glance. Actually, witli equality of the losses in th e medium, identical mean
= values Qf the amplification coefficient are established; consequently, the mean
radiation densities approximately coincide. Then, along the path from the "blind"
mirror to the exit mirror in a planar resonator, the radiation density increases by
1/?R' times 1.4;, in the telescopic resonator, by M times, that is, in the same
ratio. Hence it is obvious that p+ in these two resonator s has similar values in
- the entire volume of the active medium. As for the radiation traveling in the
opposite direction (p~), in the telescopic resonator its distribution is less ~
favorable: although the total radiation flux is approximately the same as in the
planar resonator it is distributed not with respect to the entire cross section,
_ but only with respect to part of it; worst~ of all is the f illing near the exit
mirror. As a result, the total density p+ p- is distributed over the active vol-
ume in the case of a telescopic resonator somewhat more nonuniformly, which leads
to insignificant decrease in the efficiency.
Thus, the telescopic resonator insures an eff;.ciency which is close to its maximum
value defined by formula (5) if we select the radiation lo sses 1- 1/M2 such as
the optimal planar resonator would have. ri~reover, the value of X in the vicinity
_ of its maximum varies very slowiy with M, and the variation of M within known
limits is not related to a significant reduction in the ef ficiency of the system.
This can be used so that when selecting ri the arguir~ents connected with divergence .
of the radiation are considered. For reduction of the div ergence, it is, as a
_ rule, expedient to use resonators with the largest possib le M. liere the sensiti-
vity of the resonator to the aberrat~ons decreases 3,2); in addition, the ring
52
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007102/09: CIA-RDP82-00850R000400050052-5
- FOR OFFICIAL USE ONLY
- at the exit will become less narrow. IIowever, it is necessary to proceed to values
of M significantl}r exceeding 2 with great caution. First of all, from g 3.3 it
follows that single-mode lasing with uniform field distribution is achieved
- . most reliabl}r for large N If the transverse dimensions of the active element
- equiv'
are given, N reaches a maximum for M= 2. A futher increase in M, in spite
equiv
of some increase in curvature of the mirrors causes a decrease in N as a re-
equiv
sult of a fast decrease in the transverse dimensions of the exit mirror.
Extremely large values of M can be disadvantageous also in the presence of light
dispersion, especially at angles close to 180� (usually all possible interfaces are
sources of this light dispersion). It is easy to understand the reason
- for this if we consider that with an increase in M the proportion of the radi_ation
participating in the "regular" feedback channel decreases, and the light i:itensity
mixed with it as a result of dispersion of the basic flux remains unchanged; thus, ~
the role of the light dispersion increases.
The proper choice of the resonator parameters even in the case of uniform active
medium still does not guarantee that a hioh axial luminous intensity will be obtained.
From the information presented in the preceding chapter it is clear that for. this
to occur, it is necessary to exclude the formation of converging waves with notice-
able initial intensity. In the case oF a telescopic resonator, the purely converg-
ing wave is formed, as is easy to see, with partial reflection of the basic wave
from the plane interfaces perpendicular to the resonator axis; therefore the inter-
faces existing in the laser (for example, the end surfaces of the rod) must be in-
clined noticeably.
Results of Experiments with Neodymium Glass Lasers. The above-discussed arguments
about the choice of the type and the parameters of an unstable resonator and also
a si~nficant part of the concepts developed in Chapter 3 regarding the properties
of unstable resonators were developed during the course of experimental studies of
neodymium glass resonators [5, 152, 189, 153, 190, 191, 1968, 192-197], ancl they
- were confirmed by the results of these studies. In the example of lasers of the
given type a most detailed comparison was made between the characteristics of the
lasers with planar and unstable resonators; in gractice all o.f the new versions of
the systems based on unstable resonators were tested and studied for the first time.
Let us discuss the basic results of the experiments pertaining to the lasers with
the simplest two-mirror resonators discussed in this section.
_ For a diameter ot the neodymium rod of 10 mm and length of 120 mm, the application
of an unstable resonator led only to a twofold gain in axial luminous intensity b}
comparison with the case of a planar resonator j152]. In the greater part of the
subsequent experiments, a highly efficient laser based un a rod 45 mm in diameter
and 600 mm long which was described in [198] was used. It served as a prototype
- for the series manufactured GOS-1001 lasers and various versions of them. Here the
axial luminous intensity on replacement of the planar resonator by an unstable one in-
creased by tens of times. The angular divergence of the radiation measured by the
- half intensity level decreased from 2` to 15-20"; with res~ect ~o the half energy
level, f rom 5' to 40" (Figure 4.4, curve I) [152]. Let us note that this situation
is quite characteristic: the larger the laser~ the greater the effect from us-
ing an unstable resonator in it. The achieved gain in divergence also incre.ases
. with an increase in optical uniformity of the active medium; in this respect the
_ investigated laser was entirely satisfactory,
53
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2407/02/09: CIA-RDP82-00850R000400450052-5
FOR OFFICIAL USE ONLY
1.0 ---~--~r----
/
C~S' - f
!iG -
~ 11
a
ti~.~.
4i'
~a)
~ ~ i ~ i i ~ _1
0 Z 4 6' B ' 10 1,?
~ y,Y~ A2~ri ( b ~ .
. Figure 4.4. nngular distribution of the emission of a solid-state
laser with telescopic resonator j152]: I-- resonator without~inter-
faces perpendicular to the axis; II coated glass plate was in-
stalled inside the resonator perpendicular to the axis. The propor-
tion of the energy included in the cone with apex angle ~ is plotted
on the y-axis.
Key: a. energy, relative units
b. angular minutes
In the experiments with rods 45 mm in diameter the mirrors were totally ref lecting.
The losses to emission were equal to the optimal transmission factor for.the case
of planar mirrors, and they aniounted to ~75% (M = 2). The use of a telescopic.
resonator insured approximately the same radiation energy as in the case of a planar
resonator. In tY~e case of a planoconvex system of mirrors, the output energy dropped
by 1.5-2 times as a result of worse filling of the active element with the lasing
radiation. After these experirnents with large losses to emission, only telescopic
resonators began to be used everywhere.
Subsequently, the output energy of an emission of a laser of the given type was
t~r~ught to 4500 joules, and witti series installation of two active elements in one
resonator with M= 5, to 8000 joules [194]. The angular divergence of the radiation
was: with respect to 0.5 intensity level, ~40"; with respect to half energy level,
- about 1'30".
~ Let us note the following important fact. In order to realize small angular diver-
gence, in the case of a telescopic resonator it turned out to be necessary to in- �
cline the ends of the active element by 2-3� with respect to the resonator axis,
~ which made it possible to avoid the converging waves generated by Fresnel reflection.
The necessity for taking such measures was proved by the following demonstration
experiment: a glass plate with coated surfaces was installed strictly perpendicular
to the axis in a telescopic resonator with active element, the ends of which were
- inclined; the residual reflection of the coated surfaces did not exceed 0.3%. This
turned out to bF� sufficient that the lasing pattern changed strikingly, and the "
angular divergence of the radiation increased so much that it approached the value
characteristic of a planar resonator (curve II in Figure 4.4) [153]. The corre-
sponding photographs are presented in Figure 4.5, a, b[photos not reproduced].
' S4
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2047102109: CIA-RDP82-00850R400404050052-5
FOR OFF[CIAL USE ONLY
The m~chanism responsible for poor directionality of radiation in such
~ cases ~aas studied in [197, 336]. It turned out that on introduction of a third
planar mirror into the telescopic resonator, "spurious" modes appear which corre-
spond to closed beam trajectories. Many passes through the active medium go with
one reflection from this mirror. Therefore the "spurious" modes even for the
smallest ref lection coefficients of the planar mirror have lower excitation thres~
olds than the fundamental mode of a two-ymirror resonator. Inasmuch as these mod~.~ ~n
addition, are characterized by high nonuniformity of the field distribution, some
of them are excited immediately with all of the sad consequences following from
this. And this is no surprise: in � 3.3 we encountered the situation where the
presence of even a negligibly weak converging wave generated by edge diffraction
- leads to c}egeneration with respect to losses. Therefore the e:forts sometime made
to influence the lasing mode (in particular, lower its threshold) by artificial
initiation of_ converging waves obviously always must lead to an increase in diver-
gence of the radiation [336].
However, let us continue the discussion of the properties of lasers ~,~ith "normal"
unstable resonators not having sources of converging waves. Among the discovered
peculiarities of such lasers, high stability of their output parameters is remark-
able, including the form of the angular distribution of the radiation. Such
phenomena characteristic of lasers with planar resonators as variation of the an- '
gular distribution from pulse to pulse, a gradual increase in angular divergence
during aging of the active element, and so on were not observed. This property of
lasers with unstable resonators is to one degree or another inherent in a11 systems
with spherical mirrors, and it is frequently connected with their small critical-
ness with respect to the alignment precision.Asthe experiments have demonstrated,
small rotations and shifts of the mirrors in the transverse direction cause only
small changes in the beam direction. The magnitude of these variations corres~ponds
completely to the predictions of the geometric approximation. The form of angular
distribution is essentially distorted only for such large rotations of tlie mirrors
that the axis of the resonator tightly approaches the f lat surface of the sample
[152] (an analogous cycle of studies for the case of a C02 laser was performed
later in the paper by Krupke and Suya [199]).
Also in accordance with the geometric approximation, the displaceinents of one of
the mirrors in the longitudinal direction cause variation of the curvature of the
wave leaving the resonator. In the case of a telescopic resonator it is possible
to use this means of focusing the beam at a given distance d� L from the laser,
increasing the distance between the mirrors by co~parison with the distance L for
confocal location of them by the amount ~(M + 1)L /(M - 1)d (focusing at the dis-
tance d~ L is also possible, but it is accompanied by a decrease in the output
power as a result of "tapering" of the light beam in the active element).
In reference [152J, a study was also made of the spectral and time characteristics
of the emission of a neodymium glass laser with unstable resonators. There were
no special differences from the characteristics of lasers with planar mirrors:
the same random spikes, approximately the same integral width of the spectrum; only
the duration of each spike turned out to be somewhat less, and the average time
interval between them increased.
'i'he reduction in duration of the spikes arose from the fact that the oscillations
in unstable resonators are set up somewhat f_aster than in planar resonators. The
55
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
FOR OFFICIAL USE ONL'Y '
main reason for this is the presence of some mechanism of forced "spreading" of the
emission over the cross section. We shall discuss this question in more detail ac
the end of this section when we are talking about lasers for which the rate of
esCablishment of the oscillations plays the decisive role. As for tlie spectral
distribution of the radiation, for planar and unstable reso?~ators it is essentia].1y
- the distribution of the radiation intensity between modes with different axial in-
dices (see g 2.4). Near the axis of an unstable resonator the same interference of
two counterflows and the formation of standing waves occur as in a planar resonator.
Therefore the mechanism of the spatial competition of the aaial modes in resonators
of both types is identical in spite of the fact that in the unstable resonator the
peripheral part of the active element is filled with radiation propagated in only
one direction (see also the discussion of the problem of spectral selection in
ring cavities in � 3.5).
The observations of the time expansion of the spatial distribution of the emission
[152, 153, 192] demonstrated that during lasing, insignificant shifts of the center
of synunetry of the angular disribution of the emission take place. In addition,
the angular distribution aiso in individual spiices differed from the distribution
for the ideal emitter. As a result, the integral width of the angular distribution
with respect to time for the investigated lasers noticeably exceeded the diffrac-
tion limit. Obviously, this was a consequence of thermal deformations of the
- resonator, the vibrations of the samples, and so on. Taking measures against the
effect of these f actors led to a decrease in the radiati~n divergence.
In particular, the results of experiments with a laser based on an active element
- of great length and with rectangular cross section are indicative [192]. During
the pumping pulse the sample underwent noticeable mechanical vibrations along the
- small di_mension of the cross section. Accordingly, the center of gravity of the
angular distribution completed complex oscillatory movement in the same direction;
the divergence of the radiation with respect to this direction was four times
greater than the diffraction limit, and it amounted to ~2'20". The replacement of
the concave mirror by a dihedral prism with convex surface turned into the resona-
tor and an edge parallel to the large dimension of the cross section led to.com- -
plete correspondence to the ideas developed in ~ 3.5, almost total
stabilization of the direction of radiation. The angular divergence decreased in
this case to 1'. If a telescopic resonator made of two prisms was used, the de-
gree of stabilization of the direction was somewhat less, and the divergence was
~1'10".
Extraordinarily high selective properties of unstable resonators with lar~e Fresnel
numbers were fully manifested in the test experiments performed in [190]. The
manifestations of optical nonuniformity of the medium and other similar causes were
completely eliminated here. A two-dimensional unstable resonator with bi = 2 made
of totally reflecting mirrors, one of which was planar and the other, convex cylin-
drical (Figure 4.6), was used. The active eltment, just as in the preceding case,
was a rectangular parallelepiped, the location of the flashlamps insured high
uniformity of distribution of pumping in the direction of the large dimensior. of
the cross section. The curvature of the wave front emitting from the resonator
was compensated for by an additional lens.
56
FOR OFFICIA L USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400054452-5
FOR OFFICIAL USE ONLY
- _ _ ~
_ _ _F .
- ^ _ , ~
r~ .
~ -
~ .
-
f~~
Figure 4.6. Diagram of a laser with rectangular active rod and two-
dimensional unstable resonator: a) symmetric, b) asymmetric exit of
the radiation (the crosshatched rectangles on the right depict the
exit beam cross section).
Two methods of exiting this radiation from the laser were tested which are illustra-
ted in Figure 4.6, a, b; Nequiv Was ~1700 and ~7000, respectively. In the former
case the integral angular distribution of the radiation with respect to pulse time
along the direction in the plane of the figure coincided almost with the Fraunhofer
diffraction pattern on two rectangular openings (Figure 4.5, c Iphoto not reproduced];
the long extent of the patterri with respect to the second direction is connected
with the fact that in this direction the resonator was equivalent to a planar
_ resonator; in addition, the compensating lens was not cylindrical as should be,
but spherical). The band contrast is very close to one, which indicates high
spatial coherence of the radiation (let us note that the distance between two
beams leaving.the resonator was ~120 mm). .
Noticeable deviations from the results of the diffraction at the exit aperture of
the laser and when using the system d~picted in Figure 4,6, b with exit of the
radiation in the form of a single beam in one direction from the axis of the reso-
nator were not detected. As a result of increasing the aperture width, in this
case the divergence was less than in the first case, and it was 2" or 1�10-5 rad
- (Figure 4.5, d jphoto not reproducedJ).
After performing these experiments the thesis that unstable resonators with large
N with uniform medium provide single-mode lasing with diffraction angle of
equiv
divergence of the radiation could be considered proved. It was only left to estab-
lish whether departure of the divergence of the radiation of real lasers from the
diffraction limit is a consequence of such prosaic causes as imperf ection of the
elements of.the resonator, optical nonuniformity of the medium, or the "high-order
modes" sometimes mentioned in the literature are at fault here. According to ~ 3.2,
the wave front of a light beam which is the fundamental mode of an unstable resonator
is formed in it just as on transmission of the beam through a multistage amplifier
(Figure 3.6). Therefore the best answer to the stated problem can be given by
direct experiunental comparison of the divergence of the radiation of a real ].aser
with an unstable resonator with divergence at the exit of the multistage amplif ier
57
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
FOR OFFICIAL USE ONLY
(see g 2.6) constructed from analogous active elements. This comparison was under-
taken in [195].
The basic results of [195] are presented in Figure 4.7. Curve 1 corresponds to the
angular distribution at the input of the final stage of amplification, curve 2,
at the output of the multistage system. The data for the laser with telescopic
resonator are plotted using x's; it is obvious that the multistage system in its
"pure" form insures somewhat less divergence of the emission. However, if we cover
the central part of the exit aperture of the multistage system so that the beam
acquires the same circular cross section as in the case of a telescopic resonator
the divergence of the radiation of the devices of both types comes close to
coinciding (see curve 3).
~ ' , i~
~ -
;
r
_
n.>
,
(a)
~ ~ ---1 - 1
- 0 J .T ! p; }x~ ray ~ b )
Figure 4.7. Angular distrihution of the radiation energy (the propor-
tion of the energy in a cone with ape:~ angle ~ is plotted on the y-
axis): 1-- at the entra_~ce of the final stage of a multistage system;
~ at the exit of a multistage system with circular aperture; 3--
annular exit of the radiation; x-- telescopic resonator, multi-
stage system with annular diaphragm.
Key: a. energy, relative units
b. angular. minutes
Attention is attracted by~the fact that the differences between curves 2 and 3~
cannot be explained by purely difiraction phenomena: the halfwidth of the angular
energy distribution as a result of diffraction of the plane front in a circular
opening was 5" more under the conditions of [195], and in the annular opening, a
total of 4" more. Obviously these differences were caused pri~uarily by the fact
that the optical uniformity of the central part of the pumped neodymium glass
rod is higher than its periphery (information about the nonuniformity induced in
such cases is presented in [200]); therefore the addition of the central part to
the annular exit aperture also causes a notic~able decrease in the divergence.
From Figure 4.7 it is obvious that preliminary stages and the final amplifier in the
given case make similar contributions to the total radiation divergence with re-
spect to magnitude. From the raaterials of ~ 3.2 it follows that for a telescopic
resonator used in [195] with M= 2 the distartions of the wave front coming as a ,
result of large-scale nonuniformities before the last pass through the active rod
and directly in this last pass are also similar with respect to magnitude. The
analogy between the multistage system and the telescopic resonator is quite obvious
here.
58
FOR OFFICIAL USF. ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
FOR Ol~FIC'IA[. IISf? ONLY
Thus, carefully made unstable resonators are actually capable of insuring the
same radiation divergence as multistage circuits (considering obvious corrections
connected with the differences in the exit apertures). As will be obvious in g4.3,
by using these resonators amplifiers can be constructed which provide enormous ampli-
fication of the wesk signal in one standard active element (considerable work is
~ required, in particular, in devices consisting of many channels synchronized by a
single master oscillator). At the same time, the experience of [195] demonstrated
that the problems pertaining to energy eff iciency are solved on the basis of un- ~
stable resonators much more simply than when using multistage systems (as a result
of a significantly smaller number of elements in the optical system of the device).
Therefore the sphere of application of the awkward multistage systems primarily re-
mains the rare cases where for the sake of achieving record radiation parameters
any means are considered justifiable.
The entire research cycle discussed above which was performed in the exampTe of
pulsed neodymium glass lasers with free lasing permitted sufficiently complete
discovery of the possibilities connected with the application of unstable resonators
in their simplest version. This cycle was preceeded by a total of two articles with
reports on experiments with similar resonators. The first of them is the initial
paper by Sigmen [4] which we have mentioned many times and in which, in addition :to
the formulation of a number of the most important theoretical arguments 3.1),
the preliminary results of studying a ruby laser with unstable resonator are also
discussed; the second is the paper [201] on experiments with a pulsed argon laser
having a discharge tube 7 mm in diameter. In both cases it was impossible to ob-
tain any positive effect from transition to the unstable resonator.
Gas Pulsed Lasers with Unstable Resonators. Problem of Setting up the Oscillations.
Subsequent foreign publications about the application of unstable resonators in
pulsed lasers began to appear only in 1972 [202, 203], and they pertained to the
case of C02 lasers. No new information about the properties of unstable resonators
was contained in these papers, and nothing special was presented on a purely tech-
nical level. Actually, among several of the first experiments the highest output
parameters were achie~ed in [203]: for a pulse energy of 3.5 oules, the radiation
- divergence was ~2�10 radians, and the brightness was ~2�10 1~ watts/(cm2-steradian).
For comparison we mention that in Soviet lasers with telescopic resonator based on
neodyuiium glass long before this the smaller angular divergence was "mastered" with
an output energy of ~103 joules, and in 1971-1972 there were already lasers with
- brightness of ~101~ watts/cm2-steradian) [204, 205].
Beginning with that time, unstable resonators began to be used also with invariant
success in lasers of almost all types. It is sufficient to mention, for example,
the creation of an electroionization laser with a pulse energy of 7500 joules [206].
ltowever, the results of experiments with metal vapor lasers are of the ;reatest cogni-
tive interest [207]: the specific peculiarities of these lasers forced a new look
at some theoretically known properties of unstable resonators. The fact is that
the amplification coefficient of the medium is extraordinarily high here; on the
other hand, the population inversion here exists for such a short time that during
- this time the light travels through the resonator only a few times. Since low diver-
- gence is desirable at all costs, it is of primary importance f~r the optical.cavity
to be capable of rapidly isolating the fundamental mode from noise radiation.
59
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
- FOR ONFI('lAL USF: ONI.Y
The problem of establishing oscillations in optical resonators was first encoun-
tered in 1961 by Fox and Lee [9]: the iterative calculations that they performeci
to a significant degree simulate the processes occurring in real lasers; the initial
field distribution written into the iterative procedur~ plays the role of the
"nucleatin~ center," the source of which in real lasers is spontaneous emission.
Then Fox and Lee noted the obvious relation between tlie rate of establishment of
steady oscillations and the difFerences in the losses of the individual modes:
actually, during the time of passage of the light through an empty resonator the
intensity ratio of any two modes varies by (1 - ~1)/(1 - ~2) times, where O1 and ~2
are their diffraction losses. Obviously the intensity ratio ~aill vary.in the same
way also in the presence of a medium ~aith uniformly distributed amplification coef-
ficient k with respect to volume (the eigenvalues of the integral equation of the
amp
- resonator turn out to be multiplied by the same coefficient exp(kampQ) in this case,
- (see � 1.3). If the medium ~aas uniformly excited at the time of beginning of deve-
lopment of lasing from tlie noise "nucleating center," the situation will be main-
tained until the lasing power builds up to such a degree that saturation level is
- reached.
rIence it follows that the more the losses of the individual modes differ, the faster
the generation of certain modes against the background of the others will occur; in
particular, the oscillations in unstable resonators must be set up much faster than
in plane, and especially stable cavities. For these reasons the rate of
establishment of the oscillations in the most unstable resonators increases with an
increase in IPiI.
although all of these facts were well-known, the problem of calculating the time
required for the diffraction directed beam to form in an unstable resonator from
spontaneous emission was clearly stated only in [207], and it was gradually solved
in [207-209]. It is true that the authors of the indicated papers for some reason
considering the given situation exceptional tried to get around using the known
results and methods of the theory of optical resonators, even such generally used
ones as the introduction of the equivalent resonator. Accordingly, for this quite
simple problem they obtained a very complex solution, making, in the course of the
matter, an entire series of erroneous statements (for more details see [210]). In
particular, their advice to select the resonator parameters so tiiat the converging
beam will expand to the former cross sectiona= dimensions invariably in an integral
number of passes is meaningless. Therefore it is better to discuss a signif icantly
simpler solution to the same problem presented in [210].
Let the active medium have tlie cross section 2a x 2a and be placed inside a tele-
scopic resonator (Figure 4.8). Let us follow, for example, the fate of the nucle-
ated radiation urhich at the initial point in time is emitted near the conve~ mirror
in the direction of a concave mirror. We shall take the spherical equiphasal sur-
face of the diverging wave located on the convex mirror, the center of curvature
of which is at the common focal point of the mirrors as the reference surface. The
complex amplitude of the nucleation field of one of the polarizations on this refer-
ence surface can be represented in the form of the series
` .z r
u (x, y) ~ ~in~ ~x~? /nti R ezr (l~ci ~ l, k, l - (I, ~ 1, ~ 2, . . .
n,~ ~ /
60
FOR OFF[CIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
I
~
Y~ ~ ~ ."u
I
' I
n! .
_ I ' _ -
1 jj - ~ ~ g
I ~ . ' : _ ~ - - - _
~ '
, ` b) .
~
i. , . . 0 .
I ` .
~
~
Figure 4.8. Transmission of spherical waves through a telescopic
resonator: a) one of the "diverging" waves; b), c) transmissior. of
diverging waves with centers of curvature near the zone 2a wide (li)
and outside this zone (c) o�~er an equivalent line.
This series corresponds to the set of spherical waves with randomly distributed
amplitudes ukl, the mean value of which can be calculated beginning with the power
of the spontaneous radiation for a solid angle (a/2a)2. The centers of curvature
of these waves lie in the focal plane and are shifted from tlie common focal point
of the mirrors in two directions a distance kaf2/2a, kJ~f2/2a, where f2 is the focal
length of the convex mirror, k and Q are the wave indices. The centers of curva-
ture of the waves, the radiation of which completely covers the concave mirror,
~ fills a zone 2a x 2a in size (see the figure); the number of such waves, conse-
quently, is equal to (4a2/~f2)2. As the figure ehows, some of the radiation of
waves Iying near this zone also reaches the range of the laser; however~ it very
quickly leaves the confines of the optical cavity entirely. Therefore, except
for the very earliest sta~es, the number of waves taking part in the process oF
lasing onset is (4a2/af2) , i.e. the spontaneous emission falling in a solid angle
of (2a/f2)2.
iQow let us trace the behavior of the waves; this is entirely possible within the
framework of the geometric approximation until the divergence tightly approaches
the diffraction limit. Obviously after the first reflection from the concave mir-
ror part of the cross section of each wave equal to 1/ri2 remains inside the reson-
ator; the waves themselves go from spherical to planar with propagation directions
inclined with respect to the axis at angles of (k/M)(a/2a); (R,/M)(A/2a). The width
of the entire range of angles, that is, the total divergence of the emission is
4,e' f ~ _ 2a A/
a~9-~~ ~ After each subsequent passage through the resonator, the amount
of radiation remaining in it decreases by M2 times. The slopes of all the beams,
and with them, also the total angle of divergence, decrease by M times.
_ Thus, after n passes through the resonator, the proportion of the radiation of all
of the waves entering into the "nucleating center" equal to 1/M2n remains in it,
~il
. FOR OFFIC? ~,I, USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
and the total "geometric" d~vergence is 2a/rln~2. The number of pas.ses n~ during
which the "geometric" diverbence decreases to ~/2a and thus the formation of the
diffractiollOdiverginb beam ~t~he ba~ic mode) is completed, is defined by the expres-
sion 2a/(M f)_~/2a or M = 4a /(af I3y this time the proportion of primary
"nucleating" radiation equal to 1/r12n~ ?(~f2/4a2)2 remains inside the resonator.
It is easy to see that this proportion corresponds to the radiation intensity which
initially pertained on the average to one wave.
In spite of the primativeness, the given analysis leads to the same quantitative
results which were obtained in [207-209] using somewhat more complex manipulations
with the "compressing waves." Using these results, it is entirely possible to un-
dertake specific calculations of the kinetics of such lasers. However, the most
important conclusion can also be drawn without performing such calculations. From
the above-presented relations it follows that the time of formation of a diffrac-
tion-directional beam with fixed dimensions of the resonator decreases slowly and
monotonically with an increase in M(inasmuch as np= ln [4(ri - 1)a2/aL]/ln M).
Thus, ttie thesis that to obtain ttie smallest possible divergence it is necessary,
considering the stipulations made on page 53 to use unstable resonators with the
largest possible magnifications, has received another, quite weighty substantiation.
ihis entire concept. was checked experimentally in [207]. When using a telescopic
resonator with M= 6 in a copper vapcr pulse laser, the calculated time required for
~undamental mode lasing turned out to be greater than the time during which
the radiation density inside the given laser could grow from the noise density
to the saturation level. As a result, the integral divergence with respect to the
pulse duration exceeded the diffraction limit by almost an order. For M= 200
this limit was reached, it is true, at the price of a sharp drop in radiation power
- as a result of the e:ctraordinary rise in the lasing threshold. Probably for inter-
- mediate M it would be possible to achieve both small divergence and sufficient
radiation energyl).
~ 4.2. Unstable Resonators in Continuous Lasers
Survey of Experimental Papers. Somewhat later than in pulsed neodymium glass lasers,
unstable resonators began also to be used in continuous gas lasers. Among.the
first publications only one short, but exceptionally interesting article [211]
stands out which to a great extent anticipated the future development of the reson-
ators of gas dynamic lasers; we shall return to this paper later. As for other
~ studies in 1969-1973, their subjects were low-pressure electric discharge COZ-
lasers [199, 212, 213] and chemical lasers [214~ 215]. The early paper by
Krupka and Suya [199] is isolated here. In this paper a telescopic resonator was
used in practice for the first time; as a result of the carefulness of the experi-
ment and the high optical uniformity of the active medium the authors were able
to observe the diffraction structure of the distribut'on in the far zone with full
width of the central peak on the order oF 1' (3.5'10-~ radians)~.
1This was done in the recent experiment [332].
2In this paper an analysis was made for the first time of the consequences of mis-
alignment and variation of the curvature of the mirrors in two types of confocal
unstable resonators.
62
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OF'FTCIAL USE ONLY
- It must be noted that in all of the enumerated studies eaicept j211J not only the
goals, but also the conditions differed sharply from the conditions of the.experi-
ments with neodymium lasers, primarily by the fact that in view of the modest di-
mensions of the resonator cross sections and the long wavelength, the Fresnel numbers
N were quite small. The theoretical limit of the angular divergence of these lasere,
on the other hand~ was not small. Thus, in the same paper by Krupka and Suya, the
width of the radiation ring at the exit from the laser was ~1 mm; the angle into
which half the energy went, although it was not measured, must have been equal to
5'10 3 radians under these conditions. This divergence could be completely achieved
also using a planar resonator. Therefore the basic positive result of the men=
tioned experiments is not the achievements in the f ield of angular selection, but
experimental testing of a number of conclusions of the theory of unstable resonators
pertaining to the magnitude of the losses, the nature of their dependence on N ,
and so on. A detailed summary of the results of testing the theory is availabg~uiv
in the highly substantial survey by Sigmen [216]. It is of interest that although
the majority of researchers, in accordance with the recommendations of Sigmen [167],
- have carefully selected the resonator parameters so that Nequiv Will be close to a
half integer~ no article contains data indicating that this choice actually
is useful from the point of view of angular divergence of the emission.
~ " ,i
/
~ ~
ZOcM
- 1 '
1 / / ~a~ / .
/ /j/~~~~~i.
~ /
" / `~j
e'
s ; . P~ ~,~I
- i'
~r ~ y/
Figure 4.9. Schematic representation of the active zone and resonator
of a powerf ul gas dynamic laser [211J: 1- planar mirrors, 2- con-
vex exit mirror, 3-- external concave mirror, 4-- exit beam.
Key: a. flow
Now let us more carefully consider the results of [211]. This article is devoted
to experiments witii a powerful gas dynamic laser; the schematic representation of
the active zone with the resonator borrowed from [211] is presented in Figure 4.9.
As is obvious from the figure, the resonator is installed so that the lasing radia-
tion will pass through the gas flow perpendicularly to the direction of motion of
the flow itself. This arrangement of the cavity~ which is called transverse, is
adopted because the high average powers require large flow rates of the gas mix,
and organization of uniform gas flows with large flow rates is possible only in
the case where the resonator elements are beyond the limits of the flow cross sec-
_ tion (in electric discharge lasers the same thing occurs also with the electrode
assemblies).
63
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
Tests were run on a 4as dynamic laser in j211] with resonators of two types, The
first type was a stable resonator made of two iarge metal mirrors, in one of whicli
a system of many holes 1,5 mm were made, the total area of which was on the order
of 6% of the total area of the mirror. This procedure does not withstand any criti-
cism from the point of view of divergence of the radiation 2.5), but it permits
realization of a resonator with given small losses to emission, and, as the
experience of [211] stiows, it can be used for experimental optimization of the
energy characteristics of the laser. [Jith this resonator the output power was 55
kilowatts.
The second type resonator is depi~*_ed in Figure 4.9. .It cvas formed by four mirrors
and was already unstable. One of the mirrors was convex, it served as the output
mirror, and accordingly was smaller in diameter than the others, The beam passing
near it fell on the additioi:al concave mirror and was focused on the hole in the
wall of the cavity through wtiich it was taken outside. The use of a system with
three passes throu~;h the active medium permitted, in spite of small amplification
per pass, operation of the laser with magniTication of the resonator M= 1.6; the
output power ~aas 30 kilowatts.
An almost twofold reduction in lasing power by comparison with the case of a stable
resonator indicates that the achievement of tlie maximum efficiency of energy con-
version in the gas dynamic laser resonator is not such a trivial problem as for
pulsed lasers. It is necessary to consider that such a resonator consists, as a
rule, of seve .1 carefully aligned (or even equipped with an automatic alignment
system, see [217]) cooled mirrors and is, together with the fastenings, the align-
ing slides, and so on, a quite complicated device. It is part of a still more
complicated engineering structure ~ahich is the fast-flow laser as a whole. Inasmuch
as the purely empirical selection of the optimal resonator under sucli conditions
becomes too thankless, tlie theoretical methods of analysis have been widely de-
veloped, the investigation of wliich we shall proceed with.
- Methods of Calculating the Efficiency of Flow Lasers. It is necessary to distin-
guish two cases immediately. Whereas the fast-flow laser operates in the frequency
mode where the excitation of the medium is realized by individual, periodically re-
peating pulses, the procedure for calculating its energy characteristics does not
differ in any way from the procedure for calculating the efficiency of the resonator
of_~rdinary pulsed lasers. Actually, one pumping pulse lasts, as a rule, 10-6 to
10 seconds; the medium during this time can travel such a short distance that it
can be considered stationary during the pulse (the flow velocity in the frequency
lasers usually does not exceed 100 m/sec. In pulsed lasers, as we know from g1.4,
- the state of the active medium in any elementary volume of it under the given
pumping conditions is uniquely def ined by the density of the lasing radiation pass-
ing through this volume. This makes it possible to talk not only about the
eff iciency of the laser as a whole, but a.lso about the efficiency of energy con-
version in any part of its volume, which sigr~ificantly facilitates the understand-
ing of the basic laws 1.4). The local nature of the dependence of the amplifi-
cation coefficient on the radiation density leads to signif icant simplification
also of the quantitative calculations of lasers with unstable resonators. First,
the equations describing the state of the medium themselves are simple in this case.
Secondly, it is very easy by using the threshold condition to find the radiation
density on the axis of the resonator before finding the distribution in the entire
volume (see � 4.1), which greatly accelerates the convergence of the ordinarily
used iterative procedure.
64
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2407/02/09: CIA-RDP82-00850R000400450052-5
F'nR OF1~1C'IAL USa: ONi:Y
In continuous-acti,on flow lasers the situation i~s, quit~ ~ifferent, The concept of
local efficiency~ here cannot exist in general: the previQUSly~ exci,ted active me-
dium flows through an entize beam of generated r.adiation, and the number of atoms
; reacting with the beam can be calculated only t~eginning with knowledge of the radi-
ation dist.ribution as a whole. It is also more difficult to calculate the radiaCion
density in advance on the system axis inasmuch as tt~e inverse population on the
axis d.epends not on this density, but on the entire history of the medium reaching
here, in particular, the field density on its entire path.
Similar laws occur also in the case of side optical pumping of in~uced~Raman scat-
- tering lasers frequently called Raman [combinaticn] lasers or VKF.1-converters[218].
Qn the other hand, the amplif ication coefficient of the lasing radiation on the
combination frequency is proportional to the pumping radiation density on the in-
itial frequency. On the other hand, the attenuation of the pumping radiation on
passage through the medium is almost wholly determined by its interaction with the
generated radiation ~aithout lasing, the primary pumping radiation is poorly
absorbed by the medium. It is easy to see that the pumping light density in Raman.
lasers is, from the point of view of resonator theory, the complete analog of the
inverse population densit; in flow lasers; the residual absorption in the Raman
laser medium corresponds to a decrease in the inverse population down stream with
respect to the gas as a result of spontaneous relaxation~ of the active medium of
the flow las~r.
~ In 1968 Alekseyev and Sobel'man [219] pointed out that the application of a planar
_ resonator in a Raman laser with side ptimping is fraught with highly unpleasant
- consequences. Inasmuch as the amplification coefficien~ near the edge of the
resonator from the side of which the pumping is realized, usually noticeably pre-
dominates over the losses an the combination frequency in the mirrors and the.me-
dium, the lasing radiation density here turns out to be extraordinarily high (if
its growth does not prevent the beginning of lasing on subsequent combination fre-
quencies, for which the radiation on the first combination frequency is itself
pumping). At the same time, with an increase in the density of the converted
(Ranan) radiation, the attenuation coefticier.t of the primary radiation increases
the region of powerful lasing screens the remaining volume from.the pumping ra-
diation. Thus a tendency shows up for the lasing region to contract into a very
narrow zone, and this is difficult to eliminate. Analogous phenomena must occur
also in flow lasers although usually not in such sharply expressed form (we shall
discuss the causes of this somewhat later).
In the case of an unstable resonator, independent development of lasing on the peri-
phery of the converter or the flow laser is impossible, for the lasing radiation
must come from the central section of the cross section. Extraordinary growth of
the lasing radiation density on the axis of the system is impossible, for it causes
rapid growth of the density also on the periphery, which leads to a decrease in
. the amplification on the axis. As a result, the regime turns out to be self-
balanced; the lasing radiation fills the resonator cross section, its density is
_ established on a level such that the number of pumping quanta reaching the axis in
the Raman laser or excited atoms in the flow laser insures exact satisfaction of
steady state conditions.
1jThe first letters oF the Russian words tt~at mean induced Raman scattering].
65
FOR OFFIC[AL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2407/02/09: CIA-RDP82-00850R000400450052-5
FOR (lFH'f~'fAL USN: ONLy
These arbuments are Eormulatecl iii (1~4], ancl tficy were confirmed by the experimental
data of tl~e above--quotecl reference [?11J (tli~ nonuniformity of the intensity distr~.-
- butior. observed ther~ Wltll r~s~~ect to cross sec~ion of the unstable resonator did
not exceed +50%) . In all of the suhseyueut theoretical ~~apers ~levotecl to estitnation
01 tht efficiency of the continuous lasers~ a study Is macle of rhe sel.f-halanced
lasing regim~ oii th~ lu~~~cst transversc mocl~~.
It is true that in t:t2e ~tip~ri~:i~nt oE [220] witl~ definecl resonance, a matheniatical
= ~nodel o.f a flow laser ~vas ~~rot~oy~~d irom whictl it follows ttiat the lasin~ regime must
be not steady, but autooscillatc.~ry o;ith an oscillation period on the order of the
= driFt time of ttie ~as tli~w tlirou~;li tlie reso~iator zone. If tliis moclel were correct,
- the autooscillations woul.u be ciiaractcristic of even a broader class of lasers than
the authors of ['L20~ tli~m~~~.1~~~5 pr~~osecil. liowevcr, ti:~ m~dium was considered
5ingle-compc~nent in [2':'_U], tlie s~~t~eel oC li~;i~C was consicierc~ci infi?iite, and tlie
geomerric a~proximatiun, vzilic3, even uncler the conclitions where tlic Properties ot
~ the medium vary sfiarply uv~~r eiie e::tent of sma.11 sections of
tlie resonator cross
section near its atiis. Juu~i_rl~ l>y tlie results of [221], i~ is sufficient to do away
_ with the proposition oi 5in~;lu-cumpotient miYture so that the trend toward the auto-
oscillations ~oill uccr~as~ 5h:~rply (ancl in real lasers, as a rule, mixtures are
used which contain moi-e tiian cne cc~mpon~nt). ConsicieraLion of the fact that For the
light to pass throu~;il tl~e resonator takes a finite time is extrer~ely important and
must also lead to damping of ~he oscillat~ons (from the papers at the beginning of
the 1960's devoted to tl?e ki.netic;; of solid-state lasers it is knok~n that neglect-
ing this facr usually lesds to absurd resul.ts). 'Thu~, tiie deep autooscillation
_ moue is hardly widc~E~rc~ucl. :~s fr~r th~ ordinary an~l llil3voi~lable oscillations of
intensity caused by fluctuntions of the resonator ~-factor, and so on, they can
hardly lead tu signiiicant departure ot the energy parameters of the laser averaged
.~ver a large tiuie interval fror.i tile calculation results in ttie quasistationary
approximation (see ~ 1.4).
In itseli the calculatiotl of ~}te efficiency of a laser operatin~ in the steady
state moue in the general cati~~ reciuces tu tin~ling a self-consistent combination of
- distributions of the amplif icat i_c~n coef f icient and the 13Slllb' f ield. The equations
describin~ the dependtnce oE tlie a~npli.fication coeffici~nt distribui.ion on Lhe ex-
citation conditions and the las_in~ field c?epend on the peculiarities of the medium
and are quite different. r.s Lor the lasin~; field distribution, for it it turns out
most frequentl~ to be suffi~ient t~ use the ~eometric approximation. Actually, we
have already discussed the causes by which it is possible to neglect the effect of
the edge diffraction in lasers with large ~i 3.3). The consideration of
e ~lu iv
large-scale nonunif.or~iities of the active medium does not require diffraction
approx~mation ("s 3.2; . ~ior.�ov~~r, if the medium is not too nonuniform, it is possible
also to take the patti of tii~ ueams the ~ame as wou?d occur in an ideal resonaror.
, ~~ence, it follows tt~at weak optical nonueiformity oi tEie active medium, just as the
edge dif~raction, can in gei~ert31 not be consi~'ered in the ~nergy calculation. On
- thP other hanri, inasmuch as ttie anguJ.ar divergence oi ttie radiatioa depends primar-
_ ily on the phase distribution at r_iie laser output~ and the nor.uniformity of
.lAt the end of ttie indicated article, an additional factor is erroneously introduced
~ to describe the phenomena of amplification satu.ration, at the same time as conside-
ration of these phenomec:a is alrcady built into the in:ttial ~quaticns.
66
FnR OFFICtAI. USE ORif.Y
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400054452-5
FOR OF'FICIAL USE ONLY
Llie intensity distribution influences it weakly, the amplification saturation
ptienomenon must be felt little in its magnitude; this conclusion follows from the
materials of ~ 1.1 and is confirmed by the results of sometimes undertaken specific
calculations (for example, [222]). Therefore the width of the radiation pattern
_ can be estimated in the f irst approximation without calculation of the energy
characteristics of the laser.
In order to f ind the self-consistent solution most frequently an iterative method
is used. The simplest iterative procedure used in the 1960's to study the pheno-
mena of amplification saturation in planar and stable resonators [100, 90, 109]
consists of the following. An initial field distribution (usually uniform) is
taken; this distribution is substituted in the equations of the medium; the latter
are solved, and the spatial distribution of the amplification coeff icient is found.
- Then the new f ield distribution is calculated as a result of single passage of the
initial beam through the resonator with the active medium. The newly obtained f ield
distribution is substituted in the equations of the medium, and so on. As applied
to the calculations of lasers with unstable resonators in a weakly nonuniform medium
performed in the geometric approximation, the given procedure can be written as
follows: r~+i (r) _%(tr.,,(r)], ~h�}i(r)=1%�(r)u�(rJM)'~ Where F is the aberration function
calculated considering the distribution of the amplification coefficient (see �
3.2), and the index denotes the number of the iteration. The calculations are
_ quite tedious, tor although only the Pield distrihution at the exit mirror u(r)
figures in the above formulas, for the calculation of F(r) it is necessary to deal
with the amplif ication coefficient distributions (and, consequently, the field dis-
tribution) in the entire volume of the laser.
As was noted above, the convergence of the iterative procedure can be accelerated
signif icantly by preliminary calculation of the radiation density and inverse
population on the resonator axis. In the case of lasers considered in the preced-
ing section, it was sufficient for this purpose to consider the conditions on the
_ axis itself. Later it will be obvious that this problem is also solved for flow
lasers, it is true, using more complex calculations. The data obtained on the
magnitude of the field under the state of the medium on the resonator axis are used
in the subsequent calculations; here the condition of stationarity of the regime
turns out to be automatically satisfied in all phases of the iterative procedure.
- Finding the amplification coefficient distribution next, this makes it possible for
' us to not limit ourselves to single "transmission" of the beam through the reson-
' ator with the medium and to find the steady state f ield distribution corresponding
to the given picture of the state of the medium. The iterative procedure acquires
the form ~''~a.i(r) _/[u�(r) J, ~~+i(?') = tl(0)r�(r)P�(r/M)/%�(r/fl!~)..., where u(0) is the
previously found field amplitude on the axis. As a result, the volume of the cal-
culations is reduced noticeably, especially for complex mathematical models of the
_ mediuni. The calculations of pulsed lasers with nonuniform optical pumping mentioned
in � 4.1 j188J and the calculations of gasdynamic lasers discussed below were
performed by approximately the same method.
Ot:~er procedures are also used which permit reduction of the volume of the calcu-
lations botti when finding the field distribution by the ~;ive~i parameters of the
resonator and state of ttie medium and for calculations oF lasers as a whole.
Although the authors of. each of these procedures pre~ent very convincing arguments
in its favor, it is now difficult to determine which of them is actually more
~
67
" FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFI('IAI, IISH: ONLY
effective. Therefore ttiose who desire to familiarize themselves in nlore detail witli
the method of the calculations are referred Lo numeraus. correspondinb articles
[222-227, 188, .156], and so on); at the same time we shall limit ourselves to the
fact that we shall explain some peculiarities of the calculations and the behavior
ot flow lasers in the example of gas dynamic lasers with two-mirror telescopic
resonator investigated in [188, 22S]. Al1 of the basic laws liere are the sam~ as
in the case of resonators of tlie type depicted in Figure 4.9 (if, of course, ~ae
compare lasers with identical amplification not on the beam width, but on the entire
path from one terminal mirror ot tlie resonator to another). Lasers with resonators,
the axis of which is "broken" not across, but along the direction of the gas flow
- behave differently; we shall not consider them.
Simplest ~fodel of a Gas Dynamic Laser Afedium. Procedure and Results of Energy Cal-
culations of Gas Dynamic Lasez~s with Twin-rfirror Resonator. In the overwhelming
majority of oas dynamic lasers the inverse population is created, by the proposal
of honyukhov and Proktiorov [229], by adiabatic expansion of a gas mixture consist-
ing primarily of C02 ancl N2. These two components also play the primary role in
the lasing process. C02 molecules are characterized by a comparatively short

~l oscillatory relaxation time; the laser transition is also realized in them. Fast
loss of ttle oscillatory energy reserves in this component is frequently compensated
for by resonance transmission of excitation from the :I2 molecules on collision
with them.
The relative molar concentration 1- c of the second component of the mixture is
_ larger than the first (c) and the majority of tlie total oscillatory energy reserves
is concentrated in the second component, N2, which is, therefore, a type of energy
"reservoir.'' As a result of the long natural oscillatory relaxation time of the
molecules of the second component, the energy from this reservoir is consumed pri-
marily for excitation of molecules of the first component.
~,lthough the atoms located on a quite large number of oscillatory levels of both
components participate in the operation of the laser in one way or another, Konyu-
khov [230] proposed limiting ourselves to a system of a total of two equations for
description of the relaxation processes of the medium occurring in the resoiiator
zone. These equations, being reduced to the maximum convenient fornt for calcula-
tions of the resonators, have the form [188]
dkl (r, r) ckz i- c) kl k~
dx - h - hl - -f- ~ ki,
dk2 (x, s) ckx i- c) kl ks
dx h - h=�
Here kl is the amplification coefficient of the laser radiation; it is proportional
to the oscillatory energy reserves in the fir5t component (the population of the
lower laser level is considered equal to zero, which usually does not lead to large
errors); k2 is the value having dimensionality (but not meaning) of the ampl+f ica-
tion coeff icient and characterizing the oscillatory energy reserves in N2; p and p-,
just as in the preceding section, are the densities of the lasing radiation fluxes
directed in opposite directions in the corresponding units; the designations of
the coordinates are presented in Figure 4.10; hl, h2 are the distances during the
time of passage of wllich by the flow of mixture oscillatory relaxation of the
68
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAI. USH; ONLY
individual components will occur in ttie absence of resonance energy excha.nge;
finally, h is the distance during the time of passage of which the processes of
resonance energy excha.nge, neglecting processes of other types (oscillatory re-
laxation, induced emission), cause relaxation of the ratio of the energy stored in
_ the components kl/k2 to the equilibrium value of ~c/(1 - c) (it is considered that
on collision of two different molecules the probability of exchange of excitation
does not depend on which of the molecules is excited before collision). Let us
note that as a result of the fact that the energy exchange between the components
is realized with finite velocity (h ~ 0), the total oscillatory energy reserve in
the medium cannot decrease too rapidly with as high a density of the generated
radiation as one might like. This should attenuate the manif estations ~f the
men*_ioned trend toward "constriction" of the radiation in the case oi a planar
- resonator.
- ~
: p ~r T)
L F
(a p7r., a)
i
l~ - (1 _ ~,L �
Figure 4.10. Diagram of a telescopic resonator in a f low laser.
Key: a. f low
It is possible to demonstrate that the transition from the density of the output
radiation p+ in the adopted units to the resonator eff iciency X defined as the
ratio cf the number of quanta of output radiation to the total number of excited
molecules at the entrance to the resonator should take place according to the formula
~ ,Y = f p+ (s) ds ~ f [lcl (s') /c, (s')J ds')-'~
where the f irst integral is taken with respect to the exit optical aperture of the
resonator, and the second with respect to the flow cross section surface at its
entrance to the resonator.
In spite of simplicity of the given model, its application insures satisfactory
precision of the energy calculations of the gas dynamic laser ~n a defined range
of variation of composition and parameters of the gas mixture j231]. In the greater
part of the specific calculations performed with its help, the results o� which
will be discussed below, the following initial data standard for gas dynamic
lasers were used: mixture composition 15% C02, 83.5% N2, 1.5% H2O; gas fl.ow
69
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFI('IAI. USF: ONLY
velocity 1500 m/sec; gas pressure in the vicinity of the resonator ~,1 atm, tempe-
rature in the flow 350 h, These data correspond to the following values oC tl~c
parameters which figure in the equations of tlle medium; c= 0,15, ti = 0.1 cni, I~1 =
4 cm, hZ = 250 cm. Let us also present the value of such an interesting ctiarac-
teristic of the active medium of the flow laser as the length I~ on which independent
relaxation of tlie excitation is r~alized in the absence of the lasing field. As is
known, any multicomponent mixture, the energy exchange rate between the ~omponents
of which significantly exceeds the rates of 'che remaining processes, has such a
unique relaxation length. For our medium this condition is satisf ied (h � hl, h2);
the total relaxation length is H=[(c/hl) +(1 - c)/h2]-1 ~ 25 em.
At the entrance to tfie resonator the active mediuin w s considered excited uniformly
over the flow cross section ancl in equilibrium (ki/k~ = c/(1 - c)), the total magni-
tude of ttie application coefficient of the entrance to the resonator k~L varied from
0.3 to 0.6 (L is the Flow width of tlie medium). For maximum energy pickup for the
location of the mirrors depicted in Figure 4.10, their sliape obviously must be
rectangular, which was assumed in the calculations. The reflection coefficient of
each mirror was considered to be 98%.
The calculations were performe:d L-or resonators both made of cylindrical mirrors and
made oF spherical mirrors. In the first case the calculations were not too compli-
cated inasmuch as all of the distributions are essentially two-dimensional. How-
ever, the resonator made of cylindrical mirrors can insure angular selection only
with respect to one direction. In the case of spherical mirrors which in prac-
tice is more important the calculations are greatly complicated: the gas flow
alternately intersects the planes passing through the axis of the resonator at
different angles to the direction of motion of the flow, and the solut~ons in these
planes turn out to be dependent on each other. Therefore when constructing the
solution in the entire volume it is necessary in all steps of the iterations to
manipulate the total three-dimensional field distributions and amplification co-
efficient distribution. The only exception is one plane passing through the reson-
ator axis on which the solution can be found without constructing distributions in
the remaining volume the plane in Figure 4.10. The solution of the correspond-
ing two-dimensional problem permits the field on the resonator axis to be found
immediately, which greatly facilitates subsequent calculations.
It also turned out to be convenient to divide the resonator by the axial plane
x= 0 into two parts having in ehe general case different lengths Q1, Q2, (see Fig-
ure 4.10) and to proceed with calculatiens of the distributions in the right-
hand side only after the solution on the left-hand side nas been completely con-
structed.
For optimization of the resonator, its magnification M, the widths of the left and
' right-hand sides 21 and QZ were varied. In addition to the effectiveness of the
resonator X, for each version the values of the relative losses characteristic of
flow lasers were also calculated relaxation in the volume Xrel' removal from
the resonator X and absorption in the mirrors Xmir. 1- X- Xrel - Xrem' Let
rem
us remember that X is the ratio of L-he number of qulnta leaving tlie laser in
the form of usef ul radiation to the total number of excited molecules entering the
resonator at the same time; the relative relaxation and removal losses are
70
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
FOR OFFICIAL USE ONLY
- fractions of this total number lost as a resu~t of the processes of deactivation
by collisions and as a result of removal of excited molecules thae have incom-
pletely interacted with the radiation from the resonator; the meaning of Xmir is
entirely clear.
/1.~1 ,
"
.Y~ ~ _ ~ ` ,
qb' ~a~ _
1
~4 /
n / i/
/
n, 2 ~b ~ >
_ X^ .
\ ~
n ~ s ~ ~z ~s a,,
Figure 4.11. Efficiency of the left-hand side of the resonator
X~, the rPlative relaxation losses in its volume, XQ 1 and the removal
from it Xrem as a function of the length of the leftehand side .Q1 for
rf = 1.33: curves l, 2, 4-- for k~L = Q.6, 0.5 and 0.4, respectively.
Key: a. XTe~ b. Xrel .
Let us proceed with the investigation of the results of the calculations pertaining
to the case of the rasonator with spherical mirrors. The relations are presented
in Figure 4.11 fo the efficiency of the left-hand side of the resonator XQ and
relative losses X~ , XQ as a function of the width of this part with respect to
_ , rem rel
the flow R.1. As is obvious from the figure, with a decrease in Q1 the losses to
relaxation are reduced approximately proportionally to Q1 at the same time as the
- losses to removal vary slowly; as a result, the efficiency XQ increases. The
meaning of these laws becomes clear if we consider the following peculiarity of
the solution for the left-hand side. On the axial plane x= 0 separating the left
and right sides of the resonator, the distributions and densities of the field and,
what is especially important, the amplification coefficient turned out to be quite
uniform in all of the calculated cases. Thus, over the extent of the left-hand
side of the resonator the amplif ication coefficient with respect to the entire flow
cross section decreases from the initial value of ki approximately to the threshold ~
value ki =(In M- In R')/L (R' is the mirror reflection coefficient). It is
necessary to add to this that for the selected mixture the energy exchange be-
tween components was so fast that the present radiation field could not signifi-
cantly disturb the equilibrium ratio between the number of excited molecules COZ
and N2. Hence it follows tliat the losses to removal from the le,f~t-hand side of
the re.sonator for any width must in the given case be close to kl/ki.
On the other hand, the less the width Q1 becomes, the greater rhe fields must~be
insuring such a decrease in the amplification coefficient. This leads to an in-
crease in the role of the induced radiation processes by ~omparison with the role
of the relaxation processes, that is, to an increase in X as a result of a de-
crease in ~rel'
71
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400054452-5
FOR OFFICIAL USE ONLY
Now let us proceed to the right~hand si.de~ As c~e have ~,een: the state o~ the
medium at the entrance to it can be considered in the first approximation uniquely
defined by the resonator losses. Therefore the only parameter which depends on
the conditions in the left-hand part of the resonator suhject to variation when
investigating tl~e right-hand part remains tlle radiation flux density on tlle axis
p(0, 0); this makes it possible significantly to reduce the number of variants
of the calculations of the right-hand side. ~
Ttie construction of the solution in the right-hand side offers the possibility of
- calculating its efficiency X~ defined as the proportion of the excited molecules
"processed" into outgoing radiation left after passage through the left-hand side.
The results of the calculations X~ for M= 1.33 and three values of p(0, 0) are
presented in Figure 4.12. It is obvious that ttie dependence of X~ on R2 differs
witti respect to nature from the similar dependence for the left-hand side: with
an increase in Q2, the efficiency first increases rapidly, then more and more
slowly and, finaIly, it reaches an extraordinarily gently slo~ing maximum. This
is exE~laineci by the fact that on passage of the active medium through the right-
hand side of the resonator ttie oscillatory energy reserve of the molecules is
completely extiausted; as a result of a decrease in field density down stream tiiis
process takes place more and more slowly. The maximum efficiency is achieved
when the amplification in the medium becomes so small that it compares with the
losses on the mirrors. Of cours, it is possible in practice to limit ourselves
to a significantly smaller width of the right-hand side, losing very little in
efficiency, and on the other hand gaining significantly in size of the mirrors.
For the above-indicated parameters of the medium, the value of k~ 15 cm (see
_ [228] and also Figure 4.12) can be used which is also used in the subsequent cal-
culations.
Xn
n, 4 -
- p~~~o) -nue
- U,O.~s
0,7, /.~'J~
. --------Q(K~s
-L._-- -L.----�--L--- -
0 Lj, !,'N
Figure 4.12. Efficiency of the right-hand �
side of the resonator as a function of its
length 22 for M= 1.33 and three different
p(0, 0).
Now it is possible to proceed with investigation of the properties of the ~esonator
- as a whole. In Figure 4.13 we have the relations for its efficiency X= X + XremX~
as a function of the magnification M and widCh of the left-hand part for Q2 = 15 cm.
It is obvious that the given relation coincicies with respect to nature with the
analogous f unction tor ttie left-side only (see Figure 4.11). This is also under-
standable: for small M and Q1, p(0, 0) increases, and as a result the efficiency
not only in the left-hand side, but also the right-hand side increases, and to-
gether with them, the efficiency of the resonator as a whole. The growth of X
with a decrease in M and 21 continues in the entire investigated range of parame-
ters, slowing only in the case of :ciL = 0.6 for Q1 ~ 3 cm and M~ 1.3; at this time
72
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
FOR OFFICIAL USE ONLY ~
l, already reaches 6U%. It makes no special sense to investigate the region of
still smaller values of M and kl: for ordinary sizes of the active zone of a oas
dynamic laser the geometric approximation ceases to be valid tfiere, and therefore
the direction of the radiation must become worse.
Thus, in order to acl~ieve higli efficiency of energy conversion it turns out to be
suff icient to select a total resonator width which is not too much less than the
relaxation length of tYie medium (let us remember that H= 25 cm), the width of the
left-hand side is selected approximately an order less, and the resonator losses
such that the threshold value of the amplification coefficient is approximately
half the value at the entrance to the resonator. This choice has quite clear mean-
ing and may fail to give the desired result only in case of inadequate energy
eYChange rate between the components of the mixture. Actually, ttien the total
oscillatory energy reserve will not be able to keep up with the gain reduction
in the presence of the field, and the losses to removal must increase.
In [22~3] a series of ttie corresponding calculations were made for mixtures with the
compositions 5% COZ, 90% i~2, 5% H20 and 8% C02, 90% N2, 2% H2O; in both cases the
value of k~L was 0.8, the pressure was taken equal to 0.05 atm, and the remaining
parameters were the same as in the above-investigated case. The energy exchange
rate between the components for these mistures was noticeably less (pri.marily
as a result of reduced pressure). The calculations demonstrated that for analogous
selection of the position of the axis and the dimensions of the mirrors, the
eff iciency on the order of 0.6-0.7 was achieved only when the threshold value
of the amplification coefficient was less than the input value by 3 or 4 times.
From the procedural point of view the following is networthy. Although the ampli-
fication coefficient in the plane x= 0 is as before close to threshold, the con-
tent of the excited molecules N2 here also depends on the field density. Inasmuch as,
in t-urn, in the entire indicated plane the field density is close to p(0, 0), the
- value ot p(0, 0) even for mixtures with small energy exchange rate remains the
- only parameter subject to variation for calculations of the right-hand side. .
Problem oF the Formation of Uniform Field Distribution with Respect to the Flow
Laser Resonator Cross Section. The above-investigated example is quite typical; '
it is clear from it what arguments must be and are being taken into account when
selecting the resonator For a fast-flow laser. It is also obvious that even the ~
~ x x
06 46 k,�L =Q6
0,4 k~ ~ (~6 0,4 ~
QZ " ~ry ~ QS~'~.~ 4' ' ~ '~s
- ~ ~~�~__1--- ~ ~
0 3 6 9 17, !S l~, cn /,Z 1,3 /;l �f N
n) 6l
Figure 4.13. Efficiency X of a resonator as a whole as a functioii
of its parameters with a length of the right-hand side ~,2 = 15 cm:
a) dependence of the magnitude of X on the length of the left-hand
side for ri = 1.33; b) Lhe value of X as a function of parameter i~i
Eor ~.1 = 3 cm.
73
FOR OFFiCIAL USE Ot~1LY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
F'OR OFFiCIAL USE ONLY
si~uplest unstable laser made up of syherical mirrors ~1ith accurate selection of
its parameters can entirely insure satisfactory efficiency of the energy conver-
sion. ciowever, for practical applications it is al~nost as important to have I1lOT~ ~
or l.ess uniiorm di.stribution oi the radiation intensity ~aitli respect to cross sec-
tion (otherwise the local thermal ].oads of the niirrors and angular divergence or
the radiation will increase). Although with uniformity of field disLribution in
the unstable resonators of this type things go better than in planar resonators,
they are not sufficiently good. Thus, in Figure 4.14 we have the intensity distri-
bution on a concave spherical mirror (curve 1) for the very case ~ahere efficiency of
60% (k~L = 0.6, Q= 3 cmy M= 1.3) was achieved for a mixture raith a pressure of
0.1 atmosphere. ~ere the graph is also plotted for a two-dimensional resonator
- (curve 2) for ~lie same parameters of the medium, losses and position of the axis
(let us note Cliat under tiiese conditions it has approximately the same efficiency).
From tl~e ti~ure it is obv:ious tI11C the field distribution is quite nonuniform,
~speci~ill;~ in ~he more impurtant case of spherica7. mirrors (iTi tile di.ffraction
approximatiou a sharp distribu~ion "peak" can smooth off somewhat, but the toLal
nonuniformity will still be clearly noticeable). A more favorable form oF dis-
tribution is observe~l only in versions with low efficiency, primarily with exces-
sively lar~e M when the Field inside the resonator turns out to be insuff iciently
intense. This type of situation obviously occurred in the above-described experi-
ments using a gas dynami~ laser [211], which i.s indicated by the low efficiency of
the resonator with satisfactory uniformity of distribution.
P ol
- n,zs
- i O,Z
_ ~
i~
~ 0,15
I
I ~
~ ~ 0,1
~
~ Z
i ~ -
~ -,1 D d 6 9 1Z 13 1B .z, c,w
Figure 4.14. Field density distribution in a concavc mirror: 1--
for sptierical mirrors, M= 1.3; 2-- for cylindrical mirrors, t�1 = 1.69.
1'he us~ o� multipass sy:~tems of the type depicted in Figurc 4.9 permits a sharp in-
crease in As a result of the complication of the system, a noticeable positive
eEfect is acliic:ved, in particular, tlie compactness of t}ie exi.t aperture inereases,
ancl i~s Lilling factur y increases (see l.l, 3.6; Figure 1.3, a b corresponds
to the single pass and one of the possible versions of multipass systems). How-
ever, it is still not possible to achieve a. co~bination of tiigll efficiency witli
hi~h uniformity of the field distribution here.
In order to solve this most important problem it is poss.ible to consider the prisr~
resonators investi.gated in � 3.5 in which the effect of wave aberrations of odd
order was signiFicantly attenuated by comparison with the ordinary telescopic reson-
ater. '1'he effect of the amplification coefficient gradient directed across the
74
FOR OFFICIAI. 1JSE ONI.Y
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R440400050052-5
FOR OFFICIAL USE ONLY
_ axis is identical to the influence of the gradi,ent of the i.ndex of refraction
~wedge) and the wave piiase, and it must be attenuated to the same degree.
It is tr.ue that in the far infrared range where the greater part of the flow lasers
operate, transparent total internal reflection pris.ms analogous to those used in
`solid state lasers are ha.rdly realizahle. However, for low magnif ications M which
are characteristic of the flow lasers with single-pass resonators, the application
of a confocal resonator becomes mandatory inasmuch as satisfactory filling of the
operating cross section with lasing radiation is also achieved in a resonator made
up of planar and slightly convex mirrors (see also ~ 4.1). Replacing the.planar
mirror by a dihedral 90-degree reflector made up of two planar mirrors, we obtain
the desired resonator. For equalizing the ~ntensity distribution, the edge of the
reflector must be oriented obviously perpendicular to the plane of Figure 4.10.
This possibility was investigated experimentally in the example of the f low-type
C02-laser of comparatively smaller power in reference [232]. The systems discussed
above were tested (Figure 4.15, a, b); for convenience of selecting the optimal
parameters of the resonator, the convex mirror was not spherical, but cylindrical
with regulated curvature [233] so that the unstable resonator would be two-dimen-
sional. For~the same purpose the radiation was coupled out by two auxiliary mirrors,
the position of which could be adjusted. The preliminary recordings of the radia-
tion patterns of the amplification coeff icient with respect to the resonator cross
_ section [234] demonstrated that the medium in the given laser relaxes quickly, and
the conditions are quite typical for continuous flow systems.
, p
.
~
~ ' I' I
i~ I ~ I ~ I
lloman� {
(1 ii 1 '
~ I
0
- ~ ~
P'
b) c I d ~
Figure 4.15. Unstable resonators in the flow-type lasers: a) resonator
made of planar and convex mirrors; b), c) resonator made of a corner
reflector and convex mirror; b) symmetric; c) asymmetric radiation output;
_ d) various versions of the type of projection of the exit aperture on
the plane perpendicular to the resonator axis; the axi.s passe~; through
the point 0, the line PP' is perpendicular to the plane of the figure;
a) to c).
Key: l, flow
The results of the experiments turned out to be }liglily hopeful. When using
the system depicted in Fibure 4.15, a a tenfold decrease in intensity downstream
was observed inside the generated beam. The differences between the intensities 2ad
the left and right halves of the resonator with corner reflector (Figure 4.15, b)
did not exceed 25%. Another interesting possibility is connected with the appli-
cation of the corner reflector: in order to increase the compactness of the exit
75
FOR OFFIC[AL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
apexture it is sufficient to resort to asxmmetric output o~ the radiation~ In the
case of a three-dimensional resonator tI1is is done using an output mirror, the
possible versions of the shape and arrangement of which are explained by Figure
4.15, ~1. In the two-dimensional resonator it is possible simply to remove one
of the two output mirrors (Figure 4.15, c). Ttien tl~e radiation which was incicient
earlier on this mirror and immediatelv left the resonator now makes an additional
pass through the resonator and leaves from the opposite side. The width of the ~
output zone approximately doubles, the radiation distribution in the far zone be-
comes more favorable.
- From the results of the experiments and rough estimates [232] it is also possible
to draw some conclusions relative to the energy characteristics of the flow lasers
in which an unstable resonator with corner reflector is used. If we select magni-
fication ~1 and the width of the left-hand side the same as in the case of an ordi-
nary resonator, the average radiation density here will remain as bef~re; the
efficiency of the left-hand side almost does not change. As for the right-hand
side, its width in the systems with beam "inversion" is automatically clos'e to the
width of tfie left and, as a rule~ falls far short of the optimal width
of the right-hand side of the ordinary resonators. However, as a result of much
great?r radiation density the efficiency of the right-hand side also remains
approximately on the former level. Thus, it is possible to hope that resonators
with corner reflectors will permit insurance of the same efficiency of energy
conversion as ordinary resonators with noticeably less width of the operating zone
and greater compactness of the exit aperture.
The confocal unstable resonators made of two concave mirrors must have similar
properties (see Figure 3.3, c), where "inversion" of the light beam is also realized.
EIowever, their use in many cases can cause undesirable phenomena at the common
Focal point o:E the mirrors where the radiation density reaches an enormous value.
Un the other hand, the great prospectiveness of the application of unstable reson-
ators investigated in ~ 3.6 with field rotation in continuous-action lasers is
unquestioned. The quite recently published results of the corresponding experi-
ments [235, 333] completely confirm the correctness of the arguments discussed in
this regard in ~ 3.6. The introduction of the operation of rotation of the cross
section actually cardinally e,qualizes the intensity distribution in the near zone.
- Sensitivity to astigmatism decreases so much that the latter is weakly manifested
_ even when the corner reflectors forming the llnear resonator include spherical
mirrors, the angles of incidence of the light on which are, therefore, 'ir/4.
Finally, the use of a sectional output (see Figure 3.28) instead of annular not only
increases the compactness of the exit aperture, but also leads to a significant de-
crease in divergence of the outgoing radiation without reducing its power.
It only remains to mention that sometimes reports appear in the literature and
resonators, the elements of which nave the shape of a surface differing sharply
from spherical conical, toroidal, and so on (see, for example, [236]). The
possibility of obtaining a small angular divergence of the emission in this way
still is f ar from obvious and we shall not analyze properties of such systems.
s 4.3. Unstable itesonators in Lasers with Controlled Spectral-Time Radiation
Characteristics
Simplest Types of Lasers witli Control Elements. For many practical applications
it is necessary that the stimulat~d emission have not only small divergence, but
76
FOR OFFICiAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
also given time--spectral charactezistics, Their achievement usually is insured by
tlie fact that the corresponding control elements are located insiJe the resonator.
The first publication on the creation of a monopulse laser with unstable resonator
belongs to the year of 1969 j189]. This was a solid state neodymium-doped glass
laser; a passive shutter covered the entire cross section of the active element.
The output energy was ~20 joules, the peak power was ~1.5'109 watts, the angular
divergence with respect to 0.5 intensity level was ~4"(2�10-5 radians), but a sig-
nificant part of the energy iaent to the "tails" of the angular distribution as a
result of light dissipation in the shutter liquid. As a result of rapid "spread"
of the emission over the cross section of the unstable resonators the pulse dura-
tion turned out to be noticeably shorter than when using a planar resonator.
Subsequently, monopulse lasers with unstable resonators have always been constructed
by one of two circuits depicted in Figure 4.16; here the shutter does not cover the
entire cross section of the active element, but only the exit mirror. This leads
to sionificant improvement of the output characteristics: the peripheral part of
tiie beam running "to the exit" from the laser, bypasses the shutter and does .
not undergo additional absorption and dispersion in it [204]. In addition, possi-
bilities are created for controlling the radiation flux having larger area using
a sma.~ll shutter. Zf we consider that the optically improved fast-acting~shutters
usually have small aperture, the prospectiveness of using such systems to construct
spikeless, monopulsed and other controlled-Q lasers becomes obvious. Thus, at the
beginning of the 1970's highly improved monopulse neodymium-doped glass lasers were
built with radiation brightness of ~101~ watts/(cm2-steradian) [204, 205]. Let us
also note the achievement of the quasisteady lasing mode of an analogous laser in ~
(237].
1 ~7 2 ~
- - ~ .
1 ,T
' 2
- - ~ -
I
. ~
Figure 4.16. Diagrams of lasers with modulated Q~factor: 1-- resonator
mirror, 2-- additional mirror, 3-- active sample~ 4-- shutter
'I'ite entire resonator cross section or its exit mirror can be covered, of course,
not only by ti~e shutter, but also tlie spectral selector. It is necessary, however,
when installing any controllin~; elements to ~leal witil the specifics ot unstable
resonators which impose restrictions on t}le types and mettiods of placement of these
elements. First of all it is necessary to take steps to prevent
the occurrence oF a converging wave. If the resonator is telescopic, the flat
surfaces of the controlling elements must be also inclined with respect to the
resonator axis just as any other interfaces (see � 4.1; in the light of this fact
Fibure 4.16 is provisional).
77
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
FOR OFFICIAL USE ONLY ~
Another important characteristic of unstable resonators complicating the problem
of controlling their emission is the fact that the introdu~tion of a small optical
wedge does not lead to sharply exceeding the lasing threshold, just as in a planar
resonator, but it causes only a shift of the optical axis. As a result, it is
necessary to depart from a number of traditional methods of control based on the
application of an optical wedge which varies in time':or depends on the wavelength.
Thus, the placement of a dispersion prism inside an unstable resonator leads not
to spectral selection of the emission, but only to the f act that the radiation
spectrum will be expandPd in the corresponding direction in the far zone instead
~ of one spot the spectral distribution image appears. Efforts to modulate the Q-
factor using a rotating prism can ha~dly lead to good results.
Thus, in monopulse lasers with unstable resonators it is necessary to use predomi-
nately passive or electrooptical shuttersl; for spectral selection primarily the
Fabry and Perot etalons are suitable, on passage through which the value does noC
change its direction. However, even here it is necessary to consider the fact that
in any linear, unstable resonator, not a plane wave, but a spherical wave will be
_ propagated in at least one of the two opposite directions. Under these conditions
- the introduction of the etalon will not cause intensity modulation with respect to
, the resonator cross section except in the case where the angular width of the maxi-
mum transmission of the etalon will exceed the angle of opening of the spherical
wave. The angular width of the maximum transmission of the etalon in turn is equal
to the angular distance between adjacent rings divided by the number of inferfering
beams N which depends on the reflection coefficient of the working surfaces of the
etalon. As a result, we arrive at the following condition imposed on the magnitude
of the etalc~n base t[196J:
t _ M ~.L ~
~ 2N ain A~p 1~f - 1 2NU ain ~p'
� (6)
where D is the diameter of the transverse cross section of the active element; M
and L are the magnif ication and the equivalent length of the resonator; ~ is the
" angle between the normal to the etalon surface and the resonator axis; f inally,
_(M 1)D/ML is the angle of opening of the diverging beam in the telescopic
resonatr,r (when deriving (6), the inequality a~ which usually is satisfied was
considered to be valid).
Multiple beam reflection in an inclined etalon also leads to some '~blurring" of the
position of the resonator axis, which in turn can cause an increase in the radiation
divergence. The corresponding calculations indicate that the condition of smallness
' of this increase by comparison with the diffraction angle again reduces to formula
(6). Inasmuch as the etalon base determines the width of the ragion of its disper-
_ sion (~a = a2/2t), consequently the expression (6) limits the minimum widCh of the
spectrum reached in the laser with direct placement ~f the selecting etalon in the
telescopic resonator.
1Self-Q switching of unstable resonators described in j238] and a number of
subsequent papers is realized only in the smallest lasers and leads to outp~t
parameters which are hardly recorded even for this class of laser. .
78
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-40850R040400054052-5
FOR QFFIC'IAL USF: ONLY
Lasers with 'Cllree-rlirror Resona~or. Further improvement of the methods of con-
trolling tt~e emission of lasers witi~ unstable resonators is connected with the
idea formulated and experimentally sub~tantia*ed in [153J of the effect on tlie
central section of tlie resor~ator cross section, from which the radiation "sprea~a."
For normal course of tlie beams tt~is section is the analog of the master oscillator,
and the remaining part of the cross section, a multipass am~slifier. In order to
realize this idea, it is sufficient to make an opening at the center of one of
the mirrors and install an auxiliary mirror behind it; the control elements of
very small size can be conveniently placea in the narrow "appendix" formed in this
way. This three-mirror resonator and the scheme equivalent to it without an open-
ing in the mirror are depicted in Figure 4.17.
-
- -
~ ~ ~
~
Fioure 4.1i. Diagrams of resonators with
radiation control in the central section of
the cross section.
Ttie possibility of efficient radiation control using the given procedure is limited
by the fact tliat, as follows from the materials of s 3.4, a laser with unstable
resonator is capabl~ ot lasinb even with a completely shielded central section of.._
= the cross section. Therefore, if in the "a~pendix," f~r example, the siiutter and
the axial section are "blocked" at a given point in r~me and the lasing threshold
increases insignificantly, independent lasing which is not controlled, will de-
velop in the remaining volume. Flence, it is clear what important practical sig-
nificance the nature of the dependence of the lasino threshold on the dimensions
of ttie covered central segment of the cross section has.
The results o~ the measurements of this relation performed in [191, 168, 193, 196]
turneci out to be entirely in correspondence to the theor~tical representation
~ developed in ~ 3.4. In the case oF two-dimensional resunato~s the threshold in-
- creases with an increase in hole sizes (more precisely, tha slit width) extraordi-
narily sharply. Thus, ttie shielding of the central. section ~3 mm wide has approxi-
mately tripied ttie threstiold intensity of tiie pumping of the laser described in
~ 4.1 basc~cl oii a rectanbular lar~e active element with resonator made of planar and
cylindrical mirrors (Figur~ 4.6) [168J, Therefore the ccntrol of the radiation
~ characteristics of lasers wi.th two-dimensional un~~a~le resonators is realized

~
without sE~eci,il difticulty. In particular, the use of the simplest ~3ise modulator
- has made it possiblc to convert the m~ntioned laser to the regular "spi.ke" mode
wich T'EpE.(:1C10I1 of the:;e spi.kes from 25 to ~0 kilc~hertz [168]. In reference [193]
special selection of tl:e radiation of the same laser without a noticeable decrease
~ in ir.s output power was successfully produced by th~ introduction of the Fabry and
I'erat etalon into the "ap~~endix."
Lsc~rs ~J1~I1 resonators r~~de of spherical mirrors behave entirely dif.ferently. Their
- lasi.ng t'c~resholci i~icre:tses very slawly with the s:iz:~ of the central circular
79
~ FOR OFFICIAI. USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2047/02/09: CIA-RDP82-00850R400404050052-5
, FOR nFFICIAL USE: ONLY
' opening. '1'liu:~, i.n a 1.i~~r with a~~tivu iiv~~iymium cloped ~;lass eleinent 45 mm in clia-

J meter and a telescopic re5on:~tor with magnification rt = 2 for a hole diameter i.n
the concave mirror oL 4:nm, ttw ~~ur;t~in~; tiir~~sl~al~i intensity increased Uy 1.3 ti.nir.s;
for a diameter of 8 nm~, it ~ipproxici:,tely ~ioubled hy comparison with Ll?e cas~ wher.~
; ~_il~ no1.e was absent. Ev~~i the pr~~sence af a t~ole with a di_ameter of 2t? mm and almosL
. reaching the diameter of the conve:~ mirrur (?2 nun) caused only a triple increase in
~ the self-e~ccitation tlir~.shold [ 19? ] .
;Cf'
L ~
~ \
I ~ a ~
4~
_ ^i
A
~ Q
L cti6' -
- E~ >
`u ~r ` A!z
;a.l:
~ ~ ~ ~ ~
Q3 1,' S 10 ZU 0. In this case the beam
I is the donor, and the second is amplified. From (7) it is obvious that -k~aIl
sin d has the meaning of the amplification coefficient in a medium for a second
beam in the presence of the f irst. The density of the amplified beam increases
while the condition I1 > I~ = a/(2k~~a~ sin d) is satisfied.
It follows immediately from this that for maximum use of the energy af the donor
beam it is desirable that its density decrease in the zone of interaction of the
beams to a value of I0. In the most favorable case where the densities of the two
beams at the entrance to the medium I'1, I'2 are constant with respect to cross
section, this condition can be satisf ied by using the flat layer of the medium (Fig-
ure 5.8), the thickness of which must be correspondingly selected. In Figure 5.9,
a, b, the data obtained by solution of the system (7) on the optimal thickness of
the layer of inedium for the cases depicted in Figure 5.8, a, b when the beams
enter into the layer from one or different sides are presentedl. Although for the
same I'1, I'2 the optimal thickness of the layer in these two versions does not
coincide, the attained density of the amplif ied beam I2 m~ turns out to be the same;
1The calculations for the second of these cases were performed by V. D. Solov'yev.
109
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/42/09: CIA-RDP82-00850R040400050052-5
FOR OFFICIAL USE ONLY
the data on it are presented in Figure 5.9, c. It is obvious that high energy
ef f iciency of the "transf er" (on the order of 50% or more) can be achieved only
. z ~
~I y`
~ d~ J B B dz{ T,B x
~ - ~
J II
d) d~
Figure 5.8. Geometry of the interaction of beams during "transfer"
in a flat layer of inedium: a) one-sided incidence of the beams on ~
the layer; b) counterbeams.
CO B ~~~"~(1~ ~~~,r.r.r/IO ~
1,0 ` J'/lo =q/ 4
J '
J
_ D,~
15-
nl Ji/~ .
1'
s
ne d ~ _ ~ 10 - r/I =J
~J~ - t 0- a ~ t,71
>,0 - aJ QJ
~ ~ 5-
0,5 ~
~ _i_.~_ � ~
0 5 10 15 80 ZS1~/I~ 0 ,f 10 1S I~/le
d ~ e)
Figure 5.9. Optimal thieknesses of tfie layers of the medium and m~ximum
attainable density of the amplified beam during "transfer": a), b)
dependence of the thickness ~z of the layer of inedium in the initial
values of the beam densities I'1, I'2 in the diagram in Figure ~.8,
a, b, respectively; c) dependence of the maximum attainable density
of the amplified beam I2 ~X I'1, I'2.
Key: 1. opt ~
when the initial density of the donor beam exceeds I~ by at least several times;
the initial density of the amplif ied beam also must not be too small. ~ .
Such is the theory of the interaction of beams with the holographic phase lattice
created by them in the quasistationary mode in general outlines. Now we shall
discuss the causes of the lattice shift with respect to the interference pattern
required for energy "transfer." ~
In individual cases the shift occurs as a result of a natural anisotropic medium
in which. the hDlogram is created. The classical example of this is descri~ed in
the well-known paper by Shtebler and Amodeya [298] devoted to the investigation of
- phase lattices in a lithium niobate crystal. On illumination of this ma.terial
' . 110 ~
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-04850R000400050052-5
FOR OFFICIAL USE ONLY
charge carriers are relaeased ;~n it, whi.ch is the cause of local changes in the
index of refraction. As a result of anisotropy o~ the given material, the drift of
the free carriers here is directed in an en~irely defined direction which also
causes a shift of the lattice recorded in the presence of two coherent beams. The
authors j298] observed noticeable redistribution of the beam intensities. It is
true that they used the given phenomenon not for correction of the wave front, but
_ for discovery of the previously unknown sign of the free charge ~arriers which can
be established by comparing the direction of the energy transfer process with the
direction of conductivity of the given crystal. This phenomenon can hardly be
exemplary of the dynamic correction the setup times here are tens of seconds.
In the general case of an isotropic medium a defined lattice shift can be obtained
directly during interaction of the beams, obviously continuousYy shifting the medium
in the direction perpendicular to the lattice planes. The shift must appear as a
result of unavoidable inertia of the processes of recording and erasing it. Later .
it will be seen that ~t is possible to obtain the desired result in practice
using this procedure only when using such comparatively slow recording mechanisms
as thermal recordings. According to [297] let us consider this version.
_ For the geometry of the interaction of the beams depicted in Figure 5.8, a, the
density of the thermal power dissipated as a result of absorption in the medium is
6jI1 + I2 + 2?IlI2 cos(2~rx/A)], where /l =~/2n sin A is the period of the interfer-
ence pattern, and the remaining notation was as before. The origin of the,coordi-
nates is matched with one of the peaks of the interference pattern (it is possible
to neglect its small distortions along the Y and Z axes in the given investigation).
A simple analysis shows that in the case of stationar~ medium the dependence of the
temperature on x in the presence of such peak release sources has the form T= T
_ ~ . _ , mean
a ~ ~ 9
Z llji~s x x( Zn
) coq ~2~s ~ with setup time of the spatial modulation T-- x(Zn
where T is the mean temperature of the medium slowly increasing with time, K is
mean
zhe coeff icient of thermal conductivity, c is the heat capacity and p is the density
of the medium. This leads to the occurrence of the phase lattice with modulation
amplitude L~n 2 y~ Iils K(Zn)Z~I ~7 I. ' .
If the medium is shifted continuously along the x-axis with a velocity V, the lattice
setup time remains as before; its stationary position turns out to be shifted by ~
~x =(/~/2~r)arctg w'[, the depth of the modul tion f the temperature and the index
of refraction decreases in the ratio (1 + w~T2)-192, where w= 2~rV/11. A comparison
of these data with (5) indicates that the parameters of the "transfer" theory under
- the investigated conditions assume the values
~ i .
a x 2 n dT ~1 ~o~t~) a~ 8=- nrctg wt.
As the velocity of the medium increases, d increases, approaching the optima.l value
of ~r/2 from the point of view of the "transfer," and on tfie other hand la~ decreases
rapi~ly. From (7) it follows that the intensity of the energy transfer process
from beam to beam is defined in the final analysis by the value of ~a sin 8~. This
~
value reaches the maximum equal to 2n x(i I~~-I, for w~ = 1/T; thus, the optimal
111
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/42/09: CIA-RDP82-00850R000400050052-5
F'OR OFFICIAL USE ONI.Y
speAd of the meium is V~ ~(Z y~n p 9in 0. The density o~ the "donor" beam
for which the amplification of the second beam as a result of "transfer" compensates
for its absorption in the medium; for Vp is equal to
I, - 4kx sin' Ol C n I d~ I)'
All of the relations derived above are also valid for the case of "counter" beams
(Figure 5.8, b) except here the index of refraction is not modulated along the
x-axis, but along the z-axis; movement of the medium must be realized in the same
direction.
Relation of the Idea of Dynamic Holography to the Phenomena of Induced Scattering.
Lasers Based on Various Forms of Induced Scattering. Finally the time has come to
explain what the logical development of the idea of holographic correction has led
us to. For this purpose it is sufficiez~t to compare two facts. First, when in-
vestigating the above-described "transfer" process in the coordinate system which
is stationary with respect to not the interference pattern but the medium, the in-
teracting beams acquire a def ined frequency difference as a result of the Doppler
effect. Its magnitude, as is easy to see, is w, which explains why in this coor-
dinate system the interf erence pattern is shifted at a velocity -V. Secondly, as
follows from (7), the differential amplificaiton coefficient of the radiation with
respect to beam II does not at all depend on its intensity and~is completely deter-
mined by the density of beam I. Therefore when the latter has sufficier.t power
that the "transfer" process takes place, in its presence not only the specially
formed radiation is subject to application, but also the randomly scattered or
"noise" radiation of proper frequency and direction.
The phenomenon consisting of the fact that on illumination of the proper medium by .
a powerful coherent beam amplif ication of the radiation takes place with frequency
usually somewhat shifted with respect to the initial frequency is, as is known,
called induced scattering of light. A specific amplif ication mechanism was de-
scri'~ed above connected with variation of the index of refraction as a result of
heating of .the medium during absorption of light. This type of induced scattering
is actually known. It was discovered in 1967 and since that time has been called
induced thermal scattering (ITS) [299, 300]. In accordance with the above-pre-
sented calculations, the maximum amplification of the scattered radiation occurs
on a frequency shift with respect to the initial frequency in the antistokes di-
rection (that is, larger) by w~. The ITS threshold on this frequency is defined by
the formula (8); for other frequencies the threshold increases propor~tionally to
~a sin d~max~~a sin d~ = 1/2(wT + 1/wT).
The "transfer" observed in [298] in lithium niobate pertains to the phenomena of
induced scattering on conduction electrons in semiconductors [301]. On the other
hand, al'_ types of induced scattering permit analogous "holographic" interpretation
and are ~'istinguished only by the mechanisms which cause variation of the index of
refraction and shift of the phase lattice with respect to the position of the in-
terference pattern. The reason for the shift almost always is movement of the in-
terference pattern with respect to the medium as a result.of the difference in
frequencies of primary and scattered radiation (the source of the "neucleating"
photons with shifted frequency for spontaneously occurring induced scattering which
occurs predominately in the forward and return directions, usually is the scattering
112
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
on the random dynamic fluctuations of the index of refractian~, The fact that for
ITS the frequency of the scattered radiation is shifted with respect to the initial
in the direction opposite to the usual shift direction for induced Mandelstam-
Brillouin scattering on hypersonic waves (IMBS) and induced Raman scattering (IRS)
- ar.e explained simply by the f act that the nonlinearity parameter a has different
signs in these cases.
Thus, the dynamic holographic correction reduced to the well-known idea of solving
- the problem of divergence by constructing radiation converters based on induced
scattering no other is given. Our corrector on the thermal hologram in the
moving medium is none other than the ITS amplifier with frequency shift compensated
as a result of the Doppler effect. Supplementing this amplif ier by feedback a
resonator obviously we can construct the analogous laser.
For ITS, the frequency shift is so small that it actually is easy to compensate,
~ shifting the medium: according to the estimates of [297] if in the diagram in Figure
- 5.8, a the medium is a liquid of the type of an organic solvent, the required speed
of its movement is a total of ~10 cm/sec. If the shift is compensated, it is
possible to use the part of the initial beam transmitted through the shaper as the
amplified. The first experiments with an amplifier of this type are described in
[302]; the source of primary radiation split into two interacting beams was a
single-mode ruby laser operating in the "spike" mode of free lasing. With a total
lasing pulse duration of ~400 microsec.onds, the lattice relaxation time was ~100
microseconds, which, in turn, signif icantly exceeded the time interval between
individual "spikes"; therefore for the extent of the greater part of the pulse the
lattice was in practice quasistationary. The highest energy eff iciency of "trans-
fer" was achieved for the initial ratio of the beam intensities of 10:1; after
passage of a liquid moving at a speed of 8 cm/sec, this ratio became equal to 1:3,
and the amplified beam power was about 50% of the total power of the initial beams.
High inertia of the thermal processes permits observation of the phenomenon of non-
steady "transfer" predicted in [303] and consisting in the fact that for short-
term interaction of the beams the energy transfer to the weaker one takes place
- even if the medium is stationary. This has the following e~lanation: when the
unshifted lattice begins to be recorded and the scattered radiation appears, it,
- in accordance with (6), leads to additional phase incursions of the initial beams.
As has already been noted, for a beam with lower intensity this incursion turns out
to be larger; as a result, the interference pattern, while the processes of setting
up the thermal lattice are taking place, moves through the medium which causes
"transfer." The direction of the displacement is such that the weak beam is sub-
jected to amplification. As applied to the problems of correction of the wave
fronts this phenomenon was experimentally studied in references [302, 304, 305,335].
Although the papers studying the "transf er" on the thermal lattices turned out to
be highly useful for understanding the possibilities of dynamic holography, it is
not possible now to count on the fact that by using this process we will decrease
the divergence by the radiation of real lasers. Here the mechanism of recording
the lattice itself is unfavorable. The heat release required for its formation has,
in addition to everything else, a negative effect on the optical quality of the
medium. As a result of unavoidable nonuniformity of heating of the medium, varia-
tions of the index of refraction averaged over the lattice period appear; in the
liquids, in addition, light scattering begins on the formed gas bubbles and so on.
113
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
All of this, in turn, leads to an increase in the divergence of the beam itself into
which the energy is "transferred.~' The effects of this type begin to be manifes-
ted in practice by comparatively small energy levels of the beams j335].
Idow let us proceed to other types of induced scattering. For ITS the energy
"transfer" to a weaker beam with the same frequency is achieved without special
diff iculty even in the quasistationary mode. In the presence of IMBS and, in
' particular, for IRS everything looks somewhat diff erent. The frequency shif ts here
are not so small, and the possibility of compensation for them using the Doppler
effect is for a number of reasons for the most part speculative. It is alr2ady
suff icient that in the former case the medium should be shifted at the speed of
sound in it, and in the latter case, many times f a~ter. Therefore by :using the
' given forms of induced scatter;^~ having lower thresholds in the majority of inedia
than ITS, it is possible to construct only lasers and amplif3ers of radiation
with shifted frequency. Nevertheless. the "transfer " with splitting o~ the
initial beam into the donor and amplif ied beams is realizable and in this case the
required frequency shif t of the later amplif ied beam can be obtained using the same
induced scattering. When using this system [306] conversion on IMBS was obtained
with transfer on the order of 80% of the donor beam power to the amplif.ied beam.
As a result of the conversion, the axial luminous intensity increased by more than 3
orders.
As for the IMBS and IRS lasers, their properties are quite well-known. These lasers
have, of course, many specif ic peculiarities distinguishing them from stan3ard in-
verted medium lasers. First of all here although the primary radiation frequently
is called pumping radiation as before, theoretically different requirements are
imposed on its coherence the sources of the pumping of lasers based on induced
scattering usually are other lasers with spectral radiation selection. Complex
phenomena arise as a result of the f act that in the case of induced scattering the
theoretical role is played only by the magnitude of the frequency different ~w,
but not the exact absolute values. Therefore when the density of the converted ra-
diation itself begins to exceed the induced scattering threshold, lasing is
- excited on a frequency 2~w from the initial frequency, and so on. Finally, as
already been mentioned in ~ 4.2, with respect to the nature of the interrelation
between the excitation and the generated radiation f ields the converters based on
induced scattering more resemble flow lasers than standard lasers with a stationary
medium.
In spite of all their peculiarities, the induced scattering lasers are, of course,
- the most genuine lasers. The principles of the selection of the type and parame-
ters of the resonators remain the same as in ordinary lasers; the resonator defor-
mations exist exactly the same, including those caused by heating of the medium.
I3eing the basic, theoretically unavoidable source of heating, the Stokes losses
in the IRS and IMBS lasers are much ~.ess than in the ordinary lasers which gives
rise to the prospectiveness of this entire area. At the present time a number of
experimental papers have already been published in which the conversion of the
radiation with the help of IMBS and, in particular, IRS, has led to a decrease in
the divergence (a broad bibliography exists, in particular, in [218, 306]). It is
- not appropriate to enumerate all of them; let us only mention one interesting area
of research,
In 1973 when studying the properties of the IRS converters j307] and IMBS conver-
ters [308] with pumping by the radiation of multimode lasers, it was possible to
114
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00854R004400050052-5
FOR OFFICIAI USE ONLY
observe signi~icant amplification of narrowly directional light hea~s wi.thout sig-
nif icant variation of their spatial structure. Tfie nontrivialness of the situation
consists in the fact that the multimode pumping field is nonuniform and actually
divided into a large number of randomly distributed spots with respect to volume,
khe characteristic dimensions of which are defined by the parameters of coherence
and the geometry of the illumination. The theoretical analysis of the conditions
under which the nonuniformity of the pumping field does not imply a change in the
spatial structure of the amplified beam (as a result of t!~e statistical averaging
of the effect of a large number of small nonuniformities) was performed in
references [309, 310]. The f irst purposeful experiment checking this model was
described in [311].
COPYRIGHT� "Nauka" Glavnaya redaktsiya fiziko-matematicheskoy literatury, 1979
10,845
CSO: 1862/192
115
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
NUCLEAR PHYSICS
UDC 621.384.64
LINEAR INDUCTION ACCELERATORS
Moscow LINEYNYYE INDUKTSIONNYYE USKORITELI in Russian 1978 (signed to press
21 Apr .78) pp 2-10, 244-245 ~
[Annotation, preface and table of contents from book "Linear Induction Acceler-
ators", by Yuriy Petrovich Vakhrushin and Aleksandr Ivanovich Anatskiy, Atomizdat,
1730 copies, 248 pages] �
[Text] The book preser.ts elements of the theory and engineering of new powerful
relativistic electron beam generators--linear induction accelerators. The work-
ing principle of linear induction accelerators is described, the theory is given
as well as the results of development of the accelerating system, the beam shaping
and transport systems; designs of existing accelerators and those under develop-
ment are examined, and their future is evaluated. Although the book is devoted
to linear induction accelerators, some of the problems that are considered have
wider applications; for example pulsed magnetic reversal of ferromagnetics and
accelerating voltage pulse shaping can be used in the development of pulse trans-
formers in the nanosecond range, and systems for tailoring nanosecond current or
voltage pulses
The book is intended for engineers and scientists engaged in the development and
application uf electrophysical facilities; it may also be of use to undergraduate
and graduate students in institutions of higher education that specialize in elec-
trical engineering. ~
Figures 147, tables 10, references 204.
Preface
In this book the authors have attempted t~ present the elements of the theory and
engineering of new powerful relativistic electron beam gnerators--linear induction
accelerators. Interest in this question is due to the ever increasing use of
intense electron beams in science and engineering: in research on controlled nu-
clear fusion, new efficient methods of accelerating charged particles, low-loss
long-range energy transmission, high-power electronics and so on.
Although the book is devoted to linear induction accelerators, some of the problems
- dealt with have wider applications. For example, the materials of chapters 2 and
3 may be used in developing pulse transformers for the nanosecond range, and systems
for tailoring nanosecond current or voltage pulses.
116
''~R OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007102/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
In preparing the manuscript, the authors used mainly wurk done with their partici-
pation at the Scientific Research Institute of Electro~hysical Apparatus imeni
D. V. Yefremov [NIIEFA] in connection with developing and making linear induction
accelerators for various parameters. In addition, the book uses materials published
- in the Soviet and non-Soviet literature, most of them dealing with description
of the construction of l~near induction accelerators. The book summarizes the
developments in this field of accelerator technology over the past ciecade. The
authors hope that the book will attract the attention of workers in science and
technology, which in turn will further the development and use of these effective
generators of intense relativistic electron beams.
Chapters l, 4, 5 and 9 were written by Yu. P. Vakhrushiz, chapters 7, 8 and the
appendix were written by A. I. Anatskiy, and chapters 2, 3 and 6 were written jointly
by both authors.
The authors thank the reviewers for constructive comments that were taken into
consideration in preparing the manuscript for print.
Introduction
In Ref. 1, devoted to the future of science, Academician M. A. Markov noted tnat
- side by side with the development of high-energy physics is the development of
physics of beams of relatively low energy, but high intensity. These powerful
beams have nearly limitless possibilities for practical application in engineering,
medicine and the national economy. In particular, a broad scientific vista is
opened up by the use of intense relativistic electron beams. This vista covers
- the production of plasma with heating to thermonuclear temperatures, new collec-
tive methods of ion acceleration, amplification and generation of electromagnetic
microwa,re radiation in the optical and x-ray bands, creating high pressures, study-
ing solid-state phase transitions and properties of materials and so on [Ref. 2].
For these purposes, the beams must have the following parameters: electron energy
0.5-30 MeV, beam current 103-106 A, pulse duration 5-500 ns, and beam energy
LO3-IO6 .J.
- To produce such beams, many laboratories around the world have developed and are
now operating accelerators of intense electron beams [Ref. 3]. But they have limits
on pulse recurrence rate and efficiency. However, as work with intense electron
beams makes the transition from the field of. research into the area of industrial
application (for example to produce an ion beam with high average current by using
a collective-field accelerator [Ref. 4], to produce intense x-ray bursts [Ref. 5J,
to make a powerful industrial microwave oscillator [Ref. 6, 7] and so on), acceler-
ators become necessary that not only produce electron beams with the required
parameters, but that have high efficiency, and are capable of operating at a pulse
recurrence rate of tens and thousands of hertz. It is also obvious that these
rElativistic electron beam generators must be simple to use and reliable in opera-
tion.
These requirements are met in large measure by linear induction accelerators. The
idea of developing such an accelerator was proposed by A. Bouwers as far back as
1923 [Ref. 8J; however, f.orty years elapsed before practical realization became
�easible as technology reached a level where the necessary accelerating fielcls
117
FOR OFFiCIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFIC[AL USE ONLY
could be produced in acceleration of an intense beam of charged particles. '"he
first accelerators of this type were made in the United St3tes in the early si::~i.es
under the direction of N. Christofilos [Ref. 9] in connection with work on thermo-
- nuclear f~:sion, and in the Soviet Union [Ref. 10] under the direction of V. I.
Veksler in connection with realization of the idea of an effective method of ac-
- celeration called "collective-ion acceleration." Fig. I.1 [photo not reproduced]
shows the U. S. Astron accelerator, and Fig. I.2 [photo not reproduced] shows the
Soviet LIU-3000 accelerator.
Operation of the f irst accelerators showed that this quite simple m~thod of ac-
celeration enables highly efficient production of relativistic electron beams with
high recurrence rate and with good reliability and repeatability of beam parameters.
Ma.ny laboratories around the world are doing intense research on linear induction
accelerators, developing theory and methods of designa ~nproving construction.
This work has given rise to a new field of accelerator technology [Ref. 11-13].
Right now, a considerable number of accelerators ~aith various parameters are in
different stages of development and construction. Some of them are shown in
Table I.1 [Ref. 13].
A laboratory of linear induction accelerators was set up at NIIEFA in 1968 for
producing accelerators to meet the requirements of science and industry. The re-
search done at this laboratory has been the basis for this book.
- Chapter 1 describes the working principle of the accelerator and defines the limit-
- ing ranges of parameters that accelerators of this class can have. Chapter 2 ana-
lyzes problems of design of the ferromagnetic induction system. Although in the
_ first approximation the induction system can be repre:~ented as a series circuit
of single-turn pulse transformers, the very first experiments showed that the theory
that iiad been developed for pulse transformers of the microsecond range could not
give satisfactory results when applied to the induction system. Therefore a theory
of pulsed magnetic reversal is proposed for calculation. Chapter 2 presents the
fundamentals of this theory as applied to calculation of the induction system,
compares theoretical results with experimental data obtained by studying a large
group of magnetically soft alloys and ferrites at pulse durations of 500, 250 and
150 ns typical of linea: induction accelerators. These data enabled selection
- of ferromagnetics in relation to the requirements to be met by the accelerator.
In chapter 3 an examination is made of problems of shaping the accelerating voltage
pulse with consideration of the peculiarities of the ferromagnetic induction system,
which are due to the nonlinear l.aw of behavior of the magnetic reversal current
durin~; a pulse, and the necessity of accounting for the time of commutation of
the thyratrons and the dissipative inductances of the accelerating system. This
chapter also describes the shaping arrangements that are most preferable for
' linear induction accelerators, including designs that were proposed in the process
of developing the accelerators at the institute [NIIEFA].
In accelerator design, the problem arises of the spatial distribution of the ac-
celerating field, its relation to the dimensions and construction of the induction
system. This is covered in chapter 4, where expressions are derived that relate
the accelerating field to the dimensions of the induction system, and experimental
- 118
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2407102/09: CIA-RDP82-00850R000400450052-5
FOR OFFTCIAL USE ONLY
~
~b
U fd
N/q (q is the density of the heat flux from the beam to the target).
However, when a target is bombarded by an intense electron beam, considerable x-ray
and ultraviolet emission arises, affecting the electric strength of the accelerating
gap and structural elements in the electron accelerator, and processes near the
cathode, and thus makes the operation of the accelerator during tests different
from its operation in routine use, which is of course inadmissible.
Fig. 2 shows a version of a target that is free of these def iciencies. The target
is a component part of a stand that consists of high-current steady-state electron
accelerator 8 that is to be modified, its power supply 10, working chamber 3, magnet
systems 7 and 11 and vacuum system 14. The working channel is equipped with upper
cover 1 cooled by water Z, and with side walls, and has optical observation tubes ~
and provisions for motion picture recording 4 with special protection. The dimen-
sions of the working chamber permit accommodation of various sensors of the measure-
ment system and will withstand reception of electron beams with power of up to
10,000 kW. The electron beam enters the channel through an aperture in bottom
cover 6. Acceleration tube 9 and the entire channel for beam transport in the
chamber are in a longitudinal magnetic f ield. The magnetic system terminates in
solenoid 7, which together with the system of magnetic electrodes 5 and 6 that
protect the working space from the magnetic field sets up an axial-radial magnetic
field in the beam transit region at the inlet to the chamber. Interaction of the
electrons with this field causes expansion of the beam, and consequently reduces
the density of the heat flux incident on the~reception cover of the target chamber.
Magnet systems 7, 11 can change the diameter of the surface exposed to the electron
beam over a wide range (from 2 cm to 1.5 cm).
The gas released from heated and electron-bombarded surfaces is evacuated from
working chamber 3 by a diffusion pump. Even after an experiment of only a few
seconds duration under conditions with high beam power, the pressure in the chamber
rises from the initial ~10-`` Pa to (5-10) 10-3 Pa, which is much higher than the
,p,erniissible pressur~ i~s. ~~u~u~dl operation o~ ti~:. ucc�leru~ien tube. T^ ~revent
the pressure from increasing in the acceleration tube as well, it is separated
from the working chamber by prechamber 13 and molecular overflow tube 12 located
on the axis of rotating solenoid 7. The gas leaking into the prechamber is evacu-
ated, which enables maintenance of a working pressure close to 10-4 Pa steadily
in the acceleration tube. The lower pressure also acts as a shield (except for
a small cavity in the molecular overflow tube) against bremsstrahlung and ultra-
violet radiation. This target enabled us to develop a high-current electron ac-
celerator for a power of up to 5 MW.
System for Coupling the Electron Beam out of Vacuum Into a High-Pressure Zone.
A system of transfer chambers was used for extraction of high-intensity concen-
trated electron beams. W. E. Pauli was the first to develop a system of dynamic
pressure stages consisting of an intermediate chamber and two stages designed for
_ extracting a beam with size measured in fractions of a millimeter [Ref. 5]. This
system was subsequently developed and improved by S. T. Sinitsyn and A. M. Trokhan,
who suggested substituting a cryogenic system for the pump evacuation system for
diagnostic low-current electron beams [Ref. 6J. The devices considered in all
127
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAI. USE ONLY
cases were for coupling out low-current electron beams of small diameter (less
than a millimeter), and as a rule into a region at lower than atmospheric pressure.
Calculation of the trajectory of motion of electrons with consideration of energy
- release caused by ionization losses and scattering has shown that beam transit
through transfer chambers requires openings between stages of several millimeters
(~6-8 mm). In the classical system of dynamic pressure stages (sequential transfer
chambers with evacuation), maintaining operability of the stages with deep vacuum
when the openings are of these dimensions requires a large number of vacuum units,
and this leads to unreasonably large overall dimensions of the entire facility.
Therefore a gasdynamic gate--a transverse supersonic steam nozzle--is incorporated
to reduce the overall dimensions of the lock system and minimize the vacuum equipment
used between stages with relatively high pressure (more than 100 kPa) and vacuum
stages (10 Pa or less).
- The entire system of transfer chambers has
~ 2 ~ the following appearance. The gas (see Fig. 3)
from the working chamber, which may have pres-
I sure even higher than atmospheric, goes through
a nozzle into the first lock and is ejected
~ ~ into the atmosphere under the action of excess
I pressure (about 5�10`` Pa). The gas is evacuated
y from the second stage by a supersonic gas ejector
._1 ~ 6 that brings the pressure in the stage to about
10`` Pa. Between the second and third sta~es
~ is the gasdynamic gate--a transverse supersonic
~ steam nozzle. The supersonic jet of super-
_ I_- heated steam will not pass the overflowing
B gas from the second stage to the third, and
~j~ maintains the operation of the vacuum stages
constant regardless of external~conditions.
- � The steam condenses (or more precisely it de-
= I= sublimes) on the walls of the chamber of the
9 third stage, which are cooled by liquid nitrogen.
The pressure in the stage is maintained at a
level of 10-100 Pa. The next three stages,
JJ
, I iO Y
~ !1 v ~
~ /
= I = 1~ ~ / I
~3
_ I r
S
Fig. 3. Transfer chamber system: Fig. 4. Initial section of under-
1--intake pipe; 2, 3, 6, 8, 9, expanded ~et: 1--free boundary of
10--transfer chambers; 4--steam jet; 2--hanging shock; 3--central
nozzle; 5~-vacuum valve; 7--de- shock (Mach disk); 4--reflected
sublimator-cooler; 11--focusing shock
solenoid
128
FOR OFFIC[AL LJSE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00854R004400050052-5
FOR OFFICIAL USE ONLY
like the third stage, are cryogenic pumps cooled by liquid nitrogen that are con-
nect~d in addition to a vacuum exhaust system with relatively low productivity
for expelling only the uncondensed gas that enters the stage along with the steam.
Between the working section and the first transfer chamber is the supersonic nozzle
and an adapter for intake of the gas leaking into the f irst lock (see Fig. 3).
Proper selection of the place of installation of this intake, as well as of the
intake into the second transfer chamber, considerably reduces overall dimensions
and the energy inputs to the transfer chambers. The fact is that two flow regions
are f ormed on the initial section of an underexpanded jet (Fig. 4): I--a central
region where flow is independent of ambient pressure, and corresponds to discharge
of the supersonic jet into vacuum from a tapered nozzle, and II--a peripheral region
(compressed gas flow region). When the degree of underexpansion is increased beyond
four, ten percent or less (depending on the degree of underexpansion) of the entire
flowrate of the gas passing through the critical cross section of the nozzle flows
through the cross section situated in front of the Mach disk in the central region
(see Fig. 4). Therefore, in order to reduce the amount of gas flowing to subse-
quent locks, to reduce energy losses of the electron beam and to reduce the overall
pressure of the gas entering the reducer pipe, the intake of this pipe is located
in the central zone of the underexpanded jet. The installation of fast-acting
~ remote-controlled vacuum valve 5 prevents atmospheric air from entering the third
transfer chamber during preparation of the system for testing, or inleakage of
steam as the steam nozzle is being brought up to working parameters.
~ Z .1 4 .
2,Q (I-.71 T4M3 73M6 I,Ql1=y1
K M.1 ~3 4 ~5 ~6T6 S 6 )
_ ~ M4 ~1 t
' ~I
~ . _ . -
~6 /
1 11 rn ~ ~
~ ZO
~4
,S ~ ,y ,3 ,z � ,o 9 ~ e
Fig. 5. Diagram of system for measurements and for controlling the beam position:
1--nozzle washers; 2--sectoral sensor; 3--desublimers; 4--solenoids of the ac-
celeration tube; 5---microtarget for tube conditioning; 6--envelope of the acceler-
ation tube; 7--cathode; 8, 13, 14--moving-coil solenoids for adjustment of beam
position; ~3-~6--precipitation sensors on the tubes of the lock solenoides; M3-M6--
precipitation sensors in cooler channels; 9--funnel for tube evacuation; 10--sec-
toral sensor; 11--valve of isolating vacuum gate; 12--tubes of the lock solenoids;
15--control washer; 16--beam pickup sensor
A tracking magnetic field is used for focusing the electron beam, and ensuring
high precision and stability of transport with beam confinement on a given path.
The use of a tracking magnetic field gives high precision and reliability in trans-
porting an electron beam over great distances, increases the electrical strength
of the acceleration channel, and enables variation of the beam diameter on the
129
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFIC'IAL l!SE ONLti'
path. The latter capability results from the fact that the beam is magnetized
on the patn, and during its motion the condition Br2= idem is satis�ied. In par-
ticular, changing the induction B of the magnetic field enables a reduction in
beam diameter d in the throats of the transfer chambers by local intensification
of the field through ~he addition of focusing solenoids (see Fig. 3).
The magnetic field is set up by specially designed miniature solenoids that sur-
round the electron tube and the entire transportation channel. The system for
coupling out the electron beam is equipped with a system for measurements and for
controlli~g the beam position (Fig. 5) with provisions for monitoring and correct-
ing the position of the beam during passage along the electron channel of the fa-
cility, which is particularly important because of a relatively long channel of
variable cross section and the possibility that the geometric and magnetic axes
of the system may not coincide. The beam position is corrected by pairwise-connected
deflecting moving-coil solenoids with continuous current control. Beam position
is monitored by sectoral sensors.
A distinguishing feature of the arrangement for checking the coverage of the elec-
tron channel of the facility is the capability for simultaneous observation of
the readings of ineasurements of current and temperatures on the screen of a cathode-
ray oscilloscope for each of three sets of sensors, which considerably facilitates
correction of beam position with a change in working conditions or after modifica-
tions of the working section. There is also a system for synchronous recording
of major parameters of the beam transit, and accelerator operation with digital
printout of the results.
As has already been pointed out, electron beam transportation involves the poten-
tial danger of arisal of instabilities due to energy exchange between beam and
plasma. In this connection, consideration should be given in the first instance .
to the possibility of development of waves of perturbations of electron concen-
tration in the plasma produced by the beam with phase velocity of the wave approxi-
mately equal to the velocity of the particles in the beam. (This is ~.he reso-
nance condition for energy takeoff.) Analysis shows that the distribution of pres-
sure along the electron beam transportation channel must be chosen to minimize
the extent of the most dangerous zones (from the standpoint of the possibility
of arisal of instabilities), making them coincide with the throats of the transfer
chambers. Stabl.e transportation of the electron beam was ensured by a p~~~perly
chosen law af variation in the pressure and magnetic field along the path.
Some Results of Experiments With Concentrated Steady-state Electron Beams. In -
creasingthe range of propagation of a concentrated electron beam.
It should be expected that as an intense concentrated electron beam travels through
the atmosphere, its range will increase considerably over that of the electrons
of low-current beams, since the energy release on the path of the beam should lead
to a rise in temperature and reduction in density of the medium. Another signifi-
- cant factor may be the focusing influence of scattering of electrons from the den-
ser (less heated) ambient gas.
As an example, Fig. 6 shows experimental data on the range of propagation of a
concentrated electron beam in the atmosphere. The limits of the beam were deter-
mined by registration of bremsstrahlung.
130
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
R, cM E= Z00 ke
E = ZZO keV
E=~65 keV
100
E _ /y3 keV
/00
0 0 Z, 0 I, A
Fig. 6
The maximum mean free path of an electron in air at pressure of 9.8�104.Pa, tem-
- perature of 300 K and energy of 200 keV is approximately 30 cm. It can be seen
from the data of Fig. 6 how the range of an electron beam under these same con-
ditions increases as a consequence of heating of the gas and reduction of its den-
sity along the path. Estimates show that the beam density on the path corresponds
to a temperature of the heavy gas component close to 3000 K.
Visual observations of the height of the flare produced by the electron beam agree
satisfactorily with the results given by bremsstrahlung.
~ An increase in the range of action of a concentrated electron beam has great prac-
tical significance since this makes it realistically usable for such technological
processes as welding and cutting in atmosphere, high-speed drilling and cutting
of rocks. ~
Energy efficiency of destruction of materials under the action of an
el e c t r on b eam . The problems of technological utilization of electron beams are
responsible for the great interest in investigation of the particulars of destruc-
tion of materials under the action of concentrated beams. In this article we cannot
go into any detail in discussing the physical and mechanical aspects of this inter-
esting and complicated phenomenon. We will only point out one interesting resul~
by way of formulation of the problem.
A concentrated electron beam in falling on the surface of. a material heats matter
in the zone bounded by the beam dimensions and the depth of penetration of elec-
trons. If the rate of heat release is lower than the rate of energy removal as a
consequence of heat conduction, heating will take place with formation of a hemi-
- spherical (or nearly so) molten region. And vice versa, if the rate of energy
release is much greater than the rate of energy removal (which corresponds for
practical purposes to an energy flux density q? 106-10~ W/cm2), the material is
intensively melted and vaporized an d in p art is also split off because of the
thermal stresses that arise. Under the action of excess vapor pressure, the prod-
ucts of destruction are expelled from the zone of energy release and, what is ex-
tremely important, the products of expulsion contain ma.tter not only in gaseous
- form, but also in the liquid and even the solid phase.
131
FOR OFF[C[AL U5E ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400054452-5
FOR OFFICIAL USE UNLY
Let us introduce into consideration the energy equivalent of action defined as
h= q/m, where q is the energy flux density per unit of surface, and m is the mass
flowrate per second of the products of destruction.
As a consequence of the concept presented above, it is to be expected that the
value of this equivalent will in the case of action of an electron beam on matter,
be the lower (other things being equal), the greater is the concentration of energy
in the melting zone, and the higher the electron energy, since this increases the
depth of penetration.
h�10-3, kJ/kg
6 x
x ateri 1-1Kh18B0 kW
el-
y " E - I90 - ZZOkeV
x x r oirb'.70DkJ/k
Z " _ -
/Uz I03 /0'~ ~ q~skW/cm2
Fig. 7 "
Fig. 7 shows experimental values of the energy eyuivalent of action of an electron
beam that confirm the assumption stated above. Of interest is the fact that the
quantity h is much less than the heat of vaporization, which indicates an appre-
ciable fraction of at least a liquid phase in the products of destruction. From
this we get the practically important recommendation to the effect that it is more
advantageous from the standpoint of energy expenditures to machine a material with
highly concentrated electron fluxes (and preferably at higher energies) that pene-
trate to a certain depth, than for example with high-temperature plasma jets or
laser radiation that act only on the surface of the material being destroyed. Of
particular advantage is modulated action, since the electron beam is more effective
at instants when the channel has been cleared of the vapor of the destruction prod-
ucts, as otherwise a certain amount of beam power is expended on additional heat-
ing of the products of destruction. Experiments have shown that the frequency
of ejection of matter fluctuates from 102 to 105 Hz, depending on beam parameters,
and the way that the material is being machined by this beam.
Propagation of an electron beam in a magnetic field. An experimental
study has been done on the propagation of an electron beam in air in a longitudinal
magnetic field. The results show as expected that a longitudinal magnetic field
reduces beam scattering in the transverse direction. In studying relaxation of
a comparatively low-current beam with power of about 10 kW and energy from 300 keV
to 1 MeV as the magnetic field was varied from 0.7 T to 1.4 T, it was found that
the behavior of beam radius as a function of magnetic induction is close to linear
with dr/dB =-0.35 cm/T at a depth of penetration into matter of px = 0.250 g/cm2.
It was established in the same experiments that the change in beam radius with re-
spect to depth of the target in a constant field B= 1/T is dr/d(px) = 8 cm/g/cm2.
- 132
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007142/09: CIA-RDP82-40854R040400050052-5
FOR 06FIC1AL USE ONL1~'
Nevertheless, we may speak of so-called channeled propagation of the electron beam
with a considerable degree of arbitrariness even for beams with power of more than
1000 kW, since scattering causes rather appreciable widening of the channel formed
by the beam-heated atmosphere. For example, experimental data on the distribution
of electron concentration in the beam (by registration of bremsstrahlung) show
that the beam expands "faster" than lines of force. This result agrees satisfac-
torily with the theoretical picture of relaxation of an electron beam in a longi-
tudinal magnetic field.
It is also of interest to note that experimental studies of the energy distribution
of electrons over the relaxation zone in a longitudinal magnetic field show that
the electron spectrum increases in hardness along the radius in the direction of
the beam axis.
Experiments on electron beam welding in atmosphere. The extensive appli-
, cation and advantages of using electron-beam welding in vacuum are well known,
particularly in welding parts of large thickness. However, the region of appli-
cation of electron-beam welding is limited by the volume of vacuum chambers, and
productivity is determined chiefly by the process o.f evacuating the chambers. It
is natural that the increasing overall dimensions of welded structures and the
use of materials that do not necessarily require "vacuum shielding" in welding
would bring about conditions for intense development of electron-beam welding
methods for use under atmospheric conditions.
The feasibility in principle of realizing this technique is known from research
at the Institute of Electric Welding imeni Ye. 0. Paton, the (Gereus) Company in
West Germany, Westinghouse in the United States and others.
~ We did experiments on welding with a concentrated electron beam with power of up
to 50 kW coupled out into the atmosphere with helium shielding using aluminum alloy
specimens movi.ng at a rate of 100-160 m/hr relative to the beam. The conventional
arrangement of argon-jet shielding of the molten bath that is extensively used
in welding is inadvisable when melting metal by an electron beam extracted into
the atmosphere because of the high density of argon that leads to additional losses
- of electron energy upon traversing the gas gap and to an increase in beam cross
section. These factors are detrimental to the formation of the molten zone, par-
ticularly at low rates of transportation of the workpieces.
Strength tests of welded seams, metallographic studies of weld structure and mea-
_ surements of the microhardness for three levels of cross sections of seams have
shown that the given technique can be considered quite effective, especially for
welding items of large overall dimensions with great thickness of the components
to be joined.
It has also been established that by proper choice of welding conditions it is
possible to produce high-quality welds (at least for aluminum alloy parts) even
without using special inert-gas shielding of the molten bath. This is done by
changing to increased speeds of transportation of workpieces and to a high level
of energy release, leading to the formation of a weld under conditions of active
vaporization of inetal from the surface of the melt. Radiograms of a weld made
at a rate of 160 m/hr without shielding of the bath confirm absence of defects
of the blister and pore r_ype, as well as absence of inclusions in the seam.
133
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAI. USE ONI..1'
Using electron beams to produce high-purity plasma. An investigation
was made of the feasibility of using electron beams to generate plasma streams
- of high purity. In studying high-temperature heat exchange, magnetogasdynamics,
and also For various engineering applications, use is made of high-temperature
plasma flows that are produced by heating working fluids, usually in electric-
arc plasmotrons. The working fluid always contains a certain amount of impurity
due to destruction of the electrodes; moreover, due to specific effects inherent
in an electric discharge, the flow is characterized by some pulsation of parameters.
Plasma generators based on the use of electron beams are free of these deficiencies
[Ref. 7]. A diagram of such a plasma generator is shown in Fig. 8. From the elec-
1' Z S 3 y
1 i
6 - ~ - ~
~
II
Fig. 8
tron source following the system of extraction into a high-pressure zone, the beam,
accelerated to an energy of several tens or hundreds of keV (the required energy
is selected as a function of the density of the medium being heated), is injected
through inlet 6 into working chamber 1 and forms a zone of energy release 2, heat~
ing the gas therein to a high temperature. Gas flows through intake 5 into col-
lector 3, and then through the porous wall into chamber 1. The gas flows radially
in the greater part of the chamber. The heated gas flows out through nozzle 4.
The described system has been successfully used for heating air to temperatures
of several thousand degrees at pressures up to 2 MPa. The heated gas contained
no impurities and showed no fluctuation of parameters. This system should be par-
ticularly effective at a power level of several tens of inegawatts and at high pres-
sures.
Conclusions. 1. The authors have demonstrated and realized the feasibility of
selecting a law of change in pressure and magnetic field along a system of transfer
chambers enabling extraction of an electron beam into the atmosphere with low losses
without development of instabilities.
2. The use of several stages with an intake nozzle in the zone of minimum pressure,
replacing air with components that condense or freeze out on cryogenic panels in
combination with a magnetic control system can give small and highly economic sys-
tems for extraction of concentrated electron beam.
3. The mean free path of a concentrated electron beam is greater than that of elec-
trons in low-current beams. This is primarily dua to heating of the medium by
energy released on the path.
134
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
~
4. Scattering of the electron beam in the transverse direction upon relaxation
- in the atmosphere is appreciably reduced by an external longitudinal magnetic field.
- 5. Destruction of materials by highly concentrated electron beams that penetrate
- to a certain depth in a material is energetically advantageous.
6. The use of concentrated electron beams enables the realization of new high-
efficiency technological processes and devices, and in particular the i.mplementation
of electron-beam welding at 3tmospheric pressure, and development of high-efficiency
~ low-tempera~ure plasma generators.
7. The general recommendations on methods of generating concentrated electron beams
and couplin~ them out into dense media can be used in solving specific technologi-
cal problems.
REFERENCES
1. Abramyan, Ye. A., "Outlook for Using Relativistic Electron Beams in Industrial
Technology", VESTTIIK ?,KADEMII NAUK SSSR, No 11, 1979, p 57.
2. Rykalin, N. N., Zuyev, I. V., Uglov, A. A., "Osnovy elektronno-luchevoy obra- ~
botki materialov" [Principles of Electron-Beam Machining of Materials], Moscow,
Mashinostroyeniye, 1978, 237 pages.
3. Gaponov, V. A., "Vypryamitel' na napryazheniye 500 kV i tok nagruzki 10 A" [Rec-
tifier for Voltage of 500 kV and Load Current of 10 A], Novosibirsk, Preprint,
Institute of Nuclear Physics, Siberian Department, USSR Academy of Sciences,
' 74-11, 1974, 19 pages.
4. Iyevlev, V. M., Kor.oteyev, A. S., Koba, V. V., "Experimental Facility for Gener-
ating a Concentrated Beam of Relativistic Electrons in the Atmosphere", IZVESTIYA
SIBIRSKOGO ODTELENIYA AKADEMII NAUK SSSR. OTDEL TEKHNICHESKIKH NAUK, No 3, 1977,
p 52.
5. Pauli, W. E., PHYS. LEITSCHRIFT, Vol 21, No 1, 1920, p 11.
6. Trokhan, A. M., "Coupling Electron Beams out of Vacuum Into Gas Through a Gas-
Dynamic Window", ZHURNAL PRIKL.ADNOY MEKHEINIKI I TEKHNICHESKOY FIZIKI, No 5,
- 1965, p 108.
7. Koroteyev, A. S., "Elektrodugovyye plazmotrony" [Electric Arc Plasmotrons],
Moscow, Mashinostroyeniye, 1980, 176 pages.
COPYRIGHT: Izdatel'stvo "Nauka", "Izvestiya AN SSSR, Energetika i transport", 1981
~ 6610
CSO: 8144/1589
135
~ FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-04850R000400050052-5
~ FOR OFFICIAL USE ONLY
OPTOELECTRONICS
. UDC 621.395
RADIO HOLOGRAPHY AND OPTICAL DATA PROCESSING IN MICROWAVE TECHNOLOGY
Leningrad RADIOGOLOGRAFIYA I OPTICHESKAYA OBRABOTKA INFORMATSII V MIKROVOLNOVOY
TEKHNIKE in Russian 1980 (signed to press 24 Oct 80) pp 2-4, 181-183
[Annotation, preface and article abstracts f rom book "Radio Holography and Optical
Data Processing in Microwave Technology", ed ited by Associate Member of the USSR
Academy of Sciences L. D. Bakhrakh and Candidate of Technical Sciences A. P. Ku-
rochkin, Izdatel'stvo "Nauka", 2150 copies, 184 pages]
[Text] This ~ollection examines questions of the use of holography and optical
data processing in microwave technology: me thods and equipment for visualizing
microwave fields and imaging objects; hologr aphic method of determining the param-
eters of antennas in the near zone; problems of constructing acousto-optical devices
for processing radio signals and the peculiarities of operation of such devices;
investigation of correlational optical recognition of cosmic images.
Preface
Tti4 papers in this collection cover the following topics: holographic methods
. an~i equipment for visualizing microwave and acoustic fields, and also for producing
iir.ag~s of objects exposed to waves in the microwave range; various aspects of the
~ holographic method of determining the parame ters of microwave antennas in the near

~ zone; optical processing of signals ~f antenna arrays; problems of constructing
acousto-optical devices for radio si.gnal pro cessing.
Articles by A. V. Avrorin et al. and by L. I. Bayda et al. deal with constructing
high-speed equipment complexes designed for producing microwave and acoustic holo-
- grams and images.
~ The paper by A. S. Klyuchnikov and P. U. Kukharchik investigates a new type of
displa~ for h~lograms in the millimeter and submillimeter bands--films of various
liqui~~s.
The article by 0. V. Bazarskiy and Ya. L. Kh?yavich is de~JOted to analysis of a
y generalized criterion for evaluating resolut ion of radio holograms.
Results of experimental researcti on correlational optical recognition of cosmic
- Jmages are given in the article by A. I. Balabanov et al.
~
136
FQR l;~i [~IAL USE i3iJL~l
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
The articles by A. G. Buday et al. ard by Yu. V. Sysoyev are devoted to development
- of a holographic method of determining the parameters of antennas in the near zone.
The next group of articles deals with different aspects of optical processing of
signals of antenna arrays and sources of radio emission. Two theoretical articles
by A. Yu. Grinev et al. are devoted to signal processing algorithms and evaluation
of the parameters of radio-optical antennas of systems of different configurations.
= A hybrid opticodigital system for processing signals received from pulsars is pro-
posed and studied by N. A. Yesepkina et al.
The collection concludes with articles by Ye. T. Aksenov et al. and by S. V. Kulakov
devoted to acousto-optical devices for data processing based on nonlinear acoustic
interaction, and to the investigation of the influence that shock waves and non-
linearity of light modulators have on the parameters of acousto-optical correlator.s.
The editors hope that the papers included in this collection will attract the
attention of specialists and bring about further improvement and more extensive
_ practical application of inethods of holography and optical data processing in micro-
wave technology.
UDC 778.4:534.6
REAL-TIME LONG-WAVE HOLOGRAPHY
[Abstract of article by Avrorin,.A. V., Breytman, B. A., Volkov, Yu. K., Votentsev,
V. N., Gruznov, V. M., Kopylev, Ye. A., Korshever, I. I., Kotlyakov, M. I., Kuz-
netsov, V. V. and Remel', I. G.J
- [Text] An investigation is made of questions of developing rapid-action devices
for recording long-wave holograms and reconstructing images in the c:entimeter band
of radio and acoustic waves. Results that are given from experimental studies
of discrete holographic systems show that the use of certain methods of processing
and digital reconstruction of images gives close to the limit of spatial resolution,
close to a single wavelength. An examination is also made of schemes of setting
up matrix systems for registration of acoustic and microwave holograms. A descrip-
tion is given of a specialized computer system to control multichannel devices
for collecting information and reconstructing images. Ways are pointed out for
increasing the speed of the systems.
UDC 621.396.671
ELECTRONIC EQUIPMENT FOR RECORDING AI~LITUDE-PHASE DISTRIBUTIONS OF ACOUSTIC FIELDS
[Abstract of article by Bayda, L. I. (deceased), Belash, G. P., Belyayeva, A. I.,
- Kachanov, Ye. I. and Yurkov, Yu. V.]
[TextJ An investigation is made of the particulars of construction of ineasurement
devices that operate under conditions of the near f ield of acoustic antennas. Dia-
grams are given of electronic measuring devices that process signals with a wide
dynamic range, and an examination is made of the pecuiliarities of their operation
137
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
- and of the sources of errors that limit measurement accuracy. Attention is given
to the development of matching devices for interfacing a measurement device with
a computer to enable machine processing of the measured amplitude-phase distribution
of a near field. Results of experiments are given on obtaining one-di.mensional
holograms of different types of antennas. It is shown that the given near-field
measurements have independent significance for analysis of the particulars of an-
tenna characteristics.
UDC 621.396
- INTERFERENCE-HOLOGRAPHIC METHODS OF VISUALIZING MICROWAVE FIELDS
[Abstract of article by Klyuchnikov, A. S. and Kukharchik, P. D.,]
[Text] An examination is made of a method of visualizing microwave fields in the
millimeter and submillimeter bands by using displays based on thin liquid films.
The proposed displays do not require thermostabilization or sensitization, enable
repeated use of the recording medium, and extend the range of application of micro-
wave holography. Based on the developed display, a technique is proposed for visu-
alizing the spatial polarization structure of diffraction emitters of different
shapes.
UDC 621.382.049.77
RESOLUTION OF RADIO HOLOGRAMS AND WAYS TO IMPROVE IT
[Abstract of article by Bazarskiy, 0. V. and Khlyavich, Ya. L.]
[Text] Based on the theory of statistical solutions, a generalized Rayleigh cri-
terion is constructed that accounts not only for the diffraction limitations of
forming apertures, but also for the signal-to-noise ratio in the image, and the
probability of making the correct decision on the number of resolvable sources.
The conditions of resolution of extended sources are found that ensure both separate
observation and exact reconstruction of dimensions. An analysis is made of the
possibili.ties for increasing the resolution of forming apertures beyond the classi-
cal Rayleigh limit based on analytical continuation and compression of the spatial
spectrum.
UDC 621.396.671
RECONSTRUCTION OF AN ANTENNA RADIATION PATTERN FROM NEAR-FIELD MEASUREMENTS ON
A CYLINDRICAL SURFACE
[Abstract of article by Buday. A. G., Bulkin, V. M., Kolosov, Yu. A., Kremenetskiy,
S. D., Kurochkin, A. P. and Litvinov, 0. S.]
[Text] An examination is made of problems of ineasuring the near field of an antenna
on the surface of a cylinder, and also realization of an algorithm for converting
the near field to the far field. The authors discuss the results of numerical
modeling of the problem of reconstructing the radiation pattern of an antenna with
large electrical dimensions and low level of side lobes.
138
' FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-04850R000400050052-5
FOR OFFICIAL USE ONLY
UDC 621.396.67.012.12
PROBLEMS OF REALIZING THE RADIO HOLOGRAPHIC METHOD OF DETERMINING ANTENNA RADIATION
PATTERNS
[Abstract of article by Sysoyev, Yu. V.]
[Text] A method is proposed for quantitative evaluation of the required degree
of orthogonalization of channels of correlational measurement systems for the radio
holographic method of determining antenna radiation patterns. The author gives
the results of an experimental study of random errors in measurement by this method.
Capabilities are demonstrated with regard to a graphic program package in FORTRAN
(GRAFOR) for constructing planar projections of antenna radiation patterns.
UDC 621.396.677.49
PLANAR RADIO-OPTICAL ANTENNA ARRAYS
[Abstract of article by Grinev, A. Yu., Voronin, Ye. N. and Kurochkin, A. P.]
[Text] An examination is made of the er.ergy, accuracy and dispersion character-
istics of linear and planar antenna arrays with coherent-optics signal processing
based on various space-time light moculators. A[design] is proposed for an optical
processor that has a number of advantages (in particular, it eliminates ambiguity
of direction-finding for two-band signal input to the processor). Estimates are
made of the diffraction efficiency of the processor, the influence of the pupil
of the modulator channels, and also the effect of the mutual influence between
them.
UDC 621.396.677.49
NONPLANAR ANTENNA ARRAYS WITH FORMATION OF RECEPTION BEAMS BY METHODS OF COHERENT
OPTICS ~
[Abstract of article by Grinev, A. Yu. and Voronin, Ye. N.]
[Text] Methods are described for synthesizing coherent-optics processors of non-
planar antenna arrays that operate in the parallel scanning mode. In addition
~to the general approach, special cases are examined: piecewise-plane, cylindrical
and ar.nular antenna ar�rays. An investigation is made of effects that are detrimental
to the pattern-forming properties of the processors, and methods of eliminating
them are pointed out.
UDC 523.84:534.535
HYBRID OPTICODIGITAL SYSTEM FOR PROCESSING PULSAR SIGNALS
[Abstract of article by Yesepkina, N. A., Bukharin, N. A., Kotov, B. A., Kotov,
Yu. A. and Mikhaylov, A. V.]
[TextJ The paper gives the results of an experimental study of a pilot model of
an acousto-optical correlator with time integration. It is shown that use of such
139
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
a device for processing pulsar signals eliminates the influence of dispersion of
the interstellar medium, and could improve parameters of existing radiometers.
Used as multielement photosensors with storage in the investigated processor were
bit lines of charge-coupled~de~~ices and the auxiliary buffer memory of the Elek-
tronika-100 computer.
UDC 523.84
MEASUREMENT OF THE COORDINATES OF REFERENCE POINTS OF A TERRAIN, AND DETERMINATION
OF SHIFTS IN CLOUD FORMATIONS BY USING AN OPTICAL HETERODYNE CORRELATOR
~Abstract of article by Balabanov, A. I., Korbukov, G. Ye., Feoktistov, A. A. and
Tsvetov, Ye. R.]
[Text] The paper gives the results of experimental studies on the feasibility
of using an optical heterodyne correlator to measure the coordinates of reference
points of a terrain and shifts of cloud formations in satellite photographs of �
the earth's surface. It is shown that under condition of preliminary approximate
correlation of geometric distortions, fragments of images of the terrain can be
tied in by correlational recognition with an error much less than the size of an
element of resolution. Shifting of cloud formations is well defined by correla-
tional comparison of images obtained by geostation~ry satellites with an interval
of 30 minutes.
UDC 534/535.241:621.371
ACOUSTO-OPTICAL DATA PROCESSING DEVICE BASED ON NONLINEAR ACOUSTIC INTERACTION
[Abstract of article by Aksenov, Ye. T., Yesepkina, N. A. and Shcherbakov, A. S.]
[Text] An examination is made of the feasibility of developing a new class of
acousto-optical devicrs that use nonlinear interaction of elastic waves. Results
are given from an ex~:erimental study of pilot models of such devices based on lead
molybdate and gallium phosphide crystals that realize displacement, convolution,
correlation and controllable delay cf. signals. The studies were done on frequEncies
, of 80-500 MHz, using cw and pulsed signals. With electric power input up to 0.5 W,
the relative efficiency of the device reached several percent. ~
UDC 621.317.757
INFLUENCE THAT ATTENUATION OF ELASTIC WAVES HAS ON THE OUTPUT SIGNAL OF AN ACOUSTO-
OPTICAL DEVICE FOR CORRELATION ANALYSIS
[Abstract of article by Kulakov, S. V.]
[Text] An investigation is made of the influence that attenuation has on signal
shape in an acoustic light modulator, and on the output signal of an acousto-optical
device for correlation analysis. Relations are given for selecting the medium
of acousto-optical interaction with respect to admissible error energy.
140
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
UDC 621.317.757
INFLUENCE THAT NONLINEARITY OF ACOUSTIC LIGHT MODULATORS HAS ON CORRELATIONAL
PROCESSING OF NARROW-BAND SIGNALS
[Abstract of article by Kulakov, S. V. and Bragina, L. P.]
[Text] An investigation is made of nonlinear deterministic models of an acousto-
optical device for correlational processing of narrow-band input signals and
Raman-[Nat] and Bragg diffraction modes.
COPYRIGHT: Izdatel'stvo "Nauka", 1980
6610
CSO: 1862/203
141
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
THREE CHANNEL ELECTRO-OPTICAL WAVEGUIDE COMMUTATOR
Leningrad PIS'MA V ZHURNAL TEKHNICHESKOY FIZIKI in Russian Vol 7, No 7, 12 Apr 81
(signed to press 18 Mar 81) pp 418-421
, [Article by I. G. Voytenko and V. P. Red'ko, Mogilev Department, Institute of
Physics, Academy of Sciences BSSR]
[Text] Devices for commutation of a light beam over individual channels are an
inseparable part of a fiber-optics communication line. Switches based on the elec-
tro-optical effect that have maximum speed and simplicity of design are the most
promising for this purpose. Devices based on striplines are most attractive at
the present time [Ref. 1].
This paper gives the results of an experimental study of an electro-optical commu-
tator that switches light in a waveguide over three independent channels. The
waveguide was made by thermal diffusion of tungsten oxide into a lithium niobate
Y-cut. The diffusant was sputtered by the rf-method in an atmosphere of argon
and oxygen directly from a tungsten oxide target. The thickness of the sputtered
layer was ~200 A. The waveguide was formed for an hour at a temperature of 940�C.
The waveguide could support only the TE mode with effective index of refraction
of ne = 2.2031 on a wavelength of 0.6328 um. Comaautation of light in the waveguide
was accomplished by a system of aluminum electrodes separated by a 5 um gap. Each
pair of electrodes was 0.8 mm long. The electrodes were applied to a planar wave-
guide passing into a stripline S um wide that was interrupted on a 0.8 mm section.
This section was covered by the electrodes. Effective excitation of the stripline
was accomplished by using a horn transition going from 50 to 0.5 um over a length
of 2.5 mm. To reduce losses due to the influence of the metallic e].ectrodes, a
buffer film of Si02 'L000 A thick was sputtered on the waveguide surface [Ref. 2].
A diagram of the commutator is shown in Fig. 1.
In the absence of a controlling voltage, the light passed freely beneath the elec=
trodes and was introduced into the stripline section. Electrodes 1 and 2 were
at an angle of 6= 2.2� to the direction of propagation of the light beam. With
application of potential difference V to electrodes 1, the index of refraction
of the crystal in the interelectrode gap decreased due to the linear electro-optical
effect, and the light beam was reflected in the plane of the waveguide in the direc-
tion of channel A. Thanks to the symmetry of the device, an analogous effect is
produced for the beam that is deflected by electrodes 2 in the direction of channel
C. The change in the index of refraction under the effect of the electric fieid
for the TE mode can be calculated from the formula [Ref. 3]
142
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2407102/09: CIA-RDP82-00850R000400450052-5
FOR OFFICIAL USE ONLY
. Q
4
~ s ~ + + ~ ~j-~ i
B
B - - - +
5 3
C �
Fig. 1. Diagram of a three-channel waveguide commutator: 1, 2, 3--electro-optical
cells; 4--non-waveguide region; 5--planar optical waveguide; 6--light beam
~=t2~er~Jd ~ .
where ne is the effective index of refraction of the waveguide mode, r33 is the
electro-optical coefficient, d is the width of the gap between electrodes. An
electric field of opposite polarity was applied to electrodes 3. In this case
a region was induced in the interelectrode gap with elevated index of refraction
and waveguide properties, and the light propagating in the stripline appeared at
the output of channel B.
The effectiveness of light reflection in a device of this kind depends appreciably
on the angle of incidence of the optical beam on the electro-optical cell. Assum-
ing that the distri~ution of the electric field in the interelectrode gap can be
considered uniform, the critical angle of incidence on the reflecting cell is found
from the relation [Ref. 4]
9= 2-aresin(f- Z zer~ d).
For a lithium niobate Y-cut the quantity ne = 2.2031, r33= 30.8�10-10 cm/V. A voltage
of 46 V is required for total internal reflection through an angle of 2.2� and
d= 5 um. In c~ur experiments, 100% reflection occurred at a voltage of 50 V. The
discrepancy of the results to all appearances can be attributed to disorientation
of the electric field in the interelectrode gap with the z-axis of the crystal.
To lower the control voltage, it is necessary to reduce the angle of incidence
of the light beam or the width of the gap between electrodes.
�6
100
~5 Fig. 2. Switching afficiency as a
function of the amplitude of the
So f controlling voltage (in volts):
2 1--channels A, C; 2--channel B
25
0 10 ZD 30 40 50 V ,
- 143
FOF. OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5

APPROVED FOR RELEASE: 2007/42/09: CIA-RDP82-00850R000400050052-5
FOR OFFICIAL USE ONLY
In devices of this kind the controlling voltage amplitude must be the same to switch
the channels with assurance of equal intens~ty at the output of each of the channels.
Fig. 2 shows the switching efficiency as a function of the controlling voltage
for channels A and B. It can be seen from the figure that the curves t~ehave approxi-
mately the same in the interval from 23 to 35 V. At a voltage of 27 V the curves
intersect, and the switching efficiency for channels A, B and also for B, C, becomes
equal at 65%. Such a mode of commutator operation is the optimum.
One of the main parameters of switches in optical communication lines is the modu-
lation interference at the output of the device. It can be seen from the design
of the device that such interference can arise only in channel B when the efficiency
of deflection to the other channels is less than 100%. In this case the magnitude
of the interference is determined by the mode of the substrate and by the depth
of penetration of the modulating field into the substrate. When a prism device
is used for coupling out the radiation, the mode of the substrate is weakly coupled ~
and has practically no effect on operation of the commutator. Under the conditions
of our experiment the interference was calculated by the formuia 10 lg I/Io, and
was -16 dB, where I is the intensity of the light in relative units at the output
of channel B when cell 1 or 2 is switched on, and cell 3 is switched off, and Io
is the intensity of the light at the output of channel B when cell 3 is switched
on and cells 1 and 2 are switched off. Decoupling between channels was determined
with the commutators working in the optimum mode.
REFERENCES
1. Mitsunaga Kazumaso, Masuda Masamitsu, Koyama Jiro, OPT. COMMUN., Vol 27, No 3,
1978, p 361
2. Masuda, M. and Koyama, J., APPL. OPT., Vol 16, 1977, p 2994.
3. Schmidt, R. V., Kaminow, I. P�, APPL� PHYS. LETT., Vol 25, No 8, 1974, p 458.
4. Tsai Chen, S., Kim Bumman, IEEE J. QUANT. ELECTRON, Vol 14, No 7, 1978, p 513.
COPYRIGHT: Izdatel'stvo "Nauka", "Pis'ma v Zhurnal tekhnicheskoy fiziki", 1981 '
6610
CSO: 1862/196 - E~ -
144
FOR OFFICIAL USE ONLY
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000400050052-5