JPRS ID: 10269 USSR REPORT PHYSICS AND MATHEMATICS

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JPRS L/ 10269
~ 21 Jan~ary 1982
USSR Re ort
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PHYSICS AND MATHEMATI~.S
CFOUO 1 /82)
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JPRS L/10269
21 ~anuary 1982
USSR REPORT
~ PNYS I C:S A(dD MATHEMAT I CS
. (FOUO 1/$2)
� CONTEIVTS
,
- C?tYSTALS AND SEMICONDUCTORS
- Principles o~ Thermodepolarization Analysis 1
ELEC'I'RICITY AND MAGNETISM
- Iner~ial Pile-Driver A~cumulator for Producing High-Energq
= Electric Puls~s 5
, I,ASERS AND MASERS
Producing ~and-Like High Current Ion Beama in Tetrode With
Ncn-Selfdestructing Anode for Gae Laser Pumping 9
Controlling Divergence and Spectrum of XeCl Laser 10
- Optimizing Average Power of Excimer Pulse-Periodic KrF
and XeCl Lasers 17
Multipass N~odymit~m Glass Amplifier 22
Stimulated Scattering of Light by ~emperuture Waves Excited
in Thermodynamically Nonequil9_brium Media Due to Enthalpy
of Light-Controlled Chemical Reactions 30
_ Intensxty of Ultrasound Excited in Stimulated Light
Scattering by Light-Controlled Chemical Processes 42
Nonlinear Optical Inhomogeneiti~es in Active Medirg of
Gas Lasers 50
Feasibility of Dewelopitig Excimer Lasera With Ionixation
by External Low-Power Source . 54
- a- ~III - US~R - 21.H S&T FOUO]
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Measuring Copper Vapor Concentration and Degree of Gas
- Heating in Transverse-Discharg~ Copper-Vapor Laser 57
Subnanosecond Atomic Iodine Photodissociation Laser 63
~ Using ~i.rgon in Working Mixtures of G~nl Electron P~eam-
Controlled C02 Process Lasers 66
NUCLEAR PHl'SICS
Papers on High-Energy Physics 70
Ail-Union Seminar on ~fi~sics and F.ngineering of Intensive
Sources of Ions and 7:on Beams 7b
OPTICS AND SPECTROSCOPY
Determining Spectral Dependences of Absolute Qus.ntum Yielda
of XeF Excimer Formatxon C, D) in XeF2 Ph;.~tolyais ~ 77
~
Diffractometer With Thermomagnetic Re;i~tr~ation for Checking
Wavefront ~istortions i:f Pulsed Laser Emissioc~ ~6
Tnstrument far Measuring Laser Emission Wavelengi:~a 9U
Ef.fe~t of Temperat~sre on Phase Anisotropy of Aielect~tic
Laser Mirrors 94
Dec~?eration of Atoms r~nd Rearrangement o~ Atoma.e Velocitiea
by Reso~i3nt Laser Radiation Pressure 96
Law-Frequency Spectrum Analyzer of Correlation Tqp~ 108
OPTOELEL'TRONICS
PRIZ Image Converter: Its Use in Optical Data Procesaing Syaterrs 116
PI.ASMA PHYSICS
Radiation. R.elativistic Gas Dyaamics of High Temperut.ure
Phenomena 128
STRESS, STRAIN ~1ND nEFORMATION
Calculating Internal Structure of Detonation Taarre 132
MISCF.LLANEOUS
= Survey of Research in Phyeics and Astronomy 136
- MATHEP`xATICS
Optimum Control. of S~stems Wi~h Indefiaite Information 160
- b -
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CRYSTALS AND SEMICONDUCTORS
- UDC 539.~
PRINCIPLES OF THERI~ODEFOLARIZATION ANALYSIS
Moscow OSrIOVY TERMODEPOLYARIZATSIONNOG(? ANALIZA in Russian I981 (signed to press
3 Mar 81) pp 2-8
[Annotation, preface and table of contents from book "Principles of Therinodepolariza-
tion Analysis", by Yuriy Andreyevich Gorokhovatckiy, Izdate]'stvo "Nauka"., 2800
copies, 176 pages]
[Text] The monograph contains a Systemat~zed exposition of the theory of ther:nu-
stimulated depolarization and the method based on this phenomenon for studying
ele;.trophysical properties of dielectricc, semiconductors, a.n3 also various devices
~ and components of integrated circuits that contain such materials. The principal
= ca~~,abilities and fields of application of the method of. thermostimulated depolari-
zation are pin:ied down. A sFecial section deals with exposition of the n?csliari-
ties and "stumbling blocks" of the experimental technique. '.�iadifications c~f thermo--
_ tiepolarizatzon analysis are described--thermostimulated depolarization under con-
ditions of self-consistent and fractional heatir..g, which can appreciably improve
the informatior_ content of the meth.od. An exten~ive bibliography is ~resented
' on thermostimulated depolarization.
Figur~_s 47, table 1, references 32'..
Preiace
T.he method of therm~stimulated depolarization (TSD) has found extensive application
in recent years in the investigation of electrophysical phenomena ln semiconductors,
dielectrics, and also in a variety of devices and elements of integrated circuits
madz on the basis of such materials, �
The TSD method attracrs researchers by its high informativPnass combined with com-
parative simplicit~ of hardware realization and processing of expPrimental data.
However, it is not always that this method is effectively used t~~ the full extent
- of its capabilities; in some cases the experimental technique i.s misused, and the
experimental data are improperly interpr~ted. These negative tendenciea are due
bott: to a iack of the necessary analysis of the theory of the physical phenomenon
of TSD, and to inavailability of special litarature on the experimental methods
of TSD.
In monographs dealing ~aith thermoactivation spectroscopy, which includes the TSL
- method, this technique nas remained pract.'_cally unanalyzed with the exception of
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_ a recent.ly published book by V. N. Vertoprakhov and Ye. G. Sal'man [keL-. 49]. This
~ituation can be attributed fi.rst of aIl ro the ~act that the TSD method began
- to be intensively used oniy in the late sixties, and secondly to the fact that
~ until recently it has been used primarily only in research on the electret ~ffect
[Ref. 91, 118, 129, 310], in which the first ~~tempts have been made at outlining
the ~heory and experimental methods of TSD.
However, becatise ei' the topical thrust ot this re~earch, the TSD niethod has been
super~icially treaterl, and as a rule from a quile specific ::tandpoint (in both
_ theory and experiment).
In this book the author ha:~ set him self the task of more detailed and systematic
analysis of the theory of the phenomenon and experimental technique of TSD for
the pu-'pose of further development, explanation of fundamental pecul~.arities, capa-
bilities an~i drawbacks of the method of thermostimulated depolarization.
The boolc consists oF five chapters.
The first cnapter pLese~.ts the essence of the TSD efFect, and of the technique
; based on this ezfect for studying electrophysical nroperties of dielectrics and
semiconductors. Tl~e author describes processes of polarization that take place
- in objects that cont~iin polar ~efects and free charg~ ~:~rriers. The class of phe-
nomena is pointed out for whi..:i the TSD method can be used in research, the advan-
- tages that the TSll a~ethod has o�~er other techniques usualiy used for tYiese purposes
enumerated. A Bibliography is ~iven under headings of years, subject matter
.id scieritific collectives. A sample of `_erminology is presented at the conclusion
- of the f.irs*_ chapter.
The second chapter examines the elementar:~ t:leory of TSD of homogeneous material
(semiconductor or dielectric) that conta.'_~ZS a single kind of electrically active
defects. An analysis is made of electronic and ionLc processes associated both
with orientation and ~aith space-charge poiarization. Expressions are derived that
describe the TSD current for diff~.rent models of charge migration and ionization.
Ttie author di~cusses rYie ways that the beh3vior of curves for TSD current is in-
fluenced by c~nditions of ttie contacts (bl.ocking or non-blocking electrodes), equi-
libri~im conductivity and disrupti_on of electrl.cal neutrality of a specimen. A
- list is given oE research papers on TSD in which an examination is made of different
l~miting cases and approximations.
In the thircl ch~pter, a brief examinat:~.on is made of the major metilods of analyzing
experi.cnental cur�ves to determine the paran~eters of electrically active defects
(concentration, activation energy, frequency factor). An estimate is made of the
errors oE the me~:hods that are considered. A teciinique is described f.or determin--
ing the nature of the polarization process From TSD curves by varying the conditions
of polarization of the object.
The content of the first trree chapters is essentially an introduction to thermo-
depolarization ana].ysis, providing the requisite theoretical and procedural basis
f:r. goin~ further into the specifics of l-he theory and the experimental technique
with mor~ complicated objects, as presented in the fourth and fifth chapters.
2
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In particular, the fourth chapter examines the way that curves of TSD current are
influenced by quasicontinuous energy distribution of electrically active defects
in the object. A method is described for evaluating the parameters of this d.istri-
bution from the initial section of the TSD current peak. Results are given on
_ the use of computers for calculating TSD current curves in the case of a st:ill
more complicated model of the diPlectric (semiconductor) object with two-dimen-
sional quasicontinuous distribut-�on of electrically activ~ defects with respect
to activation energy and with respect to frequency factor. Possible ca.uses of
the phenomenon of TSD current inversion frequency observed in experiments ar.e ~is-
cussed. In addition, the fourth chapter examines the phenomenon of repolarization
in the internal electric field, the s~rong internal field effect, association and.
dissociation of complexes of electircally active defects, and their influence on
the TSD current curves.
- The fifth chapter describes some modifications of thermodepolarization analysis
_ --TSD under conditions of self-consist~nt and fractional heating--which considerably
increase the information content of the met~nod and reduce ambigulty in the interpre-
tation of experimental data. It is shown that the use of self-consistent heating
- enables determination of the ordPr of the kinetics of the relaxation process, and
accordingly affor~.~ unambiguous calculation of the activati~n energy and frequency
factor of electri_ca11y active defects. Use of the fractional heating ~~tate enables
. reconstruction of the Uehavior of the distribution of electrically active defects
with respecc tr~ activation energy or frequency factor, as well as estahlishment
of the fact of existence of bivariate distribution. An examination is made of
_ the question of choosing the optimum mode of fractional heating that minimizes
measuremenr_ error ;ahile maximizing the resolutfon of the method. At the end of
the chapter, a brief survey is given of different comple~:es of inethods of studying
dielectrics and semiconductors, includine the TSD method, and their capabilities
- ara analyzed.
The experimental data used in the book serve as an illustration of the theoretical
principles and expErimental technique of thermodepolarization analysis. An exten-
, sive survey of. experimental material on investigation of some inorganic subscaaces
and compounds hy methods of thermQactivation spectroscopy, and in particular by
the metho~ of TSD, can be found in Ref. 49.
The b~ok is based on the results of studies done with direct participation of the
author. A list of Lundamental and adc~itional literature is given. Tha~ additional
literature is given as an aid to the rea~er for more detailed and complete acquain-
- tance with some questions tY:at are onl; touched upon in the text, but are not taken
un in dep~h because of the limited scope of the book.
The author considers it his plea~ant duty to thank the pe~ple at the Scientific
Research Institute of .Solid State Physics of Latvian State University ime,ni P,
Stuchkz and the Phy~ics Department of Moscow Institute of Electronic Macl~ine Build�
ing, who were of help to the author in his studiPS, and who also took part in dis-
cussing the results of these studies.
The author is particularly grateful to associate members of the USSR Aca~emy of
Sciences G. A. Smolenskiy and Yu. A. Osip'yan, as well as to Candida+tQ of Physical
and Mathema:.ical Sciences E. L. Lutsenko for thorough and extr~mely useful analysis
of the manuscript of the book during its review.
3
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The author owes a debt of thanks to do~tors of physical and mather.iatical sciences,
professors A. N. Gubkin and Yu. R. ~akis, and to Candidate of Physical and Mathe-
~ matical Sciences, Docent V. E. Eirap, who acquainted themselves with the manuscript
oF the book and made a number of coi~.str.uctive ccmments.
" Contents page
Preface 5
Principa:l abbreviations and symbols 9
C~IAPTER l: GENERAL CONCEPT OF THERMODEPOLARI'LATION r~NALYSIS
1.1. Essence of thermostimulated degolarization method 11
1.2. Basic possibilitie~ and areas of application of TSD method 16
_ 1.3. Basic stag~s of development of TSD method 20
1.4. Qeustion of terminology 23
CHAPTER 2: ELEMENTEIRY THEORY OF PHENOMENON OF THERMOSTIMULATED DEPOLARI~ATION
2.1. Analysis and cLassification of physical effects that lead to TSD cur~ent
in homogeneous object 25
2.2. TSD of maerascopically homogeneous relaxation polarization 33
2.3. TSD currents in case of electronic space-charge polarization (monoelec-
~ tret) 36
'L.4, Electronic TSD currents in electroneutral object 45
2.5. Generalized expression for electronic TSD current~ in case of space
charge "suctioning" 52
2.6. TSD currents in case o~ ionic space-charge polarizati~n 53
2.7. Influence of equilibrium conductivity on TSD curL�enLS 56
CHAPTER 3: METHOD OF PkOCESSING TSD DATA FOR OBJECTS WIT?i ONE KINll OF DIPOLES
OR CAPTURE CENTERS
3.1. Methods of calculating dipo~.e paratnsters or capture center par3meters from
TSD current curves 59
3.2. Technique for varying polarization conditions 74
CH.4PTER 4: SPECIFICSOF THERMOSTIMULATED DEPOLARIZATION IN MORE COMPLEX OBJECTS
~ 4.1. TSD in objects with Fnergy distributi.on of electrically active defects 84
/+.2. TSD in case of bivariate quasicont~nuous distribution of electrically
active deFects with respect to activation energy and frequency factor, 90
4.3. Influence r~f type of spatial distribution of space charge on TSD current 100
4.4. TSD current for objects with comparable rates of "suctioning" and
neutY~a:ltzation of space charge 104
4~5. TSD current due to effect of strong internal electric f ield 110
- 4.6. Influence of association and dissociation of complexes of electrically
active defects on TSD current curv~s 115
CHAPTER 5: MODIFICATIONS OF THERMODEPOLARIZATI~N ANAT~YSIS
5.1. TSD in self-consisteiit heating mode 121
5.2. T.SD in ~ractional heating mode 127
5.3. Research tnethod complexes izcluding thermodepolarization analysis 146
Conclusion
~ References
~ Subject and literature index 170
COPYRIGHT: Izdatel'stvo "Nauka". Glavnaya redaktsiya fiziko-matematicheGkoy
literatcry, 1981
6610
- CSO: 1862/44
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ELECTRICITY AND MAGNETISM
UDC 621.373.1
INERTTAL PILE-DRIVER ACCUMULI~TOR FOR PRODUCING HIGH-ENERGY ELECTRIC PULSES
- Moscow PRIBORY I TEKHNIKA EKSPERIMENTA in Russian No 3, May-Jun 81 (manuscript
~ received 22. Feb 8Q) pp ?99-201
- [Article by V. N. Kunin, V. J. Dorozhkov and M~ V. Sergeyeva, Vladimir Polytech-
r.ical In.stitute J
[Text] A pulse generator is describe~i that consists of a DC
electromagnet with armored magnPtic circuit, and a working coil.
Pu~ses are gene~ated when the electromagnet falls into a coaxial
coil. Mass of the facility is four metric tons, ancl the maximum
hei~ht to ;ahich a 1350 kg electromagnet is raised is nine meters.
The facility generates bell-shaped current pulses with energy of
up to 50 kJ and duration of 50-100 ms.
An inertial accumulator is described below in rahich the kinetic energy of a falling
elect.romagnPt is converted to the ener~y of an electric gulse [Ref. 1]. The accumu-
lator is a system that consists of a DC 2~lectromagnet with armored magne~ic circuit
and a coaxial working coil. When the ele~tr~magnet falls into the coil, an electro-
mor_ive induction force arises that is cloSed to a low-resistance active load.
_ The magnetic circuit of the electromagnet is cast from grade St.20 steel, has an
outside diaraeter of 930 ~n (Fig. 1[photo not reproduced] ) and masses 1350 kg. The
magnetizing coil contains 125 turns oc copper wire with 50 mm2 cross section.
Experiments have shown that the lea~cage coefficient of the magnetic field is 1.5-1.7.
In the accumulatc,r the electromagnet moves under the force of gravity along guide
_ columns by means of centerir~g rollers on bearings. The columns are mounted on
a foundation that 31so carsies the working coil. The fz~ility is fastened on
' a concrete base with shack-absorbing layer of wooden beams. Th~ electromagnet
is rai.sed by a winch with ele~tric drive. The hoisting cable is equipped with
~ a locic that permits release of the electromagnet from the cable at a predetermined
height. Tne operation of the facility is remotEly c~ntrolled from a panel situated
in a laboratoi~. The mass of the facility is four metric tons, and the height
- to which the electromagizet can ue raised is nine meters.
Fig. 2 shows oscillogr~ms of the current and voltag~ across an active load, produced
~ by the i~-115 light-beam oscilloscope. At a magnetizing current of 400 A, voltage
nf 30 V and t~eight of elevation of the electromagnet of 2.0 m, the cuzrent pu~se
- amplitude was 3 kA at voltage of 100 V. Pulse durati~n 7aas 0.11 s, and the energy
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I
0, f s U
Fig. 2. Oscillograms of current I and
voltage U across resistive load
W, icJ
B o
' ~ 1 ~
0 0,f 0,2 0,3 R~ ~
Fig. 3. Energy W released in load as a
f unction of load resistance R
released in the load was 10.1 kJ. Thus tne coefficient of amplification with re-
spect to electric poaer in this experiment is equal to 25. This parameter reaches
90 in experiments with max~mum heights of magnet elevation.
The coefficient of conversion of accumulated mechan~cal energy to the energy of
_ an electric pulse is 38%. The load resistance and res~stance of the working coil
are approximately equal (maximum power made), and therefore about 40% of the stored
energy is released ~r. ~he working coil as heat. The remaining 22% of the energy
is mechanical losses and losses in the connecting wires.
The efficiency of the pile-driver accumulator also depends on losses associated
with residual kinetic energy of the falling magnet. Actually, generation of the
- minimum attainable working voltage necessitates a certain residual veloci*_y
of the ma_~net vres xelative to the working coil, and therefore energy mvreS/2 is
_ expended, where m is the mass of tne magnet. For example when the accumulator
- is used for feeding are sources, the arc is extinguished at a voltage whPre
~res - 0.2v aX [Ref. 2], and the losses amount to 4%. Quenching of vres requires
transEer o~ moment~un P= mvres from the magnet to the base by inela~tic impact.
If the braking path is about 1Q% of. the working stroke, then in case of triangular
shape of the gene.rated pulse a constant force is reqaired that is equal to half the
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~ maximum working force of 100 metric tons. Such a force can be easily provided
by brakes of various designs, such as a rubber bumper. H~wever, the constr!iction
4nust provide for accident prevention in case the working electric circuit is run-
tured, when all the energy accumulated by the magnet is transferred to the base.
In this case the braking force is five times the maximum working force. Experience
- has shown that the required conditions are met by a leaa crusher 100 mm in diameter
and 80 mm high that spreads out between the flats or the base and the magnet upon
, impact. Energy of 1,2 kJ is expended on deformation of such a crusher by 90%,
- 'ensuring efficient braking under extreme experimental conditions.
The base of the accumulator is the same kind of electromagnet as the wcrking unit,
but turned through 180�. Shorting of ~ts coils ensures efficient braking of tne
working magnet on the concluding segment of the working stroke, when the working
- magnet begins to induce magnetic flux in ,.'ze base. The force of electromagnetic
' bra~.ing is proportional to the velocity of approach of the working magnet and base,
which i.s favorable with regard to extremum situations when the approach takes place
at vmax�
When the magnet strikes the base, a seismic wave arises that represents a certain
danger to brick structures. Therefore the accumulator is situated at a distance
of 30 m from the laboratory.
To reduce the power of the seismic wave, the base of the accumulatc~r in the graund
bears on the foundation through a wooden floor 5~ mm thick. The foundation is
built up of concrete blocks with total mass of 11 metric tQns ~uried in the ground
aac! laid on a sandstone bed. To reduce '_osses on formati~n of the pul~ed magnetic
~ fiel.d a~ound the wires of the working circuit, and to allevia~e the danger of harm-
fL~1 action of this field on the health of experimental worke*_-s, the forward and
return working wires are stretched over the entire length in direct proximity to
_ one another.
- The pulse power under conditions of ma~imum generator power is dPtermined by the
- expression
- N = 2B$v~Vplp,
where B is the induction in the working gap, v is the velocity of magnet motion,
VP is the volume of c~pper in the working coil and p is resistivity.
A disadvantage of a converter of tk~is t;~~e is that the magnetic circuit is open
before the working stroke bagins. As a result, the tcstal reluctance of the magnetic
circuit includes the reluctance of an air gap equal to the width of the working
coil (in our converter ~Z= 150 tmn), which appreciablyreduces the working value
_ of B, and as a consequence the pr.wer of the resultant pulse.
- Among the advantages of this design is moderate sensittvity of accumulator current
pulse parameters to the magnitude of the external load. Fig. 3 shows how the energy
, released in the load depends on ~oad resistance. In the experiments that yielded
this curve, H= 2 m, and the current in the magnetizing coil was 4C0 A.
It can be seen from Fig. 3 that the energy maximum is rather flat, and when the
load changes from 0.06 to 0.28 SZ, i. e. by a factor of 4, the power changes by
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only 20%. In producing powerful pulses, wP nave to reconcile ourselves to the
fact that about half the stored energy is e:~pended on internal losses. Nonethe-
less, with respect to the ratio of electric energy in a pulse to weight of the
- facility, the described design corresponds approximately =o a capacitive accumu-
~ lator i~3sed on IMUS-140 capacitors. The maximun stored potential energy for this
facility is about 110 kJ. The inertial pile-driver accumulator enables generation
of beli-shap~d current pulses with energy up to 50 kJ and duration of 50-100 ms.
REFERENCES
1. Dorozhko;~, G. V., Kunina, M. V., "Sborn3.k. Voprosy nizkotemperaturnoy plazmy
i n:agniL�~;gid~odinamiki" [Collection. Problems ~f Low-Temperature Plasma and
Ma.~net~~!~ycirodyn3mics], Ryazan', Radio Engineering Institute, 1978, p 37.
2. Kunin, V. N., Zalazayev, P. i~., Gradusov,~B. F. et al., "Sbornik. Voprosy
nizkotemperaturnoy plazmy i magnitogidrodinamiki", Rvazan', Radio Engineering
Iiistitute, 1978, n 3.
COPYRIGHT: Izdatel'stvo "Naulca", "Prib~ry i t~khnika eksperimenta", I981
6610
CSO: 8144i0423
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~ LASERS AND MASERS
UDC 533.951.2.3
PRODUCING BAND-LIKE HIGii CURRENT ION BEAMS IN TETRODE WITH NON-SELFDESTRUCTING
ANODE FOR GAS LASER PUNIPING
Tomsk IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENIY: FIZIKA in Russian Vol 24, No 9,
Sep 81 p 138
[Abstract of article ~y V. M. Bystritskiy, Ya. Ye. Krasik and S. S. SulakshinJ
(Text] The work is devoted to the study of a new type of high current proton
beam generator developed for gas laser pumping. A band-like form of proton
beams was produced, and the energy, time and spatial characteristics of the beam
were studied. It is shown that the resources of the penerator exceed the
operation by 100 to 1,000 times. Tfie possibilitp of focusing a high current
= proton beam by two types of magnetic lensec is considered. It is noted that the
application of the developed generator for Ar-NZ and XeCl laser pumping allows
new results in laser research to be obtained.
COPYRIGHT: Izvestiya vuzov, Fizika, vyp. 9, 1981.
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CONTROLLING DIVERGFNCE AND SPECTRUM ~F XeCl LASER
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 9(111), Sep 81 (manuscript re-
ceived 1 N~v 80) pp 1861-1866
[Article by V. Yu. Baranov, V. M. Borisov and Yu. Yu. ~tepanov, Institute of .:,tomic
Energy imeni I. V. ?Curchatov, Moscow]
' [Text] The paper gives the results of a study of divergence
and spectral composition of radiation from an electric-discharge
XeCl laser with non-dispersive and dispersive cavities. It is
shown here for the first time that the spectrum of the XeCl laser
can be considerably narrowed by merely reducing the level of
stimulated emission in a non-dispersive cavity. It is found
that discharge inhomogeneity in the direction across the current
has an effect on laser emission divergenca_. Lasing is achieved
with line width of 0.1 cm-1 and divergence close to the diffrac-
tion ~.imit.
- Introduction
At the present time, excimer lasers are in fairly wide use in photochemistry [Ref.
1], laser purification of material [Ref. 2, 3], separation of uranium isotopes
[Ref. 4] and also in laser-driven fusion programs [Ref. 5, 6]. Naturally, each
of the possible applications imposes certain requirements on laser characteristics.
The distinguishing feature in use of excimer lasers for nuclear fusion is that the
laser cannot be used as an amplifier in the conventional arrangement of series
amplification of a short pulse because of the short radiation lifetime of excimer
molecules. Under discussion at present are various methods of converting or com-
, ~:�essing an intense excimer laser pulse with duration of 100-500 ns into a pulse
with duration oE 1 ns [Ref. 5-7]. For example, Ref. 8 suggests time compression
of a KrF laser pulse in stimulated Raman scattering of amplif ication of opposed
beams. An approach of this kind is one of the most promising. To realize stimulated
Raman scattering of amplification of opposed beams in methane, as experimentally
shown in Ref. 8, the spectrum of the KrF laser must be narrowed from its initial
- free-running width of ~v = 50 cm ~ to ~v = 0.1 cm 1. Such narrowing should be done
in a master laser with subsequent injection of the narrow-band radiation into an
am~lif ier .
~ The following circumstznces must be taken into consideration in developing a master
. laser with narrow spectrum and divergence close to the diffraction limit. The time
~ 10
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of formatio~i of inversion in electric discharpe excimer lasers ~.s ordinarily 10-
~ 20 ns [Ref. 10]. Heating of stimulated emission from the level uf spontaneous
noise at a characteristic cavity length of about 1 m takes place in approximately
3-4 double passes of the cavity. Under these conditions, appreciable narrowing
of the spectrum and reduction of divergence can be achieved by using strongly dis-
_ persive elements, which should be accompanied by a considerable reduction of lasing
energy. For this reason, for such a master laser particular attention should be
given to reducing non-selective losses in the cavity and ensuring a high level
of stimulated emission of the electric-discharge system.
_ The purpose of our research is to develop a master laser using XeCl that gives
- the requisite emission parameters. It has been recently demonstrated that an elec-
tron beam-pumped XeCl laser may have efficiency as high as that of the KrF laser
[Ref. 9]. Besides, the XeCl laser has certain advantages: its lasing mixture
is more resistant to dissociation, and withstands a much greater number of flashes
than the KrF laser mixture, the free-running width is narrower--~v= 15 cm-1.
Therefore, to do experiments on stimulated Raman compression of excimer laser emis-
sion we have selected th? XeCl laser.
Fig. 1. Optical system of the facility:
1, 2--flat mirrors of the cavity (R1 =
~o
y 99%, R2 = 85%) ; 3, 4--lenses (f 3= 614 mm,
fy = 340 mm); 5, 6--optical wedges (~5 =
3 47', ~6 = 20'); 7--calorimeter; 8, lU--
~ 6 Fabry-Per~~t interferometers; 9--spectro-
- ;~QV~~~ r~~ ~ graph; 11-�-He-Ne laser
~ ,
I ~
I ~
~--~-e-~-~
a
- Descri.ption of Facilit~ and Method of Measurements
The optical arrangement of the facility is shown in Fig. 1. This arrangement mad~
it possible for v.s to measure energy, spectrum and divergence of laser radiation
- in each p~ilse. A laser was used with UV pre-ionization by four rows of sparks;
the eJ.ectric circuit for producing the discharge is analogous to that of Ref. 11.
The discharge was set up in a volume of 40 X 5 x 0.7= 140 cm3, where 5 cm is the
interelectrode spacing. Mainly, a cavity with external mirrors was used, and LiF
windows were installed in the chamber. The laser operated on a mixture of HC1:Xe:He
= 1:15:500 at pressure of 1.5-2.0 atm. To narrow the lasing spectrum, one or two
IT-28-30 I'abry-Perot interferometers (8) were placed in the cavity witih mirror
reflectivities of 70%. The spectrum was monitored by the STE-1 spectrograph (9)
with crossed IT-28-30 Fabry-Perot interferometer (10). To reduce absorption of
laser emission, the aluminum coatings of the interferometer mirrors were replaced
- by multilayer interference coatings. Divergence of laser radiation was determined
by photometry of one of the spots produced in the focus of lens 4 after passing
through wedge 5. Divergence was determined with respect to the level at half inten-
sity. Laser emission was attenuated upon reflection from wedge 6 and transmission
through wedge 5. Both wedges were made of quartz and had 70% interference coatings
~ on each face. The system comprising wedge 5, len.s 4 and the camera, was aligned
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.
with respect to the beam of He-Ne laser 11, coinciding with the excimer laser beam. ~
The spectrograms and focal spot were photographed on KN-2 film at normal exposures.
The laser pulse energy was measured by KTP calorimeter 7 w~th F116/1 microvoltmeter.
The c~uration of the light pulse was determined by c:oaxial photocell FK-3 and ~fl
I2-7 timer. The glass winaow of the FK-3 strongly attenuated the laser emis;;ion,
and therefore duration couid be measured only for pulses with power greater than
0.1 W.
- varrowing of Che Radiation Pattern
Lsually electrical-discharge excimer lasers give strongly diverging radiation
(6= 5-10 mrad [Ref. 11, 12]). Ref. 13 describes a laser with unstable cavity
(magnification 20-30) on which a divergence of 6= 0.5 mLad was attained with output
aperture 5 mm in diameter. To narraw the lasing spectrum, a Fabry-Perot etalon
must be placed in the laser cavity, but as pointed out in Ref. 14, the size of
the base of the Fabry-Perot etalon placed in an unstable cavity is limited by the
= angle of aperture of the spherical wave in this cavity. On the other hand it is
- known [Ref. 14] that the limiting divergence is attained more easily in lasers
with flat cavities than in thoGe with unsta~le cavities. There~fore in our research
we studied the divergence and spectrum of th~ XeCl laser with flat cavity.
Cavity Lasing PLlse Divergence 81 Divergence 6Z
characteristics duration with respect t~~ with respect to
energy, at level lar.ger dimens;_on, smaller dimen~ion,
R1, % Rz, % Z, cm mJ 0.5, ns mrad mrad
99 8 67 200 25 4 0.6
99 85 L10 S 27 2.2 0.35
- 99 85 l10 3 16 0.7 0.3
Note: In the last case a Fabry-Perot interferometer was placed in the cavity,
- d= 0.3 mm
The table summarizes the energy, time and space characteristics of laser operation
with stimi~lated emission over the entire discharge aperture (SO x 7 mm) for 3ifferent
cavities. As usual for lasers of this kind, the maximum lasing energy is realized
with a short cavity with weak coupling. In this case the cavity mirrors were in-
- stalled directly on the discharge chamber. Radiation divergence was rather large,
and on the larger dimension of the aperture it was seven times the divergence with
= r.espect to the smaller dimension. For a cavity with external mirrors and strong
coupling, divergence was about two times lower. In this case there was a sharp
reduction in lasing energy. It was found that divergence 81 with respect to the
larger dimension o~ the aperture is nearly independent of the level of energy input,
and for central regions of the discharge is about double the level for thP edge
regions, i. e. in the vicin~tv of the electrodes. On the other hand, divergence
62 with respect to ttie smaller dimension of the aperture shows little difference
in the center. and on the edges of the aperture, but is appreciably dependent on
the level of energy input. For example, when the charging voltage is increased
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from 50 to b0 kV, 6Z increases by 50%. The transverse dimension of the discharge
in this case does not change; visually it shows a large number of luminescent chan-
nels, and the increase in divergence is apparently mainly due to this deterioration
- of discharge homogeneity.
To further reduce divergence, a circular diaphragm is placed in the cavity. In
addition, the use of a Fabry-Perot interferome;.er for frequency selection of the
~ radiation is also accompanied by angular selection. By way of example, Lhe table
presents the characteristics of lasing without a dia~.~hragm when one Fabry-Perot
interferometer is installed in the cavity. The interferometer base d= 0.3 mm,
and reflectivity of the mirrors was 70%. The Fabry-Perct interferometer was in-
stalled in such a way that angular selection was in the direction of greater di-
vergence 61. It can be seen that divergence actually decreases with some fall-off
of energy and shortening of the laser pulse. By way of illustration, Fig. 2[ptioto
not repr~duced] shows focal spots produced at the focus of lens 4(see Fig. 1) for
_ various cavities and dimensions of the intracavity diaphragm D. In the case of
large image magnification (Fig. 2a-c) the fo~al spots consist of individual points,
i. e. lasing has inhomogeneous spatial distribution. Moreover, for lasing with
- non-dispersive cavity the focal spots in individual cases were stretched out in
the direction across the discharge current. The observed distortions of shape
amounted to 30-60%. The deformation of the focal spot, and accordingly the increase
- in 8, are obviously related to discharge inhomogeneity.
It was possible to eliminate deformation of the focal spot by shifting the dia-
phragm in the direction across the discharge. The reduction in 6 in one of the
- directions when a single Fabry-Perot interferometer was inst~lled in the cavity
was accompanied by compression of the spot in this direction (see Fig. 2c). The
focal spot corresponding to the state with minimum divergence and 6 close to the
diffraction limit is shown in Fig. 2d.
8, ~rad ~~E~~ Fig. 3. Divergence A(solid lines)
C uJ and lasing energy EZ (dashed lines)
o,a 4S~ as functions of the diameter of the
- J intracavity diaphragm: 1--cavity
- 46 ~ with two Fabry-Perot interferometers,
Z ~~o d= 2 mm; 2--cavity with one Fabry-
j~ o'~~~ Perot interferometer, d=0.3 mm; 3--
o � non-dispersive cavity
y /i
~ - iso
~2 � /
r ~ ~
Q - ~ ~
= J 4 D, mm
Fi~; 3 shows dependences of ~ and lasing energy EZ on the size of diaphragm D for
different lasing modes; each of the points on the graph is the average of 5-7 mea-
surements. For a cavity with a single Fabry-Perot interferometer, 8 is given for
tt~ie larger dimension of the spot (see Fig. 2c). All cavities show a common pattern:
- decre;isin~ 0 with decreasing D. This is apparently due to a reductian in the number
c~C transverse modes. Divergence close to the diffraction limit is obtained only
~il-. D= 2 mm and additional angular selection with respect to two directions by using
two Fabry-Perot interferometers (d = 2 mm). Inclusion of the Fabry-Perot interferom-
eters also reduces the energy and brightn~ss of the emission. But wherEas the
13
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total ener,y due to suppression of transverse modes falls off rapidly, the emission
brightness decreases to a lesser extent, and the spectral brightness increases.
For example fur D= 2 mm with transition from wide-band to narrow-band lasing with
two Fabry-Perot interferometers, the energy decreases by about two orders of magni-
tude, whereas the brightness falls off only to one-half, and the spectral brightness

-1 increases by a factor of 20.
In the mode with minimum divergence, the laser pulse had an energy of about 10 uJ.
Although this is not much energy, according to Ref. 15 it is completely adequate
for injection into an amplif ier that produces a pulse with energy of ~100 mJ. It
is known from Ref. 15 that for a KrF amplifier an injected pulse with narrow spec-
trum and energy of the order of a few tens of microjoules is capable of controlling
the spectrum of a pulse with energy of ~400 mJ; on the otner hand, ~ae know that
al]. major characteristics of excimer molecules XeCl and KrF and of lasers based
on these molecules are similar. Therefore we have good reason to assume that the
- resultant pulse with energy of ~10 uJ can be used for effective injectio.z into
- a powerful XeCl amplifier.
Narrowing of the Spectrum
Ref. 15 and 16 report on gettiing narrow-~and stimulated emission in KrF and XeCl
master lasers; radiation divergence was not meastired in these lasers. We have
studied the spectral composition of XeCl laser radiation for stimulated emission
both with a non-dispersive cavity and with intracavity Fabry-Perot interferometers.
The width oF eac'~ lasing line ;aas determined from a system of interierence rings
obtained from the control Fabry-Perot interferometer (IO) in the focal plane of
the STE-1 spectrograph (see Fig. 1). Systems of rings from different lines were
- separated by the spectrograph. Line width was determined with respect to the level
~ of half-intensity. Fabry-Perot interferometers were used with bases d= 1, 2, 5,
10 and 20 mm; reFlectivity of the mirrors was 85%.
An atr.empt was made to increase the spectral power of the XeCl laser by reducing
the pressure of the mixture as was done for an XeF laser in Ref. 12. Reducing
the pressure of the mixture from 3 to 0.4 atm did not lead to any appreciable nar-
rowing oF the lasing snectrum.
As an example, Fig. 4[photo not reproduced] shows spectrograms of free-running
emission and lasing with a single Fabry-Perot intzrferometer (d = 0.3 mm) in dif-
ferent positions. With a non-dispersive cavity, the XeCl laser usually emits two
lines: 3Q8.0 and 308.2 nm, corresponding to transitions (0-1) and (0-2) [Ref. 17].
The widtti of each line under our conditions caas 7-8 cm-1 at lasing power density
of 1-3 mW/r_m2. W ith 1 Fabry-Perot interferometer (d = 0~3 mm), the spectrum shows
several components. For sone positions of the Fabry-Perot interferometer (see
for example Fig. 4b, c), a single component remains with a reduction in lasing
level by a factor of 3-4.
_ Fig. 5 shows the dependence of lasing line width ~v on lasing energy density EZs
for cavities with a diaphragm. For a non-dispersive cavity and a cavity with a
single Fabry-Perot interferometer (d = 2 mm) the spectrum consists of two lines
of approxi.mately equal width. The figure shows the ~v for one of these. A com-
mon feature of all curves is th~t as EZS increases, so does ~v. This shows up most
14
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Q~~ rm 1 Fig. S. Lasing line width Ov as
- a function of lasing energy den-
4 � sity EZS: 1, 3--lasing on one
y,� line; 2, 4--on two lines; 1--
T , o~ lasing with two Fabry-Perot inter-
' � � ~ ferometers (d = 2 mm) ; 2--with
o � one Fabry-Perot interferometer
40 ~ ~c
_ (d = 2 mm); 4--lasing with non-
dispersive cavity; intracavity
diaphragm (D = 2 (o); 3 (o) and
Qa 4 mm )
_ n9 p O Q
A 0 ~
Q~l~ ~1 ~ t 1 ~ 1
a7 ~ a4 ~ as ~ 1 EZs' mJ/cm2
weakly in the case of selection by two Fabry-Perot interferometers (curve 1, the
straight line is an arbitrary approximation). The quantity ~v shows the greatest
dependence on EZS for a non-dispersive cavity (curve 4). As EZS decreases from
4 tc~ 0.8 mJ/cm , the width of each of the two lasing lines falls to half. If we
consider the fact that for EZS = 20-60 mJ/cm2, ~v = 7-8 cm 1 for each line, we can
see that by merely reducing the lasing level we can narrow the spectrum of the
- XeCl laser by a factor of 4-5. Such a technique may be useful for same applications.
The width of the spectrum can be further reduced by using a Fabry-Perot interferome-
ter; however, narrowing of the spectrum in not in proportion to the resolution
of the interferometer (curves 2 and 3). This can be attributed to the fact that
an isolated Fabry-Perot interferometer in the cavity selects the mode composition
only with respect to one direction (see Fig. 3), while selection with respect to
_ the other direction is considerably poorer. Only under conditions of "rigid"
_ selection by two Fabry-Perot interferometers is the spectrum narrowed in proportion
to the resolution of the interferometer. Typically, emission is on only one line
in this case, and a f ai.rly strong relation shows up between Ov and 6(see points
above curve 1; here an increase in A by a factor of two with a change from D= 2 to
~ D= 4 leads to doubling of ~v as well).
And so, in ~his paper we have investigated the conditions of narrowing of tt;~ spectrum
and radiation pattern of the XeCl master laser. We have attained the required
parameters: lasing line width of 0.1 cm 1 and divergence near the diffraction limit.
= In conclusion, the authors thank S. N. Borisov for assistance with the experiments.
REFERENCES
1. Wampler, F. B., Tiee, J. J., Rice, W. W., Oldenborg, R. C., J. CHEM. PHYS.,
Vol 71, 1979, p 3926.
2. Donohue, T., OPTICAL ENG., Vol 18, 1979, p 181.
3. Clark, J. H., Andersen, R. G., APPL. PHYS. LETTS., Vol 32, 1978, p 46.
4. LASER FOCUS, Vol 16, No 5, 1980, p 18.
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S. Murray, J. R., Goldhar, J., Eimerl, D� Szoke, A., IEEE J., Val QE-15, 1979,
p 342.
6. Ewing, J. J., Haas, R. A., Swingl, J. C., George, E. V., Krupke, W. F., IE~E J.~
Vol QE-15, 1979, p 368.
- 7. Krupke, W. F., George, E. V., Haas, R. A., "Laser Handbuch", Amsterdam, Vol 3,
1979, p 627.
8. Murray, J. R., Goldhar, J., SzSke, A., APPL. PHYS. LETTS., Vol 32, 1978, p 551.
9. Bothe, D. E., West, J. B., Bhaumik, M. L., IEEE J., Vol QE-15, 1979, p 314.
10. Lakoba, I. S., Yakovlenko, S. I., KVANTOVAYA ELEKTRONIKA, Vol 7, 1980, p 677.
11. Borisov, V. M., Vysikaylo, F. I., Mamonov, S. G., Napartovich, A. P.,
Stepanov, Yu. Yu., KVANTOVAYA ELEKTRONIKA, Vol 7, 1980, p 593.
12. Baranov, V. Yu., Borisov, V. M., Kiryukhin, Yu. B., Stepanov, Yu. Yu.,
K`JANTOVAYA ELEKTRONIKA, Vol 5, 1978, p 2285.
13. James, D., McKee, T. J., Skrlac, W., IEEE J., Vol QE-15, 1979, p 335.
14. Anan'yev, Yu. A., "Opticheskiye rezonatory i problema raskhodimosti lazernogo
izlucheniya" [Optical Cavities and the Problem of Laser Emission DivergenceJ,
Moscow, Na.uka, 1979.
15. Goldhar, J., Rapoport, W. R., Murray, J. R., IEEE J., Vol QE-16, 1980, p 235.
17. Tellinghuizen, J., Hoffman, J. M., Tisone, G. C., Hays, A. K., J. CHEM. PHYS.,
Vol 64, 1976, p 2484.
COPYRI~HT: Izdatel'stvo "Radio i svyaz"', "Kvantova~a elektronika", 1981
6610
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OPTIMIZING AVERAGE POidER OF EXCIMER PULSE-PERIODIC KrF AND XeCl LASERS
Mo:~cow KVANTOVAYA ELEKTRONIKA in Russian Vol 8, No 9(111), Sep S1 (manuscript re-
ceived 5 Jan 81) pp 1909--1912
- [Article by V. Yu. Baranov, V. M. Borisov, F. I. Vysikaylo, Yu. B> Kirqukhin and
N. Ya. SmirnovJ
[Text] An examination is made of the possibilities for incr_easing
the average powe�r of KrF and XeCl lasers in the pulse-periodic
mode without increasing the rate of circulatian of the gas mixture
~n a closed loop. Improvement of the homogeneity and stability
of the voltnnetric discharge resulted in an average power of about
40 W with several hours of laser operation.
There has recently been an upsurge of interest in pulse-periodic inert halide gas
, lasers because of a wide range of p~ssible applications. Attairnnent of a high
average power in such lasers involves rapid circulation of the gas mixture. For
- example in Ref. 1 an average power of 24 W was attained at a gas mixture flowrate
of about 25 m/s. In this paper an examination is made of the possibilities for
_ increasing average laser power [Ref. 2] at low gas mixture pumping velocity (about
6 m/s). On a fairly simple and compact laboratory facilit}~, the main thrust is
at attainment of good homogeneity and stability of the volumetric discharge with
high efficiency of converting ele ctrical energy to ~asing.
Fig. 1 shows the construction of the pulse- ~
periodic excimer laser. Chamber 1 is made of ~ 2 ~
stainless steel, and the removable cover 4 hold- ~ 3~~
ing hi~h-voltage electrode 3 is made of glass J[
= textolite. The surface of the cover that faces 5 ~ 6~ 9
~ the discharge was covered with sheet Teflon,
i improving passivation of the loop and extending 8 ~
the service life of the laser. Pre-ionization,
- as in Ref. 2, was produced by four rows of sparks ~
_ formed betwe~n the electrodes and four-rt~a~ of~ptns Fig. 1. Desi~n of pulse-
that were introduced into the chamber. The periodic excimer laser
length of the row was equal to the length of
the grounded (2) and high-voltage (3) electrodes ~;20 mm). The closed stainless
steel loop contained simple heat exchangex 8 and compiessor 9. .
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The eleclric power supply ~ontained an IOM-100 high-voltage source of supply that
charged storage capacitor Co (i) in a resonant diode system. Peaking capacitor C
was structuralty accommodated on the removable cover and made on the basis of
KVI-3 ~apacitors (6). A TGI-2500/50 thyratron (5) was used as the commutator.
Firing of the thyratron flash-charged the low-inductance peaking ~apacitor, and
the energy stored in it by the ti*_ne of breakdown of the main interelectrode gap
ensured high current density of the volumetric discharge. The amplitude of the
current pulse, its rise time and duration are t}:~s functions of the parameter
C/Co. As measurements show, this parameter has an appreciable effect on both the
energy input to the volumetric discharge and its stability in the pulse r~currence
mode, i. e. it determines the average power of the laser. In the measurements
- that we made, Co= 0.5 uF did nat vary, but capacitance C was varied. The limiting
current through tt~e volumetric discharge reached 35 kA at a half-width duration
of ~60 ns.
P, watts P, watts
30 2
30 1
� . . 10 , ,
2 , . . . . .
- ZO
_ ~
10
~v ~ , , ~ ,
Q14 0,78 0,42 0,56 C/Co 0
v 31 35 ~ 4f U o, kV
Fig. 2. Lasing output power Fig. 3. Lasing output power
as a function of ratio C/Co in as a function of charge voltage
mixture F2:Kr:He = 1:25:50~ (1) for unilateral (1) and bi-
and HCl:Xe:He = 1:20:500 (2); lateral (2) illumination of
p= 2 atm; Uo = 45 kV the active volume
The behavior of curves for P= f(C/Co) (Fig. 2) depends strongly on the composition
of th~~ working mixture. The presence of a pronounced maximum for the KrF laser
~ (curv~ 1) can be explained as follows. KrF* molecules are formed only as a resu?t
of inelastic collisions of F2 with Kr*. Excitation of Kr* atoms requires electrons
of fairly high energies. At values of E/p lower than 2.~ V/(cm�mm Hg) the ntunber
of such electrons falls rapidly with increasing E/p due to collisions (with energy
transferj of electrons with light t:elium atoms [Ref. 3]. Therefore the reduction
in lasing power for the KrF laser as C/Co increases past 0.28 can be attributed
- to the ~ow value oE E/p in the discharge, which is due to the stretching of the
voltage front as C increases, resulting in breakdown of the gas gap at lower vol-
tages across the high-voltage electrode. At the same time, there is no power maxi-
mum for the XeCl* molecule as a function of C/C~ (curve 2) in the investigated
range of values of C/Co.
We also studied the influence that the level of pre-ionization of rhe discharge
gap had on lastng puwer. The level of pre-ionization was varied, as in experiments
with a monopulse laser [Ref. 4] by shorting out a row of pins to one side of the
high-voltage electrode, whicn cut the intensity of UV radiation in half, since
the ~ources on both sides of the electrode are identical. It should be noted that
in this r_ase there could be a change in the degree of homogeneity of photoelectron
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distrib~:tion by changing the lighting geometry. As can be seen from Fig, 3, in
the case of unilateral illumination the lasing power is more sharply dependent
on the charRe voltage across the stora};e capacitor, the lasing power remaining
much l.ower than witti bilateral lighting.
The considerable dependence of average laser power on homogeneity and the level
of pre-ionization shown qualitatively in Fig. 3 prompted us to use a discharge
over the surface of a dielectric as a pre-ionizer and plasma electrode. Such a
~ discharge has already proved its effectiveness as a powerful homogeneous source
of W radiation in the monopulse mode [Ref. 5].
The electrode system with pre-ionization by discharge over the surface of a dielec-
- tric that we used for wark under conditions of high pulse recurrence rate is shown
~ Fig. 4a. Construction of
2 cnamber with discharge over
3 4 5 dielectric surface: 1--stain-
_ less steel chamber; 2--grounded
electrode; 3--low-voltage elec-
trode; 4--dielectric; S--high-
/6 \ voltage electrode; 6--storage
i ~ capacitor; 7--ceramic-capacitor
peaking line; 8--charging in-
ductance; 9--thyratron commutator
. g ~ + 6
- in I~'ig. 4a. As the dielectric 4, we used a ceramic plate with e= 150 of dimensions
165x 100 x 5 mm. Located on the plate were two metal electrodes 3 and 5, between
- which an auxiliary planar discharge was developed on the surface of the dielectric.
In laser chamber 1 along its optical axis were four plates. Metal electrode 2
was located at a distance of 2.6 cm from the ceramic plate. The discharge over
the surface of the dielectric was formed upon charging of peaking capacitor 7.
Detailed studies (the results of which will be published separately) have shown
that a surface discharge with high homogeneity is stable under certain conditions
evsn at quite high nulse recurrence rates (f = 10 kHz). Fig. 4b [photo not repro-
duced] shows luminescence of four sections of the plasma electrode at f= 200 Hz.
A volumetric discharge arose between the plasma and grounded electrodes. Observa-
tions of the volumetric discharge with plasma electrode showed that it is quite
honogeneous and stable. It is interesting to note that the previo usly observed
grotath of a spark filament from the r~etal surface of the high-voltage electrode
(at elevated energy inputs) [Ref. 2) is absent on the plasma electrode.
In Ref. 6 an examination is made of the problem of the possibility of arisal of
local perturbations (near the electrode) under conditions of volumetric plasma
stability. The principal causes of universal instability observed in Ref. 6 are
current focusing in the region with elevated conductivity (in the preser.ce of field
gradients along ,.:nd across the current). The threshold conditions derived in Ref.
7 for a self-maintained discharge
v~xLQ>l, v, -alnv~/alnE, ~ (1)
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and for a semi-self-maintain2d discharge
xZV~EieLa~vi; �e=c)1[1�e/C7111E; usually �eRJ , (1)
R -~1~R2 (2)
where R are organofluorine radicals. The contributions made by other radicals
to this stimulated scattering process can be disregarded.
The rate of energy release in a unit volume as a result of reactions (1) and (2) is
Q=9~~'~[Rl[J)+9~~'z[R)z, ~ (3)
where [J], [R] are the concentratior.s of unexcited iodine atoms and radicals;~l'1
and ,7fZ are the rate constants of reactions (1) and (2); q1~2 is the energy re-
- leased in recombination of one iodine atom and a radical ~.nto the initial RJ mole-
cule, and of two radicals into an RZ molecule respectively. (Let us note that
in this article the quantities Q and ~l'2 replace Q ano'. .7l'Z/2 from Ref. 4.)
To find [R] and [J], we start from equations that describe the concentrations of
particles of the working substances [N], excited iodine atoms [J*], iodine atoms
in the unexcited state [J] and radicals [R]:
- aaN~ -DNoz[N]=-~[N1+~'~[R1[JJ; (4)
a(a~~ -D,.pz~J*)=~;N]-6y([J*]- g~~~J~)4n~.wo-~zp~~ ~5)
1
(6)
_ aar ~ ~ DJO' [J] _ ~y ( [J*] - fJ] ) an~,~o - ~1 fR] (J1-- ~Tp~ ;
aaR~ -DRO'[~1=~[N1-~'~[RJ[JI-2.~2[Rl'.
where w is the probability of photodissociation of molecules of the working gas
under the action of ultraviolet pumping rad:Latiot?; Qy is the cross section of the
laser transition; gl/g2 is the ratio of statistical weights of the upper and lower
}aser levels; Tp is the time of nonradiative relaxation of}the upper laser level;
= E is the total field of the exciting (~o) and scattered (ES) electromagnetic waves;
n is the index of refraction of the medium; ~two is the energy of a quantum of
the laser field; DN, DJ~, DJ, DR are the coefficients of diffusion of molecules
of the working substance, excited ar.d unexcited iouine atoms, and radicals in the
buffer gas.
Equations (3)-(7) in combination with the :hermal diffusivity and Maxwell's equations
ar - xV'T = P~p Q, (8)
- c' adt" ^~ZE - c' `~t' L\ dT 1vT E J ~9~
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forni the complece closed system of equations necessary for solving the problem
of stimulated scattering by temperature waves. Here T is the deviation of the
temperature of thE medium from its equilibrium value To; X is the coefficient of
thermal diffusivity; p is the density of the medi~; cP is specific heat at constent
pressure; e= n2. Let us note that in (9) we have left out the term corresponding
to amplificatl~n on the resonant transition of atomic iodine, since accounting
= for amplification in the final results presents no difficulty.
3. Linearized Equations
_ Obviously we cannot get a general solution of system (3)-(9) in analyticai form.
Therefore we linearlize the system, assuming that the intensity of stimul~ted}scat-
tering ~s is considerably less than the intensity of the stimulating light ~Eo.
~ Then the deviations of particle concentrations from those that would have taken
place ir? the absence of th~ scattered field are small, and equations (3)-(7~ can
be linearized. After linearization, they will take the form
[~lo[R1~+~'~[Rlo[Jl~-( a! -DN pz +~)(N1~=0; (10)
- g~ ay/o[J]i-( ar-D,�p~+Qylo-}- tPl[J*~1=-r.a~(N]i=ay~Do~1; (11)
~ i
~'~[Jlo[R1~+~ ar -DJp2+~'~[Rlo+ g~ Qyfo)[J1~-
_(vyl�+ t ~fJ*]-vy~�!,' (12)
\ p
( a -DRp'-}-~'iIJ)a-}-4,7C$[RJo~[R1~+~'~(R1o~Jli-uull\11i=~~ ~13)
ar
Q=Qo-~Q~~ ~14)
where [N]a, [J*]o, [J]o, [R]o are the concentrations of particles in the absence
of a scattered field; [N]1, [J*]1, [J]1, [R]1 are th~ deviations of particle concen-
trations from [N] [J*] o, [J] o, [R] o; ~o-fJ*]o-[JJog2~g1; Io=ncEo/4n f~c~o is the intensity
of the exciting wave; 1,=2nc(EoEs)/4n~wo is deviation of the intensity of the resultant
field from I~ due to interference of the exciting and scattered waves; Qo=q1,~1[~jo[J1o+
9Z~~'zfRlo; Q~=9~~',([1)o[R1,-}-(Rl~[J1~)+29z~'zlRlo(R,].
In linearlizing equations (8) and (9) we will assume that Qo heats the medium to
_ temperature T'. We denote the deviation from T' due to Q1 by T1. Then equation
(8) is transformed to
aT,lat-xp2T~ =Q~~P~c~ (15)
and equation (9), transformed to the equation for ES, in the approximation of the
given field takes the form
- n~ azEs 1 de d2
at= -~ZEs- - cs ~ ar ) ars ~E~T~' (16).
_ p
In this article we will limit ourselves to the case of a monochromatic stimulating
field, and will consider only the steady-state theory. Th~ conditions of
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}pplicability of the steady-state theory will}be made clear belo}. Let total field
E consist of linearly polarized stimulating (Eo) and scattered (ES) waves with
the same polarization. Then we can consider only scalar waves. Let us represent
- E as
E=1/zEa exp (iwot-ikor)-~1/2ESexp(iwsi-ikSr)-f-compl. con~., (17)~
where w~ and wS are the frequencies of the stimulating and scattered light waves;
ko and ks are their wave vectors. Here Io=ncEo/8~~c~a, and
11=1/Zt exp (i52t-iqr)-~-~omp. conj., (lg):
where .1=2ncEoEs/8n~wo; 52=c~o-~s~ 9=ko-ks�
Let us represent [N],, [J"]l, [Jil, [R11, Tl, Ql in the same form as I1:
IN11='/,INlexp(iS2t-iqr) camp . conj . ;
[J * =1/z(J ]exp(iSZt-iqr) comp . con j . ;
[J11=1/z[J
]exp(iS2t-iqr) -E- comp . conj . ; ,
- [R~1=1/a[Rlexp(i52t-iqr) comp . con~ . ; (19)
T1=1/zT exp (iS2t-i9r) -{~~Sp . con~ . ; Q~ ='~zQ exp (iS2t-iqr) comp . conj .
Substituting (17)-(19) in equations (10)-(16), we get the following system Qf
linear equations relative to
~.i [J]o LRJ + ~i ~Rlo [ J~ - + DN9z ~N~ = p' ' (20)
g~ 6y~o ~ (iS~ + D~�9z -F aylo ~p 1 ~ j*~ ~(N] = v,,~,l: (21}
~ 1
[J]o [R] (iSZ -i- D~9' [R10 g~ ~''1~)~.~ ~ -
~
_ (QYIo p 1 ~ j+~ = oy~ol: ~22}
~ 1
(152-1-DR92-1-,71'~[~lo-I-4~'a[Rlo)~R]+~'~[R]o[J]-c~lN]=~~ (23}
Q= qi~'i ~~J)o ~R~+[Rlo ~ J~~ -I- 2qz~'a ~R)o ~R~' (24).
+ ?(92) T = Q/P~a~ (25).
aEs _ i ks ( ae 1 TEo . (26}
a~ 4ns ~ aT ~p
where r, Is the coordinate in direction ks; Io and I are determined by using Eo
and ES above. In deriving (25), we have limited ourselves to the case where there
is no amplification of the temperature wave during propagation, and in deriving
(26), consideration was taken of the fac[ that the relative change in amplitude
of the scattered field is small at distances of the order of a wavelength of light,
and therefore only the first spatial derivative of amplitude has been retained
in (26) .

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4. Sc:~k~erin~; SpecLrum
Solving equations (20)-(23) relative to [R) and ~J;, and substituting the solutions
fn equation (24), ws get the com~lex amplitude of the variable component of th~
x'ate of specif ic energy release Q:
~ i~ + p J~qa r
- Q= 9i~i ~R]oQvOo Det Iaikl I~S2 + DRq$ +
� L
i12 D q~
-+-4~'4 [Rjo ~ 1- 2q~ i~ ~N9' + ] 1. (2?)
~
where the matrix
iS2 -i- D Rq' -i- 4~fG'z [Rlo - (Dl D~.) q' - (iS? DJ�qz)
~`l'~ [~)o i52 D~q' -}-.x'~ [R1o + - ( 6yf0 Tp /
~ a ~ 1+ g' / ay!� + ~p `
~ n = . (28)
(iS2-{- DNqs~~~l'i ~~~o (iSZ -F- DN9'~ ~'l't ~Rlo (LSZ D~�Qz~
i52 DNq~ t~ ii2 DNq~ rv
+ ~D~ - D~�) qz
Substituting (27j in (25), we find the complex amplitude of temperature, and by
using (26) we find that in the region of nonlinear interaction, the scattered field
intensity proportional to ~ESI2 varies in acc.ordance with the law
; IEs~~) IZ== IEs~~=O) ~zexP~B~~)~1, (29)
where
g` = ks r ae 1 4~~'i [R1 oayDo Re ~ +~J'Qz tQ -1- p"
~ ar ~ PpCp ~(iS3 X4') Det I atn. I[ ' Rqr
P
S
4.JCz [R1o 1- 29~ ~Nq' J ~ f (30)
S. Principal Results
~,et us analyze the major features of the kind of scattering considered above. We
_ will make the following assumption to simplify the analysis: all coefficients
of difEusion will be taken as equal, i. e. DR= DpJ= D,J* = D,J = D. Then (30) takes
the Corm
c~)S2 ~ S22 _ ts~ f
rael a~~'~ [RJoQ~�eo ~ + ' ~ ~
g~~~ - ks 1~T Ip pP~P ~e{l~~ X92~ ta~ I)~2 _ a(3) + iS2 ~522 - a~~~~~ o~
\ /
~ (31)
where
a~~ 3 -'~1 ~Jlo +~i ~RJ~~ -I- 4.7~'s IRIo -1- t~ (I b':~b'1) arlo ; 3Dq2 -f- 1/ip; (32)
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_ ~D9Z ; (Dqz -t- ~ 1 ~z~g~) Qrto + 1 /ia) ~ (D9z + 4.~t'z [R)o) x
x (2Dq2 -I- rc~ -f- (1 + gx~b'~) Qy~o 1/ipj -f- .~l'i ~~10 ~2D92 + ~1 gs/gi), Qy~o -'r
. 1/~P) [R]o ~2D92 ra~ 4�~L'z ~R1o -f- Q,�~o 1/ip); ~33)
- a~3>=[(Dq2~-4.~'z~Rlo)~D9Z-}-re~)-f-.7~',[JIoDq=1(Dq2-}-~~ ~-gz~g~)~ylo~-1/ip)-I-
-F-,~c,[R]o4~'2lR lo(Dqz -}-r~+crylo -{-1 /Tp); (34)
~~i~ =2Dqz -~-4�~'z[ R ]o~ 1-92~24~) -I-~; (35)
~~~~=~D92)z-F(4~71'zlRlo~l-9~~29i)-Fr.a~)D9z-I-4.7t'2~R)ot�~. (36)
After calculating the real part of the complex expression in braces in (31), we
represent the dependence g(S2) in the form
k at~ q~ IRJoa,,eo s~ u~c>>~+ -I- U%(3)S22 'I- lY~(5) 1
~ ~ ) - S ( dT ~p eP~n -t- (X9~)' 621~) Wc2)SZ4 .{-1Y~c4152~ W(~)
(37)
where lY/cl~ _(a~'~--~~1~) -f-Y.9Z; W~z~ :a~'>z-2a~z~: W~3> -_(~~1~a~2>-a~'~~~2~)- a~3~-(at2~-a~'~~~1>~-R~2~)X92;
lY~~'> a~~~=- 2acliac'~; ly~ca~ _;aca~~cz> -}_(a~z~(it^-~- ac3~R~1~)X9~~ W~�~ =a~3~2�
It can be seen from (37) that dependence g(S2) is antisymmetric relative to the
- sign of S2, i. e. g(S2) _-g(-St) . This means thar g(SZ) will be positive either in
the Stokes region or in the anti-Stokes region, depending on the sign of (ae/8T)P,
i. e. amplification of the scattered light waves is realized. Consequently, the
temperature waves stimulated in media in which the chemical reaction rates depend
on laser field intensity should give rise to stimulated scattering of light.
Formula (37} is much simplified in two cases: when xqZ/[~~~ ~~/~k-�},
where j= 1, 2, 3, 4; k= 5; 6, and when diffusion time iD=(Dq2)-1 is considerably
less than the time of chemical reactions, the time of photodissociation and the
life~ime ot iodine atoms in the excited state.
Actually, cofactor j(S2)= (W~'>52a+W~3~~z+W~6~~~~e+~~ ~2~~a.~_ ~~a~~z+,W~o~~ in (37) varies
insignificantly in frequency band IS2i ~ S2: fzW~"~/Wt�~, and cofactor f,,(S2)=SZ/(SZZ-f-{x92)z)
reaches extremtun values at S2= fxq'. Therefore if angle 6 between the wave vectors
of the stimulating and scattered light waves is such that xq2CS2, the gain g(S2) can
be approximated as
~ ks ae 9~~'~ [R)oQYao W~S~ a a lo� ~38~
~ ar ~p ~a~p Wcs~ s~ + (x9 )
The maximum gain is
ae q~~'~ [R~aQyo ~~s~ ( )
0
_ brmax = kg I aT I p 2eP~nX9a W(5) 1~. 39
The t:ime oF establishment of the steady state in this case is determined by the
L-ime of damping of the thermal wave: ty~T~~T,.=(xq2)-1.
In the second case, the gain g(S2) can be represented as
a�1 9i~i [R~oorAo S2 (Dq9 -F- x42)
~ ~ ke ~ aT Ip EP~P ~~a -F- ~X9a)~) -f- ~~qa)~) ~o t40~
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'Piie frequ~ncics at w}iict~ g(1J.) reaches extremum vslues in this case are equal to
- ~ = f ~6 j~ DZ -r Xz ~Y 1 + 12XZDz/(~2 -I- 7(')~ - I (41)
- Tf D= X, th~ frt. 1aencies determined by (41) ,$Z -~xq2/j/~3, i. e. the frequency shift
is considerably different from that with stimulated temperature scattering or
stimulated concentration scattering [Ref. 13, 14] . The maximum g(S2) is
" g _ k( ~E ! 9i~'i [R]oar~o 3 V3 ~o (42)
, ma~ - S aT ~P E~a $ ~X91)' .
and the half-width of the scattering spectrum can be determined from the equation
- ~'-~2~3-}-3~2-2~-1=0, (43~
� where ~_L~3SS2'!(2XqZ); SS2' is the difference between the frequency where I g(S2) I is
rna::imum and tbe frequency where it has fallen to half, The real roots of equation
= (43) ~1 = 0.7 and ~2 =-0.35, implying that the half-width of the scattering spectrinn
SS~,:.2,ixaZ~y3, i. e. approximately three times lower than with stimulated temperature
scattering. The time of settling of the steady state is accordingly as many times
longer .
6. Discussion of the Results
It can be seen from (37) that in media that do not absorb the energy of the electro-
magnetic field, there is :~on-zero gain of sti.mulat?d scattering by temperature
waves. .7ust like ultrasonic waves [Ref . 4] , temperature waves are stimulated in
- this case not by the energy of the electromagnetic field as occurs in stimulated
temperature scattering or stimulated absorption scattering, but rather by the energy
of chemical rea.ctions controlled by the electromagnetic field, i. e. by the energy
of the thermodynamically nonequilibrium medium. It is clear from this that the
given stimulated scattering cannot be reduced to either stimulated temperature
scattering or stimlated Mandelstam-Brillouin scattering. Moreover, if the amplifi-
- cation oi scatterE3 light waves is realized in the anti-Stokes regi.on S210~).
u
1 6 9~~~ 5 11 13 u~t)
1 1 ~ai4
~i T T 0
B
2 12 ~ (t) . a
3 ~ -
0
6 t
Fig. 1. Optical dia~ram of the Fig. 2. Voltage ~raveshape
_ facility: 1--DKDP crystal; 2-- across the shutter (a) and
shaping line; 3--discharger; 4, transmission function of
5--cavity mirrors; 6--polarizer; the shutter (b)
7--cell; 8--pumping lamp; 9, lU--
diaphragms; 11--beam splitter; ~
12-- calorimeter; ]3--SDF-11
. photocell
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These requiremer.ts are met Uy a neodymium glass laser with periodic Q-switching
[Rsf. lJ. The purpose of this article is to ex~lain the working capabilities of
an iodine photodissor.iation laser in the periodic Q-switched mode, and to study
' its characteristics. A diagram of the measurement facility is shown in Fig. 1.
The research was based on laser chamber 7 with inside diameter of 9 mm azd length
_ of the active section of 1 m, with windows beveled at the Brewster angle. The
pumping source was two xenon flashlamps 8. The lamps were placed so as to minimize
the magnetic field on the axis of the cell. The lamp supply was from a 3 uF capaci-
tor chaiged to 50 kV through a low-inductance discharger. The main pvmping energy
was released within ths first half-period of the discharge current of 4 us duration.
Periodic Q-switching was accomplisY:ed by a'~-wave Poc:kels shutter based on DKDP
crystal l. Shaping line 2 with shorting discharger 3 produced the controlling
electric pulses across the shutter with period Tel of shape shown ~n Fig. 2a. The
corresponding transmissi.on function of the shutter is shown in Fig. 2b. The charac-
teristics of the controlling electric pulses are as f.ollows: charging voltage
4.5 kV, pulse rise time 1-2 ns, damping of pulse zmplitude by a factor of e takes
place in time of 15Te1�
The warking madium was a mixture of C3F~I (7-15 min Hg) and Ar at a total pressure
of 1 atm. Gain of ttie ar_tive medium was selected so that the lasing threshold
was slightly exceedsd�during pumping with the shutter closed.
Q-switching was star*_ed at the instant of the first zero of the pumping current.
ihis led to rapid dPVelopment of a train of subnanosecond laser pulses with period
equal to the round-trip time of lig~it through the cavity. Each train consisted
of 3-4 laser pulses. The pulses reached maxim~n amplitude after 10-15 round trips
through the cavity. The overall energy of the train was 10-20 mJ with a diaphragm
3 mm in d~~meter and cavit~ lengtr. of 220 cm. An instrument with time resolution
of -0,3 ns was used to recorc~ the duration of an individual laser pulse. Pulse
duratian wss appreciabl.y dependent on matching Tel with the round--tri~ time of
light through the cavity Tlight~ in the case af optimum matching, pulse duration
reached a minimum value of 0.4 ns at half-a;aplitude (without consideration of the
time resolution of the instrument}. It s:~ould be noted that there was little change
in pulse duration when Tl~ght and Tel weye matched within 0.1 ns. A typical lasing
' oscillogram is ~hown in Fig. 3[photo not reproduced].
Measurements of the an~ular distribution of lasing showed that radiation divergence
is close to the diffraction limit.

.I
Results on energy, pulse duration and diverge nce show that this laser could be
extensively used in multistage iodxne laser facilities [Ref. 2, 3], e. g. for
laser-dri~~en fusion.
REFERENCES
1. Basov, N. G., Bykovskiy, N. Ye., Danilov, A. Ye., Kalashnikov, M. P., Krokhin,
0. N., Kruglov, B. V., iKikhaylov, Fu. A., Osetrov, V. P., Pletnev, N. V.,
Rode, A. V., Senatskiy, Yu. V., Skli~kov, G. V., Fedotov, S. I., Fedorov, A. N.,
. TRUDY FIZICHESKOGO INSTITTJTA IMENI P. N. LEBEDEVA AKADEMII NAU;: SSSR, Vol 103,
1978, p 3.
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2. Katulin, V. A., Nosach, V. 'Yu., Petrov, A. L., KVANTOVAYA ELEKTRONIKA, Vol 3,
1976, p 1829.
~ 3. Belotserkovets, A. V., Gaydash, V. A., Kirillov, G. A., Kormer, S. B., Krotov,
V. A., Kuratov, Yu. V., Lapin, S. G., Murugov, V. M., Rukavishnikov, N. N.,
Samylin, V. A., Cherkesov, N. A., Shemyakin, V. I., PIS'MA V ZHURNAL TEKHNI-
CHESKOY FIZIKI, Vol 5, 1979, p 204.
- COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1981
' 6610
- CSO: 1862/41
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UDC 621.373.826.038.823
J USING ARGON IN WCRKING MIXTURES OF CW ELECT :vN ~3EAM-CONTROLLED C02 PROCESS LASERS
~Ioscow KVANTOVAYA ELEKTRONIKA in Rt~ssian Vol 8, No 9(111), Sep 81 (manuscript re=
ceived 2 Feb 81) pp 2063-2065
_ [Article by A. P. Averin, N. G. Basov, Ye, P. Glotov, V. A. Danilychev, N. N.
Sazhi.na, A. M. Soroka and V. I. Yugov, Institute of Physics imeni P. N. Lebedev,
USSR Academy of Sciences]
(Text] It is shown that the use of argon in workin~ mixtures
of cw electro ionization C02 lasers considerably enhances the
specific volumetric energy output (by a factor of 1.5-2) without
detriment to the physical efficiency of the laser. Substituting
argon for helium considerably reduces the cost of processes of
_ laser technolagy.
At present one of the main factors that determine the cost of laser technology
is the high price of helium, which has a content of 40-80~ in typical laser mix-
tures [Ref. 1]. Therefore a very important practical problem is total or partial
substitution of less expensive gases f~r helium in the working mixtures af electro-
ionization process lasers. One possible way to do this is to use helium-free mix-
tures such as C01-N2, i. e. to replace helium with nitrogen. However, this con-
siderably reduces lasing efficiency, due ch iefly to an increase in the threshold
, pumping energy W~, i. e. the energy carried off by the gas flow from the active
volume, a quantity that increases with the ratio of concentration of nitrogen and
C02: W~ ~(m +1), where m=[N1J/[C02]. When helium is replaced with nitrogen,
we can retain the ratio of [Nl]/[C02J and accordingly the threshol~' pumping energy
as a result of increasing the COZ content in the mixture. However, this would
_ require a corresponding increase in electron beam current density because of the
accelerated loss of electrons in the electroionization discharge plasma as a result
of stickin~ to molecules of carbon dioxide (the electron sticking rate constant
G; ~[CvZ In exis*_ing cw elPCtroionization lasers, the current density of the
electron beam je is limited by overheating of the separative foil of electron guns
_ on a l~vel of 10-15 uA/cm2 (in the plane of the anode of the discharge chamber.).
_ Therefore the content of carbon dioxide in optimum laser mixtures at the present
time does not exceed a few percent [Ref. 2J, and an increase in C02 concentration
leads to reduced pumping power, emission power and lasing efficiency.
In Ref. 3 an investi~ation was made of the possibility of increasing the specific
characteristics of helium-iree mixtures of C02 electroionization lasers by trace
66
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doping witti liydro~en, whose molecules effectively depopula~e the lower l.asing level.,
which is very important for laser operation in the powerful short pulse mode. In
C02 cw electroionization lasers hydrogen doping cannot improve lasing parameters
since HZ molecules sharply increase the relaxation rate of the upper lasing level,
and accordingly the power of relaxation losses that determine operation of the
- cw electroionization ~aser [Ref. 2J.
It was experimentally established in Ref. 1 that using xenon additives in the laser
mixture improves the characteristics of the electroionization discharge by reducing
electrode potential drops [Ref. 4]. However, the use of Xe leads to still greater
increase in laser cost as it is priced 600 times ~s high as helium.
i, Q'
_ nA/cn= O~e kJ/m3
~ Q, kJ/m3
0
40 U ~ ~,p � ~ �
� s---~ ~
C ~ 7,3 ~~?^p ~ 1,8
/ ~
zn r % n,s
Z . ~
.l ~ SQ / 4 '
% ~tr~ ,
i'
0 1 1 U~ kV ~~So/.~o
b 1.5 0 0.6
/
Fig. 1. Typical loop oscillograms of
voltage U, discharge current J and o ~1,s ~S 3~5[Arj,%
lasing power Q~S (a) and dependences Fig. 2. Lasing efficiency
of discharge current density (l, 2)
and specific lasing energy (3, 4) as n(1-3) and maximum spe-
functions of the voltage across the cific energy output QcH
discharge chamber (b) for laser mix- ~4-6) as functions of the
argon concentration in
tures COz:N2:He:Ar = 1:29:0:30 (1, 3) laser mixtures C02�N1;
and 1:29.30:0 (2, at pressure of (He+Ar) = 1:29:30 (1, 4),
60 mm Hg; interelectrode spacing 10 cm 1�14�15 (2, 5) and 1�4�S
(3, 6) � �
In this paper an experimental investigation is made of the possibility of replacing
helium with argon, and it is shown that the use of argon not only is not detrimental
to the specific characteristics of the cw electroionization laser, but also increases
the specific lasing output without reducing effl.ciency as a result of increasing
the power of the energy contribution at unaltered electron beam current. This
is due to an increase in the density of the laser mixture and accordingly in th~
number of electron-ion pairs Y formed per unit of length of the mean free path
of a beam electron (for mixture C02:N2:He = 1:30:29 when argon is substituted far
helium its molecular weight increases from 16.76 to 34, i. e. more than doubles).
The other discharge parameters remain practically unchanged [Ref. 5].
Experiments were done on a process cw laser facility (duratioii of a single opera*ing
ru~-~ about 10 minutes). Fig. la shows loop oscillograms of the luminosity-current-
voltage characteristics for a laser mixture COZN2:Ar = 1:29:30 at pressure p= 60 ~ Hg
67
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and electron beam current density j e= 12 uA/cmZ . Voltage U and discharge current
J wera measurec? by an ohmic divider and a shunt respectively. Lasing power was
measured by a wire-t,ype duct bolometer [Ref. 6]. Fig. lb shows curves for dis-
charge current density and lasing energy taken from a unit of volume of the circu-
lating gas as functions of the voltage across the discharge chamber for two mix-
tures. It can be seen t:?at in the mixture containing argon, the non-self-maintained
discharge changes from "Thomson" burning, where nearly all the applied voltage
is shielded by the cathode layer, to "electro.ionization" burning [Ref. 7] at a
slightly lower voltage than in a mixture of C02-N2-He (510 V instead of 960). This
_ is due to an increase of electron density in the discharge due to more efficiency
in ~ise of the electron beam. At the working voltages of an electroionization laser
the discharge current in a mixture of COz-N2-Ar is more than double the current
in the COZ-Nz-He mixture. The curve of lasing power as a function of voltage for
_ the mixture containing argon is also everywhere higher than for the C02-N2-He mix-
ture. However, the maximum working voltage in the COZ-N2-Ar mixture in a11 the
_ experiments was 10-15% lower than in the C02-NZ-He mixture. This is not due to
a reduction in el.ectric strength of the mixture, and can be attributed to the fact
that the gas density at the end of the active volume in the first case as a result
of energy input drops more strongly, and accordingly there is a stronger increase
in the normalized field strength E/N. The results of the experiments are in good
qualitative agreement with the formula that defines the dependence of breakdown
voltage U* on pumping power:
- U. _ ~e~P). dPo
1 w/(9~nTo) '
where (E/p)~ is the normalized breakdown f ield strength; w is pumping power; q is
gas flowrate; To is the initial temperature of the laser mixture; cP is specific
heat of the gas at constant pressure; d is the spacing between electrodes.
Fig. 2 shows the curves for maximtun specific energy outputs Q corresponding to
l~miting fiel.d strength, and lasing efficiency as functions of the argon content
in laser mixtures with predetermined concentrations of carbon dioxide and nitrogen.
The total content of helium and argon was 50%. The energy output increases mono-
tonically with increasing Ar content in the mixture. For a mixture with high carbon
dioxide content COZ:N2:(He + Ar) = 1:4:5, complete replacement of helium with argon
leads to an increase in lasing power by a factor of 2.5, which is associated with
an increase in energy input almost without any change in pumping efficiency; in
this case the laser efficiency also increases. In a mixture of C02:N2:(He + Ar) _
1:29:30 (curve 1) the lasing efficiency with substitution of argon for helium
falls from 8 to 6.5%, which is due on the one hand to overheating of the laser mix-
ture, and on the other hand--to a reduction in the rate of depopulation of the
lower lasing level in the absence of helium. In the mixture C02:N2:(He + Ar) = 1:14:15
(r_urve 2) the depende.nce of effi~iency on argon cr~ncentrati.on has a flat maximum.
The c~mparatively wide scatter of the experimental points is due to unstable behavior
of the threshold voltage of streamer breakdown of the ciischarge gap, which depends
not only on pumping power, but also on electrode surface state, which could not
~ be controlled during the experiments.
Thus, substitution of argon for. heliwc? in working mixtures of cw process lasers
increases pumping power by a factor of 1.5-2 without any change of electron beam
current, and with almost no reduction in lasing efficiency. This is especially
68
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important for Qrolonged cw laser operation when pumping power falls to half because
of the format ion of nitrogen oxides [Ref. 8] even when a regenerator is used. The
cosC of the laser mixture in this case decreases by more than an order of magnitdue,
and the total cost of processes of laser technology is cut in half.
REFERENCES
1. Basov, N. G., Babayev, I. K., Danilychev, V. A., Mikhaylov, M. D., Orlov, V. K.,
Savel'yev, V. V., Son, V. G., Cheburkin, N. V., KVANTOVAYA ELEKTRONIKA, Vol 6,
1976, p 772.
.
2. Averin, A. P., Glotov, Ye. P., Danilychev, V. A., Sazhina, N. N., Soroka, A. M.,
~ Yugov, V. I., PIS`MA V ZHURNAL TEKHNICHESKOY FIZIKI, Vol 7, 1981, p 769.
3. Danilychev , V. A. , K~:~-sh, I. B., Sobolev, V. A. , TRUDY FIZICHESKOGO INSTITUTA
IMENI P. N_ LEBEDEVA ~~KADEMII NAUK SSSR, Vol 116, 1980, p 98.
4. Averin, A. P., Glotov, Ye. P., Danilychev, V. A., Koterov, V. N., Soroka, A. M.,
Yugov, V. I., PIS'MA V ZHURNAL TEKHNICHESKOY FIZIKI, Vo1 6, 1980, p 405.
5. McDaniel, I. I., "Protsessy stolknoveniy v ionizovannykh gazakh" [Colli~~.on
Processes in Ionized GasesJ, Moscow, Mir, 1967.
6. Kuz'michev , V. M., Perepechay, M. P., KVANTOVAYA ELEKTRONIKA, Vol 1, 1974,
p 2407.
7. Aleksandrov, V. V., Koterov, V. N., Soroka, A. M., ZHURNAL VYCHISLITEL'NOY
_ MATF�MATIKI I MATEMATICHESKOY FIZIKI, Vol 5, 1978, p 1214.
8. Glotov, Ye . P., Danilychev, V. A., Kholin, I. V., TRUDY FIZICHESKOGO INSTITUTA
IMENI P. N. LEBEDEVA AKADEMII NAUK SSSR, Vol 116, 1980, p 189.
COPYRIGHT: Izdatel'stvo "Radio i svyaz"', "Kvantovaya elektronika", 1981
6610
. CSO: 1862/41
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NUCLEAR.PHYSICS
PAPERS ON HIGH-ENERGY PHYSICS
Leningrad FIZIKA VYSOKIKH ENERGIY in Russian 1981 (signed to press 9 Mar 81)
_ pp 2-3, 22-24, 26, 50-51, 54, 81-83, 115, 162-163, 200
[Excerpts from book "High-Energy Physics (Materials of the 16th Winter School
of Leningrad Institute of Nuclear Physics imeni P. N. Konstantinov)", edited by
V. Ye. Bunakov, M. M. Makarov, A. N. Moskalev and G. Ye. Solyakin, LIYaF, 500
cUples, 231 pages]
~.ext] The materials of this volume include papers dealing with various aspects
of high-energy physica. These articles discuss deeply inelastic processes at high
energies, problems of e+e- annihilation, processes with large transverse momentum.
- Material is given on three-baryon resonances. In addition, papers are presented
that are fundamental in nature even though not directly related to processes be-
tween elementary particles at high energies. Among these are items on neutrino
experiments at low energies, and effects of parity violation in nuclei.
The papers are intended for theoreticians and experimental researchers dealing
with problems of high-energy physics, elemEntary particles and the atomic nucleus.
With respect to level of presentation, they are accessible to scientific worlcers
and graduate students.
UDC 539.12
DEEP INELASTIC PROCESSES IN THE LOW-x REGION
_ (Articl.e by L. V. Gribov, Ye. M. Levin and M. G. Ryskin]
[Excerpts] An examination is made of the structure function of deep inelastic
scatterin~ at low x in QCD perturbation theory. Diagrams are summed in which the
smallness of r_he coupling constant aS is compensated by large logarithms: ln s
and ln q2. It is shown that tl-~e increase in the structure function at small x is
masked by multiple-ladder diagrams. As a result of this screening, the unitarity
conditions are not violated. The paper discusses the resultant solution and its
physical consequences for "rigid" processes.
- Conclusion. In this paper we have attempted to demonstrate a method of calculating
the asymptotic behavior of scattering amplitude at high energies within the frame-
work of QCD perturbation theory. It has been shown that in these calculations, it
70
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is not nnly the Feynman diagrams in which the smallness of the coupling constant
as is compensated by a large energy logarithm ~ln q= ln X} that are important,
but .31so graphs in which each power of as has its own logarithm of virtuality
(i. e. aSln q2~ 1), as well as a more complex class of diagrams in which the proba-
bility of parton rescattering
2
W= f~ ~'-~2
~~~1nX, q~2~ qo} dq~2
reaches values of the order of unity due to an increase in parton density It
should be emphasized that no other large parameters arise in the problem.
Summation of diagrams of QCD perturbation theory that contain at least one large
logarithm ~ln q2 or ln X~ for each power of as is accomplished by using system of
equations (11). The psrton density ~~1 X, q2, q~~ obtained as a result of such
summation is the Green's function of an effective pomeron in QCD.
To calculate contributions of order Wn to the amplitude, a cliagram method was de-
- veloped analogous to V. N. Gribov's reggeon diagram method [Ref. 3], where the
part of a pomeron is played by the "ladder" of Fig. 2a, and the vertex of interac-
tion of effective pomerons is calculated by QCD perturbation theory (for example
see Fig. 4 and expression (16) for G3p). Let us note that by gradually increasing
energy in QCD perturbation theory, we again reproduced the "r~ggeon" diagram method.
However, in contrast to the Reggeon field theory [RFT] that has recently been popu-
- lar, we started from low energies and calculated the Green's function of an ef-
fective pomeron and the vertex of its interaction within the framework of pertur-
bation theory. Our main theoretical goal has been to find the sum of the "reggeon"
diagrams at high energy, whereas RFT introduces a seed amplitude at energy s-} ~
and phenomenolo~ical vertices of interaction of pomerons, and investigates the
feasibility of self-consistency of such a theory.
In this paper we hav2 restricted ourselve~ to calculation of the cross ~ections
of deeply inelastic processes in order to avoid discussing the "confinement" prob-
lem and ttle region of small virtualities where as may be large. For this reason
we have r.~ot been able to get to the region of positive t or to verify t-channel
unitarit~~ conditions.* Nonetheless, s-channel unitarit~, the relation between
processe:~ with different multiplicity (Abramovskiy-Gribov-Kancheli rules of Regge
cuts [R~f. 11]), is totally conserved here. Moreover, our diagram method coincides
w~th the old reggeon approach fro m the phenamenological standpoint since it con-
serve.s such features of the reggeon theory as ~tntroductio n of a new quantum number
(si.gn~ture), classification of asymptotic behavior in accordance with quantum num-
bers of the t-channel, etc. In particular, exchange of a secondary "reggeon" cor-
responds to the ladder diagrams of Fig. 11 constructed from a quark and an anti-
quark. The asymptotic behavior of these diagrams differs appreciably from the
vacuum channel (Fig. 2a), and in the case of Itl> A2, the amplitude takes the form
*This limitation is fundamental, and does not allow us to move into the region
of qo ~/IZ. On the other hand, limitation lnl/x , (4?
w}iere
100) at low collector working currents (I~ ~
- 0.1-1 mA) [Ref. 13). Similar results are achieved when KT203B transistors are
_ used for the input amplifiers.
The upper frequency of flicker noises of amplif iers using transistors of these
types does not exceed 3~ Hz when the impedance of the signal source is less than
io9
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yny~
In ~ t 1 P if .
P 1 channel 1 ~B~ py~
n .
. n
IIU ruf1l re/nZ /J ii X 4~H~1 ATT
n
Input 2 ~Plif . ~,BZ PyZ ' Nn
� chanriel 2
NnyZ
Fig. 1. Block diagram of spectrum analyzer: Pem 1--first hetero-
dyne; Pem 2--second heterodyne (200 kHz); ~Bl, ~B2--phase shifters;
PY1, PY2--devices for manual and automatic gain con.trol; HIIY1, I-IITY2
--multiplier overload indicators; II--analyzer mode selector; X--
_ multiplier; ~H~i--low-frequency filter; HII--meter; u~i--digital fre-
quency met~r; ATT--multiplier attenuator
� `I~C From 1-st heterodyne
Input ATTI BMy Ar~2 ~PHy yd4 CM1 /f9~~
- ./ly/!y~ Arr3 y/ly~ Arr4 KmZ CM2 y/14Z To phase shiftF:r
Prom ~-nd heterodyne
Fig. 2. Block diagram of one amplification channel~ ATT~-ATT4--
attenuators; BMY--low-noise input amplifier with stepwise gain
control; YH~i--low-frequency amplifier with continuous gain control;
HIIC--mixer overload indicator; CM1--first mixer (128 kHz); K~1--
quartz filter with passband of 5 Hz on frequency of 128 kHz; IIYII~il--
preamplif ier of first i-f voltages; Yif~il --f irst i-f voltage ampli-
fier; K~2--second quartz filter with passband of 30 Hz or,, frequency
of 128 kHz; CM2 --second mixer; YII~i2 --second i-f voltane acuplifier (72 kHz)
- 10 k52. A diagram of the amplifier ia shown in Fig. 3. The experimental cur-~e. for
- the noi~e factor as a function of frequency is shown in Fig. 4. The wide dynamic
range (>100 dB) ie attained by making the low-frequency amplifiers in a differential
circuit with deep negative feedback (~60 dB). Commutation of the input attenuator
_ and feedback circuits is done in such a way that the input impedance of the channel
is 100 kS~ on all measurement ranges.
A schematic diagram of the mixer is ahown in Fig. 5. The mixer operates as follows.
In the differential stage based on K1NT591 microcircuit and KT312B transistor the
input voltage ischanged to antiphase collector currents of the transistors of chip
K1NT591. The current switches alternately connect the antiphase currents to the
2.2 k52 load resistors. In this way the input signal is multiplied by the pulse
signals of the heterodyne with 1 V peak-to-peak amplitude (from cycle to cycle).
110
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+~5 Knoise~ dB
73K 13n 13n' 200
T~ T2 16
6@ ~
~ � ' ~ Z40 TS
- Inpt~t _
! T4 = P Out ut ~
~ ,
T3 B
- � 2
11~K l/~K 5~6K 7~S1f _~5
2,7K 3
�B >D ZO y0 f00 200
-
! ~z F , Hz
Fig. 4. Noi~e factors of amplification
300 >,SK channel in 5 Hz band at different sig-
nal source impedances: 1--47 kSZ, 2--
4.7 kSt, 3--540 S2
Fig. 3. Schematic diagram of low-noise
input amplifier: P1, P2--sealed-contact
relays; T1, TZ--KT3107L; T3, Ty--KP303B;
TS--KT3102V
, +15.
2,2K r,2K
4ut ut ~ t
_ Heterodyne - M ~ ~
~ ~
inpu
~
t
Si$nal MZ
'ln~ut 620
T~ Ebias
J60
-IS
Fig. 5. Schematic diagram of mixer: M1--K217NT3; M2--K1NT591
T1--KT312B
111
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The wide dynamic range of the mixer (~100 dB in a frequency band of 5 Hz in combi-
- nation with quartz filter PF2P-34) is achieved by using deep negative feedback
(620 S2 res~stor) in the differential stages based on chip K1NT591, and switch oper-
2tion of the transistors of chip K217NT3. An advantage of ~he switching mode of
mixer operation is that the i-f voltage amplitude is independent of fluctuations
of the heterodyne amplitude. The balanced circuit of the mixer keeps the heterodyne
voltage on a low level in the intermediate-frequency channel ( 1 mm 1 the magnitude f~r the PRIZ modulator
is greater than the given by the PROM modulator. As a result, the dlffraction
efficiency of the PRIZ modulator is higher.
3) As kX-~0, ~~-~0, i. e. the nul.l space frequency is not reproduced by the PRIZ
modulator. Ttiis automatically leads to spatial differentiation of images.
120
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ReSUI ts are simil.ar For cut (110) , the only difference bein~ that a factor of
the order of unity depending on angle Y shows up in formula (10). It should be
noted that the external electric field in the PRIZ modulator lies in the direction
of propagation of the reading beam, i. e. geometry analogous to the longitudina~.
~ electro-optical effect is externally realized in the modulator. However, in the
recording process an inhomogeneous f ield is set up in the crystal, and the trans-
verse components of this field are actually used to modulate the light.
Exp?rimental Results
Fig. 3 shows the results of ineasurement of the diffraction efficiency of the PRIZ
modulator as a function of the space frequency. The measurements were done in
a logaritYunic arrangement with Michelson interferometer. The space frequency
was selected by varying the the angle of inclination of one of the mirrors of the
interferometer. The source of recording light
was either a helium-cadmium laser (a= 441 nm)
or an argon laser (a=488 nm). It can be
- seen from Fig. 3 that the PRIZ has high reso-
~ + lution with recording by laser light. Its
+
0.5 Z sensitivity in th is case remains practically
~ the same as in the case of recording by He-Cd
~ ~ laser light. The given experimental data
~ \3 � agree with conclusions drawn from formula
, p�> \ (10) .
.
~ 2 4 ~0 20 >00 100 80
120 b0 ~
kx, lines/mm f40 ~�ZI 40
. ~
Fig. 3. Diffraction efficiency as
�~60 ~x ~ , ~G X-x, ao
a function of space frequency for
x
- the PRIZ modulator (1 , 2) at wave- ~ '
len~ths of the recording light of '80'" x~� 0~ ~
441 nm (1) and 488 nm (2) . Shown Y~~~,x~ ,~i
for comparison is the same curve 200 f// I
for the PRUM modulator (3), a= .
441 nm, E= 200 erg/cm2 . 22p 320 x 1
�Z
~40 300 �3
Fig. 4 shows curves for diffraction ef- 260 280
ficiency as a function of the angle be-
tween the vector of the space lattice and Fig. 4. Diffraction efficienc~
the crystallographic axes for cut (111) , a~ a function of the ang].e between
The solid lines show calculated curves the vector of the space lattice
for r~ in accordance with formulas (8) and and the crystallographic axes for
(9) for linear and circular polarization circular polarization and for linear
of the reading light. The space frequency polarization parallel to axis [112]:
of the lattice was 5 lines/mm. The plane 1--recordin g fr.om the side of the
of linear polarization was oriented along negative electrode; 2--from the
axis [112]. For l.inear polarization we side of the positive linear polari-
see good a~reement between the theoretical zation r~(~) = r~~cosZ 3--circular
curve and the experimental data in the case polarization n(~) = const
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where ne~ative potential is applied to the leading electrode with respect to the
recor.din~ li~;ht. Un the other hand, if is applied t~ this electrode, the
experimental values f it satisfactorily on curve n=nocos (Y - 30�). This can be ~
explained wil:h consideration of the optical activity of the crystal by the fact
that an inhomogeneous electric field is formed in the layer situated closer to
the negative electrode [Ref. 4]. In this case, when the negative electrode is
. the trailing one wi~h respect to the recording iight, the plane of polarization
of light is turned through an angle of ~15� due to optical activity upon passage
through a crystal layer ~0.7 mm thir_k. In accordance with expression (8), this
leads to displacement of orientational dependences through an angle of ~30�. This
fact is one more confirmation of the assumption that the effective thickness of
- the layer responsible for modulation of li~;ht is considerably l~ss than the thick-
ness of the crystal.
The curves shown on Fig. 4 demonstrate that in the case of readout by linearly
polarized light, the modulator does not reproduce all spatial frequencies, but
rather only those whose vector lies in a certain angular sector, i. e. sectoral
filtration of images is realized.
~ Circularly polarized light can be used for readout of images. In this case, when
- the crystal plate has orientation (111), the diffraction efficiency in accordance
with (9) does not depend on the direction of the space lattice vector. The experi-
mental data on Fig. 4 confirm this concl.usion.
. .
.
~ A
~ ~
_ ~ r/
~
_ ~
_ � ~a.'' '
_ � Q 1
a b c
Fig. 5. Decording of hologram from PRIZ modulator: a--original
image; b--image recorded on PRIZ modulator; c--image recon-
structed from hologram
Fig. 5 shows a photograh of an image recorded on the PRIZ modulator that was read
out by linearly polarized light. It can be seen from the figure that the null
space frequency of the image was not reproduced, which led to outlining of the
image. The arrow indicates the direct-tons in which the sectoral converted image
is realized; this specific feature is reflected in the name PRIZ [PReobrazovatel'
LZobrazheniy: ima~e converter].
- The same Figure shows an example of the image reconstructed frnu a hologram that
was recorded by the PRIZ modulator. In this case the modulato:: acted as a con-
verter uf incoherent I.ight to coherent light.
122
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The sensitivity oF the PRIZ modulator is at least an order of magnitude better
than that of. the PROM modulator. This means thot the PRIZ can be effectively
used in systems Eor real-time optical processing of in~ormation. Ref. 7 has re-
ported on the use of this modulator in an optical spectrum analyzer, correlator
arid as a medium for recording holograms.
The PRIZ modulator can also be used for processing electrical signals, and specifi-
cally for compression of an LFM signal. In this case the signal is recorded as
an LFM grid on the modulator, and readout is by coherent light. At a certain
distance from the modulator, one of the diffracted beams is compressed into a
narrow band. In the same plane, another diffracted light beam and the null order
have remained defocused. The theoretical coefficient of compression in this case
is expressed by the Formula [Ref. 8]
kcomp- 2 +'Y 4 -n' n-~fl~ ~11~
4~here is the deviation of the space frequency of the grid, and Z is its length.
Fig. 6 shows the result of signal compression with deviation of 8 lines/mm,
Z= 15 mm, obtained by a PRIZ modulator. The signal was recorded on the modulator
from photographic film by He-Cd laser light.
_ The experimentally determined value of the co-
efficient of compression was ~100 (theoretical
- coefficient of compression of such a signal
is kcomp - 120) .
Dynamic Properties
Thanks to high sensitivity (-5~10-~ J/cm2 per
1% of diffraction eff iciency) and the capability
for fast erasure by a flashlamp when the elec-
trodes are shorted, the PRIZ modulator ensures
speed of the order of the television standard
~~IIIIII~,IIIIIIII~IIIII~IIIIIIII~I~IIIIII~I~~II~~~~I~~~~~~II~~~~~ mode30orrespondsrtoethedusualmwell-known cycleg
" recording - readout - erasure. However, on
Fig. 6. Result of compres- modulators with a modified current-conducting
sion of LP'M signal: a--image system, another mode of operation is possible
of LFM signal; b--image of as well, i. e. a mode that does not require
null order and compressed sig- image erasure. Since some experimental results
nal; c--scano~ram of zero order that explain this mode have already been pub-
and compr.essed signal lished [Ref. 9], we give here only the diagram
of Fig. 7. As we can see from th3.s diagram,
when the recording light is energized an image arises in the modulator that begins
- to fade ~aithln a certain time (in the given spec~.fic example within about 0.5 s),
but flares up again when the recording light is switched off. Thus a time-variable
ima~e (or part of one) is isolated in the znodulator. These effects can be attrib-
uted to redistribution of the space charge as the image changes, and they determine
the entire dynamics of operation of the device.
Available experir~ental results of investigation of the response of the PRIZ modu-
lator to unsteady controlling pulses show that this modulator is actually dynamic,
123
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eUi 1. 0
�
- H O.S
~ 0
~
~ Fig. 7. Response of device
f 0 j I
0.5 ~ I to change of light intensity
� ~ I in image being recorded
_ ~ _~:5 ~ ~
~ ~ f.a ~ I
a~ 0.5 I ~
~
H
0 0.5 f.0 5 T, s
- and can provide time-continuous image processing, whereas in most known cases,
discrete frame by frame processing is realized. In this connection, the problem
arises of describing the characteristics of a modulator that adequately reflects
their unsteady nature.
In the scope of our research, a phenomenological approach is developed to descrip-
tion of a dynamic modulator within the framework of the theory of linear systems.
The niicroscopic nature of the processes that take place in the modulator, as well
as its functional capabilities in devices for processing unsteady two-dimensional
. signals will not be discussed here.
_ Let us consider the response of a dynamic optically controlled modulator to the
action of light that has distribution of intensity in the plane of the modulator
- F(x, y, t). We will take the modulator as fairly thin to avoid accounting for
the three-dimensional nature of data recording. In the general case, the action
_ of the modulator on the reading light can be described'by a tensor of second rank
P(x, y, t). If the reading light has the corresponding wavelength and does not
influence the parameters of the mQdulator, then the amplitude of the reading light
immediately behind}the modulator Eout~x, y, t) is related to the amplitude of
the reading light Eread before the modulator by the expression
}
~out~x, y, t) = P(x, y~ t)Eread� ~12~
Under the influence of the recording light there will be a change in P(x, y, t),
so that we can write
~ y, t) = po (x~ y, t)� , ' (13)
- As we know, Po is a Jones matrix. Hereafter we will consider only ~P(x, y, t).
In accordance with the theory of linear systems, the response of the system
~P(x, y, t) ~o signal F(x, y, t) can be represented as
_ m .
015 (a, y, t) ~ks' ky' u~~ S, ~k=' kr~ ~u) e"'