JPRS ID: 10646 USSR REPORT PHYSICS AND MATHEMATICS

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12 JPRS L/ 10646
8 July 1982
, USSR Report
PHYSICS AND MATHEMATICS
(FOUO 5/82)
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JPRS L/10646
8 July 1982
USSR REPORT
PHYSICS AND MATHEMATICS
(FOUO 5/82)
CONTENTS
CRYSTAIS AND SkMICONDUCTORS
Four-Wave Acoustoelectronic Interaetion 1
FLUID TlYNAMICS
Subsonic Radiation Waves in Air Lt
Numerical 3tudy of Vibrational Relaxation With Turbulent
Jet Mixing in Supersonic Nozzle 9
Methods of 3olving Simplified Steady-State Viscous Gas
Equations 17
LASERS AND MASERS
Theoretical and Experimental Determination of Vibrational
Temperatures and Gaina in Gasdynamic C02 Laser With Additives
- of CG and NOr Part 2s Experimental Technique and Research
Results 51
High-Efficiency Photoinitiated D2-r^2-CO2 Laser 58
InfluencE of Specific Pumping Power on Working Efficiency
- of Atmospheric-Pressure Electron-Beam Controlled C02 Laser..... 60
1'nvestigation of Chemical HF Laaer Based on High-Pressure
; H2-SF6 Mixture 64
; Feasibility Study on Maximizing Specific E4niasion Parameters
of Chain Reaction HF Laser 69
' Influence of Starting Initiation on H2/F2 Laser Parameters 73
- a - [III - USSR - 21H S&T FOUO]
G'nR (1F'F'If TAT. TJ;F (1Ni.Y
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Nea Phosphate Glass for Lasers With High bnission Pulse
Recurrenc e Rate ..........0 76
Picosecond Pulse Generation in Alexandrit;e Laser in 0.7-0.8 }un
w
Range With Passive Mode Locking 79
Estimating Possibi.lities for Using Phase Conjugate
Adaptive Systems To Gompensate Laser Beam Thermal
Defocusing 84
Efficiency
of Copper
Vapor Lasers
93
'!'hermoelastic Action
of Periodically Pulsed Laser Radiation
on Solid
Surface ............................e.........a....
98
P.egenerating Worki.ng Mixture of Iodine Laser With Open-
- Discharge Pumping 112
Influence of Sound Waves on Pulsed Gse-Diacharge Laser
Emissic,n Power 116
New Working Subatances for Photodissociative Iodine Laser 122
OPTICS APID SPECTROSCOPY
Theor,r of 6bservation of�Underwater Objects Through Wave-
Covered Sea Surface 131
Wavefront Reversaa. by Foui�=Wave Mixing in Raman-Nonlinear
Medium 141
Steady-3tate Theory of flptical Striations 148
- Wavefront Reversal Theory for Radiation With Spatially
Inhorrogeneous Distribution of Average Intensity 161
Stimulated Many-Phaton Effects on Diffraction Grating 168
Laser Dispersal of Polydisperse Water Aerosol 172
MATHEMATICS
Operative Identification of Control Objects 186
- Methods of Synthesizing Low-Sensitivity Linear Control
Systems ..........................................o......... 194
Adaptive Control .............................9 202
- b -
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CBYSTALS AND 9WCONDUCTORS
FOUR-WAVL ACOUSTOELECTRONIC INTERACTION
Leningrad PIS'MA V ZHURNAL TEKiNICHESROY FIZIRI in Russian Vol 8, No 3,
12 Feb 82 (manuscript rnceived 30 Sep 81) pp 133-136 .
[Article by L. A. Slavutakiy~ and I. Yu. Solodov, Moscow State University
imeni M. V. Lomonosov]
[Text] Acaustoelectric nonlinear effects are the basis for electronic devices
used in convolution, correlation and other forms of aignal processing [Ref. 1].
Such effects are usually studied on the tasis of sqtiare-law nonlinearity of
a medium with coneideration nf only three-wave interaction of acoustic waves.
A report was given in Ref. 2 on the use of four-wave interaction oi aurface
~ waves with an electric field for signal atorage. Our paper is the first to
report experiinpntal observation of four-wave interaction of aurface and body
Acousti.c waves enabling realization of new functional operations: triple
convolution and correlation of radio signals.
h,
K b
a
K
- Fig. 1. w-k diagrams of triple convolution (a) and correlation (b)
rig. la showe an w-k diagram of f our-wave interaction of acoustic surface
and body waves. The two dispersion branches of the diagram correspond to
body (longitudinal) and surface waves with phase velocities that satisfy the
approximate condition cabw g 2casw. In the preeence of the piezoelectric ef-
fect, the axis k -0 of the diagram is a third disperaion branch of the system
in which electromagnetic perturbationa may accur. Conditions of eynchronism
with four-wave interaction take the form k4=kl+k2+k3, w4 =w1 +w2+w9, and
1
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with consideration of the possibility of interaction of opposed acoustic waves
are illustrated in Fig. la. It is clear from the diagram that when W2= w3 =
2w1 and cabW = 2casw we hav` ky= 0 and wy= Swl. Consequently, when a surface
wave interacts with an accompanying body wave [Ref. 1. 21 and with an opposed
~ surface wave [Ref. 31, for which w2 =W3= 2w1, a spatially homogeneous electric
field is formed with frequency 5w1. Such interaction can be realized under
conditions of cubic nonlinearity of the mediwn, or through two aequential
three-wave processes on a quadratic nonlinearity.
The rev-erae third-order nonlinear effect generation of a surface wave with
frequency wl [Ref. 41 as a result of interaction of an electric field on fre-
quency 5wl [Ref. lJ with opposed longitudinal [Ref. 31 and surface [Ref. 2]
waves (w2- w 3 - 2w1) is shown in Fig. lb. The conditigns of synch}onism
for this process can be written in the following form: ky= kl- k2 - k39
w4-w1'W2-W3�
The described four-wave processes were experimentally observed under condi-
tions of acouatoelectric nonlinearity of a laminar LiNbOs-Si structure. Acou-
stic surface wavea with frequenciea of 15 and 30 MHz were excited in yz-LiNb03
by interdigital transducers in the pulse mode (conversion losaes of the order
of 10 dB, band 3-5 MHz). A 30 1rIIiz longitudinal acouetic wave pulse was excited
by half-wave resonant transducere tnade of the same material and cemented to
tlie end face of the specimen (losses =15 dB, band 93 MHz). To accomplish
interaction of acoustic body and surface waves, the end face of the backing
- was cut at an angle of =10� to the axis y-LiNb03. In the region of the trail
_ of the longitudinal wave on the surface of the backing between the aur�ace
- wave traneducers was a p-Si specimen measuring 5 x 20 x 2 min with conductivity
of -10-3 (St�cm)'1. The resultant electric field was taken off by using soiid
- metal electrodes on the upper surface of the semiconductor and the bottom
plane of the backing; the signal from the el.ectrodea went to the input oi
an amplif ier tuned to a frequenr.y of 75 MHz. Upon matching of time synchroni-
zation of the pulses to corrsspond to meeting of three interacting waves under
the semiconductQr, the signal of their interaction (triple convolution) was
registered at the amplifier output.
Fig. 2. Triple convolut3on
voltage as a function of the
voltage across the transducers: 200
1--transducer for 15 M surface
wavea; 2--t,ody-wave transducer; ~
3--transducer for 30 MHz aurface ~
waves
0 900
- i~
0

.
Uiri I V
_ 2
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Fig. 2 shows the experimentally obtained dependences of the tripls convolution
signal voltage amplitude on the voltage across each of the acoustic wave trans-
ducers %(with voltage acroas the two othere held constant). We can see from
this figure that at an input voltage of =17 V, the output signal of the triple
convolution has an amplitude of the order of 300 uV and varies linearly with
increasing input signals up to 5 V. That there ia a region of saturation
- of the curves on Fig. 2 can apparently be attributed to effective energy ex-
change as a result of three wave interFtctions. Typically, since thP efficiency
of such proceasea is higher for surface waves [Ref. 31, it is for waves of
this type that saturation regions appear on Fig. 2. We should also take note
of rather high efficiency of the triple convolution process. At input voltages
of 15 V, external loases to convolution B= 20 lg U4 /U1 do not exceed 90 dB.
We used the experimental Cechnique described above to observe the third-order
inverse nonlinear effect generation of surface waves as a result of four-
wave interaction. Since the signal of the inverse surface wave ia a function
of acoustic correlation of the interacting waves, such a process represents
triple correlation. The dependences on input voltage levels in this case
are analogous to those shown on Fig. 2, and have characteristic satura*ion
regions. External losses of triple correlation are comparatively low (Uy"= 1 mV
at U1 - U2 - U3 = 10 V), and amounted to =80 dB.
This level of effectiveness of four-wave interaction is completely acceptable in
practical acoustoelectronics. Therefore the observed third-order nonlinear
effects may find practical application in electronic devices that are associ-
ated with reciprocal processing of several signals.
REFERENCES
1. Kayno, G., TIIER, Vol 64, 1976, p 188.
2. Ralston, R. W., 5tern, E., APPL. PHYS. LETT., Vol 35, No 2, 1979, p 150.
3. Bozhenko, V. V., Lyamov, V. Ye., Solodov, I. Yu., ZHURNAL TEKHNICHESKOY
FIZIKI, Vol 51, No 3, 1981, p 650.
COPYRIGHT: Izdatel'stvo "Nauka", "Pis'ma v Zhurnal tekhnicheskoy fiziki", 1982
- 6610
CSU: 1862/139
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F'LUID DYNAMICS
SUBSONIC RADIATION WAVES IN AIR
UDC 621.373.826:533.951
Moscaw RVANTOVAYA ELEKTRONIRA in Ruesian Vol 9, No 3(117), Mar 82 (manuacript
received 6 Mar 81, after xeviaion 25 Jun 81) pp 615-618
[Article by T. V. Loseva and I. V. Nemchinov, Institute of Physics of the
Earth imeni 0. Yu. Shmidt, USSR Academy of Sciencas. Moacaw]
[Text] It is ahown that fast laser emiasion absorption
wavea (with pressure in the shock wave generated by the
expanding plasma much higher than atmospheric) with pre-
dominunt role of plasma aelf-radiation in the mechanism
of propagation can exist at flux densities at least an order
of magnitude lower than those at which they have been ex-
perimentally obse.rved heretofore. The evolution of such
subsonic radiatinn waves from the initial plasma layer is
traced by ncsmerical calaulatione of the corresponding spec-
tral radiation-gasdynamic problem, and the authors detennine
- +the way tha: their major parameters depend on time (up tio
ttee quasi-steaciy etage of propagation) and on flux density
of more than 0.1 MW/cm2 for a C02 laser and 1 MW/cm2 for
a neodymiwa laser.
In Ref. 1, 2, an experimental and theoretical examinal
propagation of a laser spark in air�c;f normal denaity
mode at ratea of the order of 10 m/s. It was seaumed
gation is due to ordinary heat conduction. For small
(of the order of 1 mm) plasma radfation leads only to
plasma layer.
tion was made of the
in the slow-burning
that flame front propa-
radi.i of the laser beam
energy-loases from the
It was shown in Ref. 3, 4 that with a sufficiently large irradiation spot
size, plasma propagation relative to the barrier at which it arises will be
:determinecl by a hydrodynamic mechanism: as the plaema is heated, it expands
and praducES a shock wave. The rate of expansion of the hot plasma, which
- in essence digplaces the cool air, may be fairly high, and preasure is corre-
spondingly appreciable p- 1,QQ~/3a - 1/3. p= ISQD/381/3.
Here v is plasma velocity, km/s, qo i8 laser emiasion flux density, MW/cm2,
d is the ratio of air density to its normal value, p is preasure in bars.
4
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Since the pressure in the plasma tnay be much greater ttan atmospheric, the
optical thickness of the plaema layer will be large (for geometric dimen-
sions that are not too small), and the self-radiation of this Iayer will de-
termine the process of capture of gas particles by the plasma mass flow
through the absorption wavefront, and with it the maximwa temperature. The
ideas of subsonic radiation waves [Ref. 3, 41 have been experimentally con-
- firmed [Ref. 5-9]. Fast absorption waves (with velocities of more than 1 km/s)
have been studied at qo> 10 MW/cm2 for radiation with wavelength a= 1tw
[Ref. 5-7] and at qo> 1 MW/cm2 for X- 10 Wn [Ref. 8, 91. Our estimates and
calculations have shown that fast absarption waves generally speaking may
exist at even lower radiation flux densities.
The problem of propagation of a subsonic radiation wave was solved by a method
analogous to Ref. 3, 4. Detailed consideration was taken of the spectral
makeup of the radiation, and detailed tables of absorption coefficients were
used [Ref. 101. Since analyeis of Ref. 1, 2 shows that heat conductivity
at low radiation flux densities may play an appreciable role, in contrast
to Ref. 3, 4, molecular and electronic thermal conductivity were taken into
consideration in addition to energy transport by hydrodynamic means and by
radiation, using coefficients detetmined from tables of Ref. 11, 12. The
process of plasma origination was not considered in this work. It was assumed
that at the initial instant in the air above the barrier there existed a plasma
layer with initial temperature of 1 eV at a pressure determined by relation (1).
The initial optical thickness of the layer for radiation with a= 10 Jtm at
a mass of 20 ug/cm2 is approximately 0.2-0.3.
T,. eV
7
Fig. 1
The spatial diatribution of temperature T at different ti.ies t is ahown in
Fig. 1 for a C02 laser at qos 0.1 (a) and 5 MW/cm2 (b). The qualitative pat-
tern of the process of plasma heating and absorption wave advancement is the
same f.or these values of qo and for interntediate values. Laser radiation
is zbsorbed in a comparativety narrow zone. The gas is heated at temperatures
below 1.1 eV by radiation of the continuous apectrum emitted by the plasma.
At higher temperatures, absorption of laser radiation pla,ys a major role.
It was found that heat conduction does not play an appreciable role, which
was determined both by analysis of profiles of temperature and energy release
_ due to heat conduction and radiation effecte, and by direct comparison of
calculation with and without consideration of thermal conductivity. Radiation
effects play a decisive part in advancement of the absorption wave.
5
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T . sv
?,5
0
g b
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Pressure and velocity in the steady state at qpm 0.1-5 MW/cm2 are detemnined
by relation (1) with accuracy of t20X. The spatial maximwn of temperature
Tm, continuous-spectrimm radiation flux density de-excited from the plasma
to the wall qw, and also the flux density emauating from the plasma toward
the laser are similar functions of the' specific energy E supplied up to
the given instant t for all values of qo in the ran.ge considere�. Fig. 2
shows curvea of Tm(E) for various qo.
~
Tm, eV
At E~ 20 J/cm2, the pattern becomes quasi-stegdy.
Maximum temperaturea in the quasi-steady stage
Z change comparatively weakly with qo:
~
Tm= L1+0.251g (qo/1 MW�cm 2)]2.3 K. (2)
J
Mass f lowrate M ia nearly proportional to q o:
? at qo a 0.1 MJ/cm2 we have M= 0.7 g/cm2 �s. Total
energy losses from the plasma layer to radiation
increase with decreasing laser emission flux
density and reach 45% at qo- 0.1 MW/cm2. The
~ values of M and Tm at qo = 0.2 MW/cm2 (1.3 g/cm2�s
. 2' and 1.9 eV) and at qos 5 MW/cm2 (27 g/cm2�s and
Fig. 2 2.8 eV) differ somewhat from the values given
in Ref. 4. The differencea can be attributed to
the fact that in Ref. 4 for these values of qo the problem was solved only
in the multigroup approximation. At qa- 1-5 W/cm2 the calculated values of
the parameters of the subaonic radiation wave aYe fairly close to the experi-
mental values [Re_'. 8, 91, especially if one considers the influence of the
spike at the beginning of the C02 laser radiation pulse and the correaponding
effects of unsteadiness. In the experiments of Ref. 13 at qo> 0.2 MW/cm2 with
millisecond pulses emitted by a C02 laser, propagation of slow combustion
waves was obaerved. This ie due to the small size of the irradiated spot
(41 cm) and the correspondingly atrong influence of two-dimensionality in
expansion of the plasma jet, leading 1:o nearly atmospheric pressure.
For large spots and shorter pulse durations after completion of the stage
of plasma origination, the pattern should be close to that described by our
calculations, which are in the nature of a theoretical prediction for such
low flux densities and conditions of plane geometry of plasma expansion. In
the case of pulses of smooth shape, the stage of plasma origination looms
large for low laser radiation flux densities, according to calculations of
Ref. 14 and experiments of Ref. 13. And in addition, if the amplitude of
the spike is great enough, the apecific energy of plasma initiation is corre-
spondingly law (let us say, of the order of 2-3 J/cm2), and absorption waves
propagating due to the radiation mechanism may be observqd right down to quite
low flux densities in the main part of the laser pulse and up to the atage
of quasi-steady pulse propagation. For example, at a f lux deneity of 0.1
MW/cm2, the thickness of the plasma layer by a time of 100-200 us does not
exceed 2-4 cm, i. e. at a spot area of the order of 50 cm2 and specific energy
of 10-20 J/cm2, which �is quite sufficient fDr reaching the quasi-steady stage
of propagation, the total radiation energy or Che C02 laser is approximately
0.1-1 W.
6
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Estimates and calculations like those described above show that for a neo-
dymium laser the threshold of maintaining quasi-steady fast laser xadiation
absorption waves is higher than for the C02 laser, but such waves can also
exist at flux densities much lower than in the experiments of Ref. 5-7, and
epecifically at least at qo>- 1 MW/cm2. Qualitatively, the pattern of propa-
gation of fast absorption waves for neodymium laser radiai.ion is analogous
to that given in Ref. 3, 4 and above for the C02 laser. The pressure and
expansion rate found in the calcu'lationa also agree with relations (1). How-
ever, the ingition temperature (1.3 eV) is higher than for the C02 laser,
and accordingly the maximum temperature of the plasma is somewhat higher than
glven by relation (2). Of coursa, in this case as well at low qo special
plasma ignition is advisable, and the initial stage of development of the
effect depends on the parameters of the "initiator." At laser radiation flux
densities lower than those given in the calculations, the reduction of pressure
in the initial plasma layer due to hydrodqnamic expansion, and the correspond-
ing cooling due to the amplif ied radiation may lead to transparency of the
_ laser plasma and to a change in the nature of the proceases oc;curring there.
"Stalled" (decelerated) and "rushed" (accelerated) waves become possible, as
well as pulsating modes of wave propagation with incomplete absorption of lasex
radiation.
_ Subsonic radiation waves propagating from a barrier under conditions of plane
geometry have been considered above. However, such waves (with plaema pressure
much greater than atmospheric) are posaible in an unbounded gas medium as
- well when theq propagate from an initial plasma layer that is initiated for
example by an optical breakdown or electric discharge. The parameters of
such waves in their quasi-steady stage are not much different from those of
waves propagating from a wa11. For example, velocities'are only 23/3 times
_ less than those given by relations (1) for expansion in both directions rather
than to one side only. The maximum temperature difference ia even lessig-
nificant. The only noticeable difference is in pressures they are 2 3
times lower. The threshold of maintaining such quasi-steady fast absorption
waves is correspondingly somewhat higher. However, all the same they may
exist in the flux densiCy region where only comparatively slow waves were
observed under the conditions of the experiments of Ref. 1, 13, 15 (with pres-
sure close to atmospheric), although hydrodynamic effects had already begun
to play a part ire their propagation as well.
REFERENCES
1. Bunkin, F. V., Konov, V. I., Prokhorov, A. M. et al., PIS'MA V ZHURNAL
EKSPERIMENTAL'NOY I TEORETICHESKOY FIZIKI, Vol 9, 1969, p 609.
2. Rayzer, Yu. P., "Lazernaya iskra i rasprostraneniye razryadov" [Laser
Spark and Discharge Propagation], Moscow, Nauks, 1974.
3. Bergel'son, V, I., Loseva, T. V., Nemchinov, I. V., ZHURNAL PRIKLADNOY
MF:[CHANIKI I TEKHNICHESKOY FIZIKI, No 4, 1974, p 22.
4. Kozik. Ye. A., Loseva, T. V., Nemchinov, I. V. et al., KVANTOVAYA
ELE-KTRONIKA, Vol 5, 1978, p 2138.
7
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5. Kozlova, N. N., Markovich, I. E., Nemchinov, I. V. et al., KVANTOVAYA
ELEKTRONIKA, Vol 2, 1975, p 1930.
6. Berchenko, A. Ye., Sobolev, A. P., Fedyushin, B. T., KVANTOVAYA
ELEKTRONIKA, Vol 6, 1979, p 1546.
7. Bessarab, A. V., Dolgaleva, G. V., Zhidkov, N. V. et al., FIZIRA PLAZMY,
Vol 5, 1979, p 558.
8. Bakeyev, A. A., Vasil'yev, L. A., Nikolashkina, L. N. et al., RVANTOVAYA
ELEKTRONIKA, Vol 2, 1975, p 1278.
9. Bakeyev, A. A., NiY..olashkina, L. N., Prokopenko, N. V., KVANTOVAYA
ELEKTRONIKA, Vol 7, 1980, p 1236.
10. Avilova, I. V., Riberman, L. M., Vorob'yev, V. S. et al., "OpticheskiYe
svoystva goryachego vozdukha" [Optical Properties of Hot Air], Moscow,
Nauka, 1970.
11. Stupochenko, Ye. V., Dotsenko, B. B., Stakhanov, I. P. et al., in:
"Fizicheskaya gazovaya dinamika" [Physical Gas Dynamics], Moscow, Izd-vo
AN SSSR, 1959, p 39.
12. Kalitkin, N. N., Ruz'mina, L. V., Rogov, V. S., "Tablitsiy
termodinamicheskikh funktsiy i transportnykh koeffitsiyentov plaany"
[Tables of Thermodynamic Functiane and Transport Coefficients of Plasma],
Moscow, Izd-vo IPM AN SSSR, 1972.
13. Klosterman, E. L., Byron, S. R., .T. APPL. PHYS., Vol 46, 1974, p 4751.
- 14. Golub', A. r., Nemchinov, I. V., KVANTOVAYA ELEKTRONIKA, Vol 7, 1980,
p 1831.
15. Bufetov, I. A., Prokhorov, A. M., Fedorov, V. B., Fomin, V. K., PIS'MA
V ZHURNAL EKSPERIMENTAL'NOY I TEORETICHESKOY FIZIKI, Vol 32, 1980, p 281.
COPYRIGHT: Izdatel'stvo "Radio i svyaz t", "Kvantovaya elektronika", 1982
6610
CSO: 1862/145
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UDC 621.373.826.038.823
NiJMERICAL STUDY OF VIBRATIONAL RELAXATION WITS TURBULENT JET MIXING IN SUPER-
SONIC NOZZLE
Minsk INZHENERNO-FIZICAESK,IY ZHURNAI, in Russian Vol 42, No 4, Apr 82 (manu-
script received 27 Jan 81) pp 586-592
[Article by A. V. Lavrov and V. A. Pospelov, Leningrad Polytechnical Institute
imeni M. I. Ralinin]
[Text] The paper gives the results of a cotnputational study
of the influence that different working parametera have on
the characteristic:- of a C02 gasdynamic laser with selective
thermal excitation. �
Calculation of supereonic jet mixing with consideration of vibrational relaxa-
tion is of considerable interest in connection with the development of hyper-
sonic wind tunnel equipment [Ref. 1], investigation of spontaneous emission
in 3et engine flows [Ref. 21, and creation of gasdynamic lasers (GDLs) with
selective thermal excitation [Ref. 3-18]. Experimental research in recent
- years (Ref. 3-111 shows the possibility of using mixing in rasers to get higher
gains and specific energy outputs than in GDLs with premixing. Alongside
the further development of experimental research, a problem of some topicality
is development of an adequate numerical model of the laser and using it as
a basis for both parametric studies and analysis of the influence of separate
factors on GDL operation. However, up until now the only extensive theoretical
research that has been done on the mixing C02 GDL has been based on an instan-
taneous mixing model [Ref. 12-14]. Clearly, -calculatione using this model
= will agree well with experimental data if mixing takes place in the nozzle
assembly [Ref. 6] or the mixer unit proposed in Ref. 5 is used. Aowever,
if the C02+ He is mixed through a central plug, where the injection itself
takes place from a flat profiled nozzle [Ref. 11] or from circular orifices
in the central plug (and the distance between orifices is approximately equal
to their diameter), then two-dimensional mixing effects will play an appre-
ciable role, and disregarding them may lead to considerable overstatement
of the laser characteristics. Furthermore, in designing the optical cavity,
data on density and gain profiles are needed.
There are currently examples in the literature on calculation of jet mixing
in C02 GDLs with selective thermal excitation both on the basis of a system
of boundary layer equations (narrow-channel) [Ref. 15-17], and with the use of
9
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p 2 P
simplified Navier-Stokes equations fRef. 11, 18]. In particular, in Ref. 17
the aolution ie baeed on ueinR a yemi-empirical model of turbulence rel.ying
on an equation of pulsation energy balance with a universal set of numerical
coefficients, which had been successfully used previously in analyzing free
shear flows [Ref. 19, 20]. Satisfactory agreement between the reaults of
calculatton [Ref. 17] and experimental data [Ref. 4] on distributian of sma11-
signal gain g, COy concentration y and lasing power provides a basis for using
the proposed technique in numerical parametric investigation of C02 GDLs with
selective thermal excitation. Camparison with Experimental Results. Ref. 10 gives abundant data on tbe
influence of temperature and pressure in the gas generator chamber obtained
by using a nozzle with central plug analogous in design to that of Ref. 4.
In doing the correaponding calculations, it was assumed that the half-height
of the C02 supply jet was Aol= 0.2 mm, height of the hot nitrogen jet
~AoE - Aoi) - 0�8 mm, ratio of output cross section to critical cross section
AE/Aog = 15.7, length of the supersonic part of the nozzle xc a 60 mm. The
nozzle contour was taken from Ref. 21, which gives the results of ealculations
of nozzles of minimum length with a corner point (the contour for Mach number
M= 4.5 was used with ratio of specific heats cP:cv=2.4). The Mach numbers
at the beginning of the calculated region were equal to M013 MoE = 1.2, compo-
sition of the mixture of the secondary jet C02:He = 1:4 (by volume), initial
temperature 300 K, and the values of the other parametera are given in tha
table. The f low length of the cavity was taken as xp s 24 cm, distance between
mirrors L= 17 cm, coef�icients cf absorption of the mirrors aloa2= 0.02, coef-
ficient of tl = 0, and t2 was determined in an optimization process.
- ~ - - - - - ~y (Co)
r,. K (N,)
Parameter 1 0,05 I o,t 1.0.15 I 0,2 I 0,26 I o,s' I 0,4 1 souo I 2500 I 3000 I asoo
T, K I 207 I 213 I 21i3 I 221 I 227 I 21! ~ 2;i7
V~ t~f s 823 710 G34 575 5,33 495 941
Fig. 1. Specific energy output and 4 optimtun transmission coefficient of
output mirror as a function of the ~
stagnation pressure: I--experiment
[Ref. 101; II--calculation, a - 0.02;
III--(a + dL)- 0.05; nitrogen atag-
nation temperature: 1--To= 2000; ry
2--2500; 3--3000 K; 4--t (To= 2500 K), Z
N. J/$; P, MP8
N�0,1
2.
f ~
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1552 1940 2328 ' 9720
h(i'1 1078 1 I 50 17290
_ t
0,/2
0,J0
Q,OB
Q06
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Results of comparing experimental data with calculations are shown in Fig. 1.
The somewhat higher value of the specific energy output obtained in the cal-
culation can be attributed to the fact that in the first place no consideration
was taken of losses of vibrational energy during flow in the subcritical part
of the nozzle, and in the second place the actual losses in th e c av ity
were not considered (see Ref. 22). For example when the overall coefficient
of losses per Fas:. (a + dL) was increased to 0.05, the calculated curves agreed
much better with experimental data. Fig. 1 also showa the reaults of computa-
tional optimization of the coefficient of transmiesion of the semitransparent
mirror, evidencing the neceseity for selecting t2 in a multifactor optimization
proceas. It ia important to note that the t2 obtained in the Calculation
lie in the range of mirror transmissions used in the experiment of Ref. lU.
Results of Numerical Parametric Study. Calculations were done using the
nozzle contour taken from Ref. 4. Mach ninnbers Moi' MoE ' 1.2, static pressure
at the beginning of the computational region P1 = PE = 0.204-1.632 MPa, which
corresponds to preaeure in the gas generator chamber of 0.5-4 MPa, temperature
and flow velocity are given in the table, and the values of other parameters
are given in Ref. 17. In order to reduce the nwnber of parameters to be varied
in the given section, the calculations were done for conditions of laser oper-
ation in the amplification mode, i. e. without consideration of the losses
on the mirrors. The field intensity of the master laser was 10 kW/cm2, and
the flaw length of the cavity was 8 and 40 cm.
N�0,
7
6
5
4
3
1 a
. 4
/rv
1
Z
3
o 6
N
,75
30
?�f
20
15
IA
ZO 0,2 04 0
b
4
9
2
g
iz
5
B
1
I
/
4
,
Z
0
' 3
f
6
0
6
,
OZ
04 ~ZO
.0,2 'f
Fig. 2. Specific energy output (a, b) and average small-
signal gain (c) at the nozzle tip as a function of C02 con-
tent in the secondary flow (a--xp = 40; b--8 cm); 1-3--To=
2500; 4-6--3000 K; 1, 4--P = 1; 2, 5--2; 3, 6--3 MPa; I--
gain g< 0 at xp < 40 cm, g, m-1
Fig. 2 shows the results of calculation of specific energy output and average
Ar:
gain g= f g(y)dJ/,fla at'the nozzle tip for different values of working
0
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_ parameters. Let us note that for aome fairly large values of Y, the gain
- dropa to 0 at xp < 40 cm. As we can see from the figure, the optimum compo-
- sition of the aecondary jet depends appreciably both on pressure and on tem-
perature, an increase in P and T entailing a reduction in the optimum value
of Y. It is important to nate that in operation of a laser with w4rking param-
eters Po- 3 MPa, Tos 3000 K, the optimum mixture frotn the standpoint of maxi-
mizing energy output is C02:He -1:9, and txansition to the 1:4 mixture most
often used in experiment reducea the energy output by 25%. It is iniceresting
that for both shost and long cavities the reduction in N with increasing y at
Y> Yapt is weaker at To = 2500 K. This is because in the given case there
is a reduction of gas temperature in the cavity, i. e. greater relaxation
lossea are possible, which increase with increasing C02 concentration. The
results given on Fig. 2 show that for all working parameters the value of Y
that is necessary for attaining maximum g is much greater than is necessary
for maximizing the specific energy output. In application to GDLs with pre-
mixing, this fact has already been repeatedly mentioned in the literature
(see for example Ref. 23). The results show that for the short caiity the
specific energy output is about half that for the long cavity. Ap)arently
increasing the field strength (by increasing the spacing between mirrors)
does not appreciably increase N at xp @ 8 cm, since in addition to the limiting
influence of the rate of transfer of vibrational energy from N2 to v3C02, it
is essential for the given mixing unit that mixing continues in the cavity.
The given results do not allow us to evaluate the influence of varioua factars
on specific energy output. Therefore Fig. 3 shows data on the effici::,ncies
'lIP
~ ~ -i vs N.
p6 ~ 0,45
p 4 2
p1y 0,30
02 0,15
lf
g� /i
ge
0,6
o,4
02
~-a _�-u
L
p 0,2 0,4 0 02 014 D 02 0,4 0 02 'C
Fig. 3. Dzpendence of nozzle efficiency, mixing efficiency
(a), cavity efficiency (b, c) and small-signal gain on the
output of gas from the cavity (d) on C02 content in the sec-
ondary flow; I--xp = 8; II--40 cm; III--rmixing efficiency S
on nozzle tip; 1-6--same as Fig. 2
of the nozzle r1c and the cavity r1p, mixing efficiency 0 = cN2 (y = 0) : cN2 (y = AE)
and on the average gain as the gas leaves the cavity. As can be seen from this
f.igure, r1c decreases with increasing C02 concentration, and in all cases ex-
~ ceeds the value nc=0.65. However, for GDLs with mixing this quantity does
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not completely characterize nozzle efficiency, for the closeness of nc to
- unity is evidence of poor mixing of N2 and C02+ He. Therefore Fig 3a also
shows the values of mixing efficiency S on the nozzle tip and at tae end of
the cavity. It can be seen that B increasea with increasing C02 concpntra-
tion. This is explained by the fact that at a fixed value of Mol an increase
in Y leads to a reduction in the velocity of the secondary flow (see table);
consequently there is an increase in the difference of velocities of the flows
of N2 and C02 +Iie and accordingly in the effective coefficient of turbulent
viscosity. The pointa of inflection on the curves can be attributed to the
complexity of the process of turbulent mixing in the presence of a strong
negative pressure gradient. Mixing efficiency does not exceed 60%, which
- shows the necessity for further improving the nozzle units used. Increasing
the pressure leada to a alight drop in S, and a rise in nitro gen temperature
cauaes somewhat of an increase in which is due to an increase in velocity
VE (aee the table).
Fig. 3b and c show data on cavity eff iciency. The efficiency of the cavity
at xp= 8 cm does not exceed the value np = 0.35. At xp= 40 cm, efficiency
reaches 65% for the flow mode with parameters Tp= 2500 K, Po = 1 MPa, Y= 0.25.
As we can see from crnnparing Fig. 2a and 3b, c, at xp = 40 cm, aimilarity is
observed in the curves for N and r1p as a function of y. However, at xp= 8 cm,
such similarity is not observed. For example at xP = 8 cm, Po � 2 MPa. To=
2500 K, N reaches a maximum at Y= 0.2, whereas np continues to increase at
even higher values.
Cavity efficiency can also be evaluated from the gain on gas output from the
cavity. Therefore the corresponding calculated data are shown on Fig. 3d.
We can see from the figure that for modes with maximwa energy output a further
~
increase in th6 gas-outlet gain is possible either by reducing the length
of the cavity or by increasing field strength.
Fig. 4. Infl.uence of stag-
nation temperature and pres-
aure on GDL characteristics:
I--Po= 1; II--3 MPa; III--
Tp= 2500; IV--3000 K; 1--
- N, J/g; 2--nP;3--rtc; 4-7gain
on nozzle tip; 5--gain at
cavity outlet
Results of investigation of the in-
fluence that initial nitrogen tem-
perature has on GDL characteristics
are shown on Fig. 4. It is important
to emphaeize that at Po- 3 MPa the
energy output at To= 3500 K is little
more than half the value at the,opti-
mum temperature of 2500 K, and at
N� 0,1
'I~10
9 /OZ
9
s
4
00
2
0
2
9
3
. ~5
!o
~Z
Z 0
-IV
T /0'~ 0 2 P
the same time the gain at the nozzle tip at the maximimt temperature is slightly
lower than the maximwn gain. Analysis of the way that nozzle and cavity
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efficiencies depend on To shows that the reduction in N is due mainly to an
increase in np as a consequence of rieing gas temperature in the cavity.
IC is of considerable interest to study the way that apecific energy output
dependa on atagnation pressure aince increasing Pa simplifies the problem
of restoring presaure in the flow to atmospheric level (see for example Ref.
11). Resulte of corresponding calculations are shown on Fig. 4. We can see
that for To- 2500, 3000 K the maximum energy output is reached at pressure
of 1, 0.5 MPa respectively. Of conaiderable interest ia the fact that when
Po> 2.2 MPa the energy output for To= 2500 K is higher than for 3000 K. In
thds case, the reduction of energy output is also cauaed chiefly by a drop
~ in cavity efficiency, firstly due to the increase in gas temperature there,
and secondly due to an increase in relaxaCion losaea.
Thus the results given above show the feasibility of achieving high apecific
energy output in GDLs with selective thermel excitation when all working param-
eters are appropriately optimized. The computational data enable us to evalu-
ate the mixing efficiency, as we11 as the nozzle and cavity efficiencies,
and to make recommendations on improving them. The influence that nozzle
shape and mixing cross section have on the energy autput, and convparison of
the C02 and N20 GDLs are beyond the scope of this work aiid will be covered
in future reaearch.
Symbole
c--mass concentration; g--small-signal gain; t--mirror transmission coeff i-
cient; xc--length of superaonic part of nozzle; xp--length of cavity; Aol--
half-height of C02+ He supply jet; AoE--half-height of initial crose section
- of the nozzle; AE--half-height of output crosa section; L--spacing between
mirrors; M--Mach number; N--specific energy output; P--pressure; T--tempera-
ture; Po, To--nitrogera stagnation pressure and temperature; V--velocity;
a--mirror absorption coefficient; S--mi.xing efficiency; Y--volunetric concen-
tration of C02 in secondary flow; 6--�-~�.
that determine the solution for x> xo, lYl<
We rewrite system (1) as

ax + A~b a~ " A!~ ~ 1� ~ (a)
and consider the two aubsystems of equations

~x t A 1b (3a)
= A C ays ~ (3b)
~x
that correspond to flows in two limiting cases: negligibly small forces of
viscosity (Re-�), and large forces of viscosity (small Reynolds number).
_ The eigenvalues of matrix A-1B
V MVtC'la ~V Ca'
= ,u% _ cs
(c ='Yp p is the apeed of sound in a perfect gas) are real, and the corre-
_ sponding system of equations (3a) is tryperbolic when conditxon
_ lks+ ya 7Ca
is met. In this case, Cauchy problem (3a), (2) is correct (e. g. see Ref. 1),
and may be solved by a multistep method of integration along coordinate x from
croes section to cross section. In doing this, it is necessary that the line
- 24
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of initial data x= xo and the lines of advancement of the solution x= const
have the spatial type of Ref. 18, i. e. that condition MX= u/c> 1 be met.
In the case of subsonic flows, system of equations (3a) becomes elliptical,
and Cauchy problem (3a), (2) becomes incorrect. Since there are always local
subsonic flow zones in supereonic viscous flaw around solids near a wall,
system of equations (3a) muat be regularized near these zones. In this paper,
the simplif3ed Navier-Stokes equations are regularized by the method proposed
in Ref. 19, 20. In accordance with this method, we introduce one of the pos-
sible regularizing functions in the equation of momentum in the projection
_ of system (3a) on the Ox axis, after which matrix A assumes the form
u t o 0
o u o z/~ (5)
A- o o u o '
o YP o u
where x is a regularizing function (see Ref. 20) such that
when M. > ! (6)
when Mx < j� .
Let us consider the eigenvalues of matrix A-1B after regularization (5), (6).
T~ao of the four eigenvalues 71 and a2 will remain as before, equal to v/u.
The others will take the form
UVt C 'Ui+ 7C,(Va-C�) (7)
tie _ C2 .
, Expression (7) implies that problem (3a), (2) is correct in the subsonic zone
as well if condition
2
- za _ CIL MX(e)
is met, which can be realized by appropriate choice of function x.
Let us now consider the eigenvalues of matrix A-1C of system (3b):
'Az = 1m/U ,
(9)
c~
(x ~
System of equations (3b) is not completely parabolic (see Ref. 1), and problem
(3b), (2) is correct if eigenvalues (9) have non-negative real parts. It
is implied by (9) that J11 and a2 are real and non-negative when u> 0. Eigen-
values J13 and Xq will also be real and positive when MX > 1, since in this case
X(~-p' ,~r < o.~sMX(1+ V )1
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Howeves, if MX< 1, then a3 Q23(M = N2) (see table 2
from Ref. 1), and development of an additional channel for relaxation of vi-
brational energy of molecules of C0203), N2 and CO (see formula (10) in
Ref. 1). These factors lead to reduction of vibrational temperatures of
CO TS and the asymmetric mode of C02 T3, and to an increase in vibrational
temperature of the collective mode of C02 T2.
The experimental and theoretical data shown on Fig. 1, curves 1-4, indicate
approximately identical effectiveness of molecules CO and N2 in the process
of relaxation of the collective mode of carbon dioxide gas (6). Actually,
when nitrogen is replaced by carbon monoxide up to concentrations CCp= 0.2,
T2 remains practically unchanged. This result agrees with the data of ineasure-
ments of rate constant Q20 with M= CO (see citations 60, 61 in Ref. 1), and
contradicts studies [Ref. 4] in which it was established that the quantity
Q20 when M= CO is approximately two orders of magnitude higher than when
M= N2.
Resulta of Investigation of Nitric Oxide Additives. The nitric oxide molecule
has a lower vibrational quantum than the carbon monoxide molecule. The defect
of the first vibrational level of NO with the first level of the asymmetric
mode of C02 increases to 450 cm 1 as compared with the CO moler_ule (243 cm 1).
For the NO molecule, just as for C0, quasi-resonant exchange may take place with
the collective mode of C02 in (10).
The results of ineasurements of vibrational temperatures of NO T6 and C02 T3
and T2 when nitric oxide is substituted for nitxogen in mixture 0.1C02+ 0.5N2+
0.4He are shown in Fig. 3. The reduction in T6 and T3 as nitric oxide is
added is more appreciable than with the addition of carbon monoxide (see
Fig. 1, 3). An increase is noted in the rate of vibrational relaxation of
C0203), N2 and NO as compared with mixtures that contain carbon monoxide.
This is evidenced by the reduction of vibrational temperatures: AT6= T6(CNO s
0) - T6 (tNO = 0.5) = 500 R and AT3 = T3 (tNO = 0) - T3 (CNO = 0.5) = 500 K when nitrogen
is replaced by nitric oxide as compared with corresponding quantities ATS=
200 K and AT3a 300 K wiCh analogous substitution of carbon dioxide for nitrogen.
tHere and below, reactions are nimmbered as in Ref. 1.
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Just as in mixtures with carbon monoxide, the calculated values of T3 are
overstated by 100-250 K depending on the NO content. To correlate calculations
and experiments on determining T31 the rate conatant Q23 must be approximately
quintupled. The calculated values of temperature T6 coincide with experiment
in the concentration region Epp $0.2, and are 150-250 R higher than the ex-
perimental values at Epp^'.0.2
An increase in T2 is observed theoretically and experimentally with syste-
matic subatitution of NO for N2. The theoretical calculation of T2 is also
overstated (see cixrve 1" of Fig. 3). To bring theory and experiment into
line, it is necessary to approximately double the rate constant of reaction
(6) Q20(M - NO), or to have water vapor in the mixture in an amount of
EH2O' 0.005.
Results of ineasurements and calculation of gain with the addition of nitric
oxide are shown in Fig. 4. Addition of nitric oxide leads to a reduction
of Ro from 0.4 cm 1 at END = 0 to 0.1-0.15 m 1 at Cpp s 0.5, which corresponds
in order of magnitude to a reduction of gain with equivalent substitution
of carbon monoxide for nitrogen. Good agreement with experiment is obtained
with theoretical calculation of Ro when the rate constants of relaxation pro-
cesses are taken according to versions 3 and 4. Choosing the rate constants
in accordance with version 1 gives understated values of Ko as compared with
experimenta. Use of the rate constants of version 2 overstates Ro in region
Epp I 0.2.
On the whole, the influence of NO molecules on the kinetics of formation of
population inversions in the active medium of a C02 gasdynamic laser is in
large measure analogoue to the influence of CO molecules. Just like CO mole-
cules, the NO molecules cause a reduction in stored vibrational energy of
the upper laser level of C02(v3), N2(v) and NO(v) as a result of an increase
in the relaxation rate of this this energy in the process of V-V exchange
(7) in C02 and as a result of development of an additional relaxation channel
(10) that in fact couples the antisymmetric and collective modes of C02. The
relaxation rate of the collective mode (6) and consequently of the lower laser
level is not considerably increased as compared with collisions of C02 mole-
cules with nitrogen. The noted factors considerably reduce the gain when
nitric oxide is added to the C02 laser mixture, just as in the case of carbon
monoxide.
The following comments can be made concerning the discrepancy between experi-
ment and theory in determination of vibrational temperatures. In most cases
these discrepancies can be attributed to attendant uncertainties in choosing
the rate conetants of processes of vibrational relaxation of the multicomponent
medium of the C02 laser, or to the presence of uncontrollable trace amounts
of water moaecules in the mixture that appreciably accelerate processes of
vibrational relaxation. The more agpreciable discrepancies noted in some
cases in the given paper for vibrational temperatures of the asymmetric mode
T3 may appareatly be due to the occurrence of atomic components such as oxygen
in the medium at high temperatures. Such components are strong deactivators
of molecular vibrationa [Ref. 5]. It is also possible that the explanation
of this discrepancy under conditions of considerable vibrational excitation
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of the molecules requires examination of a more detailed scheme of vibrational
relaxation in the active medium of the C02 laser that takes consideration
of occurrence of additional channels of energy exchange.
REFERENCES
1. Doroshenko, V. M., Y.udryavtsev, N. N., Novikov, S. S., FIZIICA GORENIYA
I VZR7NA, Vol 17, 1981, p 2.
2. Biryukov, A. S.,Volkov, Yu. A. et al., KVANTOVAYA ELEKTRONIRA, Vol 3,
1976, p 1748.
3. Soloukhin, R. I., Yakobi, Yu. A., ZHURNAL PRIRLADNOY MEKHANIKI I
' TERANICHESKOY FIZIKI, No 3, 1974.
4. Levis, M., Bernatein, L., AERONAUT. RES. COUN. CURRENT. PAPERS, No 1294,
London, 1974.
5. Buchwald, M. I., Wolga, G. J., J. CHFM. PAYS., Vol 62, 1975, p 2828.
COPYRIGRT: Izdatel'stvo "Nauka", "Fizika goreniya i vzryva", 1981
6610
CSO: 1862/153
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UDC 621.373.826.038.823
HIGfl-EFFICIENCY PflOTOINITIATED D2-F2-C02 LASER
Moscaw KVANTOVAYA ELEKTRONIRA in Russian Vol 93, No 3(117), Mar 82 (manuscript
received 2 Jul 81) pp 624-625
[Article bx A. S. Bashkin, N. P. Vagin, L. V. Rulakov, A. N. Orayevskiy,
Yu. P. Podmar'kov,'0. Ye. Porodinkov, M. I. Prishchepa and N. N. Yuryshev,
Physics Institute imeni P. N. Lebedev, USSR Academy of Sciences, Moscow]
[Text] A report on investigation of a photoinitiated D2-F2-C02
chemical laser. A apecific energy output of 37 J/liter, cor-
responding to a technical laser efficiency of 18% is achieved
on a mixture of D2:F2:C02:fle - 1:5.5:4:9.5 (1021 /[F21 - 0.03,
p= 1 atm) at degree of initiation 0[F21/1F21 = 0.05X.
One of our precediag papers [Ref. 1] reported on attainment of high technical
efficiencies r1t in a large-volume fl2-F2 laser with photoinitiation by standard
flashlampe IFP-20000 (nt = 36% at specific energy output e= 25 J/liter). The
results of camparative experiments on initiation of D2-F2-C02 and H2-F2 lasers
with small volumes by a beam of fast electrons has shown that the energy param-
eters of these lasers are approximately the same [Ref. 2], which leads us
to hope for high nt in the photoinitiated D2-F2-C02 laser as well. As pointed
out in Ref. 1, the high values of nt and E in chemical lasers based on the
fluorine-hydrogen chain reaction can be realized only when using a medium
with l.arge cross sections that assure effective capture of emiesion of the
photosource (diameter of the laser cell must be of the order of 150 nu -r
more for the uaual partial pressures of fluorine of the order of 200 maa Hg
or less). Therefore the experiments were done on the same laser cell as in
Ref. 1; active voltune was about 7:3 litera.
Operation with the D2-F2-C02 laser requires the use of NaCl windows, which
could not withstand more than one use under the conditions of the experiments
done. Therefore we were unable to work with laser windows of � 160 mm as
in the case of the H2-F2 laser. However, this is not important for determinifig
the energy parameters of the D2-F2-CO2 laser since special studies on the
A2-F2 laser showed uniformity of laser energy distribution over the cross
section of the cell (cell diameter was 150 mm) throughout the entire range
of fluorine working presaures (~200 mm Hg). This demonstrates the possibility
of investigations of the D2-F2-C02 laser with the use of inedium-sized optics
'and subsequent scaling of the results to the full cross section of the laser
cell. Therefore all experimenta were done with optics of 0 70 mm and laser
beam diameter of -60 mm.
58
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~ The purpose of our research was to determine the feasibility of getting high
technical efficiencies and apecific energy outputs on a.chemical D2-F2-C02
laser initiated by flashlamp emfsaion. Iu the course of the experiments,
the above-mentioned laser output parameters were optimized with respect to
composition and paessure of the mixture, oxygen content, degree of initiation
_ and Q of the optical cavity. The best result was attained on a mixture of
DZ:F2 : C02:He - 1:5.5:4:9.5 (1021/[F2]= 0.03) at atmospheric pressure. Spe-
cific energy output e 6 37 J/liter was attained at a degree of initiation
A[F2]/[F2]- 0.05%. Considering the above statement regarding the poseibility
of scaling up to the entire crosa section of the cell, we find that the given
specific energy output should correspond to energy from the entire active
volume of the laser of 270 J. The energy of a capacitor bank supplying the
necessary degree of initiation 0[F2j/[F2]= 0.05% was 1.5 M. Consequently,
; at the attained energy output of 37 J/liter, the technical efficiency of the
laser is 18%.
It is interesting to note that on the given facility in experiments with the
H2-F2 laser an energy output of -40 J/liter was achieved at efficiency of -19X
(mixture H2:F2:He:02= 22:150:15:563, p= 1 atm). This shows that under certain
conditions the photoinitiated D2-F2-C02 laser is on a par with the photo-
initiated H2-F2 laser with respect to specific energy output and Lechnical
eff iciency.
REFERENCES
1. Bashkin, A. S., Oraevsk}r, A. N., Paziuk, V. S., Porodinkov, 0. E.,
Yuryshev, N. N., Vagin, N. P., "Investigation of a Large Voltmme H2-F2
Laser With Flashlamp Initiation", Lectures, Symposium Optika-80, Budapest,
November 1980, p 106.
2. Bashkin, A. S., Orayevskiy, A. N., Tomashov, V. N., Yuryshev, N. N.,
KVANTOVAYA ELEKTRONIRA, Vol 7, 1980, p 1357.
COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1982
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UDC 621.373.826.038.823
INFLUENCE OF SPECIFIC PUMPING POWER ON WORRING EFFICIENCY OF ATMOSPHERIC-
PRESSURE ELECTRON-BEAM CONTROLLED C02 LASER Moscaw KVANTOVAYA ELEKTRONIKA in Russian Vol 9, No 2(116), Feb 82 (manuscript
received 16 Apr 81, after revision 17 Jul 81) pp 413-415
[Article by V. G. Voatrikov, V. G. Naumov and L. V. Shachkin]
[Text] An experimental study is done on the influence that
specific pimmping power has on operating efficiency of an
atmoapheric-presaure electron-beam controlled COz laser
at f ixed near-optimum values of other parameters that in-
_ fluence laser output energy. It is ahown that an increase
in specific pwnping pawer from 2 to 7 kW/cm3 leada to an
increase in the output energy by 40% for a mixture of
, C02:N2:He = 1:6:3.
The problem 'of 'the influence that specific pumping power has on the working
efficiency of electron-beam controlled lasers is a timely question when se-
lecting optimum duration in pulse-periodic laser systems. It is evident from
general arguments that a reduction in pulse duration Tp(while retaining the
epecific pumping energy e that ia limited by heating of the gas mixture) should
lead to an increase in the efficiency of the electron-beam cmntrolled laser
due to reduced collisional relaxation as compared with radiative, and on the
other haad the reduction is limited by complication of the ionization device
and its supply system, as well as by an increase in the radiation power density
on the target, leading to gas breakdown at its surface. Besides, when the
pumping power is increased, there is an increase in the rate of electron losaes
in proportion to the square of electron concentration, which leads in turn
to a reduction of efficiency in utilization of the electron beam.
Theoretically the problem of complex optimization of the excitation pulse
parametere was considered in Ref. 1, 2. Reaearch has now been done on experi-
mental investigation of the way that emisaion energy Pe and efficiency n depend
on the normalized electric field strength E/N and composition of the working
mixture [Ref. 3, 4]. However, in all these papers, simultaneous variation
of several parameters that influence Pe and n(such as e, E/N, specific pimmping
power and so on) has precluded a detailed analysis of the influence that any
parameter has at fixed values of the other parameters near optimum.
To determine the influence of specif ic pumping pawer on output emission energy,
and efficiency on an electron-beam controlled laser using carbon dioxide, we
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did an experimental study of the way that Pe depends on n and q at fixed values
of pumping energy and E/N for mixtures of COZ:Nz:He = 1:6:3 and 1:4:5 (in parts
by volume) at pressure of 1 atmosphere and initial temperature of the gas
mixture -300 K. The experimenta were done on a facility described in Ref. 5.
The source of ionization was an electron beam with initial energy of -200 keV,
coupled through an aluminum foil 35 Itm thick into the gas-discharge chamber.
To guarantee constant composition, the working mixture was continuously circu-
lated through the mixing chamber. The discharge current was measured by a
Rogvwski loop. The research used a two-pass telescopic unstable cavity with
magnification M a 1.3, the length of the active zone along the optical axis
of the cavity was Lc= 2 x 0.75 m. Radius of curvature of the output mirror
was 33 m, and of the opaque mirror 43 m. Reflectivity of the mirrors
K= 0.985. Output energy was measured by a matrix of EP-40 cells. Lasing
pulse shape was recorded by an FSG-223 sensor with signal fed to the S8-11
two-beatn memory oscilloscope; the aignal from the Rogowski loop was sent to
the same oscilloscope. The energy input in each pulse was determined by ap-
proximate numerical integration over the course of the pumping pulse. Since
the pulse ahape for the specific pumping power is practically the same as
that of the discharge current, this recording technique enabled us to determine
the time of termination of the lasing pulse relative to completion of the
pumping pulse. Fig. 1 shows oscillograms of current and lasing pulses. The
Pe, J/Z
000
40 (B 800
00oo0
Ce
000 el
8�
q-,~tW/cm3
Fig. 1. Typical oscillo-
grams of discharge current
(top) and lasing pulse (bot-
tom)
Fig. 2. Emission output
energy as a function of
specific pumping power
variation in specific pumping power with fixed electric field and energq input
was achieved by varying the beam current and pumping puls-! duration. The
voltage across the discharge chamber (and accordingly the value of the elec-
tric field) was the maximum permissible for each mixture with consideration
of stability of the working mode at which no breakdowns were observed in the
discharge chamber either during the pulse or after its completion.
Fig. 2 shows how specific energy output depends on the pumping power density
for a mixture of C02:N2:He = 1:6:3 at E/N = 1.5�10-16 W�cm2. Output energy
was measured at two fixed values of specific energy input e1=0.25 and e2=
0.30 J/cm3. Under our conditions, lasing practically ceased at the end of ~
the pumping pulse at el, and therefore a further increase in specific energy
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input to eZ does not increase energy output. (A sianilar effect was observed
for the mixture C02:N2:He = 1:4:5 ae well.) As can be seen from Fig. 2, an
increase in specific pwnping power from 2 to 7 kW/cm2 leads to an increase
in output energy by approximately 40-50%. The maximwn attained output energy
Wgs Pemaxm 42 J/Z. For a mixture of C02:N2;He= 1:4:5 the dependence of output
energy on q is similar as a whole to that observed on Fig. 2.
Fig. 3 shows how laser efficiency
depends on specific power input for
16 both mixtures at two values of spe-
,.---r cific energy input. The curves were
10 obtained by averaging experimental
, data. As we can see from Fig. 3,
the most effective of the investigated
1, 5 q, kW/cm mixtures was a mixture of C02:N2:He =
1:6:3 (curves 1, 1'). The maximwn
Fig. 3. Laser efficiency as a func- va3.ue of n= 15% is attained at e1=
tion of specific pumping power: 0.25 J/cm3 and q= 7 kW/cm3. The
1, 1'--C02:N2:He = 1:6:3 (E/N = 1.5�10-16 higher value of n for mixture C02:N2:
W�cm2 , 1--e1 - 0.25 J/cm3 , 1' ez � 0.30 He = 1:6: 3 cannot be attributed to the
J/cm3); 2, 2'--C02:N2:He 1:4:5 (E/N e fact that the volumetric heat capacity
1.3�10'16 W�cm2, 2--e1= 0.25 J/cm3, (J/Z�deg) for the mixture with volu-
2'--e2a 0.30 J/cm3) metric ratio of components of.1:6:3
is greater than that for the mixture
with ratio 1:4:5 at about the same effectiveness of excitation of vibrational
- levels under our conditions for the given mixtures [Ref. 6, 71. It is com-
pletely possible that the decisive factor is that the optical axis of the
unstable cavity wae situated near the cathode (at a distance of the order
of 1 cm) and other things being equal (due to comparatively greater inhomo-
geneity of the discharge in the cathode zone for mixture 1:4:5), the operation
of the optical cavity was affected more by the atrong influence of inhomogene-
ity of the gain and of the index of refraction. More detailed investigation
of the dependence of output energy on the composition of the working mixture
and pumping conditions requires a�series of experimental studies of homogeneity
of the active medium and calculations with consideration of the configuration
of the discharge chamber, the cavity and homogeneity of the active mediwn.
- In conclusion the authors thank A. V. Korneyev and I. D. Dzhigaylo for assist-
ing with the experiments, and A. G. Krasyukov and P. A. Svotin for constructive
discussion of the results.
REFERENCES
1. Avrov, A. I., Glotov, Ye. P., Danilychev, V. A., Cheburkin, N. V.,
KVANTOVAYA ELEKTRONIRA, Vol 7, 1980, p 1979.
2. Avrov, A. I., Glotov, Ye. P., Danilychev, V. A., Kamenets, F. F.,
Krasovskiy, V. M., Soroka, A. M~, KVANTOVAYA ELEKTRONIKA, Vo1 8, 1981,
p 424.
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3. Basov, N. G., Dnnilychev, V. A., Ionin. A. A., Kovah, I. B., Sobolev, V. A.,
Suchkov, A. F., Urin, B. M., KVANTOVAYA ELEKTRONIKA, Vol 2, 1975, p 2458.
4. Basov, N. G., Danilychev, V. A., Ionin, A. A., Rovsh, I. B., Sobolev, V. A.,
Suchkov, A. F., Urin, B. M., RVANTOVAYA ELEKTRONIKA, Vol 1, 1974, p 2529.
5. Krasyukov, A. G., Naumov, V. G., Shachkin, L. V., Shashkov, V. M.,
FIZIKA PLAZMY, Vol 7, 1981, p 100.
6. Lobanov, A. N., Orlov, V. R., Suchkov, A. F., Urin B. M., Preprint No 199,
Lebedev Phygics Institute, Moscow, 1977.
7. Karlov, N. V� Konev, Yu. B., Kochetov, I. V., Pevgov, V. G., Preprint
No 91, Lebedev Physics Institute, Moscow, 1976.
COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1982
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UDC 621.373.826.038.823
INVESTIGATION OF CHEMICAL RF LASER BASED ON HIGH-PRESSURE A2-SF6 MI%TURE
Moscow RVANTOVAYA ELEKTRONIKA in Russian Vol 9, No 3(117), Mar 82 (manuscript
received 7 Jul 81) pp 625-628
[Article by A. S. Bashkin, A. N. Orayevskiy, V. N. Tomashov and N. N. Yuryshev,
Physics Institute imeni P. N. Lebedev, LTSSR Academy of Sciences, Moscaw]
[Text] An investigation is made of the energy character-
istics of a chemical HF laser using a mixture of H2-SF6
excited by a relativistic electron beam. Effective lasing
- is achieved at a mixture pressure up to 4.5 atm. Specific
energy output of 50 J/liter is obtained at a mixture pressure
of 1.5 atm. The authors note the capability of continuous
tuning of the lasing frequency over a range of 2.2 cm 1 about
the center of each of the vibrational-rotational lines,
which enables developmenC of a powerful tunable laser neces-
sary for laser-chemical research.
The solution o� laser-chemical problems has necessitated development of power-
ful lasers that emit radiation over a wide wavelength range. Radiation with
wavelength near 3 um is needed for resonant excitation of molecules that have
hydrocarbon bonds. Quite promising in this band is a chemical HF laser based
on a mixture of SF6-H2that has a broad lasing spectrum. The use of a stable
gas mixture as the active medium of the laser enables reliable operation at
high presaures, which not only shortens the duration of the lasing pulse,
but also enables expansion of the continuous tuning range.
Ref. 1 experimentally demonatrated the feasibility of tuning the frequency
of the AF laser in a range of 0.5 cm 1 axound each vibrational-rotational
transition. However, the energy characteristics of this laser were very low.
Beaides, expansion of the continuo~ss tuning band of the laser is quite de-
sirable.
The poseibility of aperation of the laser using an SF6-H2 mixture at pressures
up to 10 atm was demonstrated in Ref. 2. However, the explanation of the
abrupt drop in energy characteristics of the laser at mixture pressures above
3 atm by relaxation of vibrationally excited HF molecules by H2 and HF mole-
cules is unconvincing. Therefore the question of getting efficient lasing
on an SF6-H2 mixture at pressures of several atmospheres remains open.
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In ttigh-gain lasers, including chemical HF lasers, a reduction in energy char-
acteristics may be caused by "parasitic" lasing or superlwninescence [Ref.
3, 41; however, direct observation of parasitic laeing and the possibility
of overcoming it have apparently not been described in the literature as yet.
Our research is dedicated to solving all these problems. The SF6-H2 mixture
was excited by an electron beam from an accelerator described in Ref. 5. Trans-
verae excitation was used because of the low electron energy (200 keV). The
use of an external magnetic f ield of 6 kGs intensity eliminated electron scat-
tering, increased current density in the laser cell, and also permitted more
exact deteruination of the active volume of the laser and the input energy.
The electron energy lost in the laser gas medium was measured as previousiy
in Ref. 5 by a moving angle calorimeter.
.
~
Fig. 1. Lasing energy as a function
of pressure of a mixture of SF6:H2 = 7:1 ~
;a) and general diagram of the experi-
ment (b): B--direction of extarnal y
magnetic field; the axis of the "para-
sitic" cavity coindices with the di- p
rection of B ct
w
; mm Hg
n
L
_
~~iv
pnAUMMp.g.
e-beam b
Development of parasitic lasing was checked on the experiment diagrammed in
Fig. 1. Laser output energy was measured at d3.ffer.ent mixture pressures.
The occurrence of a"dip" at the top of the curve can be attributed to para-
sitic lasing. Since emission was not ubserved in the preaence of the opaque
mirror alone, it can be assumed that in the given case there was no super-
luminescence. Aluminum surfaces spaced 2.5 cm apart and parallel to one another
could serve as the mirrors of the "parasitic" cavity. The electron beam from
the accelerator was coupled in.through one of these foil sheets, and the beam
was extracted from the lacer cell for measiirement of its parameters through
the other foil sheet. Of course, the Q of this cavity was lower than that
of the main optical cavity, but aince it had a short base (2.5 cm) compared
with the main cavity (120 cm), the field was established in much shorter times.
The occurrence of the dip at the top of the curve is due to the fact that
it was at the top that tine lasing threshold was surpassed for the parasitic
cavity. The situation is aggravated by the fact that the length of the laser
active zone in these two directinns was about the same (see Fig. 1).
- To check out the above argu.nients, the length of the main cavity was reduced
to 40 cm. When this was done, the laser output energy at a mixture pressure
of 500 mm Hg more than doubl.ed upper point e on Fig. la). Also to suppress
parasitic lasing for a cavity base of L= 120 cm, a screen was introduced into
the active medium bent into a cylinder 2.5 cm in diameter, wh-ich strongly
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reduced the Q of the parasitic cavity. The current of the electron beam in
the gas medium showed insignificant change. In this case as well, a sharp
increase was observed in the lasing pulse energy (lower point � on Fig. 1).
Thus the given experiment was a kind of imitation of conditions that may arise
in lasers with large active volUmes. In such lasers, large transverse dimen-
sions may lead to spurious emission even with much lower gain than in this
case.
To eliminate the further possibility of parasitic lasing, the shape of the
cathode was altered: the circular form was replaced by a strip measuring
63 x 4 mm. The track of the electron beam [photo not reproduced] and the
general setup of the experiment are shown in Fig. 2. Laser output energy
Fig. 2. General diagratn of ex-
periment with strip cathode (a)
and track of electron beam on
surface of tin-plated sheet lo-
cated directly in the gas medium
of the laser cell (b) [photo not
reproduced]
_ Fig. 3. Output energy of laser
using mixture of SF6:H2 = 5:1 (1),
20:1 (2), 54:1 (3) and 100:1 (4)
as a function of mixture pressure
for entire lasing cross section
(a) and for a layer of 0 4 mm
closest to the point of entry of
electrons into the laser gas (b)
L
65 B
~
ve
5
T�40% e-beam r-98%
a
Elas, J ' 2
0,4
0,3 Pr'A.
012 r
was measured as a function of the pressure 0,1
of mixtures with different SF6/H2 ratios
(Fig. 3). At pressure of 1.5 atm and ~ ~p Pm~ ~atm
ratio SF6:H2 a 20:1, the lasing pulse energy .reached 0.4 J. Considering that the cross S, rel. units
section of the tasing spot as determined
from the burn left on blackened photo- b
graphic paper corresponded to the cross 4D o
section of the electron beam, we can assume JO
that the active volinne of the laser was 1 p~m, atm
about 8 cm3 . However, because of the
small laser dimensions, the accuracy of
determining the active volume is no better than 20-25X. Thus the specific
lasing energy is elS8 s 50 J/liter. Such a high value of elas shows that high
energy parameters are attainable even when a chemical reaction of other than
chain type is used under conditiona of intense initiation.
The level of initiation of the mixture was determined on the basis of data
on measurement of the electron beam energy contributed to the active volume
of the laser, and also with consideration of the fact that energy of 4.5 eV
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is expended on formation of a single fluorine atom [Ref. 6]. These estimates
give a concentration of atomic fluorine of (1.1� 0.2) 1018 cm 3 at SF6-pressure
of 1.5 atm, with laser efficiency ne of 6.6% relative to the electron energy
contributed to the active volume of the laser. Defining the chemical ef-
fiCiency nchem of the laser as the ratio of the laser pulse energy to the
energy released in reaction of atomic fluorine wi.th hydrogen, we find that
at p= 1.5 atm and a ratio of SF;:HZ s 20, nchem � 21%. Increasing the ratio
of SF6:H2 from 20 to 100 while maintaining the pressure constant at 1.5 atm
causes a drop in laser energy to 0.3 J(see Fig. 3a). There is a corresponding
drop in ne. However, aince such a reduction in the hydrogen content of the
mixture causes a sharp reduction in its energy reserve, there is an increase
in rchem� For example, at SF6:H2 = 54, n~hem = 29%, and at SF6 :HZ = 100, nchem
is 40%. Increasing the pressure of the mixture above 1.5 atm (see Fig. 3a)
causes the output energy of the laser to drop for any mixture composition
that is u.:ed.
In principle, this effect may be caused by the influence of relaxation of
excite3 HF* mol.ecules upon collision with hydrogen molecules [Ref. 21. How-
ever, an estimate of the characteristic times of the process (k = 2.4�104
(s�mm Hg)-1 [Ref. 6]) at mixture pressures of -1.5 atm shows that the drop
in output energy of the laser cannot be entirely explained by relaxation of
HF* molecules. In these estimates we have assumed that lasing pulse duration
is commensurate with the duration of an electron beam current pulse [Ref. 7].
The fact that the maxitnum laser output energy is observed at the samepressure
(see Fig. 3a) regardless of mixture composition is likewise tndirect proof
of the weak influence of relaxation of AF* by H2 molecules. Apparently relaxa-
tion begins to have an effect at more appreciable values of mixture pressure.
This is possibly manifested by the intersection of the curves on Fig. 3 at
a pressure in excess of 3 atm. The abrupt drop in output energy with pressure
_ at p> 1.5 atm to all appearances is due mainlq to the nonuniformity of initia-
tion, which shows up most strongly at high pressures. To check out this assump-
tion, 2 diaphragms were introduced into the cavity with aperture of 4 mm,
producing lasing in a narrow layer closest to the point of entry of the laser
beam into the laser cell. The output energy of the lasing pulse was plotted
as a function of the pressure of a mixture of SF6:H2= 20 (Fig. 3b). In this
case, the maximum output energy was no longer observed at 1.5 atm, but at
2.5 atm. An increase in pressure to 4.5 atm causes a drop in laser output
energy by only 1.5 times. A further increase in the pressure was limited
by the mechanical strength of the foil through which the beam was coupled
into the laser cell.
The attainment of effective lasing at such high pressures may be of interest
from the standpoint of tuning the laser frequency over the line width of the
vibrational-rotational transition. The laser line width Av in the given case
is determined by impact broadening and is related to the pressure of the mix-
ture by the expression Av=6SF6PSF6 [Ref. 11. Line broadening by hydrogen
can be disregarded.
Since 6He/aSF6= 0.2 [Ref. 8], increasing the pressure of the mixture by SF6
is more advantageous than by using a buffer gas such as helium. Since
6gF6= 0.5 (cm�atm)-1, under the given experimental conditions (p = 4.5 atm)
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taser frequency can be tuned over a range of 2.2 cm 1 around the center of
each of the vibrational-rotational lines in the emission range of the laser
(a = 2.7-3.0 um). Increasing pressure by means of the principal reagents (SF6
and fl2) without the uae of buffer gases also produced lasing with rather high
power (-10 mW) despite a amall active voltmme of the laser (-8 cm3).
The electron beam technique provides the capability of considerably increasing
the active volume of the laser not only by increasing cathode area, but by
increasing the electron beam energy. The latter also gives the possibility
for increasing the pressure of the gas medium.
REFERENCES
_ 1. Bagratashvili, V. N.,.Knyazev, I. N., Kudryavtsev, Yu. A., Letokhov, V. S.,
PIS'MA V ZHURNAL EKSPERIlMNTAL'NOY I TEORETICHESROY FIZ?KI, Vol 18, 1973,
p 110. .
2. Vol'nov, A. M., Dovbysh, L. Ye., Kazakevich, A. T., Mel'nikov, S. P.,
Sinyanskiy, A. A., KVANTOVAYA ELEKTRONIKA, Vol 4, 1977, p 426.
3. Suchard, S. N., Kerber, R. L., Emanuel, G., Whitier, J. S., J. CHEM. PAYS.,
' Vol 57, 1972, p 6065.
4. Chen, H. L., Taylor, R. L., Wilson, J., Lewis, P.,.Fyfe, W., J. CHEM.
PHYS., Vol 61, 1974, p 306.
5. Bashkin, A. S., Konoshenko, A. F., Tomashov, V. N., Yuryshev, N. N.,
KVANTOVAYA ELEKTRONIKA, Vol ,6, 1979, p 2166.
- 6. Wilson, J., Chen, H. L., Fyfe, W., Taylor, R. L., Little, R., Lowell, R.,
J. APPL. PHYS., Vol 44, 1973, p 5447.
7. Patterson, E. L.- Gerber, R. A., Blair, L. S., J. APPL. PIiYS., Vol 45,
1974, p 1822.
8. Wiggine, T. A., Griffen, N. C., Arlin, E. M., Rerstetter, D. L.,
J. MOL. SPECTR., Vol 37, 1970, p 77.
COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1982
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UDC 621.378.33
FEASIBILITY STUDY ON MAXIMIZING SPECIFIC EMISSION PARAMETERS OF CHAIN REACTION
flF LASER
Moscow KVANTOVAYA ELERTRONIRA in Russian Vol 9, No 3(117), Mar 82 (manuscript
received 7 Jul 81) pp 628-630
[Article by A. S. Bashkin, A. N. Orayevskiy, V. N. Tomashov and N. N. Yuryshev,
Physics Institute imeni P. N. Lebedev, USSR Academy of Sciences, Moscaw]
[Text] An examination is made of the energy parameters
of an H2/F2 laser excited by electron beam at a pressure
of the active volume of up to 3 atm. A specific energy
output of 180 J/liter is achieved at efficiency of SOOX
with respect to the electron beam energy contributed to
the active volume. Ar~ increase in initiation achieved by
substituting sulfur hexafluoride for helium gave a specific
energy output of 400 J/liter at efficiency of -140X and
- chemical efficiency of 22% on a mixture at atmospheric
preasure.
The development of pulsed chemical lasers is inseparably connected with in-
creasing the pressure of the active gas medium. In principle, increasing
the pressure enables us to raise the specific energy output both by increasing
the energy content of the gas mixture, and by initiation, since the concentra-
tion of radicals (such as F) that "drive" the chain reaction of fluorine and
hydrogea increases with increasing pressure of the medium at a constant elec-
tron or photon flux of the initiation source. The rise in pressure also in-
creases the chemical reaction rate, shortening duration of the lasing pulse
and thereby increasing lasing power along with energy output. Shortening
of the laser pulse necessitates the use of a short-duration pumping source.
From this atandpoint, electron beams are most convenient for pumping the ac-
tive media of high-pressure lasers.
The use of high-current, high-energy beams (55 kA, 1 MeV) gave lasing energy
of 2.3 kJ [Ref. 1, 21 on a hydrogen-fluorine mixture at pressure of 700 mm Hg,
and even 4.2 kJ at mixture pressure of 1340 mm Hg. The efficiency ne with
respect to beam energy invested in the active volime af the laser was 180%,
and maximtan chemical efficiency n h was lOX. Al1 these results admirably
demonstrate the feasibility of ef~icent laser operation on a fluorine-hydrogen
chain reaction at high reagent pressure. Unfortunately, Ref. 1, 2 do not give
69
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data on specific energy outputs, initiation level, or the way that laser param-
eters depend on mixture composition. All this makes it difficult, if not
- impossible, to do an in-depth physical analysis of the research results.
In this paper, we study the possibility of getting effective lasing on a
fluorine-hydrogen chain reaction at high reagent pressure bq using a compara-
tively law-energy electron beam (less than 200 keV) as the pwnping source.
The experimental facility is described in detail in Ref. 3. Let us note that
the use of an external magnetic field in transverse configuration of the ex-
periment eliminated electron beam scattering, enabled exact measurement of
the beam energy invested in the active volume of the laser by a moving calo-
rimeter [Ref. 4], and precise formation of the geametry of the excited volume
in the laser gas mecium [Ref. 31.
The size of the active volwne was determined on the basis of ineasurements
of the electron beam cross section in the gas mediun and the lasing spot,
the cross section of the lasing spot corresponding to the electron beam cross
section in the appropriate direction. On the basis of these measurements
we can estimate the active volume of the laser: -8 � 2 cm3.
Fig. 1. Laser output energy
Elag (1), chemical efficiency
nchem (2) and efficiency rle
with respect to electron beam
energy invested in active
volume (3) as functions of
mixture pressure
N 150
~
ti
/00
m
tv
~
~ 50
/i s0o
' 700 n
500
17
u5
g0 PFa,mm Hg .
2 p,,, , atm
Measurements were made of the output energy of a laser on a mixture of
F2:02:H2:fle - 2:0.16:0.48:5, as wo-ll as ne and nchem at different pressures
of the mixture (Fig. 1). As the pressure is increased up to 3 atm, an in-
- crease is obaerved in the laser output energy while rle drops from 900% at
a pressure of 1 atm to 500% at 3 atm with a corresponding drop in nchem from
6.6 to 3.2%. It is interesting to note that the data obtained at atmospheric
pressure correspond almost campletely to the data found in Ref. 4 for a similar
mixture in a laser with longitudinal pumping by an electron beam of the same
energy.
The influence of the hydrogen content in the mixture was studied at atmos-
pheric pressure (the cliange in hydrogen pressure was compensated by changing
the heliun presaure in the mixture). The.results are shown in Fig. 2. Despite
the fact thaC increasing the ratio pH2/pF to ~ did increase the laser output
energy, subaequent experiments were done ior mixtures with pH2/pF since
increasing this ratio reduced the value of nchea as well as conaiaerably in-
creasing the presaure developed as a reault of the reaction, which often led
70
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to rupture of the foil and damage of the
- E 1a . rel>.u n its cell windows. Since the active volwne
of the laser retained a small fraction
h7 � of the electron beam energy even at a
.sa
yo mixture pressure of 3 atm, and a further
ll.s ! 4 //J ~l1 P~y/Pr
increase in the pressure of the mixture
zn ao so BOp,i,mm $g was limited by the mechanical strength
of the laser cell, an investigation was
Fig. 2. Laser output energy as a made of the possibility of increasing
; function of hydrogen content in the degree of initiation of the mixture
the mixture by increasing che density of the medium.
This was,done by adding sulfur hexafluo-
ride, a gas with high molecular weight that is also a donor of atomic fluorine
' [Ref. 41. The total pressure of the mixture (1 atm) was not changed, and
the increased pressure was compensated by reducing the heliiaa content in the
mixture. The resultant curves are shown on Fig. 3. Addition of 400 mm Hg
of SF6 led to an increase in output energy by a factor of 2.5.. Efficiency
nchem reached a very high value (-16X) . 0,1 D,15 0,5 0,1f E. J
Aowever, the increase in Ela$ and nchem ' E~
was accompanied by a drop in ne to 200%. n X
This can be attributed to a reduction in ~?50 z~,~ ehe~ms
the length of the chain reaction due:to /0100
~
a break in the chain in trimolecular reac- s~
tions of the type F(H) + 02 + M+ F(H) 02 + M, f50 1 yvo
where M is is a molecule of SF6, which is 2 p~p
quite effective in reactions of this type. 50 _~5
Despite the reduction in ne, the addition
of SF6 may be advantageous from the view- Fig. 3. Influence of SF6
point of increasing the specific energy content in mixture of
output, chemical efficiency, and also more F2:02:H2:SF6 = 200:16:48:pgg6
efficient utilization of beam energy. Be- on Elas (1), ne (2) and on
sidas, the presence of SF6 in the mixture nchem (3)
considerably increases its stability, and
experiments have shown that it reduces the pressure developed as a result
of the reaction, which in turn reduces the requirements for strength of struc-
tural components of the cell, especially the foil and windows.
By optimizing the cavity and increasing the accelerator beam current density
through a reduction in the thickness of the coupling foil, a laser emission
energy of 3.3 J was attained on a mixture of F2:02:H2:He:3F6= 200:8:48:100:400
mm Hg. Beam energy of 2.4 J was absorbed in the active volume oi the laser,
which corresponds to a concentration of 1.25�1017 fluorine ators per cm3 that
are formed during initiation at eF = 12 eV [Ref. 5]. The value of ne was 140%,
and rlchem " 22x. As the fluorine pressure in this mixture is increased to
400 mm Hg, laser output energy rises to 4 J. Measurements of laser beam di-
vergence made'for a cavity with base of 34 cm formed by an opaque mirror with
radius of curvature of 10 m and a flat output mirror gave a value of 4 mrad,
which is ten times the diffraction limit. Hawever, no experiments were done
on imporving the divergence as this was beyond the scope of our research.
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The results demonstrate the feasibility of getting very high specific energy
outputs of -400 J/liter at ne z 100X.
The use of an external magnetic field in transverse configuration of the ex-
periment gives high initiation of the active laser medium even at low electron
beam energy. The main impediment to increasing the pressure of working mix-
tures at present is the problem of increasing the strength of laser structural
components, whereas the active volumes of the laser can be increased both
by increasing electron beam energy and by enlarging the cross section of the
beam, which ie completely feasible considering the current state of accelerator
engineering.
= REFERENCES
1. Gerber, R. A., Patterson, E. L., Blair, L. S., Greiner, N. R., APPL. PHYS.
LETTS, Vol 25, 1974, p 281.
2. Patterson, E. L., Gerber, R. A., IEEE, Vol QE-11, 1975, p 642.
3. Bashkin, A. S., Orayevskiy, A. N., Tomashov, V. N., Yuryshev, N. N.,
KVANTOVAYA ELERTRONIKA, Vol 9, 1982, p 630.
4. Bashkin, A. S., Konoshenko, A. F., Tomashov, V. N., Yuryshev, N. N.,
KVANTOVAYA ELEKTRONIKA, Vol 6, 1979, p 2166.
5. Wilson, J., Chen, H. L., Fyfe. W., Taylor, R. L., Little, R., Lowel, R.,
APPL. PHYS., Vol 44, 1973, p 5447.
COPYRIGIiT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1982
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UDC 621.378.33
INFLIIFNCE OF STARTING INITIATION ON H2/F2 LASER PARAMETERS
Moscaw KVANTOVAYA ELEKTRONIKA in Russian Vol 9, No 3(117), Mar 82 (manuscript
received 7 Jul 81) pp 6A-632
[Article by A. S. Bashkin, A. N. Orayevskiy, V. N. Tomashov and N. N. Yuryshev,
Physics Institute imeni P. N. Lebedev, USSR Academy of Sciences, Moscow]
[Text] Parameters of a chemical H2/F2 laser are studied
as a function of the level of starting initiation of the
mixture by electron beam. It is shown that conditions of
maximizing efficiency do not coincide with conditions of
maximizing output energy.
The principal initial parameters that determine the characteristics of the
emission pulse of a chemical laser are mixture composition and initiation.
Knowledge of the starting initiation enables prediction of lasing parameters
as well as verification and correction of known theoretical models of chemical
lasers. Therefore it is of considerable interest to 5tudy the way that such
laser parameters as apecific energy output e1as, laser efficiency ne, chemical
efficiency rtchem and lasing pulse duration tlas depend on starting initiation,
- i. e. the concentration of fluorine atoms [F] at different pressures of working
mixtures. Unfortunately, the question of the influence of initiation level
on the lasing parameters of H2/F2 chemical lasers has been practically un-
_ touched in experimental research. We have carried out such research with a relativiatic electron beam for disso-
ciation of molecular fluorine. Since in the given case Tinit �Tlas, the in-
vestigation of the influence of [F] on lasing parameters becomes simpler and
clearer. The degree of dissociation of F2 was varied by changing the electron
beam current density wiCl: the insertion of inesh filters in the path of the
electron beam. The use of foil of different thicknesses to do this may cause
a change in the energy spectrum of electrons, and therefore is undesirable.
The general setup $nd parameters of the accelerator are given in Ref. 1. The
use of an extemal magnetic field prevented scattering of electrons and enabled
more accurate measurement of beam energy by an angle calorimeter. The active
volimme of the laser was -8 cm3. Based on calorimetric measurements of beam
energy absorption in gas media, the initiation energy was determined. The
initial concentration of atomic fluorine was calculated from these measurements,
assuming that 12 eV is used to produce a single fluorine atom [Ref. 2].
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Fig. 1. Laser emission energy Elas (1-3) and efficiency
ne (4-6) as functions electron beam energy invested in the
active volume: mixture:F2:02:He:'H2=200:16:500:48 (1, 4),
150:12:376:36 (2, 5) and 100:8:250:24 mm Sg (3, 6)
A mixture of F2:02:fle:H2 * 2:0.16:5:0.48 was selected for the experiments.
A mixture of similar composition had been studied previously. At a pressure
of 0.8-1 atm this mixture gave elas�100 J/liter at efficiency ne = 900% [Ref.
3]. Some decrease of hydrogen in the mixture, as ahown by the experiment,
increased r1chem with a slight reduction in energy output. At the same time,
there was Also a reduction in the posaibility of damage to structural components
of the laser by explosion of the mixture.
The experiments were done at a total pressure of 1, 0.75 and 0.5 atm. Fig. 1
shows both the laser emission energy and efficiency (ne) as functions of the
energy Ein invested in the active voltmne. An increase in the level of ini-
tiation increases the output energy of the laser, although there is a tendency
to saturation of this dependence in the region of high input energies. This
effect shows up most atrongly as the pressure of the working mixture decreases.
Fig. 2. Chemical eff iciency nchem
(curves) and lasing pulse duration
T1as (points) as dependent on the
electron beam energy invested in
the active volume of the laser
(notation as ia Fig. 1)
Tlas, �s
~o
3
I
2r
I
~
~
~
U
74
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nchem, %
~ 10
B
6
4
I !1
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Specific energy output of 155 J/liter is attained at the maximum possible
_ initiation in the given experiments on a mixture with pressure of 1 atm. It
is interesting that in the region of low values of initiation the lasing energy
is higher on mixtures of lawer pressure. Efficiency nchem behaves similarly
(Fig. 2). This may be due to the fact that the length of the chemical reaction
chain is greater for low-pressure mixtures at low-level initiation. Increas3.ng
the pressure of the mixture while retaining the concentration of initial centers
leads to an increase in acts of chain breaking, which in turn reduces the
; lasing characteristics.
Fig. 2 algo shows the dependences of lasing pulse duration at different pres-
- sures on the level of initiation of the mixture. They are characterized by
weak dependence of Tla$ on the pressure of the working mixture and are steep
' only in the region of low Ein. The behavior of ne (see Fig. 1) is character-
ized by a maximum with position that depends on the pressure of the working
mixture, and shifts toward increasing initiation levels for the higher-pressure
mixttires. The maximum values of ne for all mixtures used are 800-900X. The
specific energy output for a mixture at atmospheric pressure reaches 110
J/liter.
Since it was impossible to increase initiation by raising the current density
in the given experiments, we attempted to increase the initial concentration
of fluorine atoms by substituting sulfur hexafluoride for some of the helium
[Ref. 31. A specific energy output of elas = 400 J/liter was attained at rje = 140% on a mixture of F2 :02 :HZ : He I SF6 = 200 : 8: 48 :100 : 400 mm Hg. Here the '
energy input to the active mixture was 2.4 J. If thase results are compared
- with those of our research obtained on a mixture of gtmospheric pressure at
Ein > 0.075 J(see Fig. 1), it can be seen t'nat the product rleElas changes
' by a fsctor of only 1.7 as Ein is changed by a f actor of 30. This shows that
~ the optimum conditions of initiation are appreciably different for maximizing
ne and elas�
Thus our research has led us to the following conclusions. 1. With increasing
initiation energy there is an increase in output energy and chemical efficiency
of the laser, although there is a tendency toward saturation that is most
pronounced for low-pressure mixtures. 2. The optimum values of laser effi-
ciency ne are reached at certain values of initiation energy Ein, and as the
pressure of the working mixture is increased, the optimum region of Ein shifts
toward higher values. 3. At low initiation energies the efficiency of the
chemical chain reaction drops with increasing pressure of the working mixture,
leading to a reduction in net nchem and the laser output energy.
REFERENCES
1. Bashkin, A. S., Orayevskiy, A. N., Tomashov, V. N., Yuryshev, N. N.,
RVANTOVAYA ELERTRONIRA, Vol 9, 1982, p 628.
2. Wilson, J., Chen, H. L., Fyfe, W., Taylor, R. L., Little, R., Lowell, R.,
J. APPL. PHYS., Vol 44, 1973, p 5447.
3. Bashkin, A. S., Ronoshenko, A. F., Orayevskiy, A. N., Tomashov, V. N.,
Yuryshev, N. N., RVANTOVAYA ELEKTRONIKA, Vol 6, 1979, p 2166.
COPYRIGHT: Izdatel'stvo "Radio i svyaz l", "Kvantovaya elektronika", 1982
6610
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UDC 621.373.8.038.825.3
NEW PHOSPHATE GLASS FOR LASERS WITH HIGH EMISSION PULSE RECURRENCE RATE
Moscow RVANTOVAYA ELEKTRONIKA in Russian Vol 9, No 3(117), Max 82 (manuscript
received 1 Jul 81) pp 622-624
[Article by N. Ye. Alekseyev,A. K. Gromov, A. A. Izyneyev and V. B. Kravchenko,
Institute of Radio Physics and Electronics, US.SR Academy of Sciences, Moscc,w]
[Text] The paper gives some lasing characteristics of new
LGS-T phosphate glass based on Na-Al that has higher thermal
conductivity and heat resistance than knawn grades, as well
as a rather high coefficient of thermal expansion, making
it suitable as a base fpr synthesizing athermal glasses.
The suthors demonatrate absence of concentration quenching
of neodymium luminescence in such a base at a content of
up to 6 wt.X Nd203. Average lasing pawer of more than 20 W
at a frequency of 15 Hz is attained on active elementa with
0 8 x 100 mm. The glass has good technological character-
istics and can be produced in large volumes.
Active elements made of phosphate glasses are used in pulse-periodic lasers
due to high efficiency and low lasing thresholds. The possibilities for in-
creasing the lasing power taken from the active element are limited for a
predetercnined size chiefly due to thermal stability of the elementa, which
can be increased either by hardening [Ref. 1-31 or by improving the mechanical
characteristics of the glass and improving its thermal conductivity.
Use of the first method on heat-treated acti:e elements measuring 0 10 x 130 mm
made of GLS22 athermal glass has yielded a free l3sing power of 15 W[Ref. 31.
An output power of 8 W in the free lasing mode and 5 W in the Q-switched mode
has been attained on hardened active elements measuring (d 8 x 100 mm made from
LGS-I athermal glass on a frequency of 10 Hz [Ref. 4]. At the present time,
we have obtained a free lasing power of 96 W at a frequency of 1 Hz at ef-
ficiency of 3% on a hardened rectangular active element with size of
10 x 40 x 300 mm made of LGS-I glass. Aowever, the hardening of active elements
involvea an additional technological operation that increases cost. Therefore
the aecond method of improving thermal stability of glass is preferable for
high-power process lasers.
It is known [Ref. 51 that the thermal atability of an active element increases
with a reduction in the coefficient of linear thermal expansion a, which for
76
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phosphate athermal glasses lies in a range of (105-130)�10'"7 Ic'1 [Ref. 6, 71.
Laser glasses are known with lower values of a, including Li-Nd-La ultraphos-
phate glass. Lasing pawer of 15 W at frequency of 6-8 Hz has been attained
on an active element with 0 6.3 x 100 mm made of auch glass [Ref. 8]. In this
pAper we give some results of investigation of the laser characteristics of
active elements made of a new Na-Al glass that has elevated thermal conduc-
tivity [Ref. 9] and thermal stability. The value of a for glasses of this
type is (108-120)�10-7 K-l, and consequently this base (LGS-T glass) can be
used to make athermal glasses.
The glasaes were founded in platinum crucibles with volume of 3 liters with
bottom branch pipe; the concentration of Nd203 was 3 and 6 wt.y. Cylindrical
active elements with Nd203 concentration of 3 wt.X measured � 8 x 100 mm, and
with 6 wt.X (b Sx 100 mm (a= 108�10-' K'1). Nd3+ lumineacence 13.fetime
for both concentrations was 270-280 us, which shows the possibility for further
increasing the neodymium content in the glasa. The half width of the Nd3+
luminescence band for transition Fp- I1~ft is 18 nm. The lasing character-
istics of the glasses were studied in a monoblock quartz illuminator with
mirror coating. Pwnping was by an ISP-600 stroboscopic f lashlamp, capacitance
of the capacitor bank was 200 uF, the lamp and the active element were cooled
by a 0. 2% solution of K2Cr04 at a f lowrate of at least 30 liters/minute, pump-
ing energy in a pulse was 100 J. The transmission of the output mirror was
taken as the optimwn for each type of active element, and was 30% for an ele-
ment measuring 0 8 x 100 mm, and 50% for 0 5 x 100.mm. The average power was
measured by the IMO-2 instrument with wedge-shaped reflecting plate serving
as a beam splitter. The results of ineasurements of the output pawer as a
f.unction of the pumping pulse recurrence
W, watts rate are shown on the Figure (curves
' 1, 2). Given here for comparison are
~Ei ~~s the parameters of a hardened LGS-I
12: /62 glass active element 0 8 x 100 mm (curve
3). It can be seen that on a frequency
of 15 Hz at pumping energy of 100 J
we get an average lasing power of more
~than 20 W with the active element
0 9 B f, hertz 0 8 x 100 mm, and more than 15 W with
Radiation power as a function of 0 5x 100 mm. It should be noted that
the pwnping pulse recurrence rate� the active elements were not subjected
1--LGS-T glass (3 wt.% Nd203); 2-- to any hardening operations other than
LGS-T (6 wt.X Nd203); 3--hardened ordinary pickling, and that they were
LGS-I glass capable of operation at a pumping power
of 1.5 kW for an arbitrarily prolonged
time. As a rule, deterioration of output parameters was caused by sputtering
of the lamp electrodes and reduction of light output. The element with
0 5 x 100 mm was tested in the same illuminator with the LTI-PCh industrial
laser as the light source. Under these conditiona, an average emiasion power
of 9 W was attained at a lasing pulse recurrence rate of 50-100 Hz.
Thus, LGS-T laser glass is a quite promising material for use in lasers with
emission pulse recurrence rates at least up to 100 Hz and average emission
power of 100 W or more. In addition, it has good technological properties
and can be made in large volianes.
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REFERENCES
1. Mak, A. A., Mit'kin, V. M., Polukhin, V. N., Stepanov, A. I..,
Shchavelev, 0. S., KVANTOVAYA ELEKTRONIKA, Vol 2, 1975, p 850.
2. Mit'kin, V. M., KVANTOVAYA ELEKTRONIKA, Vol 8, 1981, p 484.
3. Buzmakov, A. G., Kovrishkin, V. S., Mit'kin, V. M., Polukhin, V. N.,
Stel'makh, M. F., Stepanov, A. I., Pozdnyakov, A. Ye., Chel'nyy, A. A.,
in: "Tezisy dokladov na Vtoroy Vst oyuznoy konferentsii 'Optika lazerov
[Abstracts of Reports to Second All-Union Conference on Laser Optics],
Leningrad, GOI, 1979, p 7.
4. Alekseyev, N. Ye., Gruzdev, V. V., Izyneyev, A. A., Kopylov, Yu. L.,
Kravchenko, V. B., Milyavskiy, Yu. S., Mikhaylov, Yu. N., Rozman, S. P.,
Fisher,.A. M., KVANTOVAYA ELEKTRONIKA, Vol 5, 1978, p 2354.
5. Mit'kin, V. M., Shchavelev, 0. S., Zheltov, V. B., OPTIKO-MEKNANICHESKAYA
PROMYSHLENNOST', No 9, 1978, p 39.
6. Avakyants, L. A., Buzhinskiy, I. M., Koryagina; Ye. I., Surkova, V. F.,
RVANTOVAYA ELEKTRONIKA, Vol 5, 1978, p 725.
7. Alekseyev, N. Ye., Gapontsev, V. P., Zhabotinskiy, M. Ya., Kravchenko,
V. B., Rudnitskiy, Yu. P., "Lazernyye fosfatnyye stekla" [Laser Phosphate
Glasses], Moecow, Nauka, 1970.
8. Avanesov, A. G., Basov, Yu. G., Garmash, V. M., Denker, B. I., I1'ichev,
N. N., Maksimova, G. V., Malyutin, A. A., Osiko, V. V., Pashinin. P. P.,
Prokhorov, A. M., Sychev, V. V., KVANTOVAYA ELEKTRONIKA, Vol 7, 1980,
p 1120.
9. Alekseyev, N. Ye., Volkonskaya, T. I., Izyneyev, A. A., Kravchenko, V. B.,
Kuliknva, I. N., Parfenova, L. S., Smirnov, I. A., "Tezisy dokladov Pyatoy
Vsesoyuznoy konferentsii 'Fiziko-khimicheskiye issledovaniya fosfatov'
- ('Fosfaty-81')" [Abstracts of Reports to the Fifth All-Union Conference
on Physical-Chemical Phosphate Research (Phosphates-81)], Leningrad, 1981,
part 1, p 10.
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_ UDC 621.385.325
PICOSECOND PULSE GENERATION IN ALEXANDRITE LASER IN 0.7-0.8 gm RANGE WITH
PASSIVE MODE LOCKING
: Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 9, No 3(117), Mar 82 (manuscript
received 6 Jul 81) pp 607-609
[Article by V. N. Lisitsyn, V. N. Matrosov, V. P. Orekhova, Ye. V. Pestryakov,
B. K. Sevast'yanov, V. I. Trunov, V. N. Zenin and Yu. L. Remigaylo, Institute
of Thermal Physics, Siberian Department, USSR Academy of Sciences, Novosibirsk;
Institute of Geology and Geophysics, Siberian Department, USSR Academy of
Sciences, Novosibirsk; Institute of Crystallography, USSR Academy of Sciences,
Moscow]
_ [Text] A report on picosecond pulse generation in an alexan-
drite laser in the range of 0.7-0.8 um on vibronic transitions
4 T2 4 A2+ hwphon in passive mode locking using saturable
absorbers DS1 and DTTS. The pulse duration with DS1 in
- the range of 0.725-0.745 Mn was 8 ps, and with DTTS in the
range of 0.75-0.775 gm 90 ps.
Of particular interest among new laser materials that have now been synthesized
is alexandrite BeA1204:Cr3+ [Ref. l, 2]. A distinctive feature of this materi-
al is lasing on vibronic transitions 4 T2 4A2 + hwphon, and as a consequence
the capability for continuous tuning of the lasing frequency in the region
of 0.7-0.8 um at room temperature [Ref. 2, 3]. Relatively low thresholds,
high efficiency with lamp pumping and a considerable increase in eff iciency
- when the active element is heated to 70�C, as well as the capability for con-
tinuous-wave operation or with a high pulse recurrence rate open up extensive
possibilities for its use in science experiments and engineering, and in par-
kicular for generating ultrashort pulses with tunable frequency.
As we know [Ref. 41, ultrashort pulses can be produced in a laser with mode
lockina lf the spectral width of amplification is wide enough. II1 alexanc~rite
the amplifi;.ation band with lasing on vibronic transitions is 100 nm. The
situation is analogous in organic dye lasers, which enables generation of
sub-picosecniid pulses with tunable frequency.
In this paper we are the first to report on frequency-tunable picosecond pul.se
generation in a solid-state alexandrite laser with passive mode locking by
' saturable organic dyes. ~
-1 79
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Fig. 1. Diagram of the
experimental setup: 1--
oscilloscope; 2--spectro-
graph; 3--FEK-09; 4--output
mirror; S--Lio filter; 6--
diaphragm; 7--active element;
8--cell; 9--opaque mirror;
10--correlation device for
measuring pulse duration;
11--photomultiplier; 12--
peak-to-peak voltmeter; 13--
two-coordinate chart recorder;
on the right is the correlation
function of the laser pulse in
vector generation of the second
harmonic
8p
The diagram of the experimental setup fox mode locking is shown in Fi. 1.
The active element with 0 6 x 70 mm with chromium concentration of 103.9 cm 3
and antireflection-coated end faces and an INP 5/60 f lashlamp were placed
in a monoblock quartz illwninator. The ultraviolet part of the pumping (shorter
than 350 nm) lying in the region of inactive absorption of alexandrite and
detrimental to the efficiency of laser operation due to the development of
- photochemical and thermal processes in the active element was cut off by an
aqueous solution of sodium nitrate and a thin pyrex tube so that laser ef-
ficiency during operation was not decreased. The axis of the active element
coincided with direction of alexandrite, and stimulated emission was
polarized along . The laser cavity with length of 0.5 m was formed by
an opaque mirror with radius of curvature of 3 m and a flat output mirror
- with tranamission Tr = 3%.
Measurement of the threshold characteristics of the active medium in single-
mode operation without frequency tuning or selectors showed that the threshold
of free lasing is 48 J, whi-ch coincides with the value given in.Ref. 2. Let
us note that the measurements made in our research were done on the crystal
used in Ref. 3. The high values of lasing thresholds in Ref. 3 can be attrib-
uted to the f act that the design of the illuminator for studying the tempera-
ture dependences of lasing characteristics did not give high pumping efficiency
or optimization of lasing parameters. In the illuminator used in our research,
at a pulse recurrence rate of 12.5 Hz and putnping energy of 80 J(TP = 250 us)
on wavelength of 70 nm the average output power was 1.1 W at output mirror
transm.ission Tr = 8%. The dependence of output energy on pumping energy is shown
in Fig. 2. In the mode of generation of the TEMooq mode with spectral selector
(Lio filter) and diaphragm of 0 1.2 mm, tuning was accomplished over a range
of 718-780 nm (Fig. 3).
It is to be noted that at high levels of excitation in the active element,
considerable thermally induced stresses arise that give rise to a heat lens.
The dependence of the effective focal length of the heat lers on t'Ze average
pumping power is approximated in our case by the expression F(Pav) = 1.5/P~v
[kW]. With consideration of this, the desj.gn of the optical caviCy was changed
80
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Eout, BJ
Pav , mW
30 70 � f20 EP 9 J
Fig. 2. Free lasing output energy of Fig. 3. Spectral dependence of free
alex,sndrite as a function of pumping lasing output power for laser with
energy for a= 750 nm: rod tempera- Lio filter at Tr = 3%
ture T= 50 (0) and 15�C (o)
to compensate for thermal effects. Induced thermal birefringence was dis-
_ regarded since it was less than the natural level of An = 0.002, which was
confirmed by polarization interference in crossed polaroids. As a result
of using the geometry optimum for our case (the concave mirror with radius
of curvature of 300 cm was replaced with a convex mirror with radius of curva-
ture of 200 cm), the output power was increased to 2.5 W.
Mode locking in the alexandrite laser was accomplished by two saturable ab-
sorbers DS1 and DTTS with relaxation times of 22 and 130 ps respectively
in ethanol solutions [Ref. 4]. The absorption spectrum of DS1 in ethanol
is shifted relative to the center of the lasing band of alexandrite (750 nm)
into the short-wave region, and has a maximum on 709 nm with tialf-width of
40 nm, whic:h makes it difficult to use this substance as a saturable abaorber
in the 700-750 nm band. Because of this, the DS1 absorption line was shifted
by replacing the ethanol with dimethyl sulfoxide by 8 nm into the longer-
wave region. DTTS in ethyl alcohol, despite its considerable relaxation time,
is admirably suitable with respect to absorption spectrum fc,r mode locking
in the long-wave part of the alexandrite lasing spectrum (>750 nm).
The cell with saturable absorber oriented at the Brewster angle was placed
in front of the opaque mirror; the dye solution was circulated at a rate of
10 liters per minute, enabling operation at a pulse recurrence rate of 12.5 Hz.
All the studies described below were done in this mode. k'avelength was tuned
by a Lio filter, and the TEMooq mode was isolated by a diaphragm. The end
faces of the active element were turned through an angle of 2-3� relative
to the axis of the optir,al cavity. Mode locking was matched by changing the
density of the saturating absorber and the pumping level. The envelope of
the pulse train and the mode locking were checked by an FEK--09 coaxial photo-
cell and an oacilloscope with overall time resolution of 3 ns. The average
duration of u1.trashort pulses in the train was measured by the correlation
81
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technique of vector genei�ation of the aecond harmonic in L1I03 [Ref. 4]. In
the two-threshold mode [Ref. 5] with DS1 in dimethyl sulfoxide, the duration
of the pulse train was 200-300 ns with average duration of a pulse in the
train of 20 ps; in the mode close to autostabilization [Ref. 61, in a some-
what modified cavity geometry, where shaping was done from a series of free
- lasing spikes, the average duration of the pulse was shortened to 8 ps, and
con3iderable modulation of the train envelope was observed. With DS1, tuning
was accomplishz.d in the range of 725-745 nm at a spectral width of 0.2 nm.
The absence of structure in the emission spectrimm at high contrast of the
correlation curve shows that there were no additional pulses on the axial
_ period [Ref. 7]. On Fig. 1 we have shown the correlation curve for generation
- of the second harmonic on a wavelength of 730 run, and have indicated the
pulse duration as adjusted for a gaussian profile.
With use of an ethanol solution of DTTS, ultrashort pulses with 90 ps duration
were generated in the 750-775 nm range. Average output pawer of the laser
with DS1 on a wavelength of 735 rnn was 20 mW. When the temperature of the
active element was increased to 5.0�C (checked by a differential thermocouple
on the rod), mode locking became more stable due to increased gain of the
active medium.
There is no doubt that when the concentration af active centers in the alexan-
drite matrix is increased, we can count on a considerable increase in the
output power of the laser in mode-locked operation.
Osr research was not aimed at getting ultrashort pulses in the isolated pulse
mode at high pumping energies. Our principal attention was concentrated on
the feasibility of operation at a high pulse recurrence rate (up to 100 Hz),
enabling active use of the alexandrite laser both in spectroscopic work and
in technological devices.
REFERENCES
1. Bukin, G. V.~ Volkov, S. Yu., Matrosov, V. N., Sevast'yanov, B. K.,
Timos;zechkin, M. I., KVANTOVAYA ELEKTRONIKA, Vol 5, 1978, p 1168.
- 2. Walling, J. C., Peterson, 0. J., Jenssen, H. P., Morris, R. C., 0'Dell,
E. W., IEEE J., Vol QE-16, 1980, p 1302.
3. Sevast'yanov, B. K., Remigaylo, Yu. L., Orekhovs, V. P., Matrosov, V. N.,
Tsvetkov, Ye. G., Bukin, G. V., DOKLADY AKADEMII VALTK SSSR, Vol 256, 1981,
p 373.
~ 4. Shapiro, S., ed., "Sverkhkorotkiye svetovyye impul'sy" [Ultrashort Light
Pulses], Moscow, Mir, 1981.
5. Zherikhin, A. N., Kovalenko, V. A., Kryukov, P. G., Matveyets, Yu. A.,
Chekalin, S. V., Shatverashvili, 0. B., KVANTOVAYA ELIICTRONIKA, Vol 1,
- 1974, p 377.
6. Milenkevich, A. V., Sawa, V. A., Samson, A. M., ZHURNAL PRIKLADNOY
SPEKTFtOSKOPII, Vol 25, 1976, p 618.
82
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' 7. Sychev. A. A.. TRUDY FIZICHESKOGO INSTI'1'UTA IMENI P. N. LEBEDEVA AKA])LMII
- NAUK SSSR, Vol 84, No 3, 1975.
COPYRIGHT: Izdatel'stvo "Radio i svyaz "Rvantovaya elektronika", 1982
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UDC 537.876.23.029.7:551.510.5
ESTIMATING POSSIBILITIES FOR USING PHASE CONJUGATE ADAPTIVE SYSTEMS TO COMPEN-
SATE LASER BEAM THERMAL DEFCCUSING
Moscow RADIOTEKHNIKA I ELF�KTRONIKA in Russian Vol 26, No 11, Nov 81 (manuscript
received 24 Mar 80) pp 2334-2341
[Article by V. V. Vorob'yev]
[Text] Based on representation of the action of a nonlinear
medium as an extended aberration-free heat lens, the author
calculates the process of compensating defocusing by phase
conjugate adaptive systems. Use of such systems is effective
only in.the case of weak thermal nonlinearity when the length
of the nonlinear heat lens is less than the characteristic
length of thermal self-stress.
1. Recently there has been extensive discussion of the question of feasibility
of compensating the distortions of laser beams that arise on propagation in
the atmosphere by using adaptive coherent optics systems [Ref. 1-4]. Generali-
zation of the results of numerical calculations and experimental research
has led to the conclusion [Ref. 1] that these systems may satisfactorily cor-
rect 3istortions introduced by turbulence, but are poor at correcting thermal
defocusing. An exact solution for the problem of compensating thermal defocus-
ing in the real atmosphere can be found only by numerical methods, and in
the general case this requires repeated solution of a four-dimensional problem
of beam propagation to the target and propagation of the reflected wave to
the reception aperture. This does not permit calculations with sufficient
accuracy and over wide changes in parameters. Therefore it is advisable to
consider simple models of propagation and compensation that give an analytical
solution of the problem. One such model consists in replacing the action
of the nonlinear medium on beam propagation by the action of thin aberration-
free lenses located at different diatances from the input aperture [Ref. 5].
It has been demonstrated that it is not always possible to compensate even
the defocuaing of such lenses. The given model has the disadvantage that
the results depend strongly on the position of the nonlinear thin lenses on
the propagation path. It is not clear where to place them in the case of
- an extended nonlinear medium. In this paper, an investigation is made of
the possibflities of using a phase conjugate system to compensate for defocus-
'ing by an extended heat lens. It has been shown by various examples that
compensation is impossible when the extent Z of the nonlinear medium is greater
than the characteriatic length LT of thermal self-stress.
84
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0
z
Fig. 1. Qualitative pattern of correction: Z--thickness
of nonlinear layer; R+ Z--distance to the target; F--initial
radius of curvature of the wavefronti F+ A--distance at
which focusing to correetion occurs; F--radius of curvature
of the reflected wave
2� The following problem is considered (see Fig. 1). A beam with radius
of curvature of the phase front F on boundary z= 0 is incident in the direction
of the z-axie on a nonlinear medium ocCUpying layer (0, Z). Due to thermal
nonlinearity, the distance at which the beam is focused behind the layer (if
such is possible) will differ from F by an amount A. A diver in wave
passing
through the nonlinear layer is reflected from a target located at distance
R from the layer. The reflected wave will have radius of curvature -F. If
there were no change in perturbations of the index of refraction in the layer
with time, focusing on the target could be realized by changing the radius
of curvature of the incident wavefront from F to F. However, in a nonlinear
medium, a change in F leads to a change of the medium, and as a result, when
F is changed to F the focal point may shift away from the target. Our task
is to determine conditions under which repetition of this procedure leads
to focusing on the target, and to find the number of repetitions of the pro-
cedure (or the time interval required to adjust focusing) to get the desired
focusing accuracy.
Assuming that the thickness of the layer Z is much less that the diffraction
length Lg= kct2, where k is the wave number, a is beam sizz, and disregarding
attenuation of intensity due to absorption, we will describe beam propagation
in the layer by the equations
2 L(P 8~ '~(01~) �
(2) i � v,.(Pv1J+e1mJ' 0,
where ~ is the eikonal, J is the light field intensity, eH is the nonlinear
part of permittivtty, which in the general case is some functional of J(x, y,
z, t),
85
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3. i.et uR first consider cumPensution in a mediwn with nonlinearity of the
f orm
Eu
and intensity J may depend parametrically on time�
Where the coefficient e2
imate the integral
This dependence may approx
ae=r J(x,U,z,t~)dt'
~y~ ea~~)~eT PCv O
in time (t(8J/8t) �J)� In this case,
when intensity J changes slowly of simplicity' a dependence of form (3)
E2= -(ae/aT)�(at/pcp). For reasons see Ref. 2, 5). Its
thermal self -sTOblemsrwill be (discussed below.
is often used in tion
applicability to compensa p
In the aberration-free approximation t
[Ref. 6], solution of eqhase~front,and the (2) reduces to soluti theecase1eHS cwillurv
form
beam radius a, which in
_ 4
, s ao a'--aS,
. ~g~ . S -S LT.a. +
where LT=ao/ie,2~J0, ao is beam radius, Jo is intensity at the center Af the beam at the input of the medium. The initial curvature So of the phase front
R 1 on the
may be arbitrary. We determine So from the ~ keStplace on the,target. T~
output of the layer, i. e. so that focusing
solution of equations (5) will be
zz
(6) a= (y) aae' [ (1-SpZ) + LT7j'
z Z
' S(z) = u~)\ S,-So z-
7
From condition S(Z) = R-1 we get
(7)
21+R (1Ty 1-41z (R+l) Zli'2 Lz
SO � 2l (l+R)
1a 7) implies that focusing at distance R behind the layer is possible if
Formu (
l R+l ` ~
(8) Lr j{
Let us compare this condition with the analogous expression
_ R, (R-I-I) ~
(9) . 4sN nA-1-n,
obtained in Ref. 5 on the basis of a thir.-lens model; R1 is the distance to
he nonlinear lens from the transmitting aperture; SH is the lens power, which
t
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' as iroplied by (6) is equal to SH= z/LT. At Z�R and R1= Z, i. e. when the
thin lens is located at the end'of the nonlinear mediun, there is insignificant
dtfference between (8) and (9).
- Let us note that condition S(Z) = R-1 may be satisfied at two different values
of So. It is natural that condition (8) is necessary for convergence of the
compensation scheme. However, in the general case it is insufficient. To
demonstrate this, it is necessary to calculate the compensation in 3ccordance
with the scheme described in the previous section.
The change in curvature of the phase front S of the wave from a point source
situated at distance R from the nonlinear mediwn is described by the first
equation of system (5) with given function a(z)
a`
(10) 2=- o(
_ Z~~ \z)
and boundary condition g(Z) - -R-1. Let us make the substitution of variables
S=-b'/b in (10). Then for function b(z) we get the linear equation
(11) b�- a�4 U=0.
T77
- Considering that function a(z) is a solution of the equation
a`
a"- � =0
LTZa, ~
the solution of equation (11) can be written as
where (12) b=J(z) [C,+C, arctg g(z)
-
f(so, Z)-a(so, z) /ao; g(So, i) =-LTCf (so, Z)s(So, z)J ;
Functions a(z) and S(z) are defined by formulas (6); C1, C2 are arbitrary
constants. Considering condition S(Z)= -1/R, we get
(13) S(0)=-5,- f (1)[1-RS(1)] . R+Lrf (l) [1-RS(l) ] (ttrctg(SoLr) + urctg(g(I) ) ~
The phase conjugate compensation scheme corresponds to ar iteration scheme
for finding solution S(0)= -So of equation (13). Fig. 2 gives curves for
Fig. 2. Qualitative dependence of Che -s
curvature S(0) of the phase front of
the reflected wave on curvature S(0) 1
of the incident wavefront at Z/LT >k
(1), Z/LT= k (2), Z/LT 3-4 these quantities (in the cw and pulse-periodic modes)
reach their "quasi-steady" level in the general case, which is proportional
to Io.
3. The resultant expressions enable determination of the laser beam param-
eters Io, A, Ko, t, T, SQV that typify the stage of elastic behavior of the
material characterized by total recovery of the initial surface state when
the laser beam is switched off. However, in some cases with cw and pulse-
periodic laser action, the thermal deformation of an optical surface becomes
- impermissibly large (W >X/20). Accounting for deformations is extermely
106
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important for such laser systems as quasioptical transmission lines, tele-
- scopes, stable and unstable optical cavities, focusing systems.
4. This analysis enables us to determine the laser beam inteneity at which
the material goes into the inelastic region as a result of stresses that arise
during exposure that exceed the yield stress of the material in the cw and
pulsed modes, or that exceed the f atigue limit in the pulse-periodic mode.
The values of the maximum intensities lXi20, lQt, ITDn [Tnn is the melting point]
with cw laser action are
ITna ~ lk V Ko Tnal (Y TA), IaT = 241f Ka OT/ [If3n (1 ; v)AG aTj,
. 11/20 = XKoXco, / [20 (1 + v) aTA 1n (2YFO)I. (20)
If the physical characteriatics of inetals satisfy the inequality
a1/1(1-F'v)GaTTnnl Y3n Ko Xc0, 0I40 QT, (22)
then 1x!20l (for reference. G/QT - 103) ,+the quantity
/rnn~ I oT, and for time
- ti> 32,co,G/[400 n& (1-v)2 aT], (24)
in addition 1aT>lxco,/20�
In the case of pulse-periodic action on the solid surface, the maximum inCen-
sities are determined from the relation .
- (jHn)-1_l/SQVljenp1l-j + iMn)-1' (25)
_ where Iyenp is determined from (20), and Iy Mn is determined from (23).
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As a result of the unsteady, cyclically repeated stressed state that arises
with irradiation of the material, irreversible fatigue changes may occur if
- the amplitude of oscillations of one of the components of the heat-stress
tensor Qik exceeds the fatigue limit Qy~T as determined for crnapression or
bending respectively.
The expressiens for limiting iatensities determined for each of the components
�ik:
~y~T Y Ko Y n
lYcT(Qr') - ~ ~
acr (l -4-v) 3P01
- v) XQyc 1f Ko 2 2e , pycT / larz) = - ,qG a,i, 0 y) /'pl (26)
' ~a ~ v) Xayct ~Ko 9 - (FO ~ .
vcr zz qQ xr (1 y) 8~/ n 1
If the duration of an individual laser pulse is such that 0.02 - 81/(5127re) ~
F01 RI or 2I(2Pgp) +RI1~ I2+RI,
I( 2P p I2 I( 2p3
) + I2 , since according to the data of Ref. 24-26 the cor-
responding characteristic half-reaction times (tRi* a 1/kRi* [I(2P3/2))= 15 us
and ti2 = 1/KI2 [RI][I(2P ~2)J = 15 us) are an order of magnitude greater than
ttnax� Since autophotometry is fundamentally approximatie (up to �507') as a
method of determining absolute pumping rate, we have disregarded (averaged
out) the spikes on curve 2 of Fig. 2, and have not made corrections in the
deter.mined values of v~ for the possible understatement (up to 15% [Ref. 27, .
28]) of the measured intensity of stimulated transitions due to losses of
stimulated radiation within the cavity, or for possible overstatement (up
to 20-30%) of the intensity of stimulated transitions due to the dark reaction
R+I(2Pp) -hT*RI. (Rate constants kRI=10'll cm3/mole�s [Ref. 24, 251, which
leads to a characteristic half-reaction time of tRI = 1/kRi[I(2P 3p)] =1 us,
which is comparable with tmax)�
Under the conditions of our experiments for reactions R+ RU R2 and
R+ I(2PV2) -~U RI, characteristic half-reaction times tR2 a 1/KR2[R] and
tRi =1/kRi[I(2P V01 do not exceed 1 us (see KR and kRi in Ref. 24, 25).
Therefore in the region up to 1200-1300 K, anaiytical expression (45) from
Ref. 29
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e
- s
T(t)=T"+ Ra 1-eXp Tip
(t)dt gives the same law of temperatsre rise in the photolyzed iodide as the (funda-
mentally more exact) differential expressions of type (4) from Ref. 30 or
(14) from Ref. 31. The rise in temperature of the working gae in Table 2
was calculated by formula (1) for Q= 4 eV and CC4F9I = 42 cal/K mole (see Table
1) (Q = 4.0 t 0.2 eV is the amount of energy converted to heat in a single act
of photodisaociation as calculated on the basis of thermodynamic data [Ref.
32-341 with consideration of the fact thgt the characteristic pumping time
tp~ 45 us is nearly two orders of magnitude longer than the charac-
teristic times tR2= tRi = 1 us). Time t~d of thermodissociative lasing cutoff
was calculated by formula (67) from Ref. 29 on the basis of approximation (1)
for rate constant ktd = A exp (-AE/kT) of thercnal dissociation
C4F9I;C4F9+I(2Pp). (2)
where we have assumed AE/k = 23650 R and A= 1013-1015 s-1 in accordance with
current concepts [see Ref. 32-35].
It can be seen from *_he data of Table 2 that the experimental valuea of time
tc of lasing cutoff and especially time tmin of the appreciable drop in lasing
power are several times lower than the theoretical value of t~d. For the
less expoitential curves 4 and 5 of Fig. 2, tmin s 7 us, although it nearly
coincides with the time tmin = 8 us, where the pumping pulse has a slight mini-
miaa, but lasing power G(Imin) is only 11-13X of G(tmaX), whereas the pumping
rate Q�(tmin) is 50% of vo(tmax). Therefore, just as in Ref. 6, 36, we have
cotne to the conclusion that in our experiments the rise in temperature of
perfluorobutyl iodide undergoing flash photolysis has an effect on the infen-
sity of atimulated emission and chemical reaction rate that ie much stronger
than directly implied by formula (45) from Ref. 29, or by formulas (4) from
Ref. 30 and (14) from Ref. 31. It was ehown in Ref. 16 and 17 that the reason
f or such intensified action of temperature increase (leading to acceleration
of quenching chemical reactions and considerable attenuation of lasing power
f ar before tc) is to be found in radial gasdynamic oscillations of the working
gas of the photodissocttation iodine laser caused by the temperature gradient
that arises in the iodide undergoing photolysis. Actually, in a first approxi-
mation in each element of volume of the working gas undergoing oscillations,
density fluctuations, are accompanied by temperature fluctuations around an
average value (1). Since the rates of strongly endothern.al (e. g. (2)) or
exothermal reactions are exponentially (sharply nonlinearly) dependent on
temperature, all processes of pyrolysis of iodide take place at a rate that
corresponda to a noticeably higher tsmperature than (1). In a second approxi-
mation, corrections can be made in (1) that account for absorption and release
of heat in the periodically accelerated chemical resctions and so on. Hwever,
we did not undertake a quantitative accounting for the temperature contribu-
tion of gas dynamics to the reduction in amplitude of fluctuations of lasing
power or a comparison of the contribution 3ue to periodic misalignment of
the optical cavity as a consequence of fluctuations of optical density of
the gasdynamically oscillating gas. (The development of radial optical
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TABLE 3
Theoretical and experimental parameters
of radial oscillations of C4F9I laser
Cil
I
l~lE 013
1
P. cr
r. cr
�
a[RJ2�
-
Q/C~
so.
z,,
s;,
o.
Y~ ~
~N
r.
�e
11s
�8
us
4
1,05
0,26
0,160
i,M
716
50
34
22
l6tl
4.80
2
1,05
0,26
O,l6l
2,83
7,5
50
35
24
16t1
4,14
*First period
**Experimental value of first period of radial oacilla-
tions; p ie the inside radius of the laser cell
inhomogeneities in the working fluid of photodiseociation iodine lasera was
first experimeatally observed in Ref. 37, and the poasible gasdynamic nature
of such inhomogeneities was first pointed out in Ref. 20).
In coptraat to preceding papera [Ref. 6, 16], the uae of a grid of return
wires in this paper led to irregularity of pumping radiation pulse shape,
and consequently to additonal irregularities of the pulses of stimulated emis-
sion. However, all three pulses of atimulated emission shown on Fig. 2 show
a first appreciable minimwn at t= 7-8 us corresponding to the phase of maximwn
compression of the working gas on the axis of the cell, a second miniminn for
t m 15-17 us corresponding to the phase of maximum departure of the working gas
frrnn the axia of the cell and (on curve 2) a third minimum for t - 2 3-25 Us
corresponding to the second maximwa of compresaion of the working gas oa the
axis of the cell.
Camparison of the experimental (by data of Fig. 2) and theoretical parameters
of radial oscillations o'E the C4F9I laser is summarized in Table 3. The
sense of ro gnd a2 is given in Ref. 17. The valuea of the zeroth (TO), f irst
(T1) and second approximations of the first period of radial oscillations
of the iodide undergoing photolysis were calculated by formulas (9), (10)
and (11) respectively from Ref. 17. Since To, T1, T2 canverge to the [experi-
mental value] T3, it can be expected that exact solution of the corresponding
equations of gas dynamica will yield total agreement between the theoretical
_ and experimental valuea of the period of oscillations. Thus the experimental
data of Fig. 2 are described by the very aimple theory [Ref. 17] of nonlinear
radial oscillations of the gae undergoing photolysis, so that we can take
it as proven that there is a significant contribution of radial oscillations
of the working gas to attenuation and cutoff of lasing of the C4H9I laser
under the conditions of our experimente.
REFERENCES
1. Kasper, J. V. V., Pimentel, G. C., APPL. PHYS. LETTS, Vol 5, 1964, p 231;
Kasper, J. V. V., Parker, J. H., Pimental,' G. C. C., J. CHEM. PHYS.,
Vol 43, 1965, p 1827.
128
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2. Basov, N. G., PRIRODA, No 6, 1978, p 26.
3. Hohla, K., Kompa, K. L., APPL. PHYS. LETTS, VoZ 22, 1973, p 177.
4. Antonov, A. S., Belousova, I. M., Gerasimov, V. A., Danilov, 0. B.,
Zhevlakov, A. P., Sapelkin, N. V., Yachnev, I. L., PIS'MA V ZHURNAL
TEKHNICHESKOY FIZIRI, Vol 4, 1978, p 1143.
5. Danilov, 0. B., Yelagin, V. V., Emdina, I. M., Yachnev. I. L., ZHURNAL
TEKHNICHESROY FIZIKI, Vol 35, 1975, p 1923.
6. Skorobogatov, G. A., Seleznev, V. G., Maksimov, B. N., Slesar', 0. N.,
ZHURNAL TE[CHNICHESROY FIZIRI, Vol 45, 1975, p 2454.
7. Swingle, J. C., Turner, C. E., Murray, J. R., George, E. V.. APPL. PHYS.
- LETTS, Vol 28, 1976, p 387.
8. Hohla, K., Kompa, K. L., Z. NATUAFORSCH., Vol 27a. 1972, p 938.
9. Pirkle, R. Y., Davis, C. C., Mcfarlane, R. A., CHEM. PHYS. LETTS, Vol 36,
1975, p 305.
10. Zalesskiy, V. Yu., Kokushkin, A. M., KVANTOVAYA ELIICTRONZKA, Vol 3. 1976,
p 1501.
11. Birich. G. .I., Drozd, G. I., Sorokin, V. N., Struk, I. I., PIS'M V ZHURNAL
EKSPERIIHENTAL'NOY I TEORETICHESKOY FIZIKI, Vol 19, 1974, p 44.
12. Andreyeva, T. L.. Birich, G. N., Sorokin, V. N., Struk, I. I.,
KVANTOVAYA ELERTRONIRA, Vol 3, 1976, p 1442.
13. Tarfons, R., U. S. Patent No 3234294, 20 Dec 62; Rebfsdat, S., Sahuierer,
E., West German Patent No 1915395, 26 Mar 69.
14. Skorobogatov, G. A., Romarov, V. S., Seleznev, V. G., ZHURNAL
TEKHNICHESKOY FIZIRI, Vol 44, 1974, p 1996.
15. Volkov, V. N., Zubarev, I. G., Sorokin, V. N., ZHURNAL PRIKLADNOY
SPERTROSKOPII, Vol 7, 1972, p 735.
16. Skorobogatov, G. A., Komarov, V. S., ZHURNAL TEKHNIC73ESKOY FIZIKI, Vol 47,
1977, P 429.
17. Skorobogatov, G. A., ZHURNAL TEKHNICHESKOY FIZIKI, Vol 47, 1977, p 1551.
18. Dymov, B. P., Skorobogatov, G. A., ZHURNAL TIICRNICHESKOY FIZIRI, Vol 48,
1978, p.124. '
19. Belousova, I. M., Gorshkov, N. G., Danilov, 0. B., Zalesskiy. V. Yu.,
Yachnev, I. L., ZHURNAL EKSPERIMENTAL'NOY I TEORETICHESROY FIZIRI, Vol 65,
1973, p 517.
129
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20. Golubev, L. Ye., Zuyev, V. S., Katulin, V. A., Nosach, N. Yu., Nosach,
0. Yu., "Rvantovaya elektronika" [Quantum Electronics], edited by
N. G. Basov, No 6(18), 1973, p 23.
21. Ishii, S., Ahlborn, B., J. APPL. PHYS., Vol 47, 1976, p 1076.
22. Alekhin, B. V., Borovkov, V. V., Lazhintsev, B. V., Nor-Arevyan, V. A.,
Sukhanov, L. V., Ustinenko, V. A., KVANTOVAYA ELEKTRONIKA, Vol 6, 1979,
p 1948.
23. Ramarov, V. S., Seleznev, V. G., Skorobogatov, G. A., ZHURNAL
TEKHNICHESKOY FIZIKI, Vol 44, 1974, p 875.
- 24. Skorobogatov, G. A., Slesar', 0. N., VESTNIK LENINGRADSKOGO UNNERSITETA,
No 4, 1979, p 39.
25. Seleznev, V. G., Skorobogatov, G. A.,.VESTNIK LENINGRADSKOGO UNIVERSITETA,
No 10, 1978, p 77.
26. Dymov, B. P., Skorobogatov, G. A., Khomenka. V. Ye., Shchukarev, S. A.,
ZAURNAL OBSHCHEY KHIMII, Vol 47, 1977, p 84b:
27. Zuyev, V. S., Rorol'kov, R. S.., Nosach. 0. Yu., Orlov, Ye. P., KVANTOVAYA
ELEKTItONIKA, Vol 7, 1980, p 2604
28. Nosach, 0. Yu., Orlov, Ye. P., Preprint No 7, Lebedev Physics Institute,
Moscow, 1919.
, 29. Skorobogatov, G. A., VESTNIK LENINGRADSKOGO UNIVERSITETA, No 4. 1970,
p 144.
30. ZALESSKIY, V. Yu., Moskalev, Ye. I., ZHURNAL EKSPERIMENTAL'NOY I
TEORETICHESKOY FIZIKI, Vol 57, 1969, p 1884.
31. Zalesskiy, V. Yu., KVANTOVAYA ELEKTRONIKA, Vol 1, 1974, p 1819.
32. Laurence, G. S., TRANS. FAR. SOC., Vol 63, 1976, p 1155.
33. Tachunikow-Roux, E., J. PAYS. CHENI., Vol 69, 1965, p 1075.
34. Grygorcewicz, C., Laurence, G. S., J. PHXS. CHEHi., Vol 72, 2968, p 1811.
35. Vedeneyev, V. I., Kibkalo, A. A., "Konstanty skorosti gazofaznykh
monomolekulyarnykh reaktsiy" [Rate Conatants of MonamolecuYar Gas-Phase
Reactions], Moacow, Nauka, 1972.
36. Seleznev, V. G., Skorobogatov, G. A., Komarov, V. S., ZHURNAL OBSHCHEY
RHIMII, Vol 44, 1974, p 1293.
37. Belousova, I. M., Danilov, 0. B., Sinitsyna, I. A., Spiridonov, V. V.,
ZHURNAL EKSPERIMENTAL'NOY I TEORETICHESKOY FIZIKI, Vol 58, 1970, p 1481.
COPYRIGHT: Izdatel'stvo "Radio i svyaz l", "Kvantovaya elektronika", 1982
6610
CSO: 1862/133
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72
OPTICS AND SPECTROSCOPY
UDC 551.466.3:535.31
THEOP.Y OF OBSERVATION OF UNDERWATER OBJECTS THROUGH WAVE-COVERED SEA SURFACE
Moscow IZVESTIYA AKADEMII NAUK SSSR: FIZII:A ATMOSFERY I OKEANA in Russian
Vol 18, tJo 4, Apr 82 (manuacript received 9 Dec 80, after revision 6 Apr 81)
PP 408-415
[Article by S. V. Dotsenko, Marine Geophysical Institute, Ukrainian Academy of
Sciences]
[Text] Abstract: The article gives a theoretical
analysis of the distortions introduced
by the wave-covered sea surface in the image
of underwater features observed from the at-
mosphere. It is postulated that the spatial
structure of both observed features and
waves has a random character. The quality of
observation is evaluated using the magnitude
of the ertor in measuring the spatial lumin-
osity of the feature. It is shown that there
is an optimum relationship between the stat-
istical characteristics of the distribution
of luminosity and waves and the parameters
of the measuring instrument ensuring a mini-
mum of this error.
The possibility of observing underwater features from the atmosphere is depend-
- ent on their contrast, degree of turbidity of the water and atmosphere, super-
posing of the brightness of sir haze, light scattered in the sea and brightness
- of the water-air discontinuity on the image [1].
We will investigate the joint influence exerted on transmission of the image of
underwater features by the wave-covered sea surface and the averaging effect of
the measuring in-strument, neglecting other interfering factors, allowance for
which is poesible independently.
A problem similar in its formulation was solved in [1], where the influence of
the sea surface on image transmission was studied by an analysie of the scat-
tering function, the energy distribution in the edge image and the frequcncy
contrast of the transfer funetion. In source [2] a study was made.of the irnage
transfer of a point through a oae-dimensional sinusoidal wave and formulas were
given for computing the displacement of a point and the blurring of an ob3ect
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!J
with an increase in the exposure. An approximate model of image transfer
through the wave-covered discontinuity of two media with different refractive
indices was described in [3], where the author determines the multipoint stat-
istical characteristics of the brightness image of a self-luminescent object
or feature observed through the wave-covered discontinuity.
A feature of this study.is that it examines the observation of random spatially
elongated features using optical radiation detectors which perfora+ spatial aver-
aging of the image. Many natural formations on the bottom and in the water lay-
er can be modeled by features of the mentioned structure whose investigation
is possible by optical methods. The spatial averaginf3 of the received image
is a property of any real radiation detector. Accordingly, the combination of
such initial premises makes it possible to obtain research results suitable for direct practical application. The quality of observation is evaluated us-
ing the mean aRuaxe error between the initial and measured luminosity distrib-
utions [4]. It is shown that it is dependent on the choice of the degree of
averaging and is the highest when it has a finite value. Here we will examine
observations at the nadir as ensuring minimum image distortion [1].
In order to simplify the analysis we will examine a problem in which the ob-
ject of ineasurement and waves are assumed to be one-dimensional (FiA. 1).
'A
Z
O" ~ Y~(B) N'
I
B
al
Ha B
I
� ~ ~a) ~ U
~ C LI
~
I
Hs ~
I~ ~
a~ s~
~ o e
~L
C'
AI x
Fig. 1. Diagram explaining derivation of principal.
relationships.
Retaining the physical essence of the analyzed phenomena, such an approach makes
it relatively simple to obtain final numerical results. The x-axis of the mean
level of the wave-covered surface is stipulated in'the figure by the point 0.
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The atmosphere is situated above it and the water below. At the depth IiW below
. the sea surface there is a diffuse self-lumir.escent ob3ect to be observed, ex-
tending in the direction of ttia x-axis, whose spatial distribution of luminos-
ity is described by the random function f(x).At the height Ha above the sea
surface at the point 0" there is adetector of optical radiation whose optical
axis is directed to Che nadir. The difference in the level of the wave-covered
surface from the mean is described by a centered random function of the space
coordinate 4(x).
An analysis of the pracess of observation of an underwater feature will be
made on the basis of the premises of geome+trical optics without allowance for
the absorption gnd scattering of light in the water. The ray emerging from
Ehe point A of the obaerved feature and rECeived by the detecror at the point
0" travels the following path. It is propagated in the water medium at the
angle $0 to the vertical BB' to the puinr Q at the water surface. The tangent
. CC' to the sea surface at this point i.s slanted to the horizontal at the angle
W. , whereas the normal NN' to this surfaca also is defl2cted by the angle cx
from the vertical BB'. At the point Q there is refraction of the ray and it
- emerges from the water at the angle A to the normal NN'. The detector at the
point 0" picka it up arriving at the angle 19 to the vertical.
Since the (x) surface ia curvilinear and random, the picture picked up by
the instrument differs from the f(x) function describing the distrihution of
luminosity of the observed object and this differenc4 has a random character.
We will find the error introduced by the wave-covered sea surface and instru-
ment to the image sensed by the latter and we will evaluate the limits of ap-
plicability of such a method for obsetving underwater ob,jec:ts. For this pur-
pose we will first obtain the correlation between.the output signal Y of the
measuring instrument and the investigated ob3ect f(x).
We will find the position of the point A, situated on Che observed ob3ect, which
is sensed by the instrument as visible at the angle e to the vertical. The seg-
ment LQ is the 4(x) value. Accordingly, the abscissa of the points L and l3 is
xi-[H.-t (=i) ]tge� (l)
Since the straight line CC' is the tangent to the ; (x) curve at the point
with the abscissa x, then
1 ~g Q~ dC (x) I s~1 (XI) �
~
It follows from Fig. 1 that the distance of the point A from the point B is
equal to x3 - [liw +4 (xl)] tg.(p . Accordingly, the abscissa of the point A is
z2-X1-i-x,- [N,-C (X,).] tg 9-1- [H.-FC (xi) I t6 ip, (2)
where (P_ Ot + y. Equation (1) can be regarded as an equation for findin;; the
abscissa xl. However, due to the random character of the t(xl) parameter its
precise solution cannot be obtained. 47e will take advantage of the circumstance
that in actual practice the amplitude of the wave 1'' 1 is much less than
the height Ha at which the measuring instrument is ituated. From expression
(1) we find that xl = Ha tg e, and expression (2) assumes the form
_ xs� Ilf�-C (Na t6 e) J tB 0+ [II.-I-C (H� tg 0) ) ti6 (p. (3)
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Thus, at the angle e to the normal the measuring instrument picks up the point
of an object whose abscissa is given by expression (3). The luminosity f(x2)
- of the object at this point has the form
~ j{(I1i t(N.t88)It80+[1l.-Ft(H. tSe)] tBqp}� (4)
_ The argumQat or this function is random since the parameters y and (P are ran-
dom. Accordingl}r, the value (4) is random even for a specific f(x) record. We
will simplify its argument. For this we use the notation F, = tgoC, r1= tg 0-
Remote optical instruments usually have a very high angular resolution. Accord-
ingl.y, it can be assumed that i nI~ 1� The angles of inclination of the waves
- are usual~.y aisG small, that is i~~~A1. In this case tg y' = ti+ (11-~;)/n,
where n is the refractive index of water and the diQtribution of luminosity (4)
assumes'the form
- f rA.x, -'n n lY~(x.),, . (5)
~
where
� Ao~1 + H.
(B = w(ater) J . . . (6)
~ an3 it is taken into account that rj = xl/Na. Thus, with the mentioned assump-
' tfons the random characrer of parameter (5) is determined by the random form
- ef the function f(x) and the random character of wave slope ~E.(x) = d4 (x)/dx.
The total signal received by the optical instrumert is a superposing of the
signals (5), that 3s . . �
r~~) " J h(x)1 [ A,x + nnH.t~x) ] dx, .
(7)
_w .
where h(x) is the instrument function of the sensor of this instrument, which
is the projection of the directional diagram of the optical receiver 2Z((9)
onto the mean sea surface (Fig. 1), and characterizes the weight with which dif-
- ferent parts of the imaYe are sensed by the instrument. The Y(!~) parameter is
dependent cn the rar.dom function F,(x).
If the waves are absent and the resolution of the instrument is infinitely
high, that 3s, the conditions T,(x) = 0 and h(x) = a(x) are satisfied, the in-
strument output signal is precisely equal to thE value of the f(x) function
at the nadir point, that is, Yp = f(0). The difference between the Y(Fz, ) and
YD value is determined by the presence of waves and a finite resolution of the
measaring instrument. The mean square difference of the Y( 9) and YO values
is the dispersion of the measuretnent error '
e'(t)_[Y(t Y'Q)-2)+Y,=, (8)
dependent on the random function of slopes E(x). In expression (8) averaging
is carried out for all possible caoes of the random funetion f(x) with a con-
stant record of the random function E, (x). Assuming the distribution of lumin-
osity f(x) to be stationxry and ergodic and using expression (7), we obtain
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Y�'=l`(~) ~o=,
A � �
fh(x)B[A.x+ ]fix,
n
.
.
r _(V J~hh(z.)8IA. (xa-x.)+ n N.~t(x:)-t(x,)] }dz~dx:,
where d2 is the dispersion of the f(x) function; B(,P) is its correlation func-
tion. Expressing the latter through the S(k) spatial spectrum of the f(x) pro-
.cess, we find
� (9a)
. � Y#Y~� f fh (s) S (k) oxp ~ Ju~ [ A,x n-1.11A(z), } dx dk,
n.
~w
�
YZ(~)~ J~J h(x,)h(x:)S(k)oxp{jco[Ao(zs-s.)+
+ n-1K.~~(s:)-t(xj)),}~i~:dk�
n (9b)
Since the 4 (x) function is random, the dispersion of ineasurement error E 2(~y)
is also random. We will find the mean value of the d{spersion of ineasurement
error E 2= 0 and a> 0, the potential func-
tion V(z)--Pq0'f(x)ft-1 will be negative everywhere, and consequently the corre-
sponding state will be unstable since there is always a bound state of the
particle in a one-dimensional well [Ref. 91.
5. Numerical Modeling of Optical Striations
To find the steady-state temperature field in optical striations, we will
start with a one-dimensional model in which heat exchange of the plasma colwnn
with the ambient gas is taken into consideration as above by the model term
aT/r3 . In connection with the fact that there is actually a set of periodic
solut~ons of the problem that differ in percentage modulation and space period,
we will use a principle of solution sorting that is based on studying the
stability of the resultant laminar column. If the optical striations are
formed as a result of instability of an initially homogeneous plasma column,
the consequent final steady state can be found from the condition that the
nonlinear increment is equal to zero. It may turn out that even with the
- deepest temperature modulation the increment does noC vanish; apparently in
this case the striations should be irregular, and the state of the laminar
_ column will be inconstant in time.
tAs a rule, the distance between wells that belong to adjacent striations
is even greater.
$The method of Ref. 10 is as follows. Differentiating equation (4) with
respect to x, we get an equation for function V = dT/dx that coincides with
(8) at Ell = 0. �Since function V does not have nodes within the limits of a
_ well, we can conclude from this that the state with Ell= 0 is the ground state.
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Our numerical analysis will be based on two equations: an equation that de-
scribes the temperature distribution lengthwise of the column,
~ d s -I-F(T)=O, (dT)x- o � ( W )x= tEM 0' (31)
and an equation for eigenfunctions of perturbation of temperature T'(x):
dIT' ~~-[Eu-v(x)] T'=4,( ~ )".O=(
~ (32)
~ 1
It is advisable to limit ourselves to solution of equations (31), (32) within
the limits of one half-period, using cyclic boundary conditions and properties
of symmetry of the equations relative to the operation of inversion.
If E=E11 -}-AE,. T*, where
T* is the root of equation (dF/dT)r_T. =0, the quantity IEII I decreases rapidly
with increasing T21 the results in some cases are not very sensitive to the
method of estimating AEl.)
Most experiments on observation of long laser sparks have been done in
atmospheric air (under laboratory conditions [Ref. 3, 51 or in the open air
[Ref. 4]). Therefore it is of interest to calculate the structure of the
plasma column of a laser spark in air. To do this, we use calculations of
the coefficient of absorption based on the Biberman-Norman formula (the cor-
responding graph of uW(T) can be found for example in Ref. 2).
An example of numerical calculation for air at pressure p =1 atm is shown
on FiR. 6. The results correspond to neodymium laser emission power of 1 MW
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T, KK
f2
d
4
Fig. 6. Temperature modulation along
plastna column
length. This pattern may be masked in
next to each hot layer [Ref. 2].
(or carbon dioxide laser power of
about 10 kW). With increasing modu-
lation amplitude there is an increase
in the space period of the striations
and a reduction in the increment of
instability. Most long-lived are
states with very deep modulation,
where the temperature oscillates
lengthwise of the plasma colwnn be-
tween values of T1 = 4 anfl T2 = 14 kK
(degree of ionization varies from
_10-5 to _1). Visually one should ob-
serve brightly limminescing layers
of small dimensions separated by cool
intermediate layers of considerable
part by an "ionization halo" arising
An estimate of the correction to level energy E that accounts for two-dimen-
sional effects shows that the resultant solution with deep modulation may
be stable (or metastable). Calculations have shown that additional stability
(or destabilization) of optical striations may result from small perturbations
such as transport of the energy of self-radiation in the plasma, finite diver-
gence of the laser beam, change in power of the laser pulse with time and
the like. For example, laser illwaination of the plasma column with power
Chat decreases in time and dCP/dT < 0 gives rise to additional stabilization
of optical striations.
Atmospheric air always contains dust motes that are destroyed when exposed
to laser radiation. After the dust motes are broken down in dense vapor
[Ref. 131 each of them becomes a focus of ionization. Further evolution of
the plasma cloud will depend onthe initial size of a particle, its compo-
sition and the power density af laser irradiation. The largest motes may
become a center of nucleation of striations. Naturally, the configuration
of the striations will be chaotic. The remarks made above about the stability
of striationa apply in equal measure to these conditions since the interaction
between neighboring striations is insignificant in the most interesting case
of soliton-like solutions. (With high concentration of dust motes in air,
overlapping of plasma foci from individual motes may make itself felt, which
has been experimentally observed [Ref. 5].) In conclusion let us note that the feasibility of comparing the numerical
results with experimental data rests finally on the reliability of the cross
sections used in the calculations (including coefficients of absorption of
laser emission and so on). This applies primarily to conclusions about the
lifetime of the striations that are formed, i. e. the question about whether
the observed striations under given specific conditions will be regular
(whether they will be like the etanding striations in the positive column
of a glow discharge [Ref. 6]), or whether the inetability gives rise to hot
layers that are chaotically configured along the laser spark and that have
parameters fluctuating in time. At the same time, the very existence of
159
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optical striations atems from fairly general physical considerations, and
therefore it is to be hoped that we will soon have experimental observations
_ of their formation.
REFERENCES
- 1. Nastoyashchiy, A. F., KVANTOVAYA ELEKTRONIKA, Vol 8, 1981, p 220.
2. Rayzer, Yu. P., "Lazernaya iskra i rasprostraneniye razryadov" [Laser
Spark and Discharge Propagation], Moscow, Nauka, 1974.
3. Basov, N. G., Boyko, V. A., Krokhin, A. N., Sklizkov, G. V., DOKLADY
AKADEMII NAUK SSSR, Vol 173, 1967, p 538.
4. Parfenov, V. A., Pakhomov, L. Ye., Petrun'kin, V. Yu., Podlevskiy, V. A.,
PIS'MA V ZHURNAL TEKHNICHESKOY FIZIKI, Vol 2, 1976, p 731; Vol 4, 1978,
p 460.
5. Zakharchenko, S. V., Sintyurin, G. A., Skripkin, A. M., PIS'MA V ZHURNAL
TEKHNICHESKOY FIZIKI, Vol 6, 1980, p 1065.
6. Nedospasov, A. V., Khait, V. D., "Kolebaniya i neustoychivosti
nizkotemperaturnoy plazmy" [Fluctuations and Instabilities of Low-Tem-
perature Plasma], Moscow, Nauka, 1979.
7. Nastoyashchiy, A. F., Shevchenko, L. P., ATOMNAYA ENERGIYA, Vol 32, 1972,
p 451.
8. Peierls, R., "Kvantovaya teoriya tverdykh tel" [Quanttun Theory of Solids],
Moscow, IL, 1956 [English version, Oxford, 19551.
9. Landau, L. D., Lifshits, Ye. M., "Kvantovaya mekhanika" [Quantum Mechanics],
Moscow, Fizmatgiz, 1963.
10. Barenblat, G. I., Zel'dovich, Ya. B., ZHURNAL PRIKLADNOY MATEMATIKI I
MEKHANIKI, Vol 21, 1957, p 856.
11. Kurdyimiov, S. P., Preprint No 29, Institute of Applied Mathematics, 1979.
12. Kadomtsev, B. V., "Kollektivnyye yavleniya v plazme" [Collective Phenomena
in Plasma], Moscow, Nauka, 1976.
13. Bunkin, F. V., Savranskiy, V. V., ZHURNAL EKSPERIMENTAL'NOY I TEORETICHESKOY
FIZIKI, Vol 65, 1973, p 21.
COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1982
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UDC 535.375
WAVEFRONT REVERSAL THEORY FOR RADIATION WITH SPATIALLY INHOMOGENEOUS DISTRI-
BUTION OF AVERAGE INTENSITY
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 9, No 3(117), Mar 82 (manuscript
received 28 Ma.y 81) pp 548-553
~ [Article by I. M. Bel'dyugin and I. G. Zubarev, Physics Institute imeni P. N.
' Lebedev, USSR Academy of Sciences, Moscow]
[Text] Based on a spectral method, an attempt is made at
a unified approach to description of the various modifications
of wavefront reversal with induced scattering: in a light
guide, with lens focusing of spatially inhomogeneous and
single-mode radiation. It is shown that this necessitates
consideration of a certain.correlation between spatial spec-
tral components and decomposition of the pumping field.
Approximate solutions are found for the scattered field
in the above-mentioned cases.
Principles of the process of wavefront reversal of radiation by stimulated
Mandelstam-Brillouin scattering have now been fairly well e;overed both experi-
mentally [Ref. 1-4] and theoretically [Ref. 5-10]. The result of this research
has been formulation of the idea of existence of three modes of observation
of wavefront reversal: in a waveguide [Ref. 1-3], and with focusing of multi-
mode [Ref. 2, 41 and single-mode beams in a medium. This division of the
. effect of wavefront reversal by stimulated Mandelstam-Brillouin scattering
into three sub-effects is dictated chieflq by the fact that in g.ualitative
- description of the phenomenon, each of the three modifications of wavefront
reversal is described on the basis of its own theoretical concepts unrelated
' to the others.
For example, wavefront reversal i- a waveguide is described on the basis of
- a spectral approach, and use of the fact that the scattering medium for the
Stokes wave is an amplitude volumetric hologram that is recorded as a result
of the laser beam setting up spatially inhomogeneous negative absorption in
the mediwn on the Stokes frequency [Ref. 5, 6, 10]. This enables one to use
, volumetric hologram methods to get the pattern of formation of the scattered
' f ield correlated with pumping.
In describing wavefront reversal of focused multimode beams, a predetermined
form is assigned to the scattered field correlated with pumping (based on
161
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certain reasonable assinnptions), and then the increment of amplification of
such a field is calculated and the details of its form are refined [Ref. 7, 81.
In this approacti, the form of the field correlated with pumping, and thus
the judgments on the nature o� the process of its amplification are to some
extent arbitrary.
Wavefront reversal of focused single-mode beams is described on the basis
of concepts of constriction of the active waveguide in the region of focusing,
and strong discrimination of the modes;of this waveguide as compared with
the mode correaponding to the field of the focused bQam [Ref. 91.
Each of these theoretical approaches, while satisfactorily describing its
own modification of wavefront reversal, does not permit description of the
others. At the same time, from the experimental viewpoint these versions
of wavefront reversal are not fundamentally different, and there is the possi-
bility that by varying experimental conditions we could achieve continuous
transition from one of the methods of wavefront reversal to the others. This
shows that wavefront reversal by stimulated Mandelstam-Brillouin scattering
is conditioned by physical causes that are common to all three methods, and
that the need for dividing the effect into sub-effects is due to inadequacy
of the theoretical description of the process.
In this connection, it is of interest to describe wavefront reversal by stimu-
lated Mandelstam-Brillouin scattering with consideration of the various methods
of realization from a unified standpoint. In this paper, we solve the problem
by using a spectral approach.
In the spectral approach to description of wavefront reversal by s*imulated
Mandelstam-Brillouin scattering, the slow amplitudes of the pwnping field
eH and the scattered Stokes field ec are represented (e. g. see Ref. 15, lOJ
as a sum of planar waves:
!y_i N-1
e~= ~ a�(z) exp.(iknr); e�= J ARexp (ikn�r).
n=0 n='0
Here it is assumed that the scattering medium is concentrated in the region
- occupied by the half-space z> 0;
knz knx = 2nnx/D; kily_- lznu= 2.nny/D,
where D is the transverse dimension of the region in which the problem is
,
being considered; nX, n~, are integers that satisfy conditions nX + ~2< N2
N=[nN2], and that take on all available values inside the indicate3-inter-
vals.
Under these conditions, the equations for the amplitudes of plane waves of
the scattered field take the form
N-I N-1
- ~n = 2 Qp 7 14mAm+P-lt C'XP(IOk~lipnZ)-
p�=0 me0
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where
Ok'mzp'n = (4n'//zD2) [(nY-mx) (nY - PY) -I- (ii. - m~l) (nu - Pu)1 ;
k is the wave number of the pumping field.
In describing wavefront reversal in a waveguide, it is assumed that the slow
- amplitude of pumping e�(rl, z) at the input to the waveguide, i. e. at z= 0,
is a steady-state random process, so that
l.
However, it should be noted that this estimate has been obtained with the
assumption that the angle of divergence of plane waves of the scattered field
does not exceed the angle of divergence A of the focused pumping, and that
the amplitudes cin(0) of the plane waves are statistically independent. On
the other hand, under actual experimental conditions the initiating radiation
; on the Stokes frequency arises mainly in the region of the focal contraction,
~ and as a consequence the amplitudes an(0) are phased to some extent, and the
estimate given above requires some refinement.
REFERENCES
1. Zel'dovich, B. Ya., Popovichev, V. I., Ragul'skiy, V. V., Fayzullov, F. S.,
PIS'MA V ZHURNAL EKSPERIMENTAL'NOY I TEORETICHESKOY FIZIRI, Vol 15, 1972,
p 160.
2. Bespalov, V. I., Betin, A. A., Pasmanik, G. A. PIS'MA V ZHURNAL TEKHNICHESROY
FIZIKI, Vol 3, 1977, p 215.
3. Zubarev, I. G., in: "Obrashcheniye volnovogo fronta opticheskogo izlucheniya
v nelineynykh sredakh" [Wavefront Reversal of Optical Radiation in Nonlinear
Media], Gor'kiy, Institute of Applied Physics, USSR Academy of Sciences.
1979.
4. Dolgopolov, Yu. V., Ramarevskiy, V. A., Kormer, S. B., Kochemasov, G. G.,
Kulikov, S. M., Murugov, V. M., Nikolayev, V. D., ZHURNAL ERSPERIMENTAL'NOY
I TEORETICHESKOY FIZIKI, Vol 76, 1979, p 908.
5. Bel'dyugin, I. M., Galushkin, M. G., Zemskov, Ye. M., Mandrosov, V. I.,
KVANTOVAYA ELERTRONIKA, Vol 3, 1976, p 2467. 6. Sidorovich, V. G., ZHURNAL TEKHNICHESKOY FIZIKI, Vol 46, 1976, p 2168.
7. Bespalov, V. I., Betin, A. A., Pasmanik, G. A., IZVESTIYA VYSSHIKH UCHEBNYKH
ZAVEDENIY: SERIYA RADIOFIZIKA, Vol 21, 1978, p 961.
8. Baranova, N. B., Zel'dovich, B. Ya., KVANTOVAYA II.EKTRONIKA, Vol 7, 1980,
p 973.
9. Bespalov, V. I.., Pasmanik, G. A., DOKLADY AKADEMII NAUK SSSR, Vol 210,
1973, p 309.
10. Bel'dyugin, I. M., Zubarev, I. G., KVANTOVAYA ELEKTRONIKA, Vol 7, 1980,
p 743.
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UDC 538.3
STIMULATED MANY-PHOTON EFFECTS ON DIFFRACTION GR.ATING
Leningrad ZHURNAL TEKHNICHESKOY FIZIKI in Russian Vol 52, No 3, Mar 82 (manu-
script received 11 May 81) pp 554-556
[Article by S. G. Oganesyan and V. A. Yengibaryan, Yerevan State University,
Scientific Research Institute of Physics of Condensed Media] [Text] Ref. 1-3 covor theoretical studies of stiniulated many-photon processes
in homogeneous and inhomogeneous media. However, breakdown of the medium
and multiple scattering of a charged particle create additional difficulties
for experimental observation. As noted in Ref. 2, vacuum effects are most
suitable frotn this standpoint. Since a particle does not emit or absorb in
vacuum, the use of diffraction effects is suggested, where an electron inter-
acts with electromagnetic radiation on an opening in an opaque screen.
In this paper we examine stimulated effects when a particle passes over a
diffraction grating fRef. 4]. The percentage modulation of the electron beam
and broadening of its energy spectrum are proportional to the nunber of lines
N which in good gratings may be of the order of 105 [Ref. 51.
Classical Theory
Let a charged particle pass over a diffraction grating with period d and gap
width a, at distance zo from the grating surface. Incident on the grating from
below and normal to its surface is a monochromatic electromagnetic wave linear--
ly polarized along the y-axis, which we take as parallel to the lines of the
grat-ing. With consideration of the reflected wave, we find the Fourier com-
ponent of the vector potential
a (9:; q.) _ -t Ao I (q:) + ~ AO PCI) I i (A' -1) (n:r1/'-')l~siii X
/ia q, - siu (9:d/) -
x sin (Rsal2) 7r + co/c
~fx (9i + Vw=/t` -9s - A) (7, " Vw=~c- -q; + to)
The infinitesimal corrections �id select the pole when integrating with re-
spect to wave vector qZ.
To find the change of energy and momentum of the,electron, we use the equations
dp, dt = -lepr ~ 9:a(9=; 9.)esP {1wt-l9sr-I4::}d9d9. -
s comp. Con3.
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y --le J r.�- " 9s'�s - 7pi) �(9si 9i) tlx11 (l~nl - 19y~ - ly.Z) d~lsd~/� COmp. COAj .
dt \ r
' dp' -te~ ~ q~n ) ox Iwt - (l z) d d COIIIp . COIIj. (2)
dc - Y ~9m~ 4r P~. 9xT - ?i?s 4s !
t
and also the expression
As - v:ep: -I- u ye p y-F- u'o p.. (3)
Let us solve system (2) by perturbation theory, aubstithting the unperturbed
tra~ectory
~ x=rxo-}-vstt U=Jo. Z=zo
~
in the right-hand part.
; Integrating with respect to time from -cD to }oo, we find
as /Wso n~e /,010
APs = ~~I COS ( u= a) + APy = 0, AP, _ ~~xl ~ t- W.lc Si Il ( us �l '
� l1c~ _ Au, Cos tW;� + a~ ; (5)
where ~~~=EP mCq Slu Wd e(-~~rx)1-~~xsosii1 (Ntodl~~va:)
i Yv1- Ys 111s Si11 (1.4%: Rr) '
wd dt - Bi
a--(!y-1)2v +.arcl8
s (a)
s
and eAo/mc2 is the dimensionless intensity parameter. When condition
' ~d12u;-,),x. where a-�i; i_v;--H... (7)
is satisfied, the quantity sin (Nwd/2v,)%sin (cjd/2u=)- N. In this case, broadening
of the energy spectrum of the electron beam is proportional to the total number
of openings N. Relation (7) corresponds to the result of Ref. 4 if the angle
of spontaneous electron emission is set equal to v/2. At predetermined particle
. velocity and external field frequency w= 27rc/J1, we get the condition for the
grating period from (7):
d = nkps, where a - t; . . . .
The change in particle energy is minimiun if
1viii (wn/3u=) I= l.
(9)
Hence we get the condition for the gap size in the diffraction grating
a - ('r + 1) kpsJ", where r t ; 2; . . . . ' (11))
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With respect to order of magnitude
es' = nrEne= exl) (-8.9 sancci fXpJ) (11)
(for relativistic particles the angle between the x-axis and the direction
of electron motion is
Quantwn Theory
An analogous result (6)--equiprobable broadening of the energy spectrum of
a particle beam in the range2A6'--can be found on the basis of the Klein-
Gordon equation
-As d-fi _ 10_ (P: - Py + P;) - 2uAyPy1 + -f- m=c'+. . � (iL)
In the approximation where the change of energy and momentum Ap < p, od