JPRS ID: 10557 USSR REPORT PHYSICS AND MATHEMATICS

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JPRS L/10557
1 June 1982
USSR Re ort ~
p
~ PHYSICS AND MATHEMATICS ~
, ~FOUO 4/82)
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JPAS L/10557
1 Juae 1982
' USSR REPORT
PHYSICS AND MATHEMAT~CS
(~+'O~UO 4/8Z~ . .
CoH~Nfis
~n ~x~cs
Heavy I,~i.quid iJaves 1
LA9BR~S t+ND M1l;
BR3
- Phase F11ctLlations of Multimode I~asd~ PYeld in Turbulent
- atmosphere 5
Charecter�istica of Three-Pass At~lified Using Neoc~ymium alaa~e
Plat,e 12
' Safe Op~ration of Laser Inetalla:ion~ 18
Inveatigation of He-% Plasma Recombination La~er 3timulated
' - by ~ase~ Pulseo With a* 10.6 pm .......a 22
_ Vibr~tional ~iergy 8~cchsnge in 9ystema T~iith Optical Feedback.. 31
CW Le~~ing of Photodissxiation Laser Wlth Cy~clic '
' Circul~tion of aaseous Fluoroforn~rl Iodide !tl
Laeer Phosphate alasse8 1~8
Propagation of I~eeer Radiation in AtmAep~era 55
Spheric~.l Microtexget Irradistion by 2-Terawatt~Iodine Laser.. 61
- Rsdie~tion Mvergence in Powerfti7. Laser Ampl~fiers Using
Active Elements of Rectangula;: Cross Sectiou 65
' Using $olid ~.iel in Gaedynamic Laser 70
- a- [I~I - US6R - 21H SiT FO[10]
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OPTICS AND 3PECTR03CQPY
Laser-Induced Nonlineer Resonances in Co~ti.nuous 3pectra..... 'l6
Local Deform~tions of Cor..tinuoue Mirrors and Their
Frequency Depesndences .....................~......y........ 81
OPTOBLECTtZOrTIC3
Det,ermining Angular Coordinates of Aetronomical Ob~ects
1~en IIaing ~ptoelectronic Measurement 9yetems 86
NBU~T 1111$Q8 Converters 91
~n ~sir,s
Dense Plasma Parar,ieters, High-Pressure and Inte~se Radiation
Pulsss Tha~ Arise Y~en Powerful Proton. Flwces Interact ~
With Obstacloa 97
-b-
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l
f FLUID DYlQAMIC3 '
~
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UDC S32
H$AVY LIQUID WAVES
- Leningrad TEORIYA VO~LN NR POVERKHI~TOSTI Z~iAZflELOiY ZHIDKOSTI ia ~ussiaa 1981 ,
(~fgaed to prese 8 Apr 81) pp 2-4, 195-196
- [Anaotation, pr~face and table of contents from book "Theorq of Wawa oa the
Sur�ace of a Aeavy Liquid", by Yuriy Zosimovicr Aleshkov, Izdatel'atvo
Leningradskogo universiteta~ 2623 copies. 196 pagea]
- [Text] The textbook elucida~es topics of the theory of wevea on tha surface
of a heavy liquid, and interaction between such aaves aad solid surfacea.
Casea are examin~d ~ith high-amplitude waves in the presence of dapth~variable
- currents, witfi ~vaves in shallow water fram tlis standpoiat of the aonlinsar-
dispereion ayproximation, and also questions of wave propagation on the sur-
face of a liquid of variable depth.
For advanced uaivarsity students in mechanica and mathsmatics coursas majorin~
in applied mathematice~ and mechanice of liquids~ gases a~d plasma.
Preface
The study of mc:ion of a liquid with free surface and its fnteractiaa aith
a solid body i; of considerable intereat for such fielda of knarledga as
hydr~.ulic engineeriag. geophyaica and ship navigation. With thie in mind,
our boa~ takes wp queeCione of the theosq of aav~s oa the surfaca of a hsavy
liquid and their interaction with solid surfacea that may be eith~r stationarq
or in arbitrary motion.
As to th~ na~u~ce of the liquid~ it is taken as ideal and incompressible. and
motion ia aasumed to !+e frrotatioaal. In this case, quantitative evalustioa
of the interaction between the liquid and a solid surface ia d~tare~in~d frapt
solvtng the appropriate nonlin~ear boundary value problem of potantial tt~aory. .
Such an approach to probtems of mathemstical modeling of aome phyaical effects
cauaed by pave motioa of liquid 'enables theoretical determinatiion of the pa-
rameters of motion of the liquid and its force action on d_fferent obstacYes.
The firat chapter is introductory. It gives various forma of aquations of
motion of liquid, and foraaulates principal t,oundary conditiona iaherent in
wave motiana of liquid.
1 '
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The second chapter ie devoted to investigation of the properties of free pro-
gressive waves of finite amplitude. This topic is presented with maximwa
campleteneas for practical calculation of the parameters of auch ~aavea.
IQext, the third chapter examines problema of the theory of forced traveling
~ waves of finite amplitude. The exposition is limited to the case where ~
steady-sxate waves occur on the free surface. An investigation is made of
the ianportant case of resonance of the free surface in t:~e nonlinear approxi-
mat ion .
The fourth chapter outlines problems of the theory of both free aad forced
waves on a current that varies with depth. Conditions of existence of poten-
tial waves with such a curreat are explained. The solution of the problem
is given with third-approximation accuracy.
The f ifth chapter ofiers niaterial on quantitative ev~luation of the force
action of high-amplitude w$~vee on a vertical wall in the case of frontal ap-
proach of waves. This problea~ is generalized to the case of approach of waves
of finite amplitude toward a vertical wall at an arbitrarq angle in the sixth
chapter. .
The seventh chapter gives the deriva*ion of equationa of the theory ~cf long
waves in the three-dimensional case of g liqui~ of variable depth.
Problems of wave propagation in a liQuid of variable depth are especially
important for problems of marine hydraulic engineering. At the same time~
they are very difficult in the sense of explicit construction of a solution.
The eighth ct~apter gives an asymptotic solutioa of Che linear problem of wave
J propagation on the surface of a liquid of Wariable depth, a~nd also offers
a solution for the problem of wave passage from one depth to another~ and
wave paesage over a vertical bar~ier. .
- The ninth chapter examines problems of wave diffraction by vertical cylindri-
cal aurfaces. The case of wave diffraction.by two arbitrarily oriented verti�-
cal walls is of parti.c~lar interest for applicationa. ~
The tenth chapter presents the theory of interaction of a moving solid with
a liquid of finite depth. Final results are found for the case of a slender
body. '
The eleventh and last chapter is devoted ta questions of interaction of irreg-
ular waves with solid surfacea. The atate of the sea d.::~ to wind action muat
as a rule be described by randrna functions that are sol~itions of the corre-
sponding hydromechanical problems. Such an approach en~bles accounting for
the action of wind waves on various obstaclea.
The list of problema arising from interaction of waves with solid surfaces
requires a number of approaches for solution. ~his bo~k uses the method of
the small parameter for constructing the solution of nonlinear boundary v~lue
problema. tt~e Lyapunov-Schmidt method for etudying nonlinear integral equa-
tiona, the method of aeparatibn of variables, conformal mapping techniqusa~
2 .
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~
~
~ the method of reducing a linear boundary value problem of elliptical type
~ to an integral equation by the fundamental fonaula of the theory of haxmoaic
' functions, methods of the theory of randoa? functions.
i
~ On the whole, the book uses analytical methods both for direct construction
~ of a solution for the external problem of potential theory and for reducing
. this problem to a form convenient for using numerical tnethods and cotaputers.
In accordance with the above, this book deals with the field of applied mathe-
matics on problems of fluid dynamica. It exan~fnes determiniatic and etochas-
� tie models of wave motions of a heavy liquid.
Formation of the scientific interests of the author has been considerably
; influenced by tne ~,rorks of A. I. Nekrasov, N. Ye. Kochin, L. N. Sretenskiy,
~ Ya. I..Sekerzh-Zen'kovich and Yu. M. Krylov, who have contributed prominently
to the develop~aent of wave theory. The study of their workg has opened up
possibilitiea for solving new problems of both theoretical and praztical in-
terest.
Many points of the book have been discussed directly with Profesaor Ya. I.
Sekerzh-2,n'kovich, to whom the author is sincerely grateful for useful ad-
vice.
Contents
Preface 3
Chapter 1: Equations of Liquid Motiion 5
1.1. Description of liquid motion in Euler variables -
1.2. Boundary conditions ~
1.3. Descriptio~ of liquid motion in Lagrange variables 10
Chapter 2: Free Progressive Waves of Finite Amplitude 12
2.1. Determining velocity potential and ordinate of free eurface -
2.2. Liquid particle tra~ectory ZD
Chapter 3: Forced Asymcaetric Wavea of Finite Amplitude 24
3.1. Formulation of problem and reduction to integral equation -
3.2. Solution of problem in case uof vn 31
3.3. Solution in case uo~ vl 35
Chapter 4: Surface Waves on g Current 42
4.1. General formulation of the problem -
4.2. Free waves 44
4.3. Forced waves 49
Chapter 5: Action of Waves of Finite Amplitude on a Vertical Wall With
Frontial Approach 57
5.1. Formulation of problem in Euler variables and inethod of ~olution -
5.2. Wave height at the wall, and load.on the wall 62
5.3. Solution of the standing wave problem in Lagrange variablea 65
Chapter 6: Interaction of Waves of Finite Amplitude and Arbitrary
Direction of Propagation With Vertical Wall ~ 77
6.1. Fonaulation of the problem and method of solution -
6.2. Detenaination of velocity potential 8U
6.3. Load on the wall 86
. ~ 3
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~ i
. 6.4. Case of deep water 88
6.5. Relation between height of interference wave at wa~.l and height
of incident wave 89 ~
Chapter 7: Waves in Sl~allaw Water 9Z
7.1. Equstione of loag-rwave thoery - ~
7.2. Solitons and knoidal wavps 9S
Chapter 8: Wave Propagation Over Surface of Variable ~epth 99 ~
8.1. Raq method.for describing process of ~:~e ptopagation with con- ,
tiauous change in liquid depth - ,
8.2. Liaear ~ydrodvaamic ~problem of svave propagatioa over the surface ;
of a liquid of variable depth 104 ~
8.3. Wave passage fron~ one depth to another 110 ~
8.4. Pass~ge of ~vaves over a vertical obstacle 120 ~
Chapter 9: Ditfraction of Gravity Waves by Vertical Cqlindrical Surfaces 131 '
- 9.1. General formul~tion of groblem. Exaa~plea -
9.2. Case of gap formed by two arbitrarilq oricnted vertiaal walls 143 ;
- Chapter 10: Motion of Salid in Liquid of Finite Depth 154
10.1. Fos~mulation of problem of motion of solid in liquid -
10.2. Forced oscillations of solid in liquid of f inite depth 159
10.3. G~naral case of vibrational motioa of solid 161
10.4. Oscillatory motion of solid in the presence of travel at
constant velocity 168
10.5. Motion of slender body at variable velocitq in liquid of
~ finite depth . 168
Chapter 11: Interaction of Irregular Waves With Solid Surfaces 176
_ 11.1. Deacription of irregular developed waves on the open aea - '
11.2. Diffraction of irregular wavea 180 i
11.3. Oacillation of solid due to irregular waves 186 ~
References 192 ;
COP'YRIGAT: Izdatel'atvo Leningradskogo univereiteta, 1981 ~ '
6b10 . ~
CSO: 1862/95
4 ~ ~
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j zns~s ~ r~?s~s
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UDC 621.371.259
,
i
~ PHASE FLUCTUATIONS OF I~ATLTIMODE LASER FIELD IN TURBULENT AZMOSPHERE
.I
Mosco~v KVANTOVAYA ELERTRON?RA in Russian Vol 9, No 1(115), Jaa 82 (maauscript
j r@ceived 13 Feb 81) pp 9-13 ,
[Article by M. S. Belen'kiy and V. L. Mironov, Institute of Optics of the
' Atmosphere, Siberian Department, USSIt Academy of Sciences, Tomsk]
[Text] A method is proposed for calculating the phase fluc-
tuations of multimode radiation in a mediwn with random
inhomogeneities, uaing the concept of average diffraction
rays. An investigation ie made of the influence that the
I initial coherence of the source field and diffraction con-
~ ditions have on the radiating aperture, and the ef�ect that
turbulent conditions of propagation have on spatial atruc-
i ture of the phase function and on the variance of tremor
' ~f the source in?age. The results of the~ry are caapared
with experimental data obtained in the actual atmoephere.
Phase fluctuations of waves propagating in the atmosphere conaiderably limit
, the capabilities of varioua practical la8er systems [Ref. 1, 2~. Ho~ever~
despite the fact that taany aources uaed in systems of thia kiad have finite
temporal and epatial acales of field coherence, phase fluctuations of partly
coherent radiation in a turbulent atmosphere have not yet been calculated.
' This paper proF,oses a aiethod of calculating phase fluctuations of a multimode
laser beam in ~ medium with random inhomogeneities, and inveatigatee the way
that the structure function of the phase and associated variance of image
tremor depend on initial source field coherence, conditions of diffraction
by the radiating aperture, and turbulent conditions of propagation.
The initial distribution of the field in the plane of the radiatin& aparture
(x = 0) is given in the form [Ref . 2]
uo(P)=exp(-p'(1/2a'-I-ik/2~-i-tS~(P)1~ (1) .
where a is effective beam radius, k is the wave number, F is focal length
of the transmitter, Si(p) is random phase distributed by a normal law. The
average value of phase Si(p) is zero, and the atructure function takes the,
form '~Dgi (p)= p2/4p~. Aere 2p~, ie the initial spatial coherence radius of
the field. Phase fluctuations of the wave in the plane of obaervation (x ~ X)
in a turbulent atmosphere are described by the relation
~ 5
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' S(X, P)=S~(X, P)-~-Se(X� (2)
where Si(R, p) are random phaee distortions iii a homogeneous medium due to
fluctuatione of the field on the radiating aperture, St(R. p) is random phass
advance caused by turbulent iahomogeaeities of the atmosphere. For~la (2)
is implied by the atochastic wave equation ~itih raadom boundarq condition
(1) When it ie solved either by the ~nethod of geo~etric optics or by the
method of s~nooth perturbations. As a consequence of the statiatical indepen-
dence of quantities Si aad St, the structure function of overall phase fluc-
~tuations in accordance with (2) takea the fora
DR~X, !~)=~~i~X. t?~'FD.~~X~ ~3)
When calculating DSi(R, p) in a homogeneous field, we take consideration of
the fact that for a beam with initial f ield distribution (1), disregarding
amplitude fluctuations the relation T2(R, p)/T2(R, 0) ~ expl-~Dsi~x~ P)~ ta
satiafied, where T2 is the mutual coherence function of the second-order field.
Then a~ the coherence radiua of the unbounded plane wave po-~�� IPo'~1.45k x
CnR)-3 5, Cn is the atructure characteristic of fluctuations of the index
of refraction~, we have from the results of Ref. 3
'~:~,i~X, (~)=p=/4fp~(1-X/~'-~~X/ka)'(1-I-i~/a~l. ~4)
Formula (4) defines the change in etructure function of the phase of a multi-
mode laser bemn in a homogeneous medium due to f ield diffraction bq the ra~i-
ating aperture.
To calculate randam phaee advance of the ~oave St(R, p) due to atmospheric
- turbulence, we use the concept of average diffraction raqs [Ref. 4, 5]. In .
accordance with Ref. 4, 5:
x
. Se (X~ Pi) 2 k,~ ei (a~ P(X)) da~ P(X) Pi, ~5)
o .
where the El are fluctuations oi permittivity of the medium at points lying
on the average diffraction scay arriving at the abservation point (R, pl)�
- The trajectories of rays of a multimode beam in a medium with random inhomo-
geneities are determined analogously (Ref. 4, 5]. In accordance with Ref.
4, 5, the solution ~of the nonlinear differential equation that describes the
tra~ectories of average diffraction rays in the paraxial approximation
. (pl/X~1) with accuracy to terms of order (pl/X)2 coincidea with the expreasion
x "
P~z~ = P~ eXP v(~~ q, a) dE , (6)
x
where x is the in~stantaneous distance along the path,
y~~~ q~ a~ _ E(a -I- 2~i ~a/a
(a E a -t- ~/~~9$ 11
_ 6
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is the curvature of the average phase front of the collimated (R/F= 0) beam,
S2 = ka~ /R is the Fresnel parameter of the radiating aperture, q= R/kp~ is a
parameter that characterizes turbulence intensity on the path, a ~ 1+ a2 /p~.
According to Ref. 6, parameter a at the output of a taser with spherical cavi-
tq in the case of a large number of transverse modes of oscillations (N~1)
can be evaluated by the formula a=N.
The average diffraction rays found from relation (6) for a multimode beam
under coaditions of weak (q~l) at SZ�q-1 and strong (q~l) at n�min (qy a)
intensity fluctuations are defined by the expressions
[S2s-+-a(x/1t)~ ~~2
P (z) = Pi ~u a~ (7)
and
~ a ~
P~z) = Pi ~ 1- a~.. e/oS2qx/X, ~ 1 a-~-'/su9 , x (gi
x [a -I- ~/a~9 ~z~1~)g~b15~'` ~a ~~~~91-s~~
r~spectively. The tra~ectories of these
rays at different parameters q, a and SZ
~(~)~Pr ~ are shown in Fig. 1. It can be seen that
the spatial position and shape of the
aa average diffraction rays of a restricted
0,6 collimated beam depend on the coherent
~ y propertiea of the source and turbulent
44 J conditions of propagation. In particular,
Q? y with increasing parameter a at a~i2q the
- E 5 beams of the. multimode laser approach
~ o o,? 0,y o,6 ~qe x the rays of a apherical wave (p(x) ~
pl(x/X), curve 4), while under conditions
of strang intensity fluctuations (q~l),
Fig. 1. Average diffraction rays with the additional condition aq-1�t2~q
of multimode laser beam (X/F ~ 0, they become close to the limiting poeition
Sta 1) in turbulent atmosphere: of rays of a single-~mode (a= 1) beam (p(x) ~
1--a = 1, q= 0; 2--a m 10, q= 0; pl(x/X3~2, curve 6). In this case, the
3--a = 102, q= 0; 4--a = 104, q= rays of a multimode laser are situated
1-102 or a= 1, S2 = 0; 5--a = 10, closer to the axis of the beam even in
q= 10; 6--a = 1-10, q= 103 comparison with the r.ays of a aphericgl
wave.
Relations (5)-(8) enable us to calculate the spatial atatistical character-
istics of phase fluctuations of optical waves. To calculate time character-
istics we should use the expression for random phase advance at time delayed
by T as written using the hypothesis of frozen turbulence [Ref. 1]:
x
, S~ (X ~ P. _ ~ ~i (X~ P (X) - ~l ~x) dX~
where vA(x) is the component of wind velocity acrose the path.
?
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~ Tt~e spatial atructure of the phase function of a multimode beam in a medium
with ~olmogorov tur.bulence spectrum takes the form
~.e~X. 9~ a~ P)=Y~Q~ 9+ a)D; ~X. P). ~9)
where DgtER, p) is the structure function of the phase of a plane wave,
Y~~~ q,a) eXP - g f"(~~ p~ q, a) dg dx. (10)
~ :
At the special values t2 0, S2 formulas (9) ,(10) imply knowa results
[Ref. 1, 2j ~or an unbounded plane wave (Y = 1) and a spherical wave (Y a 3~8~
respectivel~?, and at a= 1 these formulas coincide with the corresponding ex-
pressions for a single~mode beam obtained in Ref. 5, 7. In particular, it
was showa i~ these ~apere that in the case of a single--mode spatially re-
~ stricted bE:am (a = 1, S2 = 1) under conditions ~f strong intensity fluctuations
(q~l) the parameter Y= 2/~, whereas in the region of weak ~luctuations (q�1) ,
" Y= 2/5. In tt?e c~se of a multimode laser a~l at q�1 and aq l~ttKq, formula
(lOj also impliea Y- 2/~, and when q�1 we have
~ Y~~~ 9~ a)=[1-}-acS3'sl-z/sFf~-`~e~ l~a~'~:+-~')�
From this we see that with the same scatter of observation points (p~ const)
the structure function of the phase of a spatially limited beam in the region
of strong intensity fluctuations (q�1) is less than this quantity for both
plane and spherical wavea. According to Ref. 4, 5, this is due to the ap-
proach of average diffraction rays (see Fig. 1), which reduces the average
phase difference at observation points.
Phase fluctuations of a wave received by an optical system cause image tremor
[Ref. 1]. Using the results found above, we calculate the variance of the
tremor Qa which from Ref. 1 when pb�aL (pb ie the average b~am size in ~
the plane of the receiver, aL is the radius of the reception lens) is uniquely
determined by the structure function of the incident wave phase. Taking our
lead from Ref. 1, we get from formulas (3), (9)
oa = va~ Y~~, q~ a~ a'ao~ (11)
where aq,i is variance of the tremor of t:he iyu.la~e of a fluctuating source in
a homogeneous medium, vao= 2�0.97/Ikzi2at)1~sPp/3i is the variance of image
tremor for xeception of an init~ally coherent infinite plane wave in turbulent
~ atmosphere. When a�1 and St�a , formula (4j is considerably simplified and
takes the form Dsi(X, p)~ p2/2(X/ka)2. Here oai ~(a/X)2/2, where a/X is the
angular size of the source.
Thus with increasing path length R, the.variance of image tremor for F partly
coherent source in turbulent atmosphere on the one hand decreases sinc~
Qai ~ R'2, and on the other hand increases since oao~ R. Differentiatin~
formula (11) with respect to x, we can determine from the condi*_ion dva/dx = 0
the position of the plane of minimum termor of the image on the path, Aowever,
8
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4 � '
� �
Fig. 2. Image tremor vari-
ance as a function of param- ~
eter S2 at fixed parameters q '
and qk: 1--qk= 10, q= 0.1; 0 4 ,.d,,.: . ct?
2--qk = 0-10, q s 102 ; 3--qy~ _
0-10, q= 103; 4--c~k' 10'`, q� Fig. 3. 8xperimental data .
0.1-10 from Ref. 1,0.,~Points), straight
line aa= a? al (1) and calcu-
when these results are uaed in prac- lation by formulas (10-(12) at
tice, it should be borne in mind that Lo= 1.4 m(2) and ~(3)
. formula (11) is derived without con-
sideration [Ref. 8) of the finiteness of coherence time T~ of the source or
the response time T of the receiver. If we consider the fact that for many
sources and receivers of optical radiation T~�T, then the phase fluctuations
Si(x, p) of th~ source will be averaged out by the receiver, and formula E11) '
will take the form

~
Qa = y(~, q, a) aap, ~ 12)
Relation (12) defines the variance of image tremor at arbitrary val,ues of
the parameters a, q and S2. The special case of image tremor in reception
of a single~inode beam (a ~ 1) using results found in Ref. 4, 5 was considered
; in Ref. 9. The results of that paper follow from formula (12) at a s 1.
Fig. 2 shows the dependence of the ratio aa/aao on parameter f2 at different -
values of q and qk =(a - 1) /S2. We can see that for fixed turbulence conditions
of propagation (q < 1) the variance of image tremor of an appreciably incoherent
~ source (curve 4) is 2.7 times less than for a source of the same size with
larger coherence radius (curve 1). Besides, we can see that under conditions
of strong intensity fluctuations (q�1), the image tremor variance in recep-
tion of spatially limited beams (R = 1) is less than for either a plane wave
(Y = 1) or a spherical wave (~y = 3/8) . Let us note that this result cannot b"e
obtained by the ordinary method of geometric optics (without the use of aver-
age diffraction rays) or by the method of smooth perturbations [Ref. 1, 2].
Tremor of the image of a partly coherent source in a turbulent atmoephere
was experimentally studied in Ref. 10. Tihe measurements were made with a
! thermal source of diameter 2r ` 0.3 mm and wavelength a~ 0.5 um placed in the
~ focal plane of a radiatinA lens with focal length FL ~ 250 mm and angular eize
i
' ~ 9
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of the aperture at distance X equal to 2ai,/X~ 5". The o~tical measurements
were accompanied by gradient measurements of parameter Cn on an average height
of beam propagat~on h s 2 m.
The measured values of oa and the rms deviations ?~v~ calculated from data
for Ca by formula (12) at the special value y� 3~g for path of R= 1750 m taken
from Ref. 10 are shown on Fig. 3 together with theoretical curves Qa = f(~)
computer-calculated by formulas (10), (12) at values of the parameters SZ, q
and a corresponding to conditions of experiment [Ref. 10]. Curve 2 corresponds
to the Rolmogorov spectrum of turbulence, curve 3 corresponds to the spectr~i
density of fluctuations of the index of refraction of form ~n(K) = 0.033CnK ~3x
[1 - exp(-K2~Kp~~ that accounts for finiteness of the eacternal turbulence scale
Lo ~Kp ~ 2n/Lo) �
- Under the conditions of experiment [Ref . 10] , S2 = 4, a= 1.6 �103, 1 E q~ 3. 102.
.The scale of pk was de~ermined from the formula pk = 0.61AFL/r. The estimate
Lo= 0.7h [Ref. 2] was used for the external turbulence scale.
It can be seen from Fig. 3 that the proposed method of calculation enables
quantitative description of variance of the tremor of the image of a partly
coherent source in turbulent atmosphere. The reduction of ineasured rms devia-
tions of image tremor va observed in Ref. 10 as compared with the values
calculated by the formula for an unbounded spherical wave (straight line 1,
~a ia due both to the influence of the external scale of turbulence
and to t~ie curvature of the average phase front of the beam a~d of the asso-
ciated average diffraction rays that is caused by the medium [Ref. 4, 5].
Let us note that for a single-+mode laser this effect was experimentally ob-
served in the atmosphere in Aef. 11.
REFERENCES
1. Tatarskiy, V. I., "Rasprostraneniye voln v turbulentnoy atmosfere" [Wave
Propagation in Turbulent Atmosphere], Moscow, Nauka, 1967.
2. Gurvich, A. S., Kon, A. I., Mironov, V. L., Khmelevtsov, S. S., "Lazernoye
izlucheniye v turbulentnoy atmosfere" [Laser Radiation in Turbulent Atmos-
phere], Moscow, Nauka, 1976.
3. Belen'kiy, M. S., Kon, A. I., Mironov, V. L., KVANTOVAYA ELEKTRONIKA,
Vol 4, 1977, p 517.
' 4. Belen'kiy, M. S., Mironov, V. L., "Tezisy dokladov. Pervoye Vsesoyuznoye
soveshchaniye po atmosfernoy optike" [Abstracts of Papers. First All-
Union Conference on Atmospheric OpticsJ, Part 1, Tomsk, 1976, pp 138-142.
5. Belen'kiy, M. S., Mironov, V. L., J. OPT. SOC. AMER., Vol 70, 1980, p 159.
6. Arutyunyan, A. G., Akhmanov, S. A., Golyayev, Yu. D., TU*.1'xin, V. G.,
Chirkin, A. S., PIS'MA V ZHURNAL EKSPERIMENTAL'NOY I T1:ORETICHESROY FIZIKI,
Vol 64, 1973, p 1511.
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7. Buldakov, V.-M., Belen'kiy, M. S., "Tezisy dokladov. Chetverty~?
Vsesoyuzn}ry simpozium po rasprostraneniyu lazernogo izlucheniya v
atmosfere" [Abstracts of Papers. Fourth All-IInion Symposium on Propaga-
tion of Laser Emission in Atmosphere], Tomsk, 1977, pp 183-187.
8. Fante, R. L., RADIO SCIENCE, Vol 12, 1977, p 223.
9. Mironov, V. L., Nosov, V. V., Chen, B. N., IZVESTIYA VYSSflII~ UC~BNYRA
ZAVEDENIY: RADIOFIZIICA,Vol 23, 1980, p 461. -
10. Gurvich, A. S., Rallistratova, M. A., IZVESTIYA VYSSSIRS UC~BNYI~
ZAVEDENIY: RADIOFIZIRA, Vol 11, 1968, p 66.
11. Belen'kiy, M. S., Boronoqev, V. V., Grnnboyev, N. Ts., Mironov, V. L.,
Trubachev, E. A., OPTIKA I SPEKTROSROPIYA, Vol 49, 1980, p 595.
_ COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1982
6610
CSO: 1862/114
~
11
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UDC 621.375.826
CHARACTLRISTICS OF T~tBE-PASS A1~'LIFIEA USING NEODYMIUM GLASS PLATE
Moscow RVANTOVAYA ELEKTRONIKA in Russiaa Vol 9, No 1(115), Jaa 82 (manuscript
received 10 Jun 81) pp 121-125 �
[Article by M. Ye. Brodov, V. P. Degtqareva, A. V. Ivanov, P. I. Ivashkin,
V. V. Rorobkin, P. P. Pashinin, A. M. Prokhorov and R: V. Serov, Phyeics In-
stitute imeni P. N. Lebedev, USSR Academq of Sciences, Moecow]
[Text] An experimental study is done on the enrgy charac-
teristics of a three-pass telescopic amplifier with aeo-
dymium glass active element. The paper givea the results
of a simplified model calculation of the prQCess o~ amplifi-
cation of a short laser pulse in such an amplifier with
~ compound optical arrangement. The high levels of output
energy (300 J) and gain that are achieved shaw the promise
foY the use of such amplifiers in the output stagea of pawer-
ful laser systems. ~
One of the most important probl~ms for powerful laser syetems is to impxove
the eff iciency of using stored inversion. Oae of�the ways to handle thia
problem is to use multipass amplifiera, particularly in the output stages
of such systems. The advantages of multipass telescopic amplifiers make them
feasible as the basis for effective amplifiers with large vol~mme of active
medium [Ref. 1, 2]. The outlook fo~ ueing such amplifiers ia ttie quasisteady
state has been rather well conf irmed by theory and p.xperiment [Ref. 3-5].
Far less research has been devoted to the poasibilities of telescopic empli-
~ fiera operating in a follow-up mode (for amplifqing short laser pulses) [Ref.
2, 6], and more theoretical and experimental reaearah is needed on the ques-
� tion of the efficacy and advisability of using them for powerful laser facili-
ties..
The theoretical study of energy characteristica of telescopic amplifiers in
the follaw-up mode is a rather complicated matter as the calculation of empli-
fication of aa active medium with several iatersecting and interfering wavea
requires simultaneous solution of equations for the electromagnetic field
and the active medium. S3mplifications and model approximations that are
natural in such a situation require thorough substantiation and experimental
verification. For example, careless calculation and selection of the param-
eters of a quasisteady-state telescopic amplifier is quite detrimental to
its energq capabilities [Ref. 3, 5].
; ' .
12
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This paper ia a report on an experimental studq of the energy characteristics
of a three-pass telescopic amplifier with neodymitan glass active element that
is the b~se amplifier in the powerful UMI-35 multichannel facilitq. Th~ paper
~ also gives a simplified energy model for such an amplifier, enabling optimiza-
~ tion of some amplifier parametera.
Optical System of the Amplifier
, A diagram of the base amplifier of
the UMI-35 facility is shown in Fig. 1.
The amplifier consists of active ele- .T
ment 1 measuring 40 x 240 x 720 mm and
a three-pasa cylindrical telescope.
Beam dimensions are magnified from
30 x 40 mm at the input to 210 x 40 mm
at the output of the amplifier. The ~
input beam passes the first time through Fig. 1. Optical diagram of ampli-
active element 1 and is reflected frrnn fier in side view (a) and top view
total-reflection cover prism 3. The (b): 1--active element; 2--wedges;
front side of prism 3 has cylindrical 3--total-reflection cover prism
curvature, and therefore on the second with cylindrical aurface; 4--cover
and third pass the reflected beam has prisms; 5--cylindrical half-lenses;
cylindrical divergence along the 240~mm 6---pwnping lamps
side of the active element. 1Y~o wedges
2 split the initial beam in two and prevent the radiati.:n to be amplified
from entering the input aperture of the amplifier. After reflection by two
cover prisms 4, the now separated beam passes a third time through the ampli-
fying medium, and then after the two cylindrical half-lenses 5 it leavea the
amplifier. These half-lenses compensate for the divergence of the beams,
and two parallel beams are produced at the output of the amplifier with plane
, phase front having dimensions of 40 x 105 mm each. The use of divergence in
the amplifier makes it possible to keep the radiation flux density below the
level of destruction of the glass while increasing the total beam power by
amplification. On the other hand, the radiation energy density can be great
enough to ensure more complete extraction of the stored inversion.
To increase the efficiency of the amplifier and get uniform amplification
along the 40~n side, an arrangement was used with two reflections from the
side surfa~e of the active element made of GLS22 glass. The optical path
of the rays in the side.view and the pumping geometry are shown in Fig. la.
pumping was by 36 IFP-8000-1 lamps (18 each on top and bottom) through the
24Q x 720~nm surface of the active element. Incident on the input of the three-
pass amplifier was a beam with plaae phase front and uniform intensity distri-
~ bution of the cross section obtained after the preamplification syatem of
' the UMI-35 facility. The laser pulse was aingle-frequency snd had a duration
of 60 as. ~
Results of the Experiments
~ao series of experiments were done. The energy after the first pasa through
the amplifier (in the first series) and after three passes (in the second
. series) was measured as a function of the input energy. The measurementa
13
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were done by a system of calorimeters. The relative error wae reduced to ~SX
by uaing mutual calibration of the calorimetera during the experiment. The
pumping energq per lmnp was 3.6 and 4.9 kJ. Let us note that in the second
series of experimente, a photochxomic filter with initial transmission of
30X Nas placed in front of prisms 4 to prevent self-excitation of the ampli-
f ier with 4.9 J pumping.
The gain R1 on the firat pass, and K on three passea were taken as tlie ra~tios
Qi/Ro ~d Q3/Qo. where Qo is input energy, Q1 and Q9 are the energies after
one and three pasaes respectively.
~ Q1, J/cm2 Resulta of ineasurements of gain after
~5 the first pass with 3.6 kJ pumpiag
? are shown in Fig. 2. It can be seen
ro ~ '.Z that gain falls from ~14.5 in a weak
5 ~ field to ~6 at input energy densitq
p Qa. J/~m2 _
� a' g? R o . J/cm2 ~ _ , ~ ~o
, o0
Fig. 2. Gain (1) and energq Y e�
density (2) after first pass
in amplifier as functions of ~p q~ 0,2 0,3 Qo, J/cm2
input energy density with
pumping at 3.6 kJ per lamp; gig. 3. Experimental (pointa)
experiment (points) a2O ca2- ~d theoretical (solid curve)
culation for a= 5�10' plots of energy denaity at the
(solid curvea) ~plifier output as a function
of 0:~5 J/cm2. The results of energy of input energy at pumping of
density measurements after three passes 3.6 kJ per lamp
as a function of the input energq denaity
are shown in Fig. 3 for the same pumping. The total gain is K= 3000 in a weak
field, and ~45 at input energy densitq of 0.5 J/cm2.
At input energy of 4.5 J and pwnping of 3.6 J~er lamp, the output energy
of the amplifier was 200 J. When pumping was increased to 4.9 kJ per lamp
and a photochromic filter was included (as mentioned above), an output energy
of 3000 J was obtained at the same input energy.
It is important for further optimization of multipasa telescopic amplif iers,
including for selecting the optimum telescope magnification, type of glass
and so on, to develop methods of calculating such amplifiers that would give
good agreement'pit~h experiment.
Metho~' of Calculating Amplifier
As can be seen from the optical diagram shown in Fig. 1, exact calculation
of the amplifier is a complicated problem becauae of the presence of three-
dimensional regions with intersection of two and four diverging beams. To
describe the process of radiatioa amplification in a three-pasa optical ar-
rangement we use certain simplifications that reduce the equations to one-
dimensional equations.
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The procesa of amplification of a light pulse that is ehort compared with
~ tk~e time of p~mnping and relaxation of the upper laser level when passing
through the active medium in the simplest case is described by equation [from
Ref. 8J
~ d~ ~ -
i, ~ ..A(x)[1-exp(-o~)]-~~~ (1)
where ~(x) is the number of photons passing through a unit of area with co-
oxdin~t~ x during the pulse; A(x) is initial inversion; a is the induced radi-
a~ion cross section; B is the coefficient of inactive absorption. Using the
~ ~resulta of Ref. 9 and assuming that the amplitudes of two waves are equa?
~ for regions of intersection of two beams, we get the following equation with
~ consideration of their interference:
i
i ~ _ � ~x~ r 1- /o (20~) exp ( - 2v~)] - pm~ . t2)
L
~ where Io(2o~) is a Bessel function.
i
~
j If we disregard interference in equation (2), we can write it as
!
; ~ _ ~Zx~ [1-exp (-2a~)]-~~D. (3)
' Calculations show that equation (2) by comparison with (3) gives a correction
~ in the gain on the first pass of approximately 5X at energy denaities typical
i of our experiment~.
I In theoretical calculations of the first pass of the pulse, equations (1)
and (2) were used for regions without intersection and with intersection
~ waves respectively. in numerical iutegration, technical data for K were used,
I and conaideration was taken of the transverse distribution of inversion in
the active element as previously measured in independent experimeate [Re�f. 7].
~ Generalization of equations.(1) and (2) with transition from one pass to a
three-pass arrangement of an amplifier with cylindrical divergence reduces
~ to the necessi~y of accounting for two factora: the divergence on the second
and third pass, and the presence of regions where four beams intersect in
a complicated three-dimensional configuration.
i Divergence can be simply accounted fo~ by r~dding another term to the second ~
~ member of equations (1) and (2) [-~/(xD+ x)] that describes cylindr~cal diver-
~ gence: "
; ; dro _ 0[l-exp(-o~D11-~~" X m ~ (4)
dx o -f- z
I dm ~ ~ [ 1 -1~ (2v~) exp ( - 2v~)] - am- xo -I- x ~ ~5)
I
i where xo+ x is the radius of the ~lindrical wavefront in the amplifying medi-
um, and xo is determined by the parameters of the optical cavity.
(
i
I
{ 15
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In regiona ~shere four waves intersect, we can write an equation analogous
to (5) for two wavea: '
4 [1-lo(2am)exp(-4v~)J-a~--' (6)
Here we have made the a3raplifying asswnptioa that only two pairs of wavee
; are interfering. The formalism of accounting for the crnuplex configuraltion
of three-dimensional regions of intersection reduces to the following simpli-
fication in our calculationa. A single calculation is done for the second
and third passee by equations (4) and (5) without consideriag the intersec-
tion of these passes. Then another calculation is done by equations (5) and
(6), asewning total werlap of the second and third pasaes. The final output
energy density q3 is obtained by averaging these results with specific weight
proportional to the volwae of the regione with and without intersection.
(Such a simplification seaas feasib le aince the regioae of intersection of
four waves occupy a small part of the volwae of the amplifying medium, and
besides the beama intersect at ~mall angles.)
Discussion of the Results
Specific calculation of the first pass in the amplif ier was done by formulas
(1) and (2) where the free para~aeter was the cross section of the induced
� transition. Beat agreement with experiment is obtained for a� 5�10-20 cm2
(aee Fig. 2). We were prompted to vary Q in matching experimental data with
calculated resulta by srnne acatter of the reaults of ineasuremen;:a of the cross
section of indv ed tranaition by different methods IRef. LO-12]. Besides,
we did our calculatione of the first pass by ueing the model of variable Q
propoaed in Ref. 10:
a=ln (1-1-Qom)~~. . (7)
By varying vo in this case, we wera also able to get agreement between experi-
ment and calculation at ao~ 3.5�10~20 cm2, which differs fran the ao~ 5�10-20
cm2 obtained for glass of the eame grade (GLS22) in Ref. 10 by the method
of ineasuring the lwainescence with depopulation of inveraion by a laser pulse.
The problem of the cross section for the stimulated tranaition is very impor-
tant from the standpoint of detera~ining the energy stored in the amplifying
medium. Therefore to get this quantity more exactly, and consequently deter-
mine the maximum energy that can be taken from the laser amplifier, more ex-
perimental and theoretical research ie needed.
Summing up, we can say that for the first pass of our amplifier at an input
energy of 1 J/cm2 the output energy undergoes saturation, i. e. a conaiderable
fraction of the atored energy is converted to radiation.
A second consequence of this atage of ineasurements and calculations can be
taken as their satisfactory agreen?ent, which ~ustifies the choaen computa-
tional scheme and enables complete calculation of a three-~pass amplifier.
The results of such calculation with the use of equations (4)-(6) are given
together with experimental resulta on Fig. 3. Agreement can be conaidered
16
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~ satisfactory. Some difference between e~cperimental and calculated plots can
be attributed to approximation in accounting for interference and thie induced
, transition cross section, as well as to possible reduction of in~ersion due
to amplification of lianinescence. The results show the good outlook for using
~ telegcopic amplifiers in powerful laser systems with short radiation pulse.
In conclusion, the suthors are sincerely grateful to V. V. Ravdin, Yu. N.
Sidorenkov and V. I. Ct?ernomyrdin for assisting with the experitnents.
t REFERENCES
~ 1. Anan'yev, Yu. A., KVANTOVAYA ELEKTRONIKA, Vol 6, 1971~ p 3.
~ 2. Zverev, V. A., Kulikov, V. Ya.. Ovchinnikov, V. M., Shagal. A. M.,
OPTIRO MEKHANICHESKAYA PROMYSHLENNOST', No 6, 1978, p 25.
3. Gorlanov, A. V., Kalinina, A. A., Lyubimov, V. V., Orlova, I. B., Petrov.
i V. F., ZHURNAL PRIRLAANOY SPIICTROSKOPII, Vol 17, 1972, p 617.
i
4. Anan'yev, Yu. A., Sherstobitov, V. Ye., ZAURNAL TERHI~IICI~SROY FIZIRI,
i Vol 43, 1973, p 1014.
! 5. Anan'yev, Yu. A., Koval'chuk, L. V., Sherstobitov, V. Ye., RVANTOVAYA
ELEKTRONIRA, Vol 3, 1976, p 1412.
6. Vartapetov, S. K., Vovchenko, V. I., Krasyt~k, I. K., Pashinin, P. P.,
"Tezisy dokladov. Pervaya Vseaoyuznaya konferentaiya 'Optika lazerov
~ [Abstracts of Papers. First All-Union Conference on Laser Optics], Lenin-
i grad, 1977.
I 7. Brodov, M. Ye., Gavrilov, N. I., Ivashkin, P. I., Rorobkin. V. V.,
I Nikolayevskiy, V. G., Serov, R. V., KVANTOVAYA ELEKTRpNIRA, Vol 5, 1978,
, p 1072.
i
~ 8. Mikayelyan, A. A., Ter-Mikayelyan, M. L., Turkov, Yu. G., "Opticheskiye
~ generatory na tverdom tele" [Solid-State Lasers], Moscow, Sov. radio, t967.
I
i 9. Arutyunyan, V. M., ZHURNAL EKSPERIMENTAL'NOY I TEORETICIiE3K0Y FIZIRI,
Vol 536, 1967, p 183.
i
I
~ 10. Rudnitskiy, Yu. P., Smirnov, R. V., Sokolov, V. I.. Preprint IAE-3094,
� Institute of Atomic Energy imeni I. V. Kurchatov.
; 11. Dianov, Ye. M., Karasik, A. Ya., Korniyenko, A. S., Prokhorov, A. M.,
Shcherbakov, I. A., KVANTOVAYA ELEKTRONIKA. Vol 2, 1975, p 1665.
~
. 12. Avakyants, L. I., Buzhinskiy, I. M., Koryagina, Ye. I., Surkova, V. F.,
+ KVANTOVAYA ELIICTRONIKA, Vol 5, 1978, p 725.
' COPYRIGHT: Izdatel'stvo "Radio i svyaz "Kvantovaya elektronika", 1982
~
~ 6610
CSO : 1862 /114
' 17
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t
UDC 658.328.2:621.3.038.8.004.1
- SAFE OPERATION OF LASER INSTALLATIONS
Mpgc~r BEZOpA8N03T' PRI EKSPLUATATSII IJIZERNYKH OSTANO~VOK in Russian 1981
(siqn~d to pY'ass 30 Apr 81) pp 2-5, 113
(Annotation, toret~ord and tabl~ of cantenta fraaa book "gage Operation of
Laser installations", by Boris Nikolayevich Ralchmanov and Yevgeniy ,
Dmitriyevich Chistov, Izdatel'stvo "Ma~hinoatroyeniye", 7000 copies, ~
113 pages]
[Text] ANNOTATION
Tha resuits of inveatigations oa ths probiem of safe operation of lasere are
aystmiatized tor the first time in Soviet literature. The epscific ap-
plicationa of lassrs iri industry~ the bioloqical effect of la~ser emission and
� protsction from this type of radiation are considered. The characteriatics
ot refl~ctad laser emission and air-disperssd systema are pr~s~nted. Data are
praserit~d on the persoriai protection system of personaei enqaqed in operating
lasers. The book is intended for a wids ranqe of specialiats invoived in oper-
ation ot laser installationa ~d aleo workers o! aalety asrvicea of induatrial
: . enterpriaes and the atete saaitary inspsation.
FOREWORD
Durinq the psst few years productioa processes based on local heating of
material ta be treatsd by laser a~aisaion* have qainad considerable development.
Accordinq to the estimata o! apeaialists, laeer tschnoloqy will bscaane one of
~he lesdinq tschnoloqies in the future.
'Continuous expansion of the application o~ laser instaliations in different
areae of human activity ie related to rmcruitn?ent of a large number of par-
eonnsl for asrv~icinq then~. Alonq with the wiique propsrties and advantaqas
over oth~r squipment uaed for eimilar purposes, laser inetailatione reprsssnt
a sp~aific hazard to the health of maint~nanc~ p~'sonnal�
*The term "laasr" means "liqht a~apiifiaation using stitaulatad adaission." The
word conaists of the initial lettsrs of the P~qlish phrase Liqht Amplification
, ~by Stimulst~d F~aiseion of Radiation--Laser. Thfe term ia now accepted in
, Sovist and loraiqn literature.
~
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I
i Lassr emiasion is a new physical factor which does not at prasent represent
- such a hazard as air pollutian by chemical and radioactive substanaes or high-
and superhigh frequency radio wave qeneration. This circumata~ce is related
I to localization of beuns of laser e~aission in limited spaces. I~iowever, msdi-
I cal and bioloqical research carried out in the USSR and abroad indicatss th~ ~
~ potential hazard of dfrect and reflected laser emission to the h~aaan orqanism
~ and primarily to the eyes. Accompanyinq hazardous and harmful production
facbors--radiation of pumpinq lamps, electranaqnetic fielde, noise, noxious
{ cheiaical su~~s~~nces released fram lasar installations and tarqets, X-radiation,
~ plasma phenomena and so on--xcur during operation of laser inatallations.
; Thus, one can be subjected to the canbined effects of various hazardoue and
harmful production factors which, together with laser mniaeion, cc~aprise a
hyqienic background under which laser operation oacura.
The problmn of laser safety was first posed in 1968 in [38], where tha caaplex
approach to atudy of hazardous and harmful production factors was indicated
and this pmblem was then supplemented considerably and developed in (27].
i.aser production installations generate non-ionizing radiation with energy
' below 10 keV, which has a different nature of interaction with n?aterials than
ionizins radiation. At the same time, the operation of powerful and super-
powerful lasers may be accompanied by the development of ionizinq radiation.
~ A special working qroup was aseiqned the taisk of analyzinq ths statua of pro-
j tection aqainst nonionizinq radiation (including that from laser emission) at
! the Third International Conqress on Radiation Protection (Washinqton, A. C.,
~ 1973), orqanized by the International Radiation Protection Association
QRPA). The concluaions on the w~rk of tha qroup cf specialists were outlined
, at the Eurc,pean Congress of IRPA (1975), which can be formulated in the follow-
~ ing manner: use of apparatus that qenerates non-ionizinq radiation leads to
~ increased hazard of w~orkers beinq irradiatedt the effect of thia type af ra8-
iation on the health of personnel has been little studied= the requitements
on pratection and practical safety guidelines are frequently based on criteria
differing considerably in different countriesj international cooperation sim-
ilar to that existinq in the field of protection aqainst ionizing radiation
. is required.
' The need to w~ork out universal principles of protection aqainat non-ionizinq
radiation and also criteria, standards, definitions of basic concepts and the
maximum permissible levels of non-ionizing (laser) radiation was pointed out
at the Fourth Intern~,tional Congress of IRPA (Paris, 1977). Similar psroblsms
were discussed in our country (Odessa, 1977).
The rapid rates of introducinq laser installations into the aational econaay
; contributed to intensive research bsing conducted in the field of eafe opera-
tion of thes~e installations.
~ ~
A special-purpose atudy of hazardous sources when usinq research and indus-
trial laser installatioas was required to aolve the problema that arose. Tha
~ basic requirements of safety on installation aad operation were fos~nulated
~ durinq development of the first industrial lasers. Therefore, introduction of
! production processes using laser installations was developed on the basis that
included aspects bf laser safety.
~
~ 19
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it should be aoted that the use of lasers in new production processes is
charscteri~ec] by the ir~itial phaee in development of laser technoloqy. Dur-
inq the next few years the sphera of influence of lasers will be expandad
contluiuoualy and new desiqna of laser installations v~iil be developed. There-
for�e, it is quite rratusal to expect both the appaarance of additional hazard~
ous and harmfvl produotion factors and the manifsstation to a greater deqree
of already sxiatinq factors, which represant no hazard at present.
There ara r?o special papers devotsd to the problun of laser safety in Soviet
and foreiqn literature. Hawevsr, today's requirataents indicata a nead for
euch a publication. In this raqard the authors of this book have taken oa
t.hemselvss the labor of qensralizinq and systsaatizing the results of Soviet
and forsiqn r.search and of characteriziaq ths current etate of the problem
~ of providiriq sa~a w~orkinq conditions when workinq with lasers.
The suthors will be qrateful to all who express their opinion of the qiven
Y~,ook, they will be~ grateful for commetzts and wiahes ar~d will take them into
account in their further work on this problem. it is requeated that camments
and wishes be sent to izdatel'atvo "Mashinostroyeniye" at the address:
107076, Moscow, B-76, Stromynskiy pereulok, 4.
CONTENTS Page
Foreword 3
Chapter 1. Classification of Lasers and Main Aspects of Their
Use in Production Processes 6
l. Main concepts and definitione 6
2. Cl+~ssificatfon of lasers 6
3. Uae of lasers in production pmcesses 15
Chapter 2. Gereral Problems of Laser Safety 25
1. Hazardous arid harmful production factors that aocaanpany
laeer operation 25
2. Bioloqical effect of laser emission 28
3. Effect of laser emission on the eyes 31
4. Effect of la~ser emiasion on the skin, internal orqans and
orqariism as a whole . 41
5, i~Ia~cimum permissible levels of laser emission 44
Chapter 3. Enerqy Characteristics of Laser E7mission and
Devices and Methods of Recording It 46
' 1. Enerqy characteristics of laser emission 46
2. Davices for measurinq energy characteristics af laeer
eiatesion 49
3. Methods of ineasuring the energy characteristica of
laser emission 58
4. Spatial distribution of laser emission 61
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Chh~iter 4. ~-Dispera~d Syate~as Formed Upon L^~teraction of Lsaer
~ E~hiAsiori and Materials 66
1. Mi~thods cf stiudyinq air-dispsrsed syst~s 66
2. ~eiich for exps~cimental study of air pollution of tha
v~rkiriq zon~ bp a,ir-afspe~rsed systems
3. C2i~racteristics ag air-disparsed systems and airborne -
radiolysis products
Clia'~ter 5. ,Nbise Occurrinq Durinq Operation of Laiser Installations
1. Mecli'dnism~ of aound formation upon interaction of laser
; ea?iesion ar~d mstter 80
, 2. Qiiantitative characi~eristice of noiee. formed during laser
; machininq of solide 87
Cfiapter 6. Pravidinq Safe Workinq Cvnditions When Workinq With Lasers 89
1. Laser safety system 89
~ 2. Me~tns of reducinq hazardous and harmful production factars 94
; 3. Means of monitorinq hazardous and harnaful production factors 103
~ 4. Analyzinq tha dagrea of laser safety 106
(
j Biblioqraphy 111
C
COPYRIGHT: Izdatel'stvo "Mashincstroyeniye", 1981
6521
~ CSO: 1862/104
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~
f
;
~
, ~ .
~
?
~
~
i ~
~ 21
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UDC 628.371+535.05
- INVESTIGATION OF He-Re PLASMA RECO1~lBINATION LASER STIMULATED BY LASER PULSES
WITH a ~ 10 .6 um
Moscow RVANT~VAYA ELEKTRONIRA in :4ussian Vol 9, No 1(115), Jan 82 (manuscript
received 29 Apr 81) pp 92-98 ~
[Article by V. A. Danilychev, V. D. Zvorqkin, I. V. Rholin and A. Yu. Chugunov,
Physics Institute imeni P. N. Lebedev, USSR Academy of Sciences, Moscow]
[Text] An experimental study~is done on the IR lasing char-
acteristics of a recombination laser in which the working
mixture.is the plasma produced in optical breakdown of a
mixture of helium and xenon by C02 pulsed laser emission. .
Lasing was observed on four transitions of Re I(a = 2�03,
2.65, 3.43 and 3.65 um) when it is contained in the mix*_ure
in amounts of 0.005-1.3X at a total pressure of 20-760 mm flg.
It is shown that population inversion arises due to heating
of the gas in the wave of absorption of laser emission and
subsequent rapid adiabatic cooling of the resultant plasma
during expansion. An investigation is made of the way that
the lasing paramet~rs depend on concurrent gasdqnamic pro-
cesses.
Introduction
Population invession in a nonequilibrium intenselq recombining plasma is of
considerable interest for developing new types of lasers that emit in the
RUV ansi x-ray bands, lasers with nuclear pumping, enabling conversion of tS:~:
energy released in a reactor to coherent emission, powerful lasers with ~x-
citation by electron beam or hard ionizing radiation and the like [Ref. 1].
One of the methods of getting a dense nonequilibriian plasma is to heat a vapor-
ized solid or gas by a powerful laser pulse followed by rapid cooling of the
resultant plalsma as it expands into a vacutun or into the ambient gas [Ref.
2, 3]. Induced emission in such a supercooled plasma upon recombination of
singly ionized ions and electrons has been ubserved in mixtures of gases Ar,
Kr and Xe with He [Ref. 4] and also in Cd vapor [Ref. 5]. However, many im-
portant relations of tha output parameters of the recombination laser, an3
in particular the way that these parameters depend on plssma heating coudi-
tions and on the gasdynamic processes taking place in the gas have not been
duly explained. .
~ 22 ~
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~
~
~ In this paper a detailed investigation is made of the emission characteristics
~ of a recombination laser in which the active medium is the plasma produced
; in optical breakdown of He-Xe mixture close to the surface of an aluminum
~ target by radiation of a powerful pulsed C02 laser [Ref. 6].
~ Lasing in a recombination arrangement on infrared transitions between the
, upper states of the Xe atom has been achieved recently in a different experi--
mental facility upon excitation of the He-Xe mixture at high pressure (i~r
; to several atmospheres) by a rapid transverse electric discharge [Ref. 7],
~ upon nuclear pump~ing by 235U fission fragments [Ref. 8, 9] and by products ~
! of the reaction He(n, p)3H [Ref. 10, 11], and also upon expansion of plasmoids
produced in a hypocycloidal pinch [Ref. 12].
t
' 2. Experimental Facility ~
' A dia ram of the e eriments is shown in ~ ~ ~
' Fig. g. The emiss on pulse of an electron- 1' j i~~~= 10.6 um
' beam-controlled C02 laser with energy of :~r
~ E< ~0 J and half-amplitude duration of 4
~ T s 150 ns (~250 ns on the base) (see Fig.
! 2a) was focused by cylindrical NaCl lens 1 '
(F = 150 mm) on the surface of aluminum tar-
i get 2 in a strip 1.5 mm wide with length Fig. 1. Diagram of the experi-
Z< 95 mm. The target was accommodated in ments: 1--cylindrical NaCl
~ a hermetically sealed chamber (not shown lens; 2--alwninum target; 3--
~ on the diagram) f illed with He-Xe mixture opaque mirror of the plasma
! with concentration ratio from 19000:1 to laser cavity; 4--semitrans-
~ 76:1 and total pressure from 10 to 760 mm Hg. parent cavity mirror
~ The emission of the plasma arising near the
~ target was coupled out along its axis through LiF side windows in the chamber
1 set at the Brewster's angle. The optical cavity of the plasma laser 0.8 m
long was formed by opaque spherical mirror 3 with radius of curvature of 3 m
and semitransparent dielectri~ mirror 4 with reflectivity of ~90Y in the near
infrared region of the spectrum, sputtered on a lithium fluoride backing.
The energy and shape of the lasing pulse were mea~~ured by a sensitive calorim-
eter ar~d FD9E-111 gremanium photodiode with time resolution of ~0.1 us. The
lasing spectrum was studied by an IrIDR-2 monochromator with diffraction grating
of 100 lines/mm and by calorimeter. The absolute error of wavelength measure-
ment was no more than �0.01 um.
3. Results of Experiments
Fig. 2 shows oscillograms of the laser pulse
. on a= 10.6 um that heats the plasma (pulse
shape was registered by a gremanium detector
with time resolution of ~l ns), the pulse of
plasma self -radiation in a broad spectral range
of 0.4-2 um determined by the sensitivity range
of the photodiode, and the pulse of induced Fig. 2. Oscillograms of C02
plasma radiation on a= 2.03 um. To isolate laser pulse (a), 0.4-2 um
this last pulse from the wide-band thermal thermal emission of plasma
radiation of the plasma, the photodiode was (6), 2.03 um plasma emission
covered with germanium foil transparent to (e); 1 us/div
23
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, raJiation with a>.1.8 um. Induced plasma radiation was observed in a tuned
optical cavity in which the output mirror had minimum losses at a= 2 um�
When the opaque mirror of the cavity was covered, this emission disappeared,
unlike the thermal self-radiation of the plasma, which showed almost no change
in amplitude when this was done. Comparison of the oscillograms shaws that
lasing in the plasma developed after termination of th~a C02 laser pulse,
attaining its greatest value only after ~1 us, whereas the maximum thermal
radiation corresponds to the stage of plastna heating by laser emission with
a = 10.6 um.
The measured lasing wavelength a= 2.03 um is identif ied with transition
5d[3/Z~i-6p[1/2~o in atomic Xe [Ref. 13]. When another cavity output mirror
was used with approximately the same reflectivity of ~90X in the 2.5-3.7 um
region, lasing arose simultaneously on several transitions between excited
states of Xe I: 5dI3/2li-6PL1/2lo (a=2.65 um), 7PI5/2lz-7s[3/2]i (3.43 um),
7p[1/2]1-7s[3/2]2 (3.65 um). Fig. 3 shows the dependence of total lasing energy
Elas~ uJ Eias� uJ
,so
! . .
~ /70 ' 4
. eo ,^;P
~ ~ ~n ~
40 y ~ !
� 7a SO m~p, mm Hg
o . / 2 d n,cK
Fig. 3. Dependence of lasing Fig. 4. Dependence of lasing
energy Elas in plasmg (a= 2.65, energy E1as at a= 2.03 um
3.43, 3.65 u~) on distance be- (broken line) and 2.65, 3.43,
. tween the optical axis of the 3.65 u~ ~SOlid line) on pres-
cavity and target surface h for sure p for mixtures of He:Re =
mixture He:Xe = 760:1 at pres- 19000:1 (1), 3800:1 (2),
sure p= 200 mm Hg (1) and 760. 760:1 (3), 380:1 (4) and 76:1
mm Hg (2) ; pulse energy of C02 (5) ; E= 25 J, h= 1.8 cm
laser E = 25 J
Elas in these three lines on the position of the optical axis of the cavity
relative to the target surface h. The best conditions are realized at a dis-
tance of 1.6-2.0 cm from the target, the maximwn of the curve for E188(h)
moving away from the target somewhat as the gas mixture pressure decreases
from 760 to 200 mm Hg.
- Fig. 4 shows the lasing energy El8S at the optimum position of the cavity
axis relative to the target as a function of the composition of the mixture
~ and i.ts total pressure p. The greatest lasing energy (~0.06 and ~0.15 mJ)
is reached for a mixture with Xe content of about 0.13X (He:Xe = 760:1) at
overall pressure p= 200 mm Hg. A reduction in the percent content of Xe in
the mixture, 3ust like an increase, reduces the lasing energy throughbut the
pressure range. For any mixture, the curve Elas(p) has a maximtan with position
- that is comparatively weakly dependent on mixture composition: an increase in
the precentage of Xe by a factor of 250 shifts the maximum from -250 mm? Hg
21~ ,
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i
(He:Xe = 19000:1) to 125 mm Hg (76:1). Hawever, the lasing energq in the�high-
pressure region falls off much more steeply.
Elas � uJ so eo ~ou q~ MW/cm2 Elas ~ uJ
� 'r . . ~ ' ' 'r~_~ ~s0 ' .
, ~
~ ~0
1 . ~
40
, ~ 1. .
0 %0 . - - ~ J � - .
0 ? 4 6 Q l.tM
Fig. 5. Lasing energy Elas
~ (a= 2.65, 3.43, 3.65 um) as Fig. 6. Lasing pulse energy
~ a function of C02 laser pulse Elas as function of plasma
, energy E or flux density q length Z for mixture He:Re =
I for mixture He:Xe = 760:1 at 760:1 at p= 200 man Hg (1) and
p= 200 mm Hg (1) and 760 mm Hg 760 mm Hg (2); E= 25 J
` (2) ; h = 1. 8 cm
` Fig. 5 shows Elas as a function of C02 laser pulse energy E or the correspond-
I ing f lux density q of laser emission with a= 10.6 um for mixture Re:Re = 760:1
~ at different pressures. At p= 200 mm Hg, lasing energy increases monotonical-
~ ly with increasing energy of the stimulating pulse; at values of E= 25-30 J
(q =(1.2-2.4)�l0e W/cm2) saturation is observed. This effect is more strongly
; pronounced at high pressure of the mixture p= 760 mm Ag, where there is even
~ some reduction of lasing energy at E z 16 J(q ~ 8�1Q~ W/cm2).
, Fig. 6 shows the dependence of Elas on length Z of the active region, obtained
by reducing the longitudinal dimension of the focusing spot on the target
(with a corresponding reduction in the length of the resultant plastna) by
; using diaphragms tn restrict the cross section of the laser beam. Since the
~ radiation density distribution over the cross section of the C02 laser bea~
was rather uniform (within ~20X), the energy per unit of length of the plasma
E/Z= 2.5 J/cm remained unchanged. The dependence E(Z) measured in this way
was close to linear. The shortest plasma length Z hr at which lasiag atill
~ takes place in a mixture of He:Xe= 760:1 is Zthr =~�5 cm at p= 200 nm~ Sg,
~ and Zthr = 3.0 cm at p= 760 mm4 Hg. Assuming that losses in the optical cavity
j are determined only by its transparency, we find the average gain for lines
' with a= 2.65, 3.43, 3.65 u~ in the plasma: K='~Zt}~r ln (R1R2)-1 = 0.1 cm 1
~ (p = 200 mm Hg) and K= 0.016 cm 1(760 mm Hg), where the reflectivities of
i the mirrors in the cavity are R1= 1.0 and R2= 0.9.
I
i 4. Discussion af Results
~
To interpret the relations found above, let us turn to results of lnvestiga-
I tion of gasdynamic processes that develop in a gas under the action of power-
i ful C02 laser pulses [Ref. 6, 14, 15]. After the first instant of initiation
~ associated with vaporization of the target, subsequent plasma formation takes
, place due to heating of the gas adjacent to the target in the laser emission
. 1
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absorption~wave [Ref. 14]. At the optimum preaeure for development of lasing
in the plasma p ~ 200 mm Hg and q= 1.5�108 W/cm2 corresponding to pulse energy
E= 25 J at which the principal meaeurements were made (see Fig. 3, 4, 6),
the absorption wave in He propagates in the light-detonation mode [Ref. 15].
To evaluate the velocity v~~, presaure p~A, and specific internal energy e~R
of the light-detonation wave, and the degree of compression A of the gas that
is heated in the wave, we use the follawing relations [Ref. 16]:
v~n=[2(y'-1)]lis ~9~P~l~a~ � (1)
Pcn=Pov~~~~Y~' 1)=I2 (y'-1)1'~~Po~39'~'~~Y~' 1)+ ~2)
. v 4 ~~3 Q ~~3
l ( l ; (3)
' E~~ (Ys-~)(Y-f-~) Y-~1(y~_1/ \P~/
e=P~Po=~Y-~-1)/Y, � � � ' ~4)
where Y is the effective adiabatic exponent� po and p are the initial and final
gas denaities. Setting Y= 1.3, po s 4.4�10-~ g/cm~. we get for Ae at c~~ 1.15 X
l0e W/cm2 and p s 200 mm Hg: v~~ = 3.3�106 cm/s, p~ = 2.1�108 dyaes/cm , e~~ �
8.85�1012 ergs/g = 36.6 eV/atom, 9~ 1.77. During t~e laser pulse, the wave
front propagates to a distance h= v~AT = 0.5 cm from the surface of the target.
. The temperature T of the resultant plasma as found by the interpolation formula
of Ref . 17
e=2,5 A'~0 (T � 10'~)�n (Pa~P)��1f eV/atom . ~5)
- (where pa ~ 1.79�10-4 g/cm3 is the density of He under normal conditions,
A= 4 is its atmnic weight), is 41 kR. The equilibrium degree of ionization
obtained on the basis of the Saha equation [Ref. 18~
a~ u11,797� lo-~ Tg/= eXP ~-!/kT) ~6)
1-a -u~
(where I= 24.6 eV ~ 3.92�10-11 erga is the ionization potential of He; uos 1,
ul = 2 are the statistical sums of the atom and ion; d ~ p/p8 s po9/pa is rela-
~ tive density) in this case is a= 0.87, which corresponds to an electron con-
centration in the plasma of Ne = 1019 cm 3.
Thus by the instant of completion of the laser pulse, an extended, hot, dense
plasa?a has been set up near the target with high energy concentration. As
a consequence of the high rate of collisions between particles, thermodynamic
conditions in such a plasma should be close to equilibrium; in particular,
the processes of recrnabination of ions and electrons are campensated by re-
verse processes of ionization of atoms. A reduction in temperatvre and den-
sity of the plasma upon subsequent adiabatic expansion should result in a
aituation where, beginning at a certain instant the degree of ionization pres-
ent in the plasma is greater than the equilibrium value corresponding to the
new conditions. This is due to the fact that the rate constant of recombina-
tion in triple collisions of ions with electrons (the principal mechanism ~
at h3gh particle density and not too low temperature) [Ref. 18] ~=5.2�10-'~/T�n
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i
changes with fal~ing temperature more slowly than the equilibriwn degree of
! ionization a~ d exp (-I/2kT) in the cooled plasma (a�1) . The determining
` pxocess in auch a supercooled plasma becomes recombination, whereas the proba-
~ bility of the reverse process falls off exponentially with decreasing tem-
i petature.
(
~ With the exception of photorecombination, which plays an insignificant. part
~ a,t high electron density, all other processes of recombination in triple col-
; lisions or with the participation of molecular ions lead to preferred forma- ~
; tion of atoms in upper ~nergy states [Ref. 18]. In subsequent relaxation
~ of excitation downward through energy levels with favorable ratio of proba-
' bilities of transitions, population inversion may be formed between certain
! pairs of levels [Ref. lJ. The rate of formation of excited atoms of Xe* on
~ the upper laser level, assuming that all particles formed as a result of recom-
i bindtion relax through this level, is determined by the equation
' d [Xe�J + Z '
I ~Xe ] N~-v [Xe (7)
I
i
! where [Xe*], [Xe+] are the concentrations of atoms and ions in the plasma,
~ v= aimNe + Arad is a constant that determines the loss of Xe* from the upper
laser level due to inelastic electron impacts and radiative tranaitions. The
i resultant inversion is proportional to the concentration of excited atoms
Xe* on the upper laser level, and thus depends qn the concentration of parti-
cles in the plasma and the cooling rate (S ~ T-9~2).
( To describe the gasdynamic processes that accompany expansion of the dense
hot plasma initially heated by the laser pulse into the ambient c~ol gas,
, a theoretical model of a strong cylindrical explosion is used with instan-
i taneous energy release occurring along the axis of symmetry [Ref. 19). The
. validity of such an approach corroborated by experiments of Ref. 6 in plane
: geometry, is 3ustified by the short duration of the C02 laser pulse and the
' small initial dimensions of the plasma formed close to the target ae compared
; with the lasing time of -1 us (see Fig. 2e) and plasma dimensions of ~I.6-
2.0 cm (see Fig. 3) that are typical of lasing development.
The chan~e in plasma temperature in the process of adiabatic cooling is eval-
uated by the equation of the adiabat
T cnPcn- ~ ?~v=T~t)P~t)cv-~ )/v, ~8)
Assumin~ that the pressure of Lhe gas superheated in the ]ight-detonation
wave after a fairly long time t~rbecomes equal to the pressure in the cen-
tral region of a strong cylindrical explosion with linear energy release E/Z
[Ref. 19]:
P~~) =-ka~EPo~I~)1 ~Zl-1, ~9~
where the coefficients k2 and ~ depend on the adiabatic exponent y. If we dis-
regard energy release in the recombination process and do not account for
the change in the ~.nternal energy of atoms during cooling, then, assuming
27
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Y= 1.67 = 0.58, k2 = 0.06) and E/Z = 2.5 J/cm, we get for t ~ 1 us the tempera-
ture estimate T= 1 kR. Accounting for the mentioned circumstances by intro-
ducing an effective adiabatic exponent Y= 1. 3(~ ~ 1. 3, k2 ~ 0.086) gives T=
1~4 1cR. The plasma deneity in the expansion process up to this instant falls
bq a factor of 15-30. The reduction of density and the associated slawdowa
of recambination rate are apparently factors that limit the power aud time
of lasing in the given arrangeunent.
The reduction of particle concentration in the plasma also explains the re-
duction of lasing energy at low gas preasures on Fig. 4. On the other hand,
with increasing pressure p= 200 m~n flg one also observes a reduction of lasing
energq, which in this case is due to transition to the supersonic radiative
mode of laser emission absorption wave propagation with a= 10.6 um in fle [Ref.
15J. Such a transition is accompanied bq a sharp rise in wave velocity and
a corresponding reduction of temperature and degree of ionization of the heated
plasma. Besides, the lower energy concentration in greater plasma volume
should reduce the efficiency of subsequent adiabatic cooling. These same
factors explain the reduction of lasing energy with an increase in the ener~y?
of the stimulating pulse E~ 16 J on Fig. 5; the corresponding q= 8�10~ W/cm
precisely coincides with the threshold of transition fram the light-detonation
- to the supersonic radiative wave in fle at pressure of p~ 760 mm Iig as measured
in Ref~ 15.
In the estimates given above, no consideration was taken of the influence
of small additives of Re to He on the concurrent gasdynamic proceasea and
the parameters of the heated plasma. Preliminary experiments have shown that
even a small amount (-0.1X) of Ar or Xe appreciably alters the pattern of
gasdynamic processes in fle, considerably lowering the threshold of establieh-
ment of the nltrasoni.c radiation wave. It is this circumstance that apparent-
ly explains the reduction of lasing energy observed on Fig. 4 when the Xe
~content is increased above 0.13X in the mixture rather than the occurrence
of a relaxation channel that is parasitic for the given laser arrangement
due to the formation of dimer molecules of Xe~ as suggested in Ref. 4. At
~ Re concentrations typiCal of the giveai experiments and rate constants of the
reactions .
~He '
Xe* -I ~ Xe - He - Xe2 -1- He,
Xe� -I- Xe Xe ; XeC -r- Xe,
= 1.4 � 10 ~ 32 cm6 /s [Ref . 20 ] , Sge ~ 2 .5 � 10 32 cm6 /s [Ref . 21 ] (these con-
stants are given for gas temperature T= 300 R, and decrease with increasing T)
the time of formation of Xe~ molecules is several ordera of magnitude longer
than the characteristic time of lasing development (~1 us). However, such a
mechanism can occur at a higher pressure of the mixture [Ref. 7], and also
in experiments with nuclear pumping [Ref. 8-11], where the duration of the
lasing pulse is several hundreds of microseconds.
In conclusion we note that with more detailed consideration of elementary
processes in the cooled plasma it is necessary to account for a nwnber~of
plasma-chemical reactions that may appreciably influence the rate of recom-
bination and formation of inverse population.
28
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5. Concluaion~
~ Tb~is as a result of experiments that were done an investigation was made of
i tf~ may that emission paraaneters of a plasma recombination laser using a mix-
t~re of fle-Re 'depend on conditions of plasma heating by powerful C02 laser
pulses at~d on the concurrent gasdynamic proce~ses. Despite the fact that
the efficiency of the laser arrangement considered in this res~arch ~vas quite
lo~, the method iteelf of producing a denae supercooled plasma by a pulsed
C02 iaser is,quite promising for atudying the mechaaism of formation of in-
v~rse pdpulation in recombination lasers.
t
j The principal results of this research were reported at the Fourth Inter-
i na~:~nal Conference on Lasera and Their Applications" [Ref. 22].
~ REFERENCES
1. Gudzenko, L. I., Yakovlenko, S. I., "Plazmennyye lazery" [Plasma Lasers],
Moscow, Atomizdat, 1978.
2. Kuznetsov, I. M., Rayzer, Yu. P., ZHURNAL PRIRLADNOY MEKHANIKI I
~ TEKHNICHESKOY FIZIRI, No 4, 1965, p 10.
I 3. Gudzenko, L. I. , Filippov, S. S. , Shelepin, L. A. , ZH[1RNAL EKSPERIi~TTAL'NOY
i I TEORETICHESROY FIZIRI, Vol 51, 1966, p 115.
4. Silfvast, W. T., Szeto, L. H., Wood, 0. R. Jr., APPL. PRYS. LETTS, Vol 31,
1977, p 335.
i 5. Silfvast, W. T., Szeto, L. H., Wood, 0. R. Jr., OPTICS LETTS, Vol 4, 1979,
p 271.
6. Boyl~o, V. A., Danilychev, V. A., Zvorykin, V. D., Rholin, I. V., Chugunov,
, A. Yu., RVANTOVAYA ELEKTRONIKA, Vol 3, 1976, p 1955.
i
~ 7. Chapovsky, P. L., Lisitsyn, V. N., Sorokin, A. R., OPTICS CO1~iS, Vol 16,
~ 1976, p 33.
i
~ 8. Helmick, A. H., Fuller, J. L., Shneider, R. T., APPL. PHYS. LETTS, Vol 26,
t 1975, P 327.
i
~ 9. Voinov, A. M., Dovbysh, L. Ye., Krivonosov, V. N., Mel'nikov, S. P.,
~ Kazakevich, A. T., Podmoshenskiy, I. V., Sinyanskiy, A. A., PIS'MA V
; ZHURNAL TEKHIdICHESKOY FIZIKI, Vol 5. 1979, p 422.
~ 10. De Young, R. J., Jalufka, N. N., Hohl, F., APPL. PHYS. LETTS, Vol 30,
1977, p 19.
I
~ 11. Mansfield, C. R., Bird, P. F., Davis, J. F., Wimett, T. F., Helmick, A. H.,
~ APPL. PAYS. LETTS, Vol 30, 1977, p 640.
~ 12. Lee, Ja. H., McFarland, D. R., Hohl, F., APPL. OPTICS, Vol 19, 1980, p 3343.
~
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13. Prokhorov, A. M., ed., "Spravochnik po lazeram" [Laser Handbook], Moscow,
Sov. radio, Vol 1, 1978. ~
14. Danilychev, V. A., Zvorykin, V. D., Rholin, I. V., Chugunov, A. Yu.,
RVANTOVAYA ELF.ICTRONIKA~ Vol 7, 1980, p 2599.
15. Boqko, V. A., ~iladimirov, V. V., Danilychev, V. A., Duvanav, B. N.,
Zvorykin, V. D., Rholin, I. V., PIS'MA V ZRURNAL TERHI'1IC8ESROY FIZIRI,
Vol 4, 1978, p 1373.
16. Rayzer, Yu. P., "Lazernaya iskra i rasprostraneniye razryadov"�[Laser
Spark and Discharge Propagation], Moscow, Nauka, 1974.
17. Tsikulin, M. A., Popov, Ye. G., "Izluchatel'nyye svoystva udranykh voln
v gazakh" [Radiative Properties of Shock Waves in Gases], Moscow, Nauka,
1977.
18. Zel'dovich, Ya. B., Rayzer, Yu. P., "Fizika udarnykh voln i
vysokotemperaturnykh gidrodinamicheskikh yavleniy" [Physics of Shock Waves
- and Aigh-Temperature Thermodynamic Phenomena], Moscow, Nauka, 1966.
19. Sedov, L. I., "Metody podobiya i razmernosti v mekhanike" IMethods of
Dimensional Analqsis in Mechanics], l~oscow, Nauka, 1977.
20. Pice, J. K., Johnson, A. W., J. CHF~I. PHYS., Vol 63, 1975, p 5235.
21. Werner, C. W., George, E. V., Hoff, P. W., Rhodes, C. R., IEEE J., Vol QE-13,
1977, p 769.
22. Danilychev, V. A., Zvorykin, V. D., Rholin, I. V., Chugunov, A. Yu.,
"Fourth International Conference on Lasers and Their Applications", Leipzig,
1981, p 75.
COPYRIGHT: Yzdatel'stvo "Radio i svyaz "Kvgntovaya elektronika". 1982
6610
CSO: 1862 /114
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,
UDC 621.375
VffiRAfiIONAL ENSRGY BXCHANGE IN 3Y3TEMS WITH OPTICAL FEBDBACK
Moscow KVANTOVAYA ELEKTRONIRA in Russian Vol 9, No 1(115), Jan 82 (manuscript
~ ~ received 3 Mar 81) pp 36-43
i [Article by A. S. Biryukov, R. I. Serikov and A. M. Starik, Physica Institute
imeni P. N. Lebedev, USSR Academy of Sciences, Moscow]
~ [Text] A theoretical analysis is made of a C02 ~asdynamic
~ laser aditionally pwnped by self-radiation. It ie sho~vn
that using optical-channel feedback brings about a 5-15X
improvement in efficiency of converting thermal energy to
~radiation.
There has recently been an upsurge of interest in phenomena that take place
~ when laser radiation flows through gases. The presence of absorbing dopanta
in~ga~ may lead for example to population inversion of levels. The action
of nearly all optically pwaped gas lasers is based on this effect. In same
cases the absorption of radiation is accompaaied by a temporary drop in tem-
perature. This is the so-called "kinetic cooling effect" experimentally ob-
served in Ref. 1. Additional optical pumping may also improve the ener$y
~ characterist~ics df gasdqnamic lasers [Ref. 2].
I The gasdynamic laser has the distiriguishing feature that the medivm ie at
~ appreciably different levela of deviation from thermodynamic equilibxium in
j each cross section along the flow. Excitation of the upper worki~g atate
~ and extraction of the luminous energy may be considerably separated in space
i and time. Because of this, by using the difference between relaxation rates
~ of levels and taking advantage of the resonant properties'of the system it
is possible to 3ncrease imbalance by using "positive feedback" through the
j optical channel. Additional pumping for gasdynamic lasers was considered
j ~n Ref. 2, where it was shavn that increasing the vibrational energy of a
' system of anharmonic oscillators under the action of radiation can improve
~ ' working efficiency of a CO laser. At the same time, in the opinion of the
~ authors of Ref. 2, efficiency should not be improved for steady-state C02
i gasdynamic lasers with feedback.
~ Our paper analyzes the feasibility of iiaproving the working efficiency of
~ C02 gasdynamic lasers under conditions of.additional pumping by self-emission.
The principal conclusions of the research were reached in 1974; here these
31
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conclusions are re-examined quantitatively in the liAht of recent data on
the rate constants of elementary relaxation processes.
The working principle of the gasdynamic laser is that some of the enthalpy
~ atored in internal degrees of freedom of the gas molecules ia converted to
limminous Pnergy of coherent radiation when it is heated and subaequentlq rapid-
ly cooled bq expansion. In typical C02 lasers, the enthalpy of vibrational
degrees of freedom is -10~ (at initial temperature of ~2 kK) of the total
enthalpq, and only a emall fraction of this amount can be transformed to ra-
diation. This is due to the comparatively low (41X) quantum efficiency of
' conversion, relaxation losses and entrainment of a certain amount of the
- vibrationally excited donor gas (N2) out of the optigal cavity, so that the '
overall efficiency as a rule doea not exceed ~1X. The ma~or losses of vibra- ~
tional energy are determined by relaxation procesaes in the small (~1 cm)
near-critical zo~e of the nozzle where gas temperature and denaity are high.
Nearly all the flux of lost energy goes to vibrational degrees of freedrnn
via C02 molecules. Subaequently the vibrational energy is mainly "frozen."
If a process that is free to compete with vibrational relaxation is introduced
artif~cially into the region of the critical croes section of the nozzle,
this will reduce lossas considerably. Since in this region the medium is
in the nonequilibriwa state but far from inversion, so that the populations
of the lowe.r working levels of the C02 are high, such a process may be the
absorption of COZ laser emisaion coming from the optical cavity of the same
gasdynamic laser. Conversion of particles from the rapidly relaxing lower
level to the slowly relaxing upper level increases the effective temperature
of population of vibrational states of N2 and asymmetric levels of C02 coupled
by quasi-resonant exchange by comparison with a gasdynamic laser without feed-
back. As a result, the nonequilibrium of the medium is greater whe~n it
enters the optical cavity. It w~ould seem that the increment in energy coupled
by the cavity out of the flow in the steady state should correspond to the
absorbed energy, and that efficiency should not increase. And this would
actually be the case if the relaxation rate of the lower level over the entire
extent of the nozzle were so high that its population would be determined
by the gas te~tperature. However, if we take consideration of the finite rate
of interaction of this level with translational degrees of freedom, then the
reduction of its population upon absorption of resonant radiation may lead
to an additional increase of energy in the cavity. At the same time, an arti-
f icial reduction of population of the lower level in the rapid relaxation .
zone is accompanied by local dieruption of quasi-equilibrium between the cor-
responding vibrational and gas temperatures, and as a consequence by conver-
sion of some of the energy of translational degrees of freedom to energy of
deformation vibrations (kinetic cooling effect), and then via radiation to
asymmetric vibrations, which also is conducive to an improvement of laser
efficiency.
On the basis of the simplest arguments, let us estin?ate the increase in energy
of a C02 gasdynamic laser when feedback is included.
Beyond the output mirror of the gasdynamic laser cavity we place a rotating
optical system, and direct radiation into the near-critical part of the nozzle,
as shown in Fig. 1. We will take the physical conditiona in the gas stream
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' in the absorption and cavity regions as iden-
tical with the conditions in certain average
' cross sections 1 and 2 of theae regiona re-
Z spectively. We make the following simplifq~g
y i ~ assumptions: the energies of vibrational
~ ~ 1_ quanta of N2 and asymmetric vibrations of
~ C02 coincide; due to rapid intermolecular
' W' exchange of quanta, the temperatures of
~ population of the energy levels of these modes
~ ~?~xw i~,,.! x of vibrations are the same and equal to T~ (x) ,
~ where x is the coordinate along the nozzle;
for the same reason of strong interaction
Fig. 1. .Diagram of gasdynamic w~e asswne that the temperatures of symmetric
laser witb feedbacr and deformation vibrations of C02 also are
~ the same and equal to T2(x), and that the
gas temperature of the expanding fldw behaves as in an ordinary gasdpnamic
laser without feedback (we disregard kinetic cooling). We will consider
a C02-N2-fl20 gas mixture with small mole fraction of water vapor Yg2p < SX,
so that with good accuracy we can assume YH~p +~2~~ 1. We will further assume
that the upper level in cross section 1 is frozen (T3 ~ conat at x> xl),
while the lo~wer level on section 1-2 loses the a-th part of its population
as a consequence of relaxation.
Maximum energy ~n the optical cavity is reached upon transillumination of
the working transition in section 1. Let us find the amplitude of this maxi-
mum and the energy necessary for saturation; then their difference will giv~
the output energy of the laser with feedback.
Let the average number of vibrational quanta per molecule of C02 or N2 in
cross section 1 before interaction with the eaturating radiatioa be equal ~
to E3, and for sym~netric vibrations of C02 to E~. After absorption of light
the populations of the upper and lower working levela of C02 (with consider-
ation of rap~.d exchange with N2) become equal and take on the value
Ne' =N (E~-i- EjY~OilI\~ Y~~~~
where N is the total number of partic les in a unit of ~aass o� the mixture
(here it is also assumed that absorption occurs at a rate appreciably exceed-
ing the rate of VT-relaxation of the lower level, but more slowly than rota-
~ tional relaxation). The energy necessary for transillumination of the. w~orking
transition in cross section 1 will be
i ES Ycc~, Nhv, ~ 1~
. l -I� y~p~
where hv is a quantwn of laser emission.
In cross section 2 we get F~~1=e' and e~7~=e'(1-a)and the maxiatum energy extracted
by the cavity from a unit of mass of the gas is
~ ri1'co,~ a A�~ ~l Yco~~~ ~1 ~-'p~p~~ 1Vhv~ . ~2~
Emaa = ~ ~ _ ~,co: ~ EiYco,~ ~l - a~ ~ ~'~'~co~ e~ e~Yco,~ Q~''~ ~
33
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where S is the efficiency of the cavity; Q~2~ and 0~2~ are the vibrational
stat-sum and relative threahold inversion of populations in cross section 2.
In order for the output energq of the system with additional self-pumping
tn be greater than that of a conventional gasdynamic laser with the same stag-
na~tion parameters, the condition
s= ~~F?nax Eb)lEo-1>0 (3)
must be met, Eo =(e~-e�(1---u)-0] Nh v~I (~I-~B~-'8~fx~~1-}'8~) Q1 is the output ener~y
of the gasdynamic laser without feedback; Q and o are the vibrational stat-
sum and relative threshold inversion respectivelq in cross section 2.
Substituting (1) and (2) in (3), and setting Q~g~~Q, 0~4~~0 we get with accuracq
to te~s of the second order of smallness with respect to e~, e�, A, �
e� r� ~(I-a)-YcA.(Q-~) ~4~
~
b r��-~.�(I-a)-�~ P ~ -I-Yco,) '
, i (
Estimates show that d> 0 over a fairly wide range of a, 'yco. although the
gain is low in absolute magnitude, being ~5-15x.
We can come to an analogous conclueion if we do not assume that zhe working
transition in cross section l is transillianinated. In this case, condition
(3) takes the form
6=9 (1-a)/ll-q (2-a)]>0 fo~ q