SCIENTIFIC ABSTRACT MASHKEVICH, V.S. - MASHKEYEV, A.K.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001032710020-5
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: July 12, 2001
• Sequence Number: 20
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

24(2)t 24(7)
AUTHOR: .1kiashkevich, V. S. SOV/48-22-11-6/33
-----------------
TITLE: The Method of Quasi-ITormal Coordinates in the Optics of
Crystals (Metod kvazinormalInykh koordinat v optike
kristallov)
PERIODICAL: Izvestiya Akademii nauk SSSR. 1)erlya fizichesk~xya,
1958, Vol 22, Nr 11, pp 1308 - 1311(USSR)
ABSTRACT: The present paper deals with the general principles
of the method of quasi-nofmal coordinates and its
application to ion crystals with a space lattice of the
N&C1 type. At present, 2 approximations are beinL!- ifed
in the theory of crystal lattice vibration: approxii:, tion
of point atoms (ions) (Ref 4), and of dipoles (Refs
In the point approximation the state of the crysta-1-
particles is described by means of their shifting ut
number of the elementary cell, s - number of tne
p.---ticle contained therein). In the more accura'-e dipole-
ap~jroxi-nation the dipole-moments are considered in
Card 1/4 addition to the above mentioned va-riables. Tnese dipole-

The Method of Quasi-Normal Coordinc,tes in the Optics SOV/48-22-1,--V53
of Crystals
moments are caused by the defor-ation of the electron
shell. This method is based on the idea of selecting
the coefficients c.A in slich a way that the coordinates
q12 thus obtained de:cribe both the light waves and t:.e
vibrations of other than of luminous character. In
this case H1, which already furnishes the relation of
individual Q-vibrations in hermonic approxi-ation,
will describe the single-phonon light absorption in
qualitative harmony with the results of t;-;e forced
oscillations m,Ahod. A concrete selection of co naturally
depends on the type of crystal. It can, however, also be
done in accordance with some general requirements resulting
from the observation of the inner electric field. In the
case of an ion crystal, when taking into account of
the polarization of the particles results only in
quantitative corrrctions, but does not influence the
qualitative char--cter of t."-.e spectrum (Rei's 3,5).
The vibration spectrum conni~-.ts of 8 brar-ches: 3 acoustic,
1 longitudinal, and 4 transverse optical branch~-s. Of
Card 2/4 these the transverse optical branches are important in

The Method of quasi-Normal Coordinates in the Optics SOV148-22-1-6/33
of Crystals
connection with the spreading of light. In the case
of an ion crystal, HI differs from zero alre~.dy in
the zero-th approximation of k. In tre above nentia-.ed
approximation, frequencies relating to 2 dif:'erent
polarizations are in agreement. Accordingly, all
results agree. Zero solutions are not to be taken
into account. They result in normal initial vibrations so
that:
a11D C21 0. (22)
2 '(n2 1) n2 (n2
n, 2 2 1
(22) and (6McPa (k)12 = 1, determine c 11 and c 219
so that, in principle, the introduction of quasi-n3r-::ia1
coordinates is completed. There are 5 references, 4 of
which are Soviet.
ASSOCIATION: Kiyevskiy politekhnicheskiy institut (Kiyev Polytechnical
Card 3/4 Institute)

AUTHOR- Mashkevich,__V. S. SOV120-121-2-14153
TITLt: The Normal Coordinates of a Crystal LatticeWith Allowerree
MW Interaction Lag (Normallnyye koordinaty k-istallicheskoy
reshetki pri uchete zapazdyv&niya vzaimodeystviya)
PERIODICAL: Doklady Akademii nauk SSSR, 1958, Vol. 121, Nr 2.
pp. 247 - 249 (USSR)
ABSTRACT: For the theoretical Investigation of a number of properties
of crystals it becomes necessary to introduce normal coordinates.
An elementary solution of this problem can be found for purely
mechanical oscillations without consideration of the inter-
action lag. In the following the author demonstrates the
introduction of normal coordinates in the general case for
a crystal lattice in dipole approximation. Starting from the
equation of motion (disregarding the inertia of the dipole
moments) and the expressions for
__1' V1
U, and p the author sets up the amplitude equ,tion ( for
Card 1/3 plane monochromatic waves); furthermore the equations for

The Normal Coordinates of a Crystal Lattice With AUm- SOV/2o-121-2-14/53
&me for Interaction Lag
--r --V -0
UCI as well as for 6 (r, t and j are given as
8 a OAF
functions of q k,t). The expression
I - - +1j 2 1 qa(-+ ;a(l) is obtained for
;~ E 4" (k) ia (k) OL (k ~k)
the energy of the lattice. The equation of motion Is
0 a (-kj + 6j 2-'P a ( 1k -~r " ; --3P 4
q a (k)q - 0 with p"(k) q"(k) and p'(lk 4L(kj-
Expressions for Land H Ftre also given. e denotation is
-.0 1?
the usual one ; u -atom.displacement, the dipole
moment caused by the deformation of the electron shell;
the index I serves for numbering the unit cells, and 9 for
the atoms or ions, respectively; electric field intensity
in the lattice point with the coordinates The asterisk
denotes the cc n ugated complex quantities which are obtained
by rFl cin *3 -1). Thus for example there holds
a g k by (-
Card 2/3 QCL ja (-kj.There are 3 references, 1 of which is Soviet.
I

The Normal Coordinates of a Crystal Lattice With SOV/2o-121-2-14/53
AUoume for Interaction Lag
ASSOCIATION: Kiyevskiy politekhnicheakiy institut (Kiyev Polytechnical
Institute)
PRESENTED: April,8, 1958, by N.N.Bogolyubov, Member, Academy of Sciences,
USSR
SUBMITTED: April 7, 1958
Card 3/3

24(2)
MHORs Ma&hkevich- V- 5- SOV/ 5 -6- 36-1, - 16162
TITLE# The Electrical, Optical, and Elastic Properties of the
Crystals of the Type of a Diamond (Elaktricheakiye,
opticheskiye i uprugiye evoystva kristallov tipa almaza)
III. Di.spersion and Absorption of Light (Ill. Dispersiya
i pogloshcheniye eveta)
PERIODICkLi Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1959,
Vol 36, Nr 1, pp 108-115 (USSR)
ALBSTRACT s The author develops a quant.Ltative theory for the lattice
vibrations of a homeopolar cryetal. Four parts of the present
paper deal with dispersion and double refraction far from the
singular point, with the quasinormal coordinates, with
dispersion and double refraction in the neighborhood of the
singular point, and with the absorption of light. In the
fifth part, the parameters of the theory and the numerical
results are given. The following conclusions can be drawn
fron the considerations discussed in the present papers
1) The theory oonfirms the presence of dispersion and double
refraction, which are caused by the vibrations of the atoms
Card 1/2 in the crystal. Both effects have their maximum intensity

The Electrical, Optical, and Elastic Properties of SOVI/56-36--l-16/62
the Crystals of the Type of a Diamond. III. Dispersion
and Absorption of Light
in the neighbourhood of the extreme frequency of the
optical vibrations where the difference of the refraction
indices for the 2 polarizations amounts to 10-4. 2) A crystal
of the diamond type has 7 axes, and the directions
of the optic axes coincide with the directions of the edges
and diagonals of the lattice cube. The theory asserts a
one-phonon absorption of light with the extreme frequency
of the optic vibrations and further gives the dependence
absorption on the propagation direction and on the polariza'
of light. 4) An experimental verification of these results
of the theory would be very advantageous, for it would permi,
comparison with experimental results of that part of the
theory which concerns the optical properties. There are 1 table
and 8 references, 6 of which are Soviet.
ASSOCIATIM Kiyevskiy politekhnicheskiy institut (Kiye-, Polytechnic Institutel
SUBMITTEDs May 16, 1958
C ard 2/2

24(2) SOV/56-36-6-17/66
AUTHORs Mashkevich, V. S.
TITLEo Electrical, Optical, and Elastic Properties of Crystals of
the Diamond Type (Flektricheskiye, opticheskiye J uprugiye
avoystva kristallov tip& almaza). IV. Interaction Between
the Conductivity Electron and Lattice Vibrations (IV. Vzai-
modeystviye elektrona provodimosti a kolebaniyami reshetki)
PERIODICALs Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1959,
Vol 36, Nr 6, PP 1736 - 1742 (USSR)
kBSTRkCTs The interaction between an electron and the lattice vibrations
of an ion crystal may be dealt with already in point ion
approximation if the polarization connected with the vibra-
tions is taken into account. In the case of a homeopolar
crystal no polarization occurs in this approximation. This
makes it possible to operate either with Bloch- or with de-
formation potentials. The author of the prosent.piLper, by
taking the atoaic dipole moments iato account, develops a
quantitative theory of interaction between electron and
lattice vibrations, and, by using this theory, investigates
Card 1/3 the problem of the existence of polarons in homeopolar crystals

Electrical, Optical, and Elastic Properties of Crystals BOV/56-36-6-17/66
of the Diamond Type. IV. Interaction Between the Conductivity Electron
and Lattice Vibrations
and calculates the mobility of the conductivity electron.
For the purpose of simplifying calculations, the complexitv
of iscenergetic surfaces in the conductivity zone is not
taken into account and the simplest model of spherically
symmetric surfaces with the center at pointt - 0 is used.
With respect to the problem of the existence of large radius
polarons the author arrives at the same conclusion as Deygen
and Pekar, namely that the zonal state of the electron is
stable (or metastable) and that polarons with a large radius
do not exist. The interaction between electron and lattice
vibrations is investigated by means of the perturbation theory.
The results concerning electron mobility and its temperature
dependence are compared with theexperimental results obtained
by other authors, viz. for diamonds (Table 1) and germanium
(Table 2). Table 3 shows the experimentally determined electron
mobility at 3000K and the effective masses for diaaonds, si-
licon, and germanium calculated herefrom by means of the
equation (22) of this paper. A comparison with the experiments
Card 2/3 shows that the-theory leads to satisfactory results. The

Electrical, Optical# and Elastic Properties of Crystals BOV/56-56-6-17/66
6f the Diamond Type. IT. Interaction Between the Conductivity Electron
and Lattice Vibrations
author finally thanks K. B. Tolpygo for discussing the results
obtained. There are 3 tables and 16 references, 7 of which
are Soviet.
ASSOCUTION3 Kiyevskiy politekhnicheakiy institut (Kiyev Polytechnic Insti-
tute)
SUBMITTEDs December 4, 1958
Card 3/3

S/139/60/000/004/026/033
3032/E5A
AUTHOR: Mashkevich, V.S.
--==wpm - -- ------------
TITLE: Higher Approximations in Equations Describing the
State of Matter in Blectrodynamics 1~
PERIODICAL: Izvestiya rysshikh uchobnykh zavedeniy, Fizika,
1960, No.4, pp. 217-221
TEXT: The electrical and magnetic state of matter in
usually described by the polarization and magnetization vectors
P and 1, assuming that the relation between these vectors and the
displacement and magnetic induction is:
D 9 + 41fP (1)
8 H + 4V 1
(2)
The equations describing the electromagnetic state of matter are
then established by deducing the polarization and magnetization as
a function of the fields E and H. When the wavelength of the
electromagnetic wave X is large compared with molecular
dimensions d, the fields can be expanded in powers of d/k. In
Card 1/2

alsher
Appro
oe t 0 x1ft
r dy4 4tio
ejr,M,ft ca'ses 441 CS 4* in equations 'De S113 9/6
ord* P-1 0 the
r 0 in aer Z032/a 0/
000
Of t9rma C4.1c 0- 514
428 C' Oust ions Opp /004/026/03
C ubt u.1 a t order scribing the state of'
0 (7w 1 Cry -0 1 3
0 be Cone jr
Concern pye Ital n Joe ti
0 a cluded erned On
der ed and iva quire
i V*d Irl th ('90, vit In
quant. ror th shkev., a th n h ive t
4tio es e int f 'Rot, opt. 8urr.
so lri e a. tile 4 0 hl Ch I I ) Acal acl ent.
t Th ac Cher Re'r rodt, , act.
0 t rose -0 .2) C ti 'rhi I A %r - Por
re--6-rej,coreat OPIC 2-der on Of 0 at
ASSOC optl~
ftent VOC t 4ppr rho see Cal rat-
I a en or's G-Vj Pres Ond e 131 a
t 1., 0 1 144 ti en t -0 0 tr(,p
friy e1 n t e1'.48 00 8 . a er er t
skj Y Cj Of PO is erfts
y assical. U.14
Yet' P0 poli t fticros e are
Ytech eichni rher, CO ic
toy '20, ni C al ell 0skj
0 are
card 1959 xnstlt -instit t
2/2 te) 4

"SHOTIM I. S.
RUO~r approAmations In the Xw&M mthod. Fix. tver. tela 2
a0,,5:908-912 NY I" (XIM 13:10)
1. politskmichookly Institut, "T.
(lattice theory)

84617
8/181160/002/010/045/051
lit 0) BOI 91BO56
AUTHOR: Mashkovich. V. S.
TITLB. Dipole Approximation in the Micro-theory of Crystals.
I- Lattice Vibrations Taking in Consideration the Electron
Dispersion
IN
FIRIODICAL: Fizika tverdogo tela, 1960, Vol. 2, No. 10, pp. 2629 -2636
TUT: X.- B. Tolpygo, in the Born theory of the crystal lattice improved
by him, proceeded-frou the assumption that the potential energy of the
crystal depends on the displacement and the electron dipole moments of
ions. At the same time, he neglected the inertia of the electron dipole
moments or of electron dispersion. In the present paper the electron
dispersion for lattice vibrationa, the frequency of which is *&all com-
pared to that of the electron transitions, is taken into account. Be-
side#2 *sub-cells* are assumed to be crystal elements, which are con-
sidered to be parts of the unit calls belonging to the nuclei. In the
first part, the Hamiltonian of the electron system is set up in harmonic
PAkrd 1/3

84617
Dipole Approximation in the Micro-theory of 3/18 60/002/010/045/051
Crystals. I. Lattice Vibrations Taking in B019/BO56
Consideration the Electron Dispersion
approximation, after which the delayed interaction of the lattice vibra-
tion~ with the electroaagnetic field characteris*d by the vector poten-
tial I is investigated. For the perturbation operator 'HII in the Hamil-
ii( + )
tonian of the system the expression HI - Oxp(-iWt) + h exp(iwt)(9)
is obtained. With the aid of N for the wave function the expression
is . v(+)*xp[_i~jo + O)tj + vk-)Oxp[-i((,)o - w)tj (11) is obtained, where
V(�) j(njh(-�)j0~n/4(wo - Wn + W). Moreover, from the *equations of
otionO of the electron dipole soaents and the equation of action of the
:
*ntors of same of the "sub-cello", the amplitude equations are derived.
Finally, several properties of the coefficients of the two amplitude
equations are discussed. The results given here represent a generaliza-
tion of the theory developed by Tolpygo in the following resp*ots:
1~ lo assumptions are made about the existence of the potenti4l energy.
2 The electron dispersion is taken into account. 3) The difference
Card 2/3

846!'?
Dipole Approximation in the Micro-theory of $/lei /60/002/010/045/051
Crystals. 1. Lattice Vibrati-ons Taking in BOl9/BO56
Consideration the Electron Dispersion
between the nucleus coordinate and the coordinates of the centers of
mass are taken into account. 4) A zero dipole moment is assumed. 5) No
assumptions art made as to the binding of the electrons in the ions and
the approximationsof the wave functions. In a following paper, vibra-
tions of dipole moments with frequencies lying within the range of
electron transitions are to be investigated. The author thanks
K. B. Tolpygo for discussion of the results obtained. There are 7 ref-
erences: 6 Soviet and I German.
ASSOCIATION: Xiyevskiy politekhnicheakly institut (Kiyev Polytechnic
Institute)
SUBMITTED: March 14, 1960
Card 3/3

P~l
3/056J60/038/03/22/03~
3006/B014
AUTNORs Mashkovich, T. S.
TITLEs -Electromagn*tic Waves in a Medium With a Continuous Inergy
3yeatrum ilkI
PnIODICALt Zhurnal skeps,risentellnoy i t*or*tich*skoy fisiki, 1960,
Vol. 38, Do. 3, PP. 906-911
TEM In the case of spatial dispersion it in possible to consider
pol&ris&bility to be a factor of proportionality between polarization
vector and field strength. The effect of spatial dispersion was studied
by P*kar (Ref. 1) far the exciton #tat*. In the article under review, the
author studies certain curr*ntl*ss state* and approach** the dependence
of the polarisation vector on the field strength by using the p9rturbatiGa
theory. go uses a modification of the Weieskopf-Wigner method similar to
that employed by Born et &I. (Ref. 2). The Ramiltonian of this system in
set up as the sun of the unperturbed R&miltonian R 0of the dissipative
perturbation 91 and the electronagnotio perturbation 11. The wave function
Card 1/2

82421
Electromagnetic Waves In a Medium With a 3/056 60/038/03/22/033
Continuous Inergy Spectrum. I B006%BO14
of the system in similarly composed. H
^A is determined from the interaction
between electrons and lattice vibrations. It is assumed that when twO the
system to in the ground stat*, and that the interferences of energy
dissipation of the various states and the width of the ground state are
negligible. ~(+)exp(-iwt) + ^(-)Oxp(iwt) , and the corresponding
h
steady-state solution of the wave function If' can be written down.. Next,
the author studios the dop*ndonce of polarization on the electric field,
and derives a number of relations. In conclusion, he studies the
dispersion relations for the so-called kernel of polarisability, and dis-
cusses the solutions of the Maxwell equations. There are 4 Soviet roftr-
onces.
ASSOCIATIONs Kiyovskiy politekhnicheakiy Inatitut (KiZov Polytechnic
Institute)
SUBMITTEDs September 3, 1959
Card 2/2

BANPADZF.,, R.V.; MSHMICHp V.S.
PLapproximation in the tbeory of & diamond-typs, crystal Uttice. Lm.
v7soucbsbeswo; Me zw*105-40 161* (KEM 14:7)
1e Kiyevskly politekhnicheekly institut.
(Dipole moments) (Crystal lAttices)

A, 7
25200
031
S/056/61/040/006/021/
~
.
B108/B209
(,#o/ /n -3)
M Mashkovich, V. S.
0
R

-TITLE: Electromagnetic waves in a medium with's continuous energy

T
L
E
IT
spectrum. II
PERIODICALt Zhurnal eksperimentallnoy I teoreticheakoy fisikior V. 40,
PJMIODICA
no. 6, 1961, 1803 - 1011

EXTI In
T
TEXTs In a previous paper (Ref. Is ZhETF, L8, 9o6, 1960), the author has
derived equations for a electromagnetic field In a non-conducting medium
erive 0
dd
with spatial dispersion. The results are now applied to exciton states of a
'crystal. Calculations are made on the basis of the integro~differential 0,
,i,equation
+ T6 (r) + UT (r, r) Sk (r) ~r' 0. (1) 01
4ig Kke (r, r) (e) dr', (2)

whioh automatically accounts for the additional conditions and requires n
0
1
Card 1/7

25200
5/05~/61/040/006/021/031
Electromagnetic waves in a ... B108/B209
the selection of the exciton wave functions; as the latter, the author used
thos6 of S. 1. Pekar (Refs. 2,3s ZhETP, U, 1022, 1957; ZhETF, a, 117 6
1958).' In Eq. (1), J/o2j the polarizability'kernol is given by
+ Kel,,, (r,
(0 1 ar W I R) (" I or, W) 10) (n I Oe (r) 10? (0 1 Ov. (3)
hW - is. (W) Es + AW Is,,
rot, 1(,'. (r, r,) = 0, (4)
730
where E0 is the ground-state energy and En that of the exnited'statel F_n is
related to the lifetime of the state as usuall G(r) is the operator of the
electric moment per unit volumel the operator "rot" indicates "curl". For
waves in an infinite crystal, Sq. is transformed into
Card 2/7
...........

5 )0
S/o5y6l/040/006/021/0131
Electromagnetic waves in a ... B108 B209
Ke'. (r, r') K,",' + K,-ee (r,
LI
K ',, (r, r') :] ~ r� (k, a) x
X,
(21t)J Aw .. ) I t
x (b, W, k. k. at) ex pA (r r') T- i2n (br b.'rj I dk; .(6)
bb, E (k. - Es
r� (k, a) :F WX :gw) - Ea t
g+.Y, (b, W, k, W, g,, (b. k. o,) g,, (b', W, a), g-
with the exciton quasi-momentum k and the vector of the reciprocal lattice.
Taking into account that the generatrix of _k in (6) cannot be ara~ytic at
the point 0, one may rewrite Eq. (1) in the form
Card 3/17

25200
3/056/61/040/006/021/031
Electromagnetic waves in a ... B108/B209
(r) + 11,~ (r) + 4nr (r. r') 11,4 (r') dr- 0. (7)
Wo a) (0, 0, a i .-al
0, -al ai a
+ a Wr g,, -Fr 7 W) )1.+*- 45'-
'The primed sum in (8) indicates that terms containing a singularity are
112
neglected. The wave function 2- is used for the case of
k (TIX k
a wave passing through a plane-parallel plate of a cubic crystal.)('-`~ is the
kk.
wave func~~n of the infinite crystal.
-'04
ka k& k I -ka . ka k
1,2 1,2 1,2 3 3 3 'VVAN + 1),
V= I ...... NJ a1,2 are the parallel surfaces of the plate, N the number of
Card 4/7

25200
5/95 61/040/006/021/031
Electromagnetic waves in a.... B108YB209
unit calls across the thickness 1 of the plate. When the z-axis is per-
pendicular to the surf aces of the plate, the integral-kernel has the form
hy Pl

K V F� (k, a) exp (:F i fk3buz +
$
24)
(2:q
bb'
+ It, (x x~ k,, (Y - Y') + (kibl, + k2b2.) (z - z') + 2:t (br-b'r') 1) x
x Igt -, (b, W, k, k. at) exp (� ikabuz

t
- 9-V (b, W, k, i, a) exp (T ik3b3,zj I A, dk,,. (13)
where k 'Tr./(z. + 1 ). In this case the equation of the field is glv*n by
+ (Z) + X (z, z', b, b'. a) 9(2') dz' = 0. (14)
2F
W

provided
9(z) lies in .
O
the y-direction. The.sum over(Y- concerns transverse
excitors only, b nb n integer number) VZ 4yL21/ji 0;
' z

Card 5/7

25200
S/056/61/040/006/021/031
rilectromagnetic waveB in a ... B108/B209

"Z
(z, z', b, o', a) exp (2,t (bz b r- (k, a) g. (b, k, a) x

x exp (ikz) (g. (b', k, a) exp ikz') -go (b' .- k, a) exp (ikz') 1,

where f f 7,g.
(b,k) f(nt kj
9 The solution of Eq. (14) has
0 C)
k
3
x9y
the form
9 (2) c, exp Ux,z), (16)
where r are the roots of the equation

g- (0, o, x, x,, a) r-
-4- TI + 0 (x, a) o. (17)

Card 6/7

25200
S/056/61/040/006/021/031
Electromagnetic waves in a ... B108/B209
Pinally, the absorption of an electroinag-netic wave with spatial dispersion
is investigated, leading to the term
2i, 8,~*.(r) 8~-(r') dr dr'.
where R y is the anti-Hermitean part of the kernel K x y
There are-
7 Soviet-bloc references.
ASSOCIATION: Kiyevskiy politeklinicheskiy Institut (ICiyev Polytechnfe
Institute)
SUBMITTE"D- January 11, 1961
Card 7/7

DUOUDE, V. A., MASHKEVICH, V. S., PRIMIOTIKO, A. F., PROKOPTA, N. F. , SGSKIN, 1% S.
ONEWARON6
ffind:uced radiation in molecular crjstals."
A four-level scheme for a quantum generator was discussed. It was shown
that optics.I properties of molecular crystals provide a basis for the reali-
zation of a quantum generator.
The report presented to the 22th Conference on Luminescence (Nolecular
luminescence and luminescence analysis) Minsk, 10-15 Sept. 1962.

D2
2
12 /31 '2'
11. hk e v 4- c hY
Condi ti~ns for the occ-,;rrel-11ce -,f si~at-
crystals
--,J zika tverdoCc te' a, 4 , no - 6
EXT The spatial d is.-je rsior. contained in the ocal re'- at
;-7)/4n is examMed usinC,
PA, f K., (r') dr'
(r, r') (E. Ej X
x !(() G,,(r).n)(n C,.(r','O) (n G,,(r) 0)(0 Gv.-(r') n)-,
Ell - EO
Here C"L(r) is the solenoidal part of the amplitude of the
Card 1 13

Conditions for the occurrence -Z 12 r
-'Ih the frequency (J. P(r) is the -)ola7izatic)
w
ener_cy of the ground state, and s t e n e r y 3 f h e e x c 3 t
'p', is the probability, per unit o f me , o f it 4- 3-:. Z, t-
7 rl /
interval of the frequency that correspor,,:s to szi:-tes u*---"---,-L C.
ene=y 2 + and G(~'*' is the' oolarization ot;erator. e d e e
0
- is determine' b
spatial disper340n - y H e r t: S e
radius of the kernel cf -olari'zabiI4.ty ant4 the f
-h-. . The s atial. dis,---arsJon of the !,-,cai or -Iil).11-.3c~- .
L
corresp~Dnds to the polarization causel ,-Y eXci1ta-.-:J:.-;.
i t h 1 tr,at. these tViG Va:-4.U11t3 (Ii,cai and
considerably froin one another. -.here is :-1-G
for impurity states -ith lar--e rad-Ju s or t h I o c a e r-.-:
In the case of spatial dispersion of *he nor.-I(J-~al
excited states causing polarization .iust ljeion,~ to
-0, ~ . ,
S)/ 1 must hold. This condition car, be
a ectrum and i(
as where 1(-80) 20. 1// --s -~ha
Ll
lifetime of the excitons with respect to the tia.-.3itiOnS t'~
Card 2/3

ConAitions for t1le Occurrerce ...
states s + -tw N
- - 0 S) k S " .11-er, exciton,
Of he electrons tten y may j e 1)
ex0iton band at suf,- - - end con5'.d6r4b!~, on the
,!cje,-,t,y of
Probably spatial dis ~0*11 tem")eratu'res. c; 0 ") 'r, e
'De ra i or: Of the non-loc
excep: al to t,-v
"w ter:'Peritures.
_1 t s
lr'st"Lut f4ziki A21 USoR) Kiyev /Instit.t. of
~rx-rSSR, Kiyev) -ys:cs ;,-z
9052
Card 313

/~A# 1W211t
5/18 1/62/004/010/055/063
B102/B104
AUTHORS: Broude, V. L., Mashkevich, V. S., Prikhotlko, A. F.,
Prokopyuk, N. F. and Sookin, M. S.
TITLE: Possibility of obtaining induced radiation in systems with
electron vibrational levels
PERIODICAL: Fizika tverdogo tela, v. 4, no. 10, 1962, 2976-2976
TEXT: A possibility of obtaining negative temperatures and induced
radiation in a four-level scheme of molecular systems is discussed. The
scheme (Figure) consists of the ground state (1), a vibrational level of
the electron ground state (2), the first excited electron level (3), and
the totality of all higher levels (4). 1"-4 is a transition due to light-
quantum absorption, 4-3 a radiationless transition, 3-2 the transition
used for obtaining the induced radiation and 2-1 again a radiationless
transition. The lifetimes of the radiative transitions are
T , 10-7 _ 10 -9s*c, those of the radiationlese transitions are k 'f" v/.
r n r
r has to be small for obtaining the induced radiation. Generation of
Card 1/4

S/181/62/004/UlD/055/063
Possibility of obtaining induced ... B102/B104
2 C7 2,&,-
coherent induced radiation begins if n -n 4 ax i, v r I-R where n n are
3 2 o 1 29 5
the mean numbers of molecules in state 2 or 5 per unit volume, V is the
wave number of the 5-2 transition, v the halfwidth, H the reflection
coefficient of the resonator mirror, I is the length of the sample, and
ro is the lifetime of state 5 with respect to the 3-2 transition.
n3 4 U K," N, where IV is the lifetime of state 3 with respect to all other
transitions to lower states, K is the mean absorption coefficient on the
region of the 1-4 transition, ILis the number of states 3 produced from
one state 4, and N is the number of photons of the optical excitation
1-4 per unit of time and per unit of surface area. Numerical estimates
for the anthracene molecule are presented. For K&2 cm
'r - 3-10- sec and 'r - 10-7sec one obtains N - 4-10 21 ca2sec -1 which can
0
be realized by means of an WOK-2000 (IFK-2000) pulsed lamp. If besides
,,Irr, n 39 N will depend on 'Al, not on Valone. This makes it
Un "\ An I;o
possible to draw conclusions as to the most effective form of luminescence
spectrum to obtain, induced radiation. A system of layers of dielectric
Card 2/4

3/1 a IJ62/004/010/055/06 3
Possibility of obtaining induced ... B1021D104
coatings with a certain R(&A) dependence
induced radiation frequencies other than
peak. Thus such a system can be used as
figure. The most important English-langaage
et al. Phys. Rev., 123, 765, 1961; E. G.
35, 759. 1961.
allows of annihilating all
a chosen one, where R has a
an "antifilter". There is 1
references are: W. Kaiser
Brock @t al. J. Chem. Phys.
ASSOCIATION: Institut fiziki AN USSR, Kiyev (Institute of Physics
AS UkrSSR, Kiyev)
SUBMITTED: June 6, 1962
Card 3/4

S/181/62/004/010/055/063
Possibility of obtaining induced ... B102/BI04
I -%%~ M-3 -4
I
- j
I
I
--- I -
11,78' -1
Fig.
Card 4/4

9/181/62/004/011/034/049
Dios/siol
IUTBORj Mashkovich, V. S.
TITLEs Absorption and dispersion of light in the region of exciton
junctions
PERIODICALt Fisika twerdogo tela, v. 4, no. 11, 1962. 5279 - 5285
TEXTv The effect of spatial dispersion on-ths, dispersion and absorption
of light around oxciton transitions is studied for the case of weak
xciton-phonon coupling. The Maxwell equations are solved by a method
:
eveloped previously (ZhETF, 58, 906, 19601 40, 1805, 1961). The effect
of spatial dispersion increases with increasing oscillator strength of the
transition, with increasing mean free time of-the virtual exciton, and
with increasing width of the exciton band. This effect say be considerable,
particularly at low temperatures. The spatial dispersion leads to a
violation of the Kramers-Kronig relations when the seen free time of the
virtual exciton is long enough. When linearly polarized light falls per-
pendicularly onto a plane parallel plate, the width of the region in
which the spatial dispersion becomes effective to small as compared with
the width of the exciton band.
Card 112

8/181/62/004/011/034,/049
Absorption and dispersion of lignt ... B108/B102
ASSOCIATIM Institut fiziki AN USSR, Kiyev (Physics Institute AS UkrSSR,
Kiyev)
SUBMITTEDt June 1, 1962 (initially) z
July 3, 1962 kalter revision)
Card 212

S/056/62/042/001/0k2/048
U B100102
AUTHOR: Mashkevich, V. S.
TITLE: Electromagnetic waves in a medium possessing a continuous
energy spectrum. III
PERIODICAL: Zhurnal eksperimentallnoy I teoreticheskoy fiziki, v. 42,
no. 1, 1962, 135-143
TEXT: The theory of electromagnetic waves In a crystal in the presence of
spatial dispersion due to exciton states was applied to a number of
problems in previous papers (ZhETr, je, 9o6, 19601 AQ, 1803, 1961). The
solution of Maxwell equations for a nonconductive medium was presented in
The pro agation of perpendicularly incident waves through a plate (cubic
crystalT was examined in II without allowing for birefringence. The
birefringence due to spatial dispersion is now taken into account. Using
results and symbols of the previous papers and assuming optical anisotropy
for a cubic crystal, the following relations are obtained for the
amplitudes of incident, reflected, and transmitted waves:
Card 1/4

Llectromaenetic waves in a medium... B104Y13102
R. I - 0% + Fl. D. 9. i20, exV iho
Gs +(I + IFJI ' 01. + 0 + JF.)' (4).
F.-=f,,ctgx,"l+f,,,ctgx,,j, G,=f,,/sinx.,I+f,,/sinx,,,I,
XM / As
(X2.1 - k2.)
f is obtained from f by permutation of subscripts 1 and 2; K2 are
n2 nl nl,2
the roots of the equation
X9 + Y V + UP) + BI(IXXI ic. 0.
B 4xVL'l I P..L IE (0. al) Es I/ U,
As / W., E,, + Aw E (0, al),
5/05 62/042/001/022/048
Card 214

B/056/62/042/001/022/048
Electroma6,netic waves in v. medium. B100102
where mn denotes the eifective mass for the direction 9, Wpendicular to
the plate; P allows for the local part of polarization; k n is the root of
-1 2_
the equation , k it o. if M and m differ noticeably,
n n 1 2
birefrineence will take place. The penetration of a plane-parallel plate
by a wave incident at an arbitrary angle is considered. Restricting
oneself to a semi-infinite crystal, the following generalized Fresnel
formulas are obtained:
f__ f .p (12x4) f--
R,w = 4, Is +-+ 14
it-2- to + e- p(12xj) I-,,- f
(14).
D,, IL44PS 91 q2 94 exp I i (x,, A.) 11 x
PI_ A- P;
x + exp (21M.4 I- /~+I-
14
Card 3/4

S/056/62/042/001/022/048
Electromagnetic waves in a medium... B104 B102
-11
Lhe longitudinal components of the electric field of a light wave are
calculated, and the results are compared with the corresponding results
-f S. I. Pekarts theory (ZhETF, .3A, 1176, 1958). The latte~r is criticized
-ri connection with the case of oblique incidence of a longitudinal and a
.r-ansverse wave field. There are 11 references: 10 Soviet and 1 non-
iviet.
..~__-,OCIATION: Kiyev skiy politekhnicheskiy institut (Kiyev Polytechnic
Institute)
,11*: -ITTED: April 25, 1961

10 Egg 9-9~ AratM LIA-1
PIP
-S 'Eff wl~

MASHUVICHP V.S. [lbahkovych, V.S.)
A 3,aster based on Raman scattering. Ukr. fiz. zinw. 8 no-91
1032-1035 5 163.
Nonlinear optical properties of a threo-level system in a
resonator with several modes, Ibid.slO35-1039 (MIRA 170)
1, Institut fiziki AN UkrSSR, Kiyev.

-_ , I I I : .. -
~ ; ~, -: 1 i, - I , . ~: - .: . I ~ .~ - - -: 11 . - ~ ~ , . . - ? --., Z 7 ' I -- -
-
=-,m - . "- 1~ -

L 33166-66 EWT(1) IJP(c ) JV-W/GG
ACC NR, AR6Oi6i�~---- SOURCE CODE: W(5o58j65/OW/OL1/DO30/DO31-
27
AUMOR: Mashkevich. V. B.; StrashalWya.-14. I
TITLE: Pogilble manifestation of additional waves in the reflection of 1 from
crystals
SOURCE: Ref. zh. Fizika, Abs. 11D234
REF SMM.: Tr. Komis. po spektros~x
.211. AN SSSRf t- 3, VYP- l.- 1,964., 448-453
Topic TAGS: light reflections exciton absorption# refractive index, cadmium sulfide
AMTRACT: Xt Is indicated tbat usually the manifeefttlon of additional ligft veves
in the region of e=iton absorption of the crystal be& been considered only in con,-
nection with the passage of two waves tbrowgb a thin plate. At the saw time, adA'-
tional. vaves can alvays greatly influence the reflections too. Zspecia.1.1y ebaracter-
istic is the case Aen the refractive indices of the two myes satisfy the relation
mf m r?l > 0. O= the additional vave can greatly influs=* the pbase of the re-
f1wted vwm. The CdS crystal is considered " an examWA. [Translation of abstractil
SUB'CODE: 2D/
6

ACCESSION NR: AP4041706 S/0181/64/006/007/2037/2046
AUTHOR: Vinetskiye V. L.; Mashkevich, V. S.; Tomchuk, P. M.
TITLEs Theory of stationary radiation induced by interband transi-
tions
SOURCE: Fizika tverdogo tela, v. 6, no. 7, 1964, 2037-2046
TOPIC TAGS: laser effect, laser emission, laser pumping method,
stimulated emission, transition frequency
ABSTRACT: A kinetic equation method developed by the author for the
analysis of stimulated emission (UFZh v. 8, 918, 1963) is used to de-
termine the parameters of the singular modes at which laser action
can be achieved. These parameters are then used to determine the
threshold value of the pump signal. It is assumed that only direct
transitions are effective, the electron and hole bands are spherical,
the electrons and holes have equal effective manses, each band is in
Card 1/2

ACCESSION NR: AP4041706
statistical equilibrium, and the system is spatially homoqeneous.
it is shown that an important factor in the feasibility of IaBer ac-
tion is the spacing of the singular modes, and monochromatic emission
is possible in principle if the spacing is large. Future plans call
for investiqations of induced emission for system with impurities
and the use of x-rays or gammia rays for pumping. Orig. art. has:
56 formulas.
ASSOCIATION: Institut fiziki AN UkrSSR Kiev (Institute of Physics,
AN UkrSSR)
SUBKITTED: 24Feb64 ATD PRESS: 3076 ENCL: 00
SUB CODE: EC , QP MR REP SOVt 004 OTHER: 004
Cord 2/2

PASIBC.-I'VICIII V.S. [Mas~Lcevyoh, V.j. j
Laser with two Vpes o' active centers. U~x. fiz. zhur. ~ n-l-.1-1:
1260-1263 N 164. (: az LA l'i : ~, )
11
1. Institut fiziki A:i "iyov.

ACCES=X Us. AM12027 3/0185/64/009/001/0014/0025
I
AVMRs Dwyakivalkwey, as Ya. I X&shk*V*Qh' VO 3
Tr=s Theory of stationary madiallon of a homogeneous mWaten in -9 multimode
resonator, 1. Dvadom of ndation on the aft
SOMM MMSYIWIWy AWdu" --hunal. V. 9. no. 1. 19&. 14-25
MPIC TLOSs laawo maser, resonator, resonator nods, laser theory, rAng, multi-
mods resonatore IdwUo equat4ons
-ABSTUCTs The present waric was wulertaken to mays the proUss, in laser theory,
of determining the nodes at which generation Ah*WA occuro In previous work by
one of the authors It was shown that, by using the method of kinetic equations, a
nwibor of true results can be obtained in the case of a stationary reglme; he
succesded in investigating nonlinear properties during weak swings and in proving
the existence of a sharply expressed threshold of generations. In doing so, a
large noiber of modes and. since the field was considered in a quantm mechanical
sense, *cutaneous radiation won consistently taken Into account. The present
work continues the, Investigation. Using- the nothod of kin*Uo equations the
Card 1/2

AC4==N Us AP4=27
authors develop the theory of the stationary radiation of a homogeneous sYstem in &
resonator where there is a great nwbar of resonator nodes within the width of the
radiation line. (Because of the "Ume ooaplwdty of the problem of heterogeneous
systems, invosugstdon of Seneous systaims Is a necessary step, ev thou& It
must still be detemined iftether a laseroalkn be gonsidared a hanogensous system.).
Tas finding that the intenatir of radiation of the resoator nods is a function of
the swing In reglops of weak and strong swings is a real st4V forward %hich per-
mitted obtaining vow deta" Womation on the PrqPwties of the syst4m and the
geners-
radiation. It is shown that it the mabar of nades at *Lcb
tion of induced radiation oomrs Is niall In comparison with the amber of
modes, there in a pronounced thredwId. value of the amino lbe w14th of the
threshold region is found. Or1g. art. has 85 fanolas.
Insty0tat fis~ AN UkrLSR, Ziff (ISBUtlate of ftsiose AN MQM)
SMTM OWAY63
M (MIX: PA. AS
Card 2/2.
DM ACQ& 147ob&
--NO MW XN& 002
2=3 00
0=3 0"

ACCESSION MR: AP4017404 S/0185/(A/00/00VO226/0229
AUTHOR: MshkewV*ch, V. S-
TITLE: Radiation of the second optical harmonic
SOURCE: UkrayIns'ky*y flz"chny*y zhurnal. v. 9. no. 2, IWA, 226-229
TOPIC TAGS: electrodynamics, loser, quantum mechanics, crystal radiation. optical
harmon1c, perturbation analysis. combinatorial scattering, phal
ABSTRACT: The high paier levels bbtained from present day lasers create condi-
tions favorable to the generation of the second optical hqrmonIcs In crystals.
The classical theory of electrodynamics Is not applicable because of relatively
high second harmonic power levels and because the reverse process, I.e. recombine-
tion of the second harmonic radiation to give the fundamental frequency. Is non-
singular (I quantum of the second harmonic radiation yields 2 quanta at the funds-
mental and vice versa). Hence, a quantum mechanical analysis becomes necessary.
The simplest model, having only-one mode at the fundamental frequency and one mode
at the second harmonic, Is assumide" For a stationary sptem, with spontaneous
radiation at the second harmonic frequency, the condition under which the second
harmonic radiation offlclemyg 0 1 IF-0- appnolmately 100% Is
*~ " &%,c
Cord 1/3

ACCESSION NRS AP4017404
where a, and a are losses associated with the actual propagation modes of the
fundamental 8:3 the -second harmonic components, respectively. The Inequality (1)
assume$ very large values of N,. the pump level at the frequency and the mode of
the fundamental component. if q, Is the -, 6er of quanta In the fundamental W -1-
and If q, >> I then the assumption of large N, simplifies to:
jV, 3, 1!
28' (2)
where 8 Is the probability of transition of two quanta of the fundamental mode
Into I quantum of the second harmix (c mode. Thus. when the basic Izequality (1)
is satisfied and when the external losses at the second harmonic fr uency are
low, the pump levels which satisfy (2) giv*4
)- 1. The classical approach gives
the erroneous answer that 17 -%s, I can be &chi owed I ndependent I y of the va I ues of
al and c%2. Perturbation a lysis of the spontaneous stationary system with the
above assumptions shows that It Is stable. When the refractive Indices at the
fundamental and second harmonic frequencies are equal, a maximum transition pro-
bability 8 rejj!ts tnd, for Items realistic parameters, the Inequality (2) gives
N >> O.S x 10 oc" . This level Is achievable with ruby loser radiation. It Is
t9 author's opinion that values ofo7g= I were not achieved untl I now because the
bas I c requ I remant as expressed by I nopm I I ty ( I ) was not understood and not fu I -
f I I led. UmInailon of an Indoced redlation systain shows that the generation of
the 9 hennonic Is awlepus to con6inatorlel scatterinjo The basic diffl-
W

ACCESS I ON KRt AP1401740
culty arises from the fact that the coherency volume Is limited by the free path
length of a phonon. Indicating the requirement of low tempetratures for Induced
generation of the a PoW harmanic. Orig. art@ has: 25 formulas.
ASSOCIATION: INSTY*TUT F1 AN UASR, WW. (institute of "sics, Academy
of Sciences of the Ukrainian SSA)
SUBMITTED: O8Oct&3 DATE ACIS 19PAr" FACI.S ad
sue COUS op NO R9F SWs 003 OTHFAs 003
Card 3/3

'~. --: ;I - ~'.. I...,- .- . -- I- -- w :- - - - .- : 11 .~ ~ I ., .
Z- - - --- - - ~z : -'- -, Z-, I - --- - - - -, --
-- . .
, ~ . -~ , , , ~ ~7 ~~ . - , '- I .~ - ~- 1. . . - -
ig, ~ :a~ If z - -
,- -,--.,cy,7-,- f- jz~-
~- tT- -?~ i . , .- -

j.
FF-_ - - - - - ---- - . . . - . -
-1 .. - - .- I . . 1:.... ., - w, .: - -. . . . .
:~ ~ -Z.~ , -.1 - ., . - - - - - N'. - . . .
. . :, ~w% , ~ .: ;l . - .-
! ~ t, .. . ~ I
I . . - i. . I . 1 .1 1 .. . I I .- x - . . - . G
I ; - . . . . I

aiw-
i. rld -6 ... I ~ - 11 , 1. ,

I I I. I . . : - -,i . . I- i- . -, . .
:1 ;7,; -;~;: - : .., .: q - ~ -1. :-_ - - . '. L , -; .- ~~ ~ -: "-,.- ,, ~,-- --:,- --- . ,.., - -
~ -! ~ ~a 1, ml 1 1, -
. - "
11 - o., - -,
.4 Wall RIMPIN . ).,

rR I .
Z_g
nl
MOXV t W-PM -4, P; Pi--
WN
1m,
VV 600 21-rz
10
41t
~W7
A -- ~ ---
CV.--
omit,
-my
r7t
AL, altIL
f Virr
j;RX
AS
AK
I'A
r r~i - -w-ard,
Ac _M
9- P-1: ..,.q
~_N
M_
MWN
ROME:
i_ PEW-- MW W_e7
-61 wt
J;717
'&VA it
wto M
UZI
OM
1,
WtoW.:. a
7~~ Z~AS_W_ -5. 95i

Ut 'Ef-Ru
z 'Ra 1, ,r I .
M

-- -:- - --. - - . - 1 -1 i - . . . - I I
7
- -- -7,-- - --
IN, -- - - -- , , '. I- , - 7 . --

1: NPR 7

sommosimalM. M

;--_7 --- - - ~ . ~. .. . ~ i ~- - . - . . : .
".-;. -.- i --I - - -, - ". -I ~ . - -,-- . I ..
~ ~ 1.- -1 !-.-- Llll -- ,
!:. - - - - ~ 7A.11- - i -.' , . ~. ~~:, ..... :: ~-
-71 - .1 ~ .. d.,.J.- 1 . .. I . . - . .
I I-. . . I !
I - -t ~, 1. -, -, ~~: ~ -4 -~-.
" .-

w
. I I ... . r - I - . I . .
~: ~4---;7~ - --- - - - -.-' -. - - - -- --', -;, -.;
, - - ,, , . I -: 7 .. - I . ~ ~ %~* - ~ -:. ~
r ,
", - ~ - I !!!!. ~. . . . . ., 71 !;~ -7 '1 ~- 4,--- , :- I -t-'L & ~ Q.

VINF.TSKIY, V.L.,, MASHMV1,211 V.S.
~~ensration of la3er recliat-'.on in direrc tranaltiong -In $1
meWconductor. Fiz. tvor. tela 7 no.6-1898-1899 Js 161,.
(MIRA 18t6)
1. Tnetitut flzlki AN UkrSSR, Kiyev.

I'M
ton
miw V~ MORT M
W97
OX
_1 R
~Ra I
A2
MaMMMIM
z-N R, OP- -A,
R~
M M; WIT
RIMMME, wo 1j",
~ ow I W~_011111
0
~W_ s

MAIMISHKOf I*A. [Ma-ruchko., ...0.1; RASUKEVIC,
Gsneration of the soo-ond optical ha=outa in a laser
-Mts fiz. zhurs 10 no.301i-322 Kr 165.
1, InOtitut fizJ-ki AN Ukr3SR, Ki."v.

-or, witii
riaisilon of spr*

A-11

MARUSHKOv I.A. I jgmmvICHC V.S.
- "WmlfW~
Idw width of induced Raman scattering, Opt* i spairtr. 19 no.U136-
1 138 A 965- (KMA 1818)

Apir.,
a SpOctria
P.
The

A---
0- w
AIDA
if do
2-
'y ig
'Al
Mgt RMS
3Yn,---
lk,

L 32632-66 HD/E (1)/EEC(k LW
W-T
ACC NP, AP601882o SOURCE CODE: UR/0056/66/050/005/1410/11414
.,A7LJniOR: 14ashkevich, V. S.; Vinetskiy, V. L. -1 -
ORG: Institute f Ph sics, AcadeaW of Sciences Ukrainian SSH (Institut fiziki,
oi-
!nauk Ukrainskoy SS137
f
TITIX: Role of absorption by free carriers in a semiconductor laser
SOURCE: Zh eksper I teor fiz, v. 50, no- 5, 1966, 14lo-1414
TOPIC TAGS: light absorption, 1zxMM2WW% charge carrier. semiconductor
laser, carrier density, laser emission, photon. exciton, laser pWTing
ABSTRACT: The authors present a consistent analysis of the interaction between
radiation and the medium in a semiconductor laser whose characteristic parameters
without allowance for absorption by free carriers were determined by them earlier
(FTT, v. 6, 2037, 19a) - It is shown that when absorption of photons by the free car-
riers is taken into account,the kinetic equation for the radiation-medium system can
have three solutions corresponding to different carrier densities. Only two are
stable and only one of these gives stable laser emission. The analysis is restricted
to the simplest case of interband transitions in an Impurity-free semiconductor, neg-
lecting the binding between the carriers and the excitons, although the latter assump-
tion turns out to be in disagreement with the actual physical situation. The stable
laser solution is obtained in the case of weak absorption by the free carriers, and a
criterion for the realizability -f this solution to derived The threshold pump ener-
C,,d 1/2

L 32632-66
ACC NRI AP6018820
gies of the different solutions are found. The second stable solution, which does notl
correspond to a laser mode, and the unstable laser solution, occur when the carrier
density is high, so that the screening of the electron-hole gas becomes appreciable.
The results indicate that when attempts are made to obtain laser action in a semi-
conductor by app W ng excessive pump power, there in the danger of producing condi-
tions corresponding to one of the additional solutions. This is borne out by some
recently published data (G. Burns and M. J. Nathan, Proc. I=, 52, &2, 1964). Orig.
art. has: 1 figure and 20 formulas. [021
SUB CODE: 2D/ UMM DATZ: 07Dec65/ OPAG REF: 007/ OTH FJW: 002 / ATD PRESS:
,5'e 2 67

L 45861-66- EWT (1) /EEG W -2/T/-EWP.(k) VIG/GD
ACC NRt AT6015142 SOURCE CODE: UR/0000/66/000/000/0214/OZZ7
:AUTHOR: Vinetskiy, V. L.; Kolychev, N. N.; Mashkevich, V. S.
'ORG: Institute of Physics, AN UkrSSR (Institut fiziki AN UkrSSR); Institute of
Semiconductors, AN UkrSSR (Institut poluprovodnikov AN UkrSSR)
;,TITLE-. Theory of laser r diation from impurity-band transitions
SOURCE: Respublikanskiy seminar po kvantovoy elektronike. Klvantovaya elektronika
~(Quantum electronics); trudy seminara. Kiev. Naukova dumka. 1966, 214-227
TOPIC TAGS: laser. solid state laser, semiconductor laser, IlLser theory) iA-5f *V--
Rf? 0i#9 7-,oo A*4 IfnpuRory 43AAlo
ABSTRACT: The semiconductor laser operation based on radiative transitions of
current carriers from impurity-band state to bound state is examined by the method
of kinetic equations. A semiconductor having M identical impurity centers with a
11evel in the forbidden band in considered. Pumping drives the electrons from the
!valence band into the conduction band. Electron-hole recombination takes place at*
Ilevels. Hole capture by an impurity level in accompanied by radiation of a photon.
lKinetic equations and a neutral -condition equation are set up. Solutions for the case

ACC NR, AT6015142
iof acceptor and donor centers (Boltzmann distribution and strong degeneration in the
hole band) are given. Absorption by free carriers is allowed for. This special
feature of the impurity-band laser is noted: In some cases (medium pumping),
populations of m, p, n levels and generated frequency vary when pumping produces
1
!higher -than-threshold number of electrons (holes) the number of quanta radiateC
iby the special mode per unit time increases with pumping in a slowe r-than -linear
manner; this deviation from linearity is pronounced with '0 approaching (m
is the number of electrons at impurity levels; p is the number of holes in the valence
,band; n is the number of electrons in the conduction band). This feature is due to them
absence of thermal equilibrium between the impurity and the band. Orig. art. has:
~2 figures, 80 formula@, and 2 tables.
ISUB CODE: 20 / SUBM DATE: 12Feb66 / ORIG REF: 006 / OTH REF: 00 1
Cad Z/2

T, o1059-67 EWr(I)IT TJPW GI)
ACC Nit, AT6015131 SOURCE CODE: UR/0000/66/000/000/0034/0076
AUTHOR: rushko, I. A.; Mashkevich, V. S.
ORG: Institute of Physics. AN UkrSSR (Inatitut fiziki AN UkrSSR)
TITLE: Method of kinetic equations in the theory of generation of
SOURCE: Respublikanskiy seminar po kvantovoy elektronike. Kvantovaya elektronika,
~(Quantum electronics); trudy seminara. Kiev, Naukova durnka, 1966, 34-76
TOPIC TAGS: laser theory, solid state laser, kinetic equation
ABSTRACT: 1. Deduction of kinetic equations from a density-matrix equation for them
case of generatian of the second optical harmonic. Only stationary conditions of
generation and only the process of frequency summation are considered. The
analysis is made in the first nonvanishing approximation of the disturbance theory;
contribution of multiphoton processes is neglected. The kinetic equations are:
2m
j- B V [~2 Q, + 1)(j! + 1) + 1)Wo?. 6 (E, + E. - Ej) cg,'Wo + JV.
.91, AW
-F8Aj1(i2+ Oqil;?i -~24i'+ 1)(4-it+ 1)1
. d. a

L 01059-67
ACC NR1 AT6015131
Applicability of these equations to near-stationary conditions of generation is briefly
discussed. 2. Generation of the second harmonic in a plane-parallel slab. It is
clarified which field vector potential should be used for calculating the nonlinearity B
in the above kinetic equations. In each particular case of solving the kinetic
equations, construction of orthonormalized solutions of the Maxwell linear equations
is required. Kinetic equations and total -quanta -number equations for the second-
harmonic generation in the slab are derived. From them, this formula for efficiency
%( r)
is derived: -k= 4 + P - 20' (e2 + q2 _. The second-harmonic intensity in the
NA&I N
transmitted and reflected light dependent on the angle of incidence (formula given) is
convenient for determining the degree of agreement between the calculated and
observed data. 3. Line shape in the second-harmonic generation with a speoified
pumping at fundamental frequency. The above generation case is also used ior
investigating the line shape. An integral equation describing the time shape is
solvable only in two particular cases: (A) Gaussian curve (weak and strong
generation regions); and (B) Lorentzian curve (weak generation). 4. Second-
harmonic generation in the laser resonator. The harmonic generation depends on the
nonlinearity B, photon density q, in the beam, and the lose ratio at fundamental and
harmonic frequencies. Hence, an efficient harmonic generation can be achieved by

ACC NRs AT60IS131
placing the nonlinear crystal into the laser resonator. The generation efficiency is
qual to a ratio of the harmonic power to the dominant -mode -plus -harmonic power:
k= To find the effect of laser pumping
~6 27B,?,(-l+as)+cLja, i
ion the harmonic efficiency, the dominant-mode equation is solved for these cases:
j(A) The near above-threshold pumping region for which this condition holds true:
I !
- 27BB, nllp > 8BB. B. nil at. (m, - nil); (B) The pumping region in which this
7 a") - 0
condition i a satisfied: 104B. (m, - nil) - 2B8, n"12 < 8B, B. nil at, (In, - nil). (C) The at rong
0 -
11) Ills> 1).
pumping region with this condition satisfied: I- B" (m, 2BBn 8TIB, nil a, (m, - n'
MI_nII