SCIENTIFIC ABSTRACT FEDOROV, D.P. - FEDOROV, F.I.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000412620006-0
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: March 20, 2001
• Sequence Number: 6
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

Fed orov, A D. P.
i se-i in ge mar) wrm
!~ez,hvuzovs~,aya nauchno-tckhniche(k~ya
e rk
i kantaktnyyc
ya%-leniya v
T- - !n I
germanium transistor
authors s-,u&y the nelationship betw~c!,)
-C--~Qr ilin-tions In P4 allayel- Junct
.)f temperature on ncises in *hf:sr-
t,- detr-: -in ine the c-,-nbine,~ n, ise
o-f the

ACCESSION NR: AT5020464
ir Iv ~n~levondfmt of tho rmprmont ,f
-A A: ii, ~1~ I iRqi

0
L 3-133-66 EWT(l)/EEC(k)-21*Z/EWA(h) IJP(c) GS
ACCESSION M AT5020479
UR/OOW/64/000/000/0328/0334
4
AUTHORS3 Kuznetsov V. I.j Shchevelevs M. I I Fedorov D. P.
q.~
TITLE: Temperature dependence of parameters of plate silicon diodes
SOURCE: Mezbvusovskays nauchno-tokhnicbeskaya konrerentelya flzlke
po.~,qpr9yodnikoy (p2verkhnostrAyy9 I kontakt! vleni . TOM IWO
, =L" L_" L
Poverkhnostmyye i kontaktwjyo yavlaniya v poluprovodnikakh ce and- 0 tact
I phenomena in semiconductors), Tomsk, Isd-vo Tomokogo univ.p l9u+j 328-334
J
TOPIG TAGSs :volt ampere characteristic, silicon diode, electric curront / D202
diode, D20 diode
ABSTRACTj Results from experimental investigation of the temperature dependence
'of tho back volt-ampere characteristics and break-through voltage of plans silicon
high-voltage liodon of the typo D2(P--M051 *re reported,, P-mr-imters of -the diodes
were meas&ad in,~he texperatwv interval of 20-1700. At low return voltages the
current Increases with the temperature, while at high voltepa. the opposite takes
place, leadl~g'to the increase of the break-through voltage of the diode. Figure
I on the Enclosure shove characteristic curves for the temperatwe dependenob of
the break-through voltage* It in obnaludod that two processes occur in aillcon
diodes.
, one of vhich leads to an iam-sase In the return ourr at with tesperaturs,,
Card 113

L 3-133-66
ACCESSION NRt -AT5020479
the other to a decrease. The first process is related to the generation of beat
in the current carriers and Is practically independent of the voltage on the
transitions. The second pvassa is connected with the surface changes occurring
on the silicon oxide,, due to.the changes in concentration of chemisorbed moisture
with temperature., To support this latter aisumption, temperature dependencolof
30 silicon transitions on the break-down voltage was recordedi The transitions
were then dried for 8 hours in vacuum at 2200p then maintained In moist atmosphere
for 5 days, each time recording Vv(T), A detailed chemiftl exp1mustion of the
process is given. Or1g, wt, bast .4 figures
'31
ASSOCIATIONi am
SUMITrEDs 06Oct64 ZWLt M SM 001XI Ba
NO REF SOVt 003 OTHERs 003
Card 2/3

L 3.133-66
ICCESSION MR'S AT5020479
IVA

n

M

-1.11, ~ - ~ '- ~- i I.- ,. - -
i -. - i~ , 'I . . !- . - 1-1 ~ ... 1-.1
-R-. [lyi- --- -- -- - - -
Fedorov, D.S., Temperature regime of ocean currents as an indicator of their
variability, Tr. Leni~gr. gidrometeorol. In-ta (Works of the Leningrad Rydrometeorological
Institute), 110 7, 1956, p 211-216; (RZhGeofJ,z 12/58-8872)

FEDOROV D.T.(Chiia)
A3.1'depote of the railroad boaame profit bringing units, Zheladoretranspe
45 no.2.-73-7/+ F 163. (min 16t2)
1. GlavVy insh. Zabaykallskoy dorogi.
(R-ailroads-kreight)

ACCESSION NRs AP4017788" 5/0083/64/0004002/0024/0023
AUTEIORt Fedcrov,, go
TIM: Satellites and weather forecasting
SOURGEs Kry*llya roditW*~ no.-2# 19&* 24-23
or
TOPIC TAGS: mote ologyg telemeteringe v"tbAr satellite
ABSTRACTs Ground meteorological observatories have the disadvantages of being
located unevenly over the surface of the earth* with large areas covered very
poorly (especially water areas); being able to penetrate only the lower layers
of the air, so that upper air soundings are too scanty to be of much use in
woathor forecasting; and are unable to transmit their observation data U
central processing offices# in many oasest until they are too old to be of
maxim= value. Weather satellites would not be subject to these disadvantageso
Images of cloud cover over extensive areas obtained from satellites are
especially valuable for forecasting storms mid cyclones. Tho heat balance of
the earth is also easily measured from satelliteag as are the atmospheric
temperatures at various alUtades~ the composition of the atmosphere# and the
upper boundaries of cloud covert Active radar tracking from satellites can
Card 1/2

ACCESSION XR: AP4(a"88
trace cloud movements and the nataro of prealpitation. Satellites may also be
used as-co=,Wcatton r*LW points for observation stations located in remoto
regions. Meteorological satellites should hAve orbits *Us* to a polar orbit
so that they can cbserve alLlatitades of the slabs* OrU. art. has 2 diagrams.
ASSOCIATION: none
SUR-MTED: 00 AM nN&rf4 MMS 00
SUB CODEs AS* CO 30 MY SOVS 00 OMM: 00
Car,d 212

L __~--54 FEO-2/EVT(d'/FSF(h)/FS--,I , - -,. -,., -, - 'L r
L
A 14 ~IR: A, P 5 /FWI
13 "rom the COz-:MO,-. ~;uidi-ng airplanes e r, j f r3 a r tLa
~a Ba Ie 111 tea
K7y]'ya rorliny, no, 2, 1965, 22-2)
T`IFI,~ -AL'S: Inavi n satellitl~ navigation system, sr-tolil- -r-, aircraft
gliidance equ i unO I
ABSTRACT: New vistas in the realm of airplane nnvigation arq
earthIq artificial satelllte6, Ajij7-,:I a --ror,i I nn
`3 r r,F
ma
y b-ic mp u
?i"Cular (Ind q-~ a he~g~

L
ACCESSION, INT.: AP5006235
The apVaratus in each ri-atal I I
f and --In the plaiae-=at-b zym6ranized that the planar cowuter
will cale-alate the coardimtos, course, velocity, and altltwie In
rint only planes but a!,;,)
Sy a !-~3m. rlis a -'1a S
A36;,-),~ LAT WN t none
SUB'1437"TZI)t 00 ENCLi SUT CC'r--- IrG
OW OTHb 000

7XDOROT, NoTee
1,
"' - gronlits 'ia'truvton In ths Tabs and 4rda Basin$ (KmnOYarsk Urrito27)o
Nate TM11I Ob. my. soiSsI06-in J48o (Ni" USO
(&onoprok UrritoW-Woultes)

--.,
Devonian igneous aotivity in the Mimwinsk Basin. Trudy VSEGEI
58:125-133 161. (KM 15:5)
(Minusinsk Basin~-Rocks., Igneous)

TMJNOV, A., glavMy Inzhennr; IMMINNYT, L. . inth h.
Converting to central control system at the grain elevator of
the Kirov Milling Combine. Muk.-elev.prom. 25 no.6:9-10
je 159.~ (MIRA 12:9)
1. Leningradskly mellnichWy korbinat im. S.M.Kirova (for Trunov).
2. Odesekiy proynictno-konstruk-torskiy Institut Pishcheprom (for
Reynennyy, Fednrov).
(Grain elevators-zquipment and supplies)
(,,kutomatic control)

, 11 ,
"Rationalization Serves Pmduction.," Tokst. prom., 12, lio.43 1952
,
~. A,

FEDOROVP F. A.
"Mechanical ~Iethod for Rermving Droppirws from Under the 11fackling Machine,"
Tekst. prom.2 12, No.8. 1952

FIDDROV, P.A.
Device for planlvg grooved metal rollers for spinning looms,
Obm.tekh.opyt. (MLPJ no.20:5-6 '56. (14IRA 12:11)
(Planing machines)

M
FEDOROV, f.A.
Addition of 300-200-brand cement to tho BF-2 glua for in-
creRsing Itn strength. Obm.takh.opyt.[Wj no.20t19-20
156. (MIRA 12:11)
(Glue)

FIDOROV. N.A.
Improved design of T-uhaped brass clamps for fastening the
R and D- system atomizers. Obm.takh.opyt.[MU] no.20:28-29
'56. (MIRA 12:11)
(Spraying)

FEDOROV.9 F.A.
lap for repairing sliding oalipers. Tzm.tekh. no.3jl2 963.
(Calipers) (MM 1684)

7EWROT 7 27,
trollin
pectors W99ti -.-..g,4oisting machinery. Besop.
truda v prom. 1 no.407 Ap 157. (MM IWO
(Hoisting machinery)

TEGORUMIN, V.Te.; KRAMOMMKOV, N.A.; RA2XTSLOVICH, I.R.; FXWROVv
F.F: - SMEMOVICH, P.V.; TSVYRKUH, N.A.; BUYLIN, G.,
2-.&-T re ,
UU-CHITS, G., tekhn.red.
(Handbook of a tractor driver] Spravochnik traktorista. Minsk#
Gos.izd-To BSSR. Red.selikhos.lit-ry, 1959. 578 P. (MMA 1):3)
(Highway transport workers--Handbooks, manuals, etc.)

GOLOYNIT, I.F., kand.tekhn.nauk; PANOT, A.A.1 YICDOROT, F.F.; YUTACIIEVA,
N.Ta.; TALAGINA, T.A., tekhn.red.
(Press forging; bibliography with annotations for publications
in 19571 Obrabotka metallov davleniam; annotirovannyi biblio-
grafiohaskii sprovochnik literatiwy Sa 1957 god. Leningrad.
Mo .1, [Haating and drop forging) Nagrev, kovka I goriachais
shtampovks. 1958. 132 p. (KIRA 13:2)
1. Laningradskly dom nauobno-takhnichookoy propagandy.
(Bibliography-Irorging)

TATNTRAUB, D.A.; PANOY, A.A.; FXDOROV,_Y.V.,- TUTACHSTA, N.Ta.; TILAGINA.,
?*A., takhn.red.
(Press working of metals; annotated bibliography of publications
for 19373 Obrabotka metallov davlanism; annotirovannyi bibliogra-
ficheskii spravoohnik lit^ratury za 1957 god. Leningrad. No.2.
(Die stamping] K61odnaia.shtampovka. Pt.l. 1959. 99 p. Pt.2.
1959. 77 P. (MIRA 13:3)
1. Leningradskiy don nauchno-tekhnichaskoy propagandy. Nauchno-
tekhn1cheskqa bibiloteka.
(Shest-metal work)

RIMMYY9 Lavinzhs; YXDOROV, P.,insh.
Devices aM eqnipment for the automatic control of 'various
operations in grain elevators. Muk.-eleveprom. 25 no,2:8-
10 1 159. (KMA 12:4)
1, Odeaskiy proyektno-konstruktorskiy institut Pishchaprom.
(Grain elevators) (Automatic control)

FEL)C,ff)v,
Theory of elautle itavee in cryBtalD. Comparison with an isotrople
medium. Xrlsta-Uografila 8 no.2:213-220 Yx-Ap 163.
(MIRA 17: 8)
2.. Inotitut flziki. AN BSSR.

U . I)rlr. -1 !.,
-r i
r , I, -k -
Fedorov, F. 1. - 'On the superposition of physieal magatudesm, rzvestiya Akad. nauk
BSSR, 1949v No. 2, p. 17-18.
SOt U-411, 17 July 53, (tatopla tZhurnal tnykh Stateyl, No. 20, 1949).

FEDOROV9 F. I.
USSR/Physics - Relativity Wave Equation 11 Avg 51
"Kiniman Polynomials of the Matrices of Relativistic
Wave Equations," F. I. Fedorov, Belorussian State U
imeni Lenin
"Dok Ak Nauk.SSSR" Vol LMX, No 5, PP 787-790
Purpose is to show that the condition' which states
that among the states possible for particles those
must be absent corresponding to energy density equal
to zero' also permits oneessentially to limit the
form of the minimum polyn of the matrices of
the following equation: ik)P=O, where P repre-
sents the psi-function. ted by Acad V.A. Fok
16 jun 5l.
21OT90

1 Genert.

c I.S
18
;03-733
tj "r Vk
iF.4
mi" I?
ut 10. Shi I
U.6 "Pec
or all c-,~st'.v'Co an
t4
t4~

WSSR/Physics Crystallograpby, Optical 21 Jun 52
Parameters
"Determining tl!.%e Optical Param terB of Monoaxla7 Cry a-
tale According to Reflected Light," F. I. Fedorov,
Belorussian State U iment Lenin
"Dok Ak Nauk SSSR" Vol LXXXIV, No 6, PP 1171-1174
Subject investigation is based on the relations
among the amplitudes of reflected and incident waves
for the case of incidence of light from an isotropic
medium or, to a monoaxial nonconducting nonmagnetic
crystal. Designates the unit vectors of the wave
Mormals of the incident reflected, ordinary and
eXtraordinary waves; vectors of the elec and magnetic
223rI02
fields; Indices of refraction of the isotropic
medium; ordinaz7 and extraordinary rays; =it vector
of optical axis of crystal; tensor of dielec per-
mobility; unit vector of normal to the surface of
sepn. Submitted by Aced D. S. Belyankin 24 Apr 52.
223T102

--~ -1.1
.6
Use of the method of functionals In certain problamg of milatlon **
theory. Uch. sap. WU no.146-33-73 '52. (KIRA 11:W
j0pautum theOr7)

Pu a)
PAnRIVICH. I.G., kandidat f iz Lka-matematychnykh rAruk, reclaictor;
nMARAU 'I kaudydat fizika-matemstychnykh navak, redaktor;
1b., takl=edaktar.
[Radio and its role in the davtlopmeat of culturer and technical
progress) Radylo i itho Yolia u razvitstei kulitury i takhnichnaba
pragresu. Minsk, Vyd-va AN BSSR, 1953. 30 P. (KLRL 8-.2)
(Radio)

r T F- I I
YEDOROT, Fedor Ivenovich
-PiDOROV, Fedor Ivanovich (Belorussian State U Iment Lenin), Academic Degree of
Doctor of Phystoo-Mathematical Sciences, based on his defense. 3 Dec-
ember 1954, In the Council of the State Order of Lenin 0
ptioal Inst
imeni Vavilov, of his dissertation entitled: "InvariMle methods In
:the optics of anisotropic mediums.1 For the Academic Degree of Doctor
of ScIencas.
SO: Byulletan' Kint" terstra, Vysshego Obrasovantya SSSR, List No 20, 8 OctoUr
1955, Decision of Higher Cartifteation Commission Concerning Academic Degrees
and Titles.

MARAU,F. 1.
- - 0. - O~! 0- RM; ,
Invariable Indications of the polarization of light. Testsf
AN BSSR no.6:78-91 N-D '54. (KIRA 8:9)
(Polarization (Light))

11 1
: -,:: I- - . ~ ~ - - .;; ~ 1. :-1 ~F- - t, -;, . ; ,~ .. - - . ..
, , '. - -. 4' , , V " ; -, , ... - -
:, ~ r ~-. :1,)7,1i.~1 '.
~;, - I j ~ ; ;. . -
~i-- I .I

USM/Physics Elect. magn. wave polarization
QU4 1/2 Pub. 22 - 17/49
AnVion I Fedorovi F, I*
Title S About. the polarization of electro-magnetie. waves
Periodical i Dok. AN SSSR 102Am 69-71, May 1, 1955
Abetraot I An anAlysis of electro-magnetie-wave polaiitation is preserdood, Monochro-
Matic homogeneous " non-homogeneous waves are considered. Two m6thods
for analyzising the ho=geneous waves are suggested. 1he first method
starts from a consideration of the wave ariplitude in the fom
E a 1~ + iE . where the real vector parte E~ and 3 are conjugated semi-
damet6rs of2~he ellipse of oscillations. ilia pecoRd method consists in
the consideration of the complex vector E = E0elf , where is a phase
Institution The Acad. of So., USM, Physico-Technical Institute
Presented by t- Academician A.A. Laboday, December 13, 1954

Card 2/2 Pub. 22 - 17/49
Periodical i Dok.,AN SSM 102/lp 69-71s M&Y lo 1955
Abstract I of the oscillations. A consideration of the nen-homogeneous wave
polarization is suggested# starting 4ith the reduction of Fammll's
equation to the following formt
JxHj, "H a [mEj
As a result of such a treatment of Yjmell's equation a series of
properties of non-homogeneous slectro-magnetic waves is listed. Two
referencess 1 USS and'l Oem. (1929 and 1952).

-f _i-__ - --_ - .- - - -
I . j

Crystals. B-5
Abs Jour: Beferat. Zhu=al'Xhiziym,, No 3, 1958, 7082.
Author ?.I. Fedorov.
Inst,
Title "Transfer Principle and General Theory of Optical Pro-
Parties of Absoxting Crystals.
Orig Pub: Oj?tiki% i spektroakcpiya~ 1956, ls No 6s W7-W8-
Abstract; Me lack of foundation for the "transfer principle" is enoa-
sized. According to this principle,, all the relations of optics
of transparent crystals my be transferred to the cases of
absorbing ned'a (aouiprising mmonlilmi a and triclinic crystals)
on condition that corresponding magnitudes receive coaWlex va-
lues. Cited conputations show that the tensor of dielectric
permeability has not generally three ova linearly independent
vectors, it has not even ccMlex vectors.. consequently, the
theory based on the "transfer principle" cannot be applied to
Card 1 1/2 .27-
-4w
17

I . .
ff-~- ill 1~ t3l I

YEDDROT, : ~ - - -
Determining the optical parameters of absorbing crystals. Isr.A)i
SSSR Ser.fis.ac.5064-369 056. (KI2A 9:9)
LInstitut fluild i matematiki Akademli saidt BSSR.
(Crystallography)

USSR/Theoretical Physics B-6
Abe-Jour Referat Zhur Fizika, No 5. 1957s No 10898
Author
Inst Institute of Physics and Mathematics, Academy of Sciences,
Belorussian, SSR.
Title Reduction of Wave Equations for Spin Zero and One to the
.Hamiltonian Form.
Orig Pub Zh. eksperim. i teor. fiziki, 1956s 31,, No 1, 140-142
Abstract A method is given for the reduction of the equation for
particles with spine zero and one
019 VA -I- Y
to the Hamiltonian form. The method is independent of the
actual choice of natrixes(3 k and is based only on Eq. (1)
Card 1/2

nwiRov, T. I.
Certain dot-product representations of tbree-dimensional
tensors. Trudy Inst.fis. i mt. AN BSSR no-2:230-234 1 57.
(MIRL 12:1)
(Calculus of tensors)

AUTHOR: Fedorov, R.I. 51-3-12/24
TITLE: Optics of magnetic crystals. II. Binormals and biradials.
Optical.surfaces. (Optika magnitnykh kristallov.
II. Binormali i Biradiali. Opticheskiye Poverkhnosti).
PERIODICAL:"Optika i Spektroskopiya" (Optics and Spectroscopy),
1957, Vol.2, No-3, PP. 361-370 ~U.S.S.R.)
ABSTRACT: Continuation of the author's paper in "Optika i
Spektroskopiya", Vol.1, p.926, 1956. Theoretical electro-
magnetic calculations give directions of binormals in a
general type of magnetic crystal. It is found that, in
general, transparent magnetic crystals (just like non-
magnetic ones) have two binormals. A principle of
duality, i.e. parallelism of the systems of equations, is
established for normals and rays in infinite magnetic
crystals. Binormal and biradial surfaces are found to be,
in general, different. The limiting values of the refractive
indices are obtained. The optical normal surface and its
cross-sections are derived and shown in figures. There are
Card 1/1 5 figures; 3 references (2 Slavic); a mathematical appendix
(matrices and tensors).
SUBMITTED: June 2 1956
ASSOCIATION: Physics ana Mathematics Institute,Ac.Se. of Byelorussian
.-SSR (Institut Fiziki i Matematiki Ak.Nauk BSSR). ,

AUTHORt Fedorov, F.I. 51-4-17/25
TITLE:,6_pMT5q ZI-Magnetic crystals. III Uni-axial and uni-refringent
magnetic crystals. (Optika magnit~Wkh kristallov. III
Odi~ow~We 1i odnoprelom1,yayushch!34,f magd,~nve kristally).
PERIODICAL: "Ontika i-Spektroskoviyall (uptics and Spectroscopy)
~ .. .-1957, Vol.2, No.4s PP-514-Y23 (U.S.S.R.)
ABSTRACT: This purely theoretical paper is the continuation of the
author's papers in Optika i Spektroskopiya, Vol.1, p.926,
1956 and Vol.2, P-361, 1957. The electromagnetic'theory of
~wave propagation is applied here to particular cases of
magneto-anisotropic media. Uni-axial magnetic crystals, de7
fined as those which possess a unique axis along which both
normal velocities are identical) are considered. Optical sur-
faces are derived and illustrated for these crystals. It is
established that, in general, in uni-axial magnetic crystals;
(a) binormals do not coincide with biradials; (b) ray velocity
along a biradial is not equal to normal velocity along a
binormal. It is shown, in principle, that there also exists
a group of anisotropic magnetic crystals for which birefrin-
gence is absent (they are called uni-refringent). In other
words in such crystals light velocity depends ondirection
Card 1/2 but has only one value for each direction. Linear polarization

AUTHOR: Fedorov, F.I. 51-5-10/26
TITIR: Optics of the Absorbing Crystals. (Optika pogloshchayu-
shchikh kristallov) I. General Relationships. (I. Obshchlye
sootnosheniya)
PERIODICAL: Optika i Spektroskopiya, 1957 Vol.2 No-5
ppe &6 - 6L (USAR).
ABSTRACT: The fundamentals of the optical theory of the absorbing
crystals were given by'Voigt and DrIlde at the end of the last
and beginning of the current centuries. Their theory, however,
is not absolutely general since it has limitations due to using
a special system of co-ordinates, the -so-called"principal a:kes"
of the complex tensor of dielectric permittivity. this theory
is also very complicated and leaves certain important questions
un-answered. In the current paper (which is to be followed by
further parts), a fully-general theory of the optical proper-
ties of the absorbing crystals is developed on a new invariant
basis and this now theory is free of many limitations of the
Voigt and Drdde theory.
.Starting from Maxwell's electro-magnetic equations, general
relationships are put forward for propagdion of plane, in
particular, non-uniform,waves in the-absorbing crystals. A
Card 1/2 general equation for normals in an invariant form is obtained.
Optics of the Absorbing Crystals. 51-5-10/26
The conditions for linear and circular polarisation of waves
are discussed* The directions of the wave-field vectors are
determined for a given vector of refraction-Theh?aRe5 is ent-
irely mathbmatlOal-TheTe` "0' 8:, -references 9 . or. w c are Slavic.
ASSOCIATION: Institute of Physics and Mathematics of the Ac-Sc.
Belorussi'an SSR. (Institut Fiziki i Matematiki
AN BSSR)
SUBMITTED: July 6, 1956.
AVAILABLE: Library of Congress
uard 2/2

AUTHORs Fedorov.. 51-6-13/26
TITLE: Optics of Absorbing Crystals. II. Crystals of Middle
Syngonies. (Optika pogloshchayushchikh kristallov
II.. Kristally arednikh singoniy.)
PERIODICAL: Optika i Spektroakopiya, 1957, Vol.11, Vr.6,
ppe 776-780. (USSR)
ABSTRACT., A theoretical paper. Optical properties in an
Invariant form are discussed for absorbing crystals
of trigonal, tetragonal and hexagonal syngonies.
General equations are obtained for the refractive
Vector and for field vectors of the orcHnary and extra-
ordinary waves. Both uniform and non-uniform waves
are treated. The conditions for linear and circular
polarisation of waves are given. In uniaxial absorbing
crystals for uniform waves polarisation properties are
obtained similar to those of transpareAt uniaxial
crystals. It is found that absence of double refraction
occurs in absorbing uniaxial crystals not just fbr a
single direction of the incident of wave, as in trans-
Card 1/2 parent uniaxial crystals, but for a range of directions.

61-6-13/26
optics of Absorbing Crystals. Il. Crystals of Middle Syngonies.
r There are 4 references, all of which are Slavic.
ASSOCIATIONs Institute of Physics and Mathematics) Academy of
Sciences of the Byelorussian SSR. (Institut fiziki
i matematiki AN BSSR)
SUBMITTEDs July 6, 1956.
AVAILA.BLEs Library of Congress.
Card 2/2

- 1 ~~ I I %F I I ~w %I / j . -A- ,
I%- . SUPRUNEM , D.A.; NEWSHEVICH, I.G.
History, of development of physicomathematleal
White Russia. Vestsi AN BSSR Ser. fiz.-takh.
157. (White Rusaia--Physica)
(White Russia--Mathematics)
sciences In
nav. no-3:17-20
(MIRA 11:1)

Light reflection and refraction laws In a vector form. Uch.zap.
BOU no.32:169-lV. 1 57. (MIRA M12)
(Light)

PHM I BOOK Z-21A.-UATION 663
OYtIkA anizotropufth are& (Optics of Antootropic Media) Minsk,, Izd-vo AN BBSR"
190. 379 p. 2pOOO copies printed.
Zdat Stepswvj, B. L# Prof.; Ed, of Publishing House: Barmichey, V,
Tech. Ed.; Als"androvich., Xh.
PURPOSE: This book in intended for the use of students and specialists in the
field of optics with special emphasis on aniacytropic media,
COVERACIN: Thin book is a presentation of the phenomenological electromagnetic
theory of light propagation in homogeneous, mainly sainotropiczedla. It also
covers the theory of reflection and refraction of 11*tt on the surface of these
media, The first three chapters contain well known resulteg but many of them
are obtained by methods different from the ones employed in available vorks in
theoretical optics. Along the same lines chapters 1., 11,, and 311 present a
series of.new results concerning pol6rization., heterogeneous waves, total
reflection, etc. The majority of results presented in chapters IV., V, sn& VI
are said, to be original. Pertinent mathematical relations are found in
paragraph 4 of chapter I., and paragraphs 16 and 20 of chapter 133.
Card 116

Optics -of--Arxisotropie-Media----------o"0'3
Sow are also found throuatout chapters V and VI, Recognition is given to
Professor Z.,I. Stepanoy for,his invaluable advice and observations and to
Be Ve Bokutf for his help in reading the manuscripts and getting the book
ready foi the printers. There are 210 references, 72 of Aich are Soviet,
.104 Clemmt 25 English., 8 French imd 1 Svedish.
TAZX OF CONTENTS:
Fare rd 3
Cho Io Plane.Electromagmetic Waves 7
lo. Mamalfs equations and boundary conditions, The Law of Conservation
of Znerg-. 7
2, Plane electromagnetic wav a 14
3, Polarization 23
4. Invariant form of relationships characterizing polarization 33
3* Addition of vaves with different polarization 46
6* Reflection and refroation of plane vayes 56
Card 2/6

(Ypties.of Anisotropic Media 66,4
Ch, II. Isotropic Media 62
7. Continuous plane waves in isotropic dielectrics 62
8. Heterogeneous plane waves in an isotropic dielectric 68
9. General solutions of Maxwell's equations for heterogeneous plane waves 78
10. Plans wav a in isotropic conducting media 03
3.1, Plane wave on the boundary of two isotropic media. Freenel's fbr=Llas 91
12. Light intensity and polwization in reflection and refraction 103
13, Total reflection 3-12
14, Total reflection at arbitrary polarization of incident waves.
Reflection f conducting media 3.19
ch, III, Propagation of Plane Waves in TraMwent Normagnetie Crystals 129
15. Tensors of dielectric and sagnstie penetrability 129
3.6. Certain data fron linear algebra 135
17. Plans vaves in a nonmagnetie anisotropic dielectric.
Equation of normals 141
18, Analysis of plane ways vectors in a crystal 145
19, Density and, flow of energy* Principle of reciprocity 151.
20, Invariant representations for tbree-dimansional. real synntrical,
tensors 157
Card 3A

Optics of Anisatropic Media 663
21* UnlWal crystals 263
22. Biwdal crystals 167
23. Optical surfaces 171
Ch. IV. Reflection and Refraction of Ught in Transparent Nomiagnetic
crystals
24o Introduction 174
25. Oeneral statement of the problem 17
26, Reflection and refraction in unimdal crystals 179
27. Rotation of the plans of polarization in reflection, Angle of
total polarization 1W
28. Reflection and transmission coefficients, Total reflection
from uniWal crystals. 203
29., Buie vectors of reflection and refraction waves 209
30. BiWal crystals 221
31. Methods of determining optical parameters of transparent crystals 234
32a Determining paramters of unimdal crystals 237
33. Determining parameters of biwdel crystals 248
34, Small angles of incidence nethod applicable to biaxial crystals 259
Card 4/6

Optics of Aninotropic Media
Cho Ve Propagation of LiSbt in Magnetic -Anisotropie Media
35o Buie equations for magnetic crystals 263
36o Equation of nozmls 265
3T. Flow of energy and the first principle of reciprocity 272
38. Binornals and birsdials 276
39. Uniazial magnstia crystals. Optical classification of savetie
crystals 284
40. Invariant representations for tensors of uniwdal magnetic crystals 290
Cho VI, Absorbent Normwoetit Crystals
41. Introduction 300
42. General relationships 309
43, Absorbent crystals of average syngony 316
44, Absorbent crystals of poor syngony 320
45o General classification of absorbent 4;,,.-yatals according to optical
properties, 330
46o Reflection of light from absorbent crystals of average ewwny and
deteminatlon of their optical parameters 344
47. General rules for the reflection of 31&tt from crystals 350
48. Determining optical parameters of absorbent crystals of poor
syngony according to reflection of ligbt 355
Card 5/6

0
Optics of Anizatrople Media 663
. Supplement to Chapter VI. 365
Bibliography 3T3
AVAILABIZ: Library of Congress
Card 616 MKIM"
10-15-58

rSDINI?(%v
Reflection and refraction of light In biaxlal crystals. Inzh.-fis.zhur.
no,1:41-52 Ja 158. (MIRA 11:7)
I.Institut fiziki i mtematiki AN BSSR, g.Minuk.
(Crystallography)

FEDOROV,
Compogition of parameters of a rotation grrAip. Dokl.Ali BSSR
2 no.10:408-IPIP H 158. (HIRA, 12:8)
(Gronpa. Theory of)

AUTHOR: Fedorax.-YE.-I. SOV/r/0-3-1-8/26
TITIS: ---Invarialit Methods in the Optics of Transparent Non-
magnetic Vrystals (Invariantnyye metody v optike
prozrachnykh nemagnitnykh kristallov)
PERIODICAL: Kristallografiya, 1958, Vol 3, Nr 1$ pp 49 - 56 (USSR)
ABSTRACT: According to the electromagnetic theory of light, the
optical properties of non-magnetic crystals are determined
by the symmetric dielectric constant tonsor, e .
Usually a special system of co-ordinates is used in the
case of such crystals.so that this tensor assumes a
diagonal form. However, in spite of the fact that it is
widely used, this method is neither unique nor the best
for solution. of problems in the optics of anisotropic
media. Invariant vector-tensor methods which do not
employ any special co-ord1nate systems have considerable
advantages. The author has shown in Refs 1 and 2 that
the latter methods may be used to develop a general theory
of the optical properties of media having an arbitrary
magnetic ahisotropy and absorption anisotropy. A particu-
larly useful simplification of the theory is obtained
Cardl/3 by the use of special invariant dyadic representations

SOV/70-3-1-8/26
Invariant Methods in the Optics of Transparent Non-magnetic Crystals
for 3-dimenaional tensors. The present work is concerned
with the application of the methods developed in Ref 3
by the present author to some of the main problems in the
optics of transparent non-magnetic crystals. The second
section of the present paper (Section 1, is an introduction)
is concerned with the definition of a "canonical" represen-
tation of a tensor. Such a representation is defined by
Zq (3). Section 3 treats uniaxial crystals. The
"canonical" tensor representation is applied to ddrive -the
usual properties of plane, monochromatic waves N - 1)
in tri- tetra- and hexagonal crystals. Section 4 deals
with bi1xial crystals and again the "canonical" represen-
tation formalism is applied and among other things it is
shown that the biradials of the crystal coincide with the
axes of the dielectric constant tensor, or the binormals
of a non-magnetie transparent crystal ire the axes of the
inverse dielectric constant tensor e- . The final
section deals with optical surfaces and it is shown that
invariant methods may lead to the usual results in a much
simpler way. In general, even in the case of the simpler
Card2/3 problems in the optics of anisotropic media, there is no

SOV/70-3-1-8/26
Invariant Methods in the Cptios of Transparent Non-magnetic Crystalb
necessity to use any special system of axes since t!~e
invariant approach is both more general and simpler.
There are 5 Soviet references, 1 of which is a translation
from German.
ASSOCIATION: Institut fiziki i matematiki AN BSSR
(Institute of Physics and Mathematics, Ac.Sc.
Belorussian SSR)
SUMITTED: Janua37 15, 1957
Card 3/3

AUTHOR: Fedorov, F.I.
TITLE: On Certain e
Light from Crystals
yakh pri otrazhenii
PERIODICAL: Kristallografija,
70-3-3-11/36
Regularities in the Reflection of
(0 nekotorykh obshchikh zakonomernost-
sveta ot kristallov)
1958, Vol 3, fir 3, PP 322 - 324
(USSR).
ABSTRACT: It has been theoretically established that on the
reflection of light from a crystal of any type (transparent,
absorbing, magnetic, etc .) for every given di-ection of the
wave normal of the incident wave, there exists a unique pair
of mutually perpendicular directions of polarisation of the
incident wave, to which correspond two mutually perpendicular
directions of polarisation of the reflected wave. For these
polarisation conditions, the coefficients of reflection assume
the maximum and minimum values. It is assumed that the
relations between D and E and B and H are linear. The
results follow dire7ctly fro! an analysis oCMaxwell's equations.
The reflected wave has a magnetic vector HI connected with
the magnetic vector of the incident wave F by HI = R H
(R being a matrix). R+ is the Hermitian-conjugate to R
.The reflected energy is H'kH' and the coefficient of reflection
Cardl/4--

70-3-3-11/36
On Certain General Regularities in the Reflection of Light from
Crystals
2 2 2
r / /E/ /H'/ HIR+RH = HI"TH where
T-R+R = T+ is the Hermitian self-conjugate matrix. If
/ 2 is made 1 then r = HXTH - The task is to find the
extrema of the Hermitian quadratic form r(H) = HATH with
the supplementary condition H'*H=l . As is known the
vectors H corresponding to the extrema correspond to
vectors of the matrix T of the Hermitiali form. As these
vectors H and HI are each determined by two complex
components in corresponding phaseplanes, the matrix T
then has two rows and two columns and consequently the two
corresponding vectors Hl and H2 are determined by the
conditions TH `~rlHi and TH2=r where r and r2
1, 2H2 1
denote the corresponding special values of the matrix T.
From this it is deduced that HjJ~ ' = r
'H~ 2Hl'OH2 = 0
The following conclusions are drawn:
1) For l' ht falling from an isctropic medium (non-
conductinIg5 onto an arbitrary medium for a given direction
Card2/4 of the wave normal of the incident wave, there exists one

70--3-3-11/36
On Certain General Regularities in the Reflection of Light from
Crystals
and only one pair of magnetic ve,,-tors H1and H2
connected by HwA,"H' 2=O, which correspond to a pair of vectors
for the reflected wave Hiani % which are connected by
Hjm~' = 0 .
2) These vectors are eigen ve~.,toors of the Hermitian
matrix T.
3~ They correspond to extrema of the reflection coefficient.
4 For the usual case of reflection from a transparent
medium T and H, and H 2 are real.
5) If H, and H2 are non-linear then the maximm mi3ection
will be obtained for elliptically polarised incident waves.
6~ For total reflection R 'must be a unitary matrix.
7 For reflection from isotropic media H1and H2' are
linear and together with Hi and H~ , the incident ray
and its perpendicular lie in a plane.
Ca-rd3/4 There are 6 references, 3 of which we Soviet and 3 German.

70-7 11/36
,On Certain General Regularities in the Reflectic from
Crystals
,ASSOCIATION: Institut fiziki i matematiki AN BSSR
.(Institute of Physics and Mathematics, AS
BSW
SUBMITTED: October 30, 1957
Card 4/4

SOV/r/0-3-5-9/24
AUTHORS: Goncharenko, A.M. and Fedorov, F.I.
TITIS: The Surfaces of Refraction an ion in Absorbing
Crystals (Poverkhnosti refraktsii i absorbtaii
pogloshchayushchikh kristallov)
PERIODICAL: Kristallografiya, 1958, Vol 3, Nr 51 PP 58?-592 (USSR)
ABSTRACT: A theoretical ans sis is made of some of the properties
of the surfaces representing the refractive index and
absorption in absorbing crystals. Only the propagation
of uniform waves is considered where wave and amplitude
normals are parallel. The refractive index surface is
defined by a radius vector R, of length proportional to
the r.i. n, for the wave normal direction n - Hence,
El - nl n and n. is the real part of the r.i.2
n - n, -in2, n2 being the absorption coefficient. The
absorption surface is defined by E2 = n2 n . The task
is to describe these two surfaces as functions of the
wave normal n .
The coeffici-ents in the expression:
Card 1/3

SOV/70-3-5-9/24
The Surfaces of Refraction and Absorption in Absorbing Crystals
2 1/2
13~,2 nmn] 2
- a + b fne 11 [ne"I
+ Z-j
have to be found. The parameters come from the reciprocal
complex tensor for the dielectric susceptibility:
v-1-1 - a + b(01.0" + 0".cl) .
A graphical method for finding the directions of the
extrema, in principal sections of both the r.i. and the
absorption surfaces is explained. Zxplicit values for
the parameters in the above equation are given in terms
of thq real and imaginary parts of the r.i. andthe
directions are given. There are 2 figures and 4 references,
3 of which are Soviet and 1 German.
Card 2/3

SOV/70-3-5-9/24
The Surfaces of Refraction and Absorption in Absorbing Crystals
ASSOCIATION: Institut fiziki i matematiki AN BSSR
(Institute of Physics and Mathemtics of the
Ac,Sc. Belorussian SSR)
SIMMITTBD; March 17, 1958
Card 3/3

AJThO1W:
.51-A -1-20/26
Fadorov, F. 1. and Tomillchik, L. 1.i. xial
the Optical properit;ies of Bia.
On ~the ' ~naorY~ of
I
Elaonctic Crystals, (K teorii opticheskilul --voys'uv
dvuosiiylch magnitnykh kristallov.)
Optiltu i Spelctroskopiya, 1958, Vol. IV, IxTr. 1,
pp. 109-112. (USSR)
Er. 1. Fodorov (Refs. 1-4) developed a theory of the
optical prope rties of ma~;netic crystals in an in~,rariaat
form. From this theory lie deduces the m-An lavis of
propaGation of liE;ht in magnetic crystals of all
synL,,onies. In the case of biaxial crystals the
problem was complicated by the presence of two nop---
commutins tensors c and ~L. The theory can be
considerablZr simplified by usine a special "canonical"
dyadic representation of tensors. In Ref.5 such a
representation of the symmetric tenser c mas applied
to the case of transparent non-mab-notic cry~~,tals. In
PI~RIUDNAI.b:
A 13 62 RA G T
Card 1/2

1 - A -3. - 2 021-6
a rT-, r; t i c
On tho 'cory of tile Optic 1 P--op xtiez ol Biaxial L
the case of maLrgietic biaxial crystals, the optical
properties depend greatly on the non-syuunetric tensor
~. = V.-lp -A canonical dyadic repro sentation for t'he
latter tonsor was obtained in Ref.6. The present
(oatirely thoorotical) paper gives the main optical
relationships for transparent magnetic biaydal crystals.
There aiy-. 6 reforen,ces, all of which are Russian.
ASSO%JJ1.k2IO1T; Belorussian 0-itate University imeni V.I. I-enin.
(&-lorusskly .-Osudarstvennyy universitet im. V.I.
Lenina. )
SL1M1-.OZjD-- April 17, 1957.
AVAIIAB14;: Library of Congress.
Card 2/2
1. Hognetic crystals-Biaxial-Optical properties

51-1- 4 -3-13/30
AUTHORS: Sotakiy, B.A., and ~dorov, F-L&
TITIA,j: Molecular Theory of Reflection and Refraction of Light.
I. LiOat Incident from Vacuum on-to an Isotropic Medium.
(K molelollyaln-loy teori-i otrazheni a i prelomieniya
ly
sNeta. 1. Padeniye S--reta iz zakirina na izotropnuyu
sredu . )
EBRIODICAL: Optika i Spektroskopiya, 1956, Vol-IV, Ur-3,
PP. 365-372 (USSR).
ABSTRACT: Molecular theoi-j of propagation and no-fraction of light
in it-otropic Laedia was developed by Eviald, Esmarch,
Oseen, Landblad and othera This theory
Is based an the followixiE; as-amptions. Under the
action of an electromagnetic wave, inoident frou vacuuLt
onto the aesdium, moleculaz dipoles are ex-,it-ed into a
state of degr-i:erate vibrationo-, and emit 6econdary waves.
Both the incident und secondary waves obey 111amjelllc
equations for --,,a,.~uucj. -SUporpositior', cT all the
z-Eicondary waves and of the 14'ricident, wave the
xefracted gaVe 4nsdde the, and 1-he ::,~~,flected
wave outsLde it. This mr.-Iccular t1aeory hac a number
Card 113 of fallits of

,
!1- 4 .3-13/30
J
Molecular Thoory of Rof I rj,.t L olrt an d 14).Crar;l, ioc- r, f IA~~it . L .
formulae for the L;enerai case of obligae incAdence are
obtained, only in approximate form by using, tile method
of Oseen and Lundblad (Ref.10--12). In none of the
papers on the molecular theory of reflection and
refraction is the case of total reflei:~tion of light
dealt with. The present paper is an attempt to
develop a more complete and exact -molecular theory of
reflection and refraction, including in particular the
case of total reflection. All the main relationships
(such as the relationship between the refractive index
and polarizability the quenching theoi-j of Oseen,
Fresnel's formulae~ are obtained exac;tly and in a
comparatively simple way. The present authors also
generalize Oseen's theory to tile case of non-horAogeneous
waves. The paper is entirely theoretical. There are
2 figures and 21 references, of which- 14 are German,
4 Soviet, 2 English and I a translation of Born's
"Optics" into Rl-ssian.
ASSODIAIMIT; Belorussian State University (Belorzsskiy
Card 2/3 gosudarstvennyy uni:versitet.)

51.- 4 -3-13130
Molecular Theox-j of Reflection and Refraction of Light. T.
SUBLITTED: May 4, 1957.
- ~ 1. Light-Reflection-Theory 2. Light-ROTaction-Theary
3. Ligh+,-P"Pipticm-Thavry
Card 3/3

5 Oil5l -.-1 -1 - 10/19
AUTHORSs Sotskiy, BA. and Fodorov, F.I.
TITLE t On the Molecular Theory of Reflection and Refra-z-Lllon of Light-
~K moloicalyarnoy toorii otrazheniya I prolomleniya svota)
II. Light Incident on the Boundary Between an Isotroplu, Medium
and Vacuum or Another Isotropic Medium. Total Refle-Aicin.
(II. Padeniye eveta. na granitau izotropnoy sred a valmunitga III
a druGoy itotropnoy srodoy. Polnoye otrazheniye~
PERIODIGALs Optika I Spektroalcopiya, 1958, Vol 5, Hr 1, pp 57-C5 (USSR)
ABSTROT; In the preceding part of this work (Ref 1) the authcrs considered
the came of an Infinite plane monochromatic electronugnotic wave
incident from vacuum on to an isotropic medium. The present paper
gives the molecular theory of reflection and refraction of light
at the boundary of two media, of which the first consists of
molecular dipole& and the second is vacuum or consists of dipoles
of another typo. The molecular theory of total refleetvion is givea.
Card 1/2 It is found that, under certain conditions, the vacim vavo -which

SOV161-5-1-10,1,19
On the Molecular Theory of Reflection and Refraction of Light - II - Light
Incident on the Boundary Between an Isotropic Medium and Vacuum or Another
Isotropic Medium. Total Reflection.
appears as the result of superposition of primary waves produced by
vibrations of dipoles, may be damped in spite of the fact that the
dipole vibrations are undamped. This Is the converse of the =so
discussed in Part I (Rof 1) where a damped dipolo wave produced an
undamped vacwam viave. There are 3 figures and 5 referen.-as, 2 of
rhich are Soviet, 1 translation of a Western work into Ruasian,
1 German and 1 English.
ASSOGIATIONs Belorusskiy gasudarstvannyy universitet ( Belorussian State
University)
SUELITTED Attgast 15, 1957
Card 2/2 1. Light - Reflection 2. Light - Refraction 3. Light -
1461scular theory

ii C, R Fadorov, F 3 011/51 -5-3 -17/ 21
TITLY.t Optics of Absorbing Crystals. (Optika pogloshcha,~ushchikh
kristallov). III. Crystals of Lower Syngonies. Optical Axes
kIII- Kristally nizshikh singoniy. Opticheskiya oul).
FERIODICALs OptikM i Spektrookopiya, 1958, Vol 5, Nr 3, pp 322-3,',3 kUSSH)
AM TRAC T s In eariier parts (Refs 1,2) the autJ-.or established an invariant form of
general relationanips for propagation or plane monocnromatic waves
in absorbing crystals and discussed the case of crys+Als of medium
r,yr.:,0nio5- ',"he prajent pupar deals with the optical properties of
cryatals of lower syngonles using a canonical lLvariaut reprasenzUtioa
of the reciprocal complex tensor of partaitdvity. Gan,3ral expressions
are obrAined for polarization of plane viuvos in crystals of loNer
syngonioa with canplex. rafractiva indices for uniform vmves. A
Card 1/2

SOV/51-5-3-17/21
Optics- of Absorbing Crystalu. III. Urystald of Lo.-;er :;~mgoniaj- Optical A7.3a.
0 -
general expression Is found for the apocial 31rections -,ihich have a
aingle value of tha rafractive indeam. The puper is antir3ly
theoretical. There are 2 figuras, 1 appendix and 19 references,
14 of whicn are Soviet,
into Ru3sia:a.
iWSO~XLTIONsInqtltut fizIkI j lzato:aAtiki, XT B3JR (Instituts of Piysics and
Mathawatics, Academy of Sciences of th, Belorussian SSR)
~;UBIJTTEDi October 28, 1957'
1. Crystals--Optical properties 2. Cryutals--Theory

AUTHOR s Fedorov, F.I.
TITLE optics of Absorbing Crystals (Optika pogloshchayushchikh kristallov).
IV. Classification (IV. Klass Ifilcatsiya)
PMUODICAL i Optika I Spektroskoplya, 1958, Vol 5, Nr 4, pp 450-461 (USSR)
LBSTR&CT% The author discusses all possible types of absorbing crystals of lower
apganies, frota the point of view of the number and nature of the
optical axes. It is shown that isotropic optical axes may be present
in such crystals. In contrast. to transparent crystals the cptical
properties of absorbing crystals of rhowbic, monoclinic and triclinic
syngonies differ essentially between each syngony. The -total nnber
of various types of absorbing crystals roaches 16, instead of 3
according to' Voigt--Drudeve theory. Octaplate classification 0~
absorbing i~on-active non-magnetic crystals according to their

-SOV/51-5-4-14/Zl
Optics of Absorbing Crystals. IV, Classification.
optical pioperties is given. The.paper is entirely theoretioal.
Thera are 9 references, 7 of which are Soviet and 2 German.
ASSOCIATION tInstitut I itiki I matematik:i, AN SSSR (Institute of Physics and
Mathematti s . Academy of Science of the U.S.S.R.)
SUEMMD% October 21 , 1957.
1. Crysta3s--Optieal properties 2. Crystals--Classification
Card 2/2 3. Crystal3--Theory

AUTHORS s Tomillchi1c, L.M. and Fedorov, F.I* SOV/51-5--t-15/21

TITLE. Optics of Absorbing gnetic Grystals. (Optiks. pogloshchayushchikh
magnitnykh kristallov). I. Polarization of Uniform Plane T(Aves
(I. Folyarizatsiya odnorodnykh plookikh voin).
MRIODICAL; Optilm i Spektrookoplya, 1958, Vol 5, Wr 4, pp 462-468 (USSR)
ABSTRACT. Applicution of invariant methods (Refs 1-8) simplifies considerably
the theory of the optical properties of absorbing crystals. Such a
theory is, however, incomplete without allowing for the magnetic
properties of crystals. Although 1A transparent bodies the magnetic
susceptibility is negligibly small, it may reach conparatively large
values in absorbing crystals. Thus crystalline hydrates of organic
and inorganic salts of rare earths and of metals of the iron group
(Fe, Ni, Go) are strongly param gnatic (ILdiffers frou 1 in the third
decimal place) and exhibit strong magnetic anisotropy (20% of the
absolute value of magnetic susceptibility). There are also Many
organic and inorganic diamagnetic crystals in uhichii differs from I
only in the fourth or even sixth decimal place but vhich are nevertheless
strongly anisotroplo, e.g. graphite. In such substances the magnetic
susceptibility and its anisotropy are of the same order as the
Card 1/2 anisotropy of the permittivity tensor F_. The authors deal 'with

'Optics of Absorbing Magnetic crystals. I. Polarization of Uniform Plane Waves.
polarization of plane uniform electromagnetic waves propagated in
a non-active medium-with an arbitrary anisotropy of the dielectric,
magnetic and conducting properties. The discussion is given in a
general invariant form. The folloning results are obtained.
(1) The most general case of polarization in absorbing orystals is
elliptical polarization and the polarization ellipses of the transversefield
vectors D! and B are pot similar and are not Lautually orthogonal.
(2) Elliptically polarized vqves v4th similar and Identically
distributed ellipses of transverse vectors of induction are propagated
along optical axes. (3) circular polarization to possible only for
maves propagated along optical axes, and then only in crystals %hose
parameters obey an additioMl.special relationship involving the
permittivity and parmeability vectors. (4) Linear polarization
of one of the transverse vectors produces linear polarization of the
Ga rd 2/2 other vector. The paper is entirely theoretical. There are 15 references
8 of which are Soviet, 5 Englishand 2 translations,
AS-30CLITIONsBalorusakly gosudaretvannyy universitat im. V.I.Lenina (1~rolorussian
State University Dneni V.I. Lenin) 1. Crystals-Magnetic factors
SUBLUTTSDs October 29, 1957 2. Electromagnetic waves-Polorization

ME
MTHORS s Torall'ohik, L.M. and Fodorov, F.I. SOV151-5-5-15123
TITLE: Optics of Absorbing YLagnetic Crystals. (Optillca pogloshchayushchikh
magnitnykh lcristallov). II. Field Vectors for Plane 7.,Tavos. Refractive
Indices and Optical Axes. (11. Vaktory polya ploskikh voln. Polmuitali
prolomleniya I opticheskiye osi)
PSUWICAL: Optika i Spektrookoplya, 1958, Vol 5, Yr 5. r-p 601-605, (USSR~'
I
A,~ TRU T In Part I (Rat 1) it was shown that the difforance between the equations
for plans electromagnetic waves in absorbing r4arnotic crystals and
the corresponding equations for transparent vagnetic crystals can be
reduced to replacement of the real permittivity tensorE by a complex
tensor el . Following Refs 2, 3 it is concluded that optical properties
of abaorbin6,uagnetic crystals should be determined primarily by the
tensor Ir = (FIJ-1 I'll The I I tensor Is in general couplex and asymmetric,
bat it may be made symetrical using the real sy=otric permeability
Card 1/2

SOV151-5-5-15123
Optics of Absorbing Magnetic Crystals. II. Field Vectors for Plane 1aves
Refractive Indices and Optical Axe&.
tensor p- Using a canonical dyad representation for the tensor
the authors obtained general Invariant expressions which give complex
refractive indices and polarization of plans uniform monachromtic
-waves, as wall as the directions of optical axes. The paper Is
entirely theoretical. There are 8 Soviet references.
SUBLaTTED: December 3, 1957,
1. Magnetic crystals--Optical properties 2. Electromagnetic waves
Card 2/2 --Analysis

24 (5)
AUTHOR:
TITLE:
PERIODICAL:
ABSTRACT:
Card 1/2
Fedorov, F. I. SOV/56-35-2-25/60
Projective Operators in the Theory of
Elementary Particles (Proyektivnyye operatory v
teorii elementarnykh chastits)
Zhurnal eksperimentallnoy i teoreticheskoy fizikip 1958,
vol 359 Nr 2, pp 493-500 (USSR)
By means of the minimal polynomials of the matrices of the
relativistic wave-equation and the apin-matrices projective
matrices are written down; dyadee are concerned here by means
of which every possible particle-state can be described in
the case of any spin. The physical fundamental quantities
(energy-momentum, current-charge, transition probability)
can be represented immediately by means of these projective
operatorsp viz. in an invariant manner (independent of the
manner of representation). The calculation of various
effects for particlea with spin can be reduced to the
evaluation of the traces of definite combinations of
matrices. In application of the method described the general
conditions for the definiteness of energy and charge for

Projeotivo Operators in the Theory of SOV/56-35-2-25/60
Elementary particles
particles of the same mass are derived. Furthermorep a
derivation of the commutation relations for particles
with any spin is given. It is shown that the two formulae
a V f (2)),Zpk
2k m A -'� "2k' 2k 1 "2k' 2k (x/X22po
can be used also for the purpose of dealing with all sorts
of other problems in which the spin of particles plays an
important part. There are 9 references, 8 of which are
Soviet.
ASSOCIATION: Institut fiziki i matematiki Akademii nauk Belorueskoy SSR
(Institute of Physics and MathematiesiAS Belorussian SSR)
SUBMITTED: March 269 1958
Card 2/2

"? Y. V 00 6,%V/58-59-7-16463
Translation from: Referativnyy Zhurnal Fizika, 1959, Nr 7, p 257 (USSR)
AUTHOR: Fedorov, F.I.
% X
TITLE: Reflection and Refraction of Li&h Iin Transparent Uniaxial Crystal
PERIODICAL: Uch. -zap. Belorussk.-un-t. 1958, Nr 41, pp 219 - 230
ABSTRACT: Using the invariance method, the author solved 'the problem of the
reflection and refraction of light in unbounded transparent uniaxial
crystals in the case of arbitrary orientation of the optical axis,
division plane, and plane of incidence. The resulting formulae for
detem.ining the amplitudes of the waves reflected and refracted on a
uniaxial crystal have the same value as the Fresnel formulae for Iso-
tropic media. The following particular cases are examined: a) the
optical axis is parallel to the division plane, b) the optical axis
is perpendicular to the division plane, c) the optical axis Is ar-
bitrarily oriented relative to the division plane but parall *el to the
plane of incidence, and d) the normal incidence of light.
Card 1/1 B.V. Bokut'

TOMILICHIII, L.M.-,-F=R()V, F.I.
Optical characteristics of absorptive magnetic crystals
with average and rhombic eyngony. Trudy Inst.fis.i mt.
All BSSR no.3:142-151 159. OURIL 13:4)
(Crystals--Optical properties)

MOROZ, L. G. ; rAWROV, F. L
Wave functions of an electromagnetic field in a vacuna.
Trudy Inst.fiz.1 mat.AV BSSR no.1:154-166 '59.
(KRA 13:4)
(Wave mechanics) (Blectromagnatic waves)

SOV/70-4-4-6/34
AUTHORS: Tomillchik, L.M. and Fedorov, F
TITLE: Magnetic Anisotropy as a Metric Property of Space
PERIODICAL: Kristallografiya, 1959, Vol 4, Nr 4, pp 498-504 (USSR)
ABSTRACT: It is shown that the theory of the optical properties
of homogeneous magnetic crystals can be derived from the
corresponding theory for non-magnetic crystals by intro-
ducing a metric, the metric tensor g being determined
by the magnetic permeability tensor ji . A covariant
tensor A in denoted by A and a contravariant tensor
by 2: . (0-1 = I . g converts from a space with an
orthogonal Euclidean metric to a space with some other
metric. In Maxwellts equations E Is a covarlant
vector and B a contravariant pseudovector.
As V = 1/81T (ED + 1W) is scalar, 5 is a contravariant
vector and R a covariant pseudovector. The refraction
m Is a covarlant vector. In this notation these
quantities are denoted by
Cardl/3 0

SOV/70-4-2-6/34
Magnetic Anisotropy an a Metric Property of pace
The dielectric and magnelic iermeabilities are doubly
contravariant.tonsors III * A marks a pseudo-
vector. For non-magnetic crystalsw Maxwell's equations
and the equation for a plane wave take the form:
I R Lis B, a
For a magnetic crystal:
A 4 n A
ITY 0 L*6j
These quantities are.transformed by the metric tensor as:
A A r-.,t t% - k
R [;Kj I B
H I k~MEJ
~7g ~ 0 \[Tg~
The sets of equations for the two cases can be made to
Card2/3 coincide if

SOV/-78-4-4-6/34
Magnetic Anisotropy as a Metric Property of pace
IL -T
IL or and IL
0.
This statement is poved and two examples are given.
There are 9 Soviet references.
ASSOCIATION: Institut -f&:bik:L i mat*matikI AN BSSR
(Inditute of Physics and Mathematics of the Ac.Sc.,
Byelorussian SSR)
SUBMITTED: March 22, 1959
Card 3/3

I SOV/51-ti-1-14/30
AUM-10R. Fedorov, F.I.
- .11~
TI7L,E.- Tha,~ry -,f the Opft~-%2 A:-ti-r-Ity of Cryytala. (K t,3orii optichaskoy
a"Ivr.o.M. &iutall-c7). I -, 11-ka Law -~Jr Conzarvation of Bnergy and
Opti~sl A,Aivity Temqcrz (I. Zakaa soUiraneniya energii i tenzory
akt1,,tc!xtt)
PERIODICAL: Optik-a 1 5pAtraF.L,.*riya, 11c.-1 E. Nr 1, p? 83-03 (USSR)
ABSTRACT; Thio raprat sri-7as a tntory of t4i,~ optical activity of
cryetalu in an invarl-&-it fv= .vhirh -is ln4apendvat of zoordinatox.
Starting from the assumption of Jzdapsndenco of the electric and
m9gneti,~, in4m,.-tion vosctorx D anl A of -che gradienta of the corresponding
flold4 t:ia autbor applien the law d r-=zarvatiot of energy to obtain
the baf:i-! ralatlounhip of B-arnIc moleralar theory of the opticaily
a,itlve -.!rystrilc. It was found thitt the 'rector of the energy flow density
in the optically aA1-T6 media ditforis from the u,3,--al Umov--Foynting
vector P Thir rector 1,T nc, given by
'S 0
P +
^41 / ulti
where it. pare transposezef third-rank teasors d., 15, called electric
and ma~paetl~ ft;,~ttvlty tanaorc. The author obtains invariant expressions
Card 1/2

4/aO
Theory of the Optical Aebirity of Oryai,.Alu 4_,ii of Conservation of~
Energy and Optical Activity Tensors.
for the activity tonsort cL and 19 of all classes of the optically
active crystals. Of the 32 z1asses of crystals the activtty tensors
become zero for all cantrai. and plamaxial classes (there are 11 of
them) which possoss Inversicn o~metry. Also both inversion classes
of hexagonal syngony (with sixth-order Inversion axis) and the planar
class of -.ubic ayugony have zero activity tonsor4. Only the remaining
classes of crystal symetry may exhibit optical activity. The paper
is entirely theoretical. There are 10 references, 7 of which are Sooit,
1 French, I Gaman and I translation.
SUBMITTED: March 15, 19SP
Card 2/2

AUTHOR: Fedorov, F.I. SOV/51-6-3-15/28
TITLE: On the Theory of Optical Activity of Crystals. 11 Crystals
of Cubic Syngony and Planar Classes of Middle Syngoniea
(K teorii opticheskoy aktivnosti kristallov. II Krialally
kubicheskoy aingonii i planallnykh klassov srednikh aingonly)
PERIODICAL: Optika i Spektroakopi-ya, 1959, Vol 6, Nr 3, pp 377-383
(USBR)
ABS~TRACT: The author showed that Maxwell's equations together with
constitutive equations far plane waves in optically active
media have.the following form;
- cng ], (1)
CIA 1, (2)
+
+ (4)
where m A is the refraction vector, k /0 is
the wave number in vacuum and ~cc, 0 are the electric and
Card 1/3 magnetic activity tensors respectively. Using EqB.(I)-(4)

SOV/61-6-3-10/28
On the Theory of Optical Activity of Crystals. II Crystals of
Oubie Syngony and Planar Classes-of Middle Syngoniea
the author studied propagation of light in anisotropio
media with the highest symmetry, i.e. in crystals of cubic
syngony and planar classes of middle syngonies. As in
the preceding paper (Ref.1), invariant treatment was
employed. The author found that in planar classes of
middle syngoniea there is no rotation of the plans of
polarization on propagation of light along the optical
axes. Neverthelesaproperties of such crystals differ
essentially from properties of optically inactive crystals,
since the light reflected at such crystals is elliptically
polarized. The author points out that optically active
.substances do not necessarily exhibit the property of
rotation of the plane of polarisation. He proposes that a
medium should be called optically active if its constitutive
equations have the form
-0 4 -J,
D = eB + (0CVj' E]J' B = JAH + [,6q, HI (45)
Card 2/3 F-,03~ :~- plane waves these equations have the form given by

sov/51-6-3-15/28
On the Theory of Optical Activity of Crystals. II Crystals Of
Cubic Syngony and Planar Classes of Middle Syngonies
Eq.( 3) -Eq.( 4) with, & and P not equal to zero. From
this definition it follows that a medium which rotates the
plans of polariaation for one or more directions of propa-
gation of light is necessarily an optically active medium,
,.but, in general, the reverse is not true. The paper is
entirely theoretical. There are 8 references, of which
6 are Soviet, I translation from German into Russian and
1 German.
SUBMITTED: February 15, 1958
Card 3/3

24(4), 24(2) SO'1/51-6-4-21/29
AUTHORS t Bokut', B.V. and Fedorov, Fa.
TI TIZ: On the Theory of the Optical Activity of Crystals. (K toorii
oDticheskoy aktivnooti kristallov). III. 'the General Equation of
Normals (III. Obshcheye uravneniyo normaley)"
FERIODICALs Optika i Spektroskoplya, 1959, Vol 6. Nr 4, pp 537-541 (USSR)
ABSTRACTt In the earlier part3 of this work (Refs 1, 2) the author developed an
invariant phenomenological theory on the optical activity of crystals
of all types of sy=etry. The present paper deals with the general
ec,pation. of normals for the optically active crystals when magnetic
effects are allowed for. 'rho theory shows that three types of waves
are possible in the optically active crystals, and the phase velocity
of the tbird Tave should be very small ccmpared with the velocity of
light. The paper is entirely theoretical. There are 6 references. 5 of
which are Soviet and 1 translation from German into Russian.
SUMffTTZD,- March 15, 1958
ca rd 1/1

SO'1/51-7-4-20/32
AUTHORSs Bokat', B.V. and Fedorov, F.I.
------------
TITMz Propagation of Light in Absorbing Magnetic Active Isotropic Media and
Cubic Crystals
FMODICALs Optika I spektroskopiya, 1969, Vol 7, Wr %, pp 558-561 (USSR)
AM TROT s The authors discuss propagation of plane electromagnetic waves in an
optically isotropic medium, possessing optical absorption, optical
activity and magnetic properties.. It in shown that when the magnetic
tems of the optical activity are taken into account, circular
dichroism should occur. The paper is entirely theoretical. There
are 8 references, 6 of which are Soviet and 2 translations.
SUBMITTFjD: March 23, 1959
Ca-rd 1/1

LOBKO, S.I.; ;$
Spin 1/2 - 312 particle In a homogeneous magnetic field,
Dokl.AM BSSR 4 no. 5:194-198 My 160. (HIRA 13:10)
1. Beloruashy gosudaretvanVy univereitat im. Y.I.Imnina.
(Particles (Unclear physics))