Multiplexing and switching of laser beams based on cross-correlation interaction of periodic fields

1.8 MB·

by  S. A. Bugaychuk

OPTICS, LASERS, AND QUANTUM ELECTRONICS
7
1
doi: 10.15407/ujpe61.04.0301
0
2 S.A. BUGAYCHUK,1 V.O. GNATOVSKYY,2 A.M. NEGRIYKO,1 I.I. PRYADKO1
n 1InstituteofPhysics,Nat. Acad. ofSci. ofUkraine
a (46, Prosp. Nauky, Kyiv03028, Ukraine; e-mail: [email protected])
J 2PhysicalDepartment, TarasShevchenko NationalUniversityofKyiv

7 (4, Prosp. Academician Glushkov, Kyiv 03022, Ukraine)
1
MULTIPLEXING AND SWITCHING

] OF LASER BEAMS BASED ON CROSS-CORRELATION
s
c INTERACTION OF PERIODIC FIELDS
PACS71.20.Nr,72.20.Pa
i
t
p
o
s. Theworkisdevotedtothestudyofthecorrelationtechniqueofformationoflaserbeamsunder
c conditions of the interaction of coherent fields spatially periodic in the transverse direction. It
i is aimed at the application of this technique to the multiplexing (splitting) of an input laser
s
y beam to several output ones, management of the energy of these beams, and their clustering
h and debunching according to required time algorithms.
p
Keywords: opticalcorrelators,phaseperiodicstructures,spatialswitchingandmultiplexing
[
of laser beams.

1
v
0 1.Introduction cording to [6]. The purpose ofthe work is to increase
1
the factors of influence on the formed field and, con-
7 The idea to use periodic diffraction elements for a
sequently, to enlarge the area of practical problems,
4 directional transformation of light beams was ap-
0 peared simultaneously with the invention of these el- which can be solved in such a way. We are consider-
. ing the task, when the interference pattern created
1 ements. Wellknownistheimportanceofadiffraction
by two laser beams illuminates a flat phase diffrac-
0 grating, which splits the incoming beam into several
7 secondary ones. In dependence on the structure of tion grating, which can be moved in the transverse
1 direction. This problem represents a special case of
a groove of the grating, one can amplify, decrease,
v: or make equal the intensities in the diffraction or- the correlationapproach(two-stagemethod) to form
i an optical field, which has a complex structure and
X ders [1,2]. Taking into consideration that the auto-
a required distribution of the energy at a technolog-
correlation function of any periodic distribution rep-
r ical target [7]. In addition, it can be considered as
a resents also a periodic structure [3], the diffraction
an extension of the dynamic holography [8,9] to the
gratingsare applied to practically important correla-
casewherethephaseelements,inwhichastronglink
tion schemes for the information processing (in par-
between the distribution of the phase of the grating
ticular, to the schemes with synthetic aperture [4],
andtheintensityfringesoftheinterferencepatternis
holographic correlatora with discrete representation
broken,areinuse. Inourmethod,the lightfieldillu-
of the signal [5], and so on). In the present work,
minatingaphasemaskhasaperiodicstructure. Inso
we are developing further capabilities to use periodic
doing,boththephasedistributionofthefieldandthe
structures for the management of laser beams, ac-
phasemaskitselfmaybevariedbychangingtheirpe-
riods,thestructureofphaseindices,andtheirmutual
(cid:13)c S.A.BUGAYCHUK,V.O.GNATOVSKYY,
shift. In particular, this distribution of the illumina-
A.M.NEGRIYKO,I.I.PRYADKO,2016
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ISSN 2071-0186. Ukr. J. Phys. 2016. Vol. 61, No. 4
S.A.Bugaychuk,V.O.Gnatovskyy, A.M.Negriykoetal.
The main idea of the proposed technique consists
in the fact that one should create a “coupledsystem”
of the light grating and the material grating. In such
coupled system, each diffraction order on the output
is formed as a result of the interference of partial
waves of the light grating.
The purpose becomes to find the special condi-
tions to manage the intensity in each diffraction or-
der. Thatmaybeeithertheamplificationorsuppres-
sionofsomeofthem,nullification,ordoingthemwith
Fig. 1. Basic optical scheme of the correlation method with
two periodic structures. Two input plane waves Iinp and Iinp equal intensities, what is made in the multiplexing
1 2
converge at the angle θ to form the interference pattern on schemes.
the phase grating M2.The periods of the phase grating and The theoretical framework of the correlation tech-
the interference fringes are either equal or multiple to one nique with periodic structures involves the known
another. The objective O forms the angular spectrum of the
theorems for the displacement and for the convolu-
resulting field.The notations {±k}, k = 0,1,2,... mark the
tion of two functions. They are used to find match-
diffractionorders onitsoutput plane
ing between the product of the distributions of two
fields and the convolution for the Fourier transforms
tion field, which is created by the interference of two
(angular spectra) of these fields. Thus, the correla-
or more beams, can be replaced by its synthetic ana-
tion method of the formation of beams in differ-
log, which forms an “equivalent” field. The specially
ent diffraction orders lies in the consistent impact of
calculated synthetic hologram, which is illuminated
amplitude-phaseconvertersonapreviouslydiffracted
onlybyonebeam,maybeusedassuchanalog. Inour
field. In the frame of this work, this is a transforma-
work,wewillinvestigatethe“equivalent” fieldformed
tion of the periodic light field by means of a phase
by a periodic phase grating, which has the rectangu-
grating.
larprofile. Wewillprovealsothatthefieldformedby
Now, let us consider the case where a plane light
suchgratingsubstitutesagenerallyknownpatternof
wave propagates through two sequentially arranged
interference fringes. The lack of the obligatory corre-
modulators M and M . Note that the description
spondence of the distributions of phase profiles be- 1 2
of one of the modulators (M ) will correspondto the
tween the input field and the diffraction grating also 1
fringepatternofthelightintensityintheinterference
promotes to introduce new dynamical algorithms for
area (see Fig. 1).
the multiplexing, scanning, and switching of shaped
Theangularspectrumoftheoutputfieldisdefined
beams.
as the Fourier transform of the diffraction field after
these both modulators:
2.Mathematical Background of the
Correlation Method for Periodic Functions 1
Fˆ{M M }= Fˆ{M }⊗Fˆ{M }=
Thebasic schemeofthe correlationmethodbasedon 1 2 4π2 1 2
the periodic structures for a transformation of laser 1
= m ⊗m , (1)
beams is shown in Fig. 1. 4π2 1 2
Accordingtothisscheme,twoplanewavesformthe
interferencefringepattern(letuscallitthelightgrat- where Fˆ and ⊗ are the operators of Fourier trans-
ing), whichilluminates a periodic phase grating. The formation and convolution of functions, respecti-
periodic intensity distribution on the input is trans- vely:
formed into a set of diffraction orders at the back
focal plane of the objective O on the output of the m1,2(ξ,η)=Fˆ{M1,2(x,y)}=
system. The intensity ofeachdiffractionorderis eas-
∞ ∞
ily controllable by changing the parameters of the
scheme, including the mutual spatial shift of the pe- = M1,2(x,y) exp[2πi(ξx+ηy)]dxdy. (2)
Z Z
riodic structures relative to one another. −∞−∞
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ISSN 2071-0186. Ukr. J. Phys. 2016. Vol. 61, No. 4
MultiplexingandSwitching of LaserBeams
Here,(x,y)arethespatialcoordinatesintheplaneof of grooves, i.e., L = NT . The parameter a deter-
gr
the modulators(in the front focalplane of the objec- mines the shift of the grating along the coordinate x
tive, which makes the Fourier transformation of the and relative to the interference fringes.
light field), (ξ,η) are the angular coordinates in the Theinputinterferencefieldisformedbytwobeams
plane of the formation of diffraction orders (in the Iinp and Iinp that have equal intensities and plane
1 2
back focal plane of the objective). wavefronts:
In the case of one-dimensional periodic structures, E =Eexp[i(k r−ωt+ϕ )],
1,2 1,2 1,2
wecanpresentthetransmittanceofthemodulatorsin (8)
E=(0,E,0),
the form of the convolution between the distribution
in a single “window” S(x) (of an individual groove) where ω is the frequency of the laser radiation, k
1,2
and a comb function: are the wavevectors of the beams, and ϕ are their
1,2
input phases. The wavevectorshavethe components
M(x)=S(x)⊗comb(x),
∞ θ θ
(3) k = ±ksin ,0,kcos ,
comb(x)= δ(x−bT), 1,2
(cid:18) 2 2(cid:19)
Xb=1
and their interference occurs at the plane (x,y).
where T is the width of the “window” S(x). In the Let,attheinitialtimemoment,ϕ =0andϕ =π.
1 2
extended form, we have the integral Then the expression for the interference pattern has
the form
∞
M(x)= S(x−y)comb(y) dy. (4) E (x)=2Esin ksinθx exp[−i(ωt−π/2)]. (9)
Z int
(cid:18) 2 (cid:19)
−∞
The angle of convergence of the beams θ is chosen
Thus,theoutputangularspectrumwillbecalculated
from the condition that n numbers of the periods of
according to formula (1) with regardfor integral (4),
the interference pattern fits on the aperture L of the
which contains the specific profile of a converter.
diffractiongrating. Thenformula(9)canberewritten
as follows:
3.Calculations of Algorithms
for Switching and Spatial Multiplexing E (x)=2Esin(2πnx/L)exp[−i(ωt−π/2)],
int
(10)
for the Correlation Scheme x∈[0,L].
Asanexample,weconsiderthetransformationofthe
The period of the interference pattern T will be
field
interferencefieldwithasinusoidalintensityprofileby
related to the aperture of the grating L by the ex-
means of a phase diffraction grating, which has ei-
pression T = L/n. The distribution of the inten-
field
ther rectangular (meander) or triangular phase pro-
sity of the interference pattern on the plane (x,y) at
file. Then we will have the following expressions for
an arbitrary time in dependence on the coordinate x
the rectangular and triangular phase profiles in the
will be proportional to the expression
“window”, respectively:
I (x)∝sin2(2πnx/L), x∈[0,L]. (11)
int
S (x)=−Φsgn(x), x∈[−T /2,T /2], (5)
rect gr gr
The position and the intensities of diffraction or-
Stri(x)=Φ(1−2|x|/Tgr), x∈[−Tgr/2,Tgr/2], (6) ders are determined by the following important pa-
rameters: byarelativespatialshiftbetweenthegrat-
and
ing and the interferences fringes, by the multiplicity
∞
Tgr of the periodof the diffractiongratingrelative to the
comb(x)= δ x− (2b−1)+a , (7)
(cid:18) 2 (cid:19) interference pattern, and by a phase profile of the
Xb=1
grating.
where the constant Φ sets the phase profile of the We have found the conditions of the implementa-
grating. We choose the physical size (the grating tion of several scenarios to make the spatial multi-
aperture) L so that it includes an integer number N plexing, as well as the management of the intensities
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S.A.Bugaychuk,V.O.Gnatovskyy, A.M.Negriykoetal.
In Figs. 2.1 and 2.2, the period of the interfer-
ence pattern is doubled in comparison with the pe-
riod of the diffraction grating. The central peak in
Fig. 2.1, which is created under the conditions of
a = 0 and a = T /2, may be redistributed to two
gr
channels (left and right) with equal intensities under
the condition a=T /4. Therefore, the parameter of
gr
theswitchingofchannelsisthemutualspatialshift a
between the light periodic structure and the diffrac-
tion grating.
If we replace the rectangular grating by a tri-
angular one, then the left and right channels will
become doublets, as it is seen from Fig. 2.2 un-
der the condition a = 0. Thus, one can create four
beams with the same intensity. We have obtained
the possibility to form either one, or two, or four
beams of equal intensities by changing the grating
profile and the mutual transverse shift. Owing to
the simple structures of the phase profiles, the in-
tensities of created beams can be easily adjusted
with the use of computer-controlled phase mo-
dulators.
In Figs. 2.3 and 2.4, the periods of the light pat-
tern and of the diffraction grating are the same.
For the rectangular grating profile, one can create
two channels for the switching: we can either leave
only the left one (Fig. 2.3 for a = 0), or only the
right one (a = T /2), or the both simultaneously
gr
(a = T /4). In the case of a triangular grating pro-
gr
file (Fig. 2.4) under the condition a=0, four diffrac-
tion maxima (communication channels) with equal
intensities are created. If the shift is changed by the
Fig. 2. Control over the intensities in the diffraction orders
underashiftofthediffractiongrating.Positions(a)showthe value of a = Tgr/4, only two left channels appear,
normalizedintensitiesI/I0.Positions(b)showtherelativespa- and there are only two right channels for the shift
tial position of the phase profile of the grating and the in- a=−T /4.
gr
tensities in the interference pattern, which are denoted by a Each of the described scenarios for the change of
dashcurve. Thenotations {−0}and{+0}designatethemain
both the intensity and the location of the diffrac-
diffraction orders, which correspond to the positions of the
tion orders are determined due to the shift, phase
beams, which form the interference pattern. The first diffrac-
tionorders aremarkedby{−1}and{+1}.Thevalueashows relief, and mutual dispositions of the periodic struc-
the spatial shift between the maxima of the grating and the tures. Therefore, all these factors are important to
interference pattern. In Figs.2.1and 2.2, n=20 and N =20 make manipulation of the spatial channels on the
aretaken. InFigs.2.3and2.4,thesequantitiesaren=10and output of the correlation scheme. On a practical
N =20 level, controlling these parameter may be imple-
mented with the help of a spatial electro-optical
modulator of phases, which is placed on the area
oftheoutputbeams,whenthefringeinterferencepat- of the formation of interference (or created by an-
ternilluminatesaphasegrating,whichhaseitherthe other way) fringes. This modulator could create a
rectangularortriangularformofgrooves.Theresults grating, parameters of which can be changed with a
are given in Fig. 2. computer.
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MultiplexingandSwitching of LaserBeams
4.Experimental Study
Wehavestudiedtheangularspectraofthegenerated
fields,namelythedistributionoftheintensitiesinthe
diffraction orders of the correlation scheme. The op-
tical scheme of the experimental set-up corresponds
to Fig. 2.1. The radiation of a He–Ne laser was ex-
panded by a telescopic system and filtered by a sys-
temofdiaphragms. Theresultingbeamwithuniform
distribution of the energy in the cross-section and
with a plane wavefront is forwarded onto a beam-
splitter device to obtain two beams for their later in-
terference. Moreover, the block of the beam-splitter
device provides a fine adjustment of the angle be-
tween two beams. These two beams form the inter-
ference pattern, which illuminates a diffraction grat-
ing. The grating is mounted in a holder, which ad- Fig. 3. Experimental measurements of the redistribution of
the intensities in the diffraction orders for arectangular grat-
justs a requiredorientationof the grating in the hor-
ingwithdoubleperiodrelativetotheinterference fringes (see
izontal and in the vertical directions. The necessary
case 2.1 inFig.2), and their comparison with theoretical cal-
ratio between the period of interference fringes and
culations: the photos of thediffraction orders (a); histograms
the period of the diffraction grating is achieved by of the measured intensities (b); calculated intensities (c).The
the adjustment of the convergenceangle between the notations {−0} and {+0} denote the angular spectra of the
interfering beams. beams, which form the interference pattern. The mutual shift
The angularspectrumofthe diffractionfield is ob- isa=0
servedonabackfocalplane ofa high-qualityFourier
objective. Thebeamsofthediffractionorders,aftera
necessarymagnification,havebeendirectedtophoto-
diodesbyasystemofprisms. Theiroscillogramshave
beenregisteredandthenprocessedbyacomputer. In
the experimental investigations, we used the phase
gratings, which had a rectangular profile.
The results of experimentalresearchesof the man-
agement of the angular spectrum and their compari-
sonwith the theoreticalcalculations are presented in
Fig. 3. The grating has the rectangular phase profile
with the modulation depth equal to π/2. Such value
of the modulation depth can be easily controlled ex-
perimentally, because, in this case, one can observe
the appearance of a strong maximum between {−0}
and {+0} diffraction orders together with a strong Fig. 4. ThesameasinFig.3.Themutualshiftisa=Tgr/4
decrease in the intensities in these main diffraction
orders. This effect is well observed in Fig. 3. In the
experiments, we apply a usual interference pattern Moreover, the measured values of the normal-
on the input of the system that was formed by two ized intensities practically coincide with the theo-
plane wavesof equal intensities. In Figs. 3 and 4, the retical calculations: in Fig. 3, the measured values
data of the experimental implementation of two sce- are I/I0exp = 0.6 for the central maximum and
exp
narios depending on the spatial shift of the diffrac- I/I0 = 0.14 for the side peaks, whereas corre-
theor
tion grating relative to the interference pattern and sponding calculated values are I/I0 = 0.8 and
the comparison with the theoretical calculations are I/I theor = 0.12. In the Fig. 4 the measured in-
0
exp
given. tensities are I/I = 0.4 for the side peaks and
0
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ISSN 2071-0186. Ukr. J. Phys. 2016. Vol. 61, No. 4
S.A.Bugaychuk,V.O.Gnatovskyy, A.M.Negriykoetal.
I II
1 1
(a) 0.5 0.5
0 0
{-0}{+0} a=0 {-0}{+0}
1 1
(b) 0.5 0.5
0 0
Fig.5. Basicopticalschemeforthecorrelationtechniquewith
a=Tgr/4
periodicstructures basedonthe“equivalent” interference pat-
tern.TheinputplanewaveisIinp,theequivalent phasemask 1 1
isM1,i.e.thisisanadditionalphasegratingwithdetermined (c) 0.5 0.5
phaseprofile. Thediffractiongratingandtheequivalentmask
haveeitherequalperiodsormultipleperiods.Theotherdesig- 0 0
nationsarethesameasinFig.1 a=Tgr/2
1 1
I II
(d) 0.5 0.5
1 1 0 0
(a) 0.5 0.5 Fig. 7. Comparative calculations of the intensities in the
diffraction orders for the scheme with “real” interference pat-
0 {-0} {+0} 0 {-0} {+0} ternI(schemeinFig.1)andfortheschemewith“equivalent”
a=0
patternII(schemeinFig.5).ThephasediffractiongratingM2
1 1
hastherectangular profileofthereliefshowninFig.2.3. Fig-
(b) 0.5 0.5 ure(a) showsthemaindiffractionorders ontheoutput plane
of the scheme in the case where the diffraction grating M2 is
0 0 absent. The value a determines the spatial shift between the
a=Tgr/4 periodicstructures
1 1
(c)
0.5 0.5 intheexperiments. Weexplainitbythefactthatthe
two input waves could not be entirely equal in a real
0 0
a=Tgr/2 experimental set-up.
1 1
5.Equivalent Mask with one Plane Wave
(d)
0.5 0.5 for the Substitution of Interference Pattern
0 0 For practical using of the correlation scheme, there
Fig. 6. Comparative calculations of the intensities in the will be appropriate the exclude the interferometer,
diffraction orders for the scheme with “real” interference pat- which play a role of a “generator” of a light periodic
ternI(schemeinFig.1)andfortheschemewith“equivalent” patterninaformofinterferencefringes. Thebestde-
patternII(schemeinFig.5).ThephasediffractiongratingM2 cision for this purpose is the substitution of the in-
has the rectangular profile of a relief shown in Fig. 2.1. Fig-
terferometer (as well as the interference pattern) by
ure(a) shows themaindiffraction orders on theoutput plane
someamplitude-phasemask,whichhassuchthecom-
of the scheme in the case where the diffraction grating M2 is
plex amplitude of the transmittance that is identical
absent.The value a determines the spatial shift between the
periodicstructures to the complex amplitude describing the interference
pattern, and therefore, it has the following form:
exp
I/I =0.15forthecentralpeak,thecalculatedin-
0 M (x)=|sin(2πx/T )|×
tensitiesforthesidepeaksareI/I theor =0.37. Note, equ field
0
that the central maximum is damped not completely × exp[iπ/2sgn(sin(2πx/T ))]. (12)
field
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ISSN 2071-0186. Ukr. J. Phys. 2016. Vol. 61, No. 4
MultiplexingandSwitching of LaserBeams
After the illumination of this mask M (x) with similar results, and they are completely suitable
equ
thehelpofoneflatwave,weobtainthesamedistribu- in practical schemes of the switching and mul-
tion of the fringe pattern, like in the previous cases, tiplexing.
on the plane (x,y), where the diffraction grating is We have carried out the experimental researches,
set. The calculations with the use of this mask give, whicharesimilartothosedescribedinSection4. The
naturally,thesameresults,asinthecaseofusingthe same diffraction converters M are used in this ex-
2
interferencepattern. Forthe only exception,thatthe periments, but, instead of the interference pattern,
amplitude of distribution (12) takes a half of the en- we apply the equivalent phase mask M placed be-
1
ergy of the beam illuminating this mask. Therefore, fore the converterM . So that, the plane wavefirstly
2
it has the sense to consider the case in the correla- diffracts on the equivalent mask. After that, the cre-
tion technique where one uses a distribution similar ated fielddiffracts on the grating. The latter is setin
to (12), but another mask, which contains only the the near field ofthe mask M at the distance ≤200λ,
1
phase part of Mequ(x), i.e, according to our estimations. We have obtained that
the equivalent mask very efficiently replaces the in-
M (x)=exp[iπ/2sgn(sin(2πx/T ))]. (13)
equ field
terference pattern.
One can see that such mask represents a simple
periodic phase structure with rectangular profile of
a relief with the depth equals to π radians, in 6.Conclusion
fact, the diffraction grating with rectangular profile
The application of the correlation technique based
of the grooves. Such grating can be easily fabri-
on a periodic structure expands capabilities of the
cated or be simulated on the controllable phase mo-
schemes forthe multiplexing ofa laserbeamfor such
dulator.
problems, where one needs changes of the intensities
The experimental set-up of the correlation scheme
intheoutputbeams,theirlocationonatechnological
with equivalent mask is shown in Fig. 5, and it
target,aswellasfortheswitchingoftheopticalchan-
is differ only by the input part comparing with
nels. Duringthisprocess,onecanimplementdynamic
the scheme in Fig. 1. In the case of the “artifi-
scenariosof the multiplexing, that are almostnot at-
cial” interference pattern,only one plane wavecomes
tainable during the traditional use of one diffraction
on the input of the optical scheme, and it goes
gratingevenwith acomplicatedprofileofanindivid-
through two diffraction gratings, which are sequen-
ual groove. These advantagesof the correlationtech-
tially arranged close to each other. The phase dis-
nique are achieved due to increasing the number of
tribution in the equivalent grating is rectangular ac-
factors,whichimpacttheformationofbeams. Inpar-
cording to expression (13), but the phase distribu-
ticular, they are the dynamics of a transverse shift
tion for the grating of a converter may be arbitrary,
of two gratings relative to each other and the possi-
in particular, like it was described in the previous
bility to change the multiplicity of their periods. At
section.
the same time, the correlation approach conserves
In the Figs. 6 and 7, we present the results of
a relative simplicity of a phase relief in individual
calculations corresponding to the use of the “equiv-
grooves in both used modulators, which facilitates
alent” mask (13) together with the converter grat-
their practical application as computer-controllable
ing with the rectangular profile of a groove.In
converters.
Fig. 6, the diffraction grating of a converter has
the rectangular phase profile with the modulation
depth ±π/2 and the double period compared with
the period of the equivalent mask (see Fig. 2.1). In 1. V.A.Soifer,V.Kotlar,L.Doskolovich,IterativeMethodsfor
DiffractiveOpticalElementsComputation (London,Taylor
Fig. 7, the converter has the rectangular phase pro-
andFrancis,1997).
file with the modulation depth ±π/4 and the same
2. Yu.V. Miklyaev, W. Imgrunt, V.S. Pavel’ev, V.A. Soifer,
period as the period of the equivalent mask (see
V.G.Kachalov,V.A.Eropolov,L.Aschke,M.V.Bolshakov,
Fig. 2.3). V.N.Lisochenko,Komp’yuter. Opt.35,42(2011).
One can see that the substitution of the inter-
3. A. Papoulis, Systems and Transforms with Application in
ference pattern by the equivalent mask gives very Optics (McGraw-Hill,NewYork,1968).
307
ISSN 2071-0186. Ukr. J. Phys. 2016. Vol. 61, No. 4
S.A.Bugaychuk,V.O.Gnatovskyy, A.M.Negriykoetal.
4. A.N.Malov,V.N.Morozov,I.N.Kompanets,Yu.M.Popov, С.А.Бугайчук, В.О.Гнатовський,
Kvant.Elektr.4,1981(1977). А.М.Негрiйко, I.I.Прядко
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voi,SPIE3055,186(1996). ЛАЗЕРНИХПУЧКIВПРИКРОС-КОРЕЛЯЦIЙНIЙ
6. V.O.Gnatovskyy,S.A.Bugaychuk,A.M.Negriyko,I.I.Pryad- ВЗАЄМОДIЇПЕРIОДИЧНИХПОЛIВ
ko,A.V.Sidorenko, IEEECFP13814,378(2013).
Резюме
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8. V.L.Vinetskii,N.V.Kukhtarev,DynamicHolography (Ky- формуваннялазернихпучкiвпiдчасвзаємодiїперiодичних
iv,NaukovaDumka,1983)(inRussian). упоперечномунапрямкукогерентнихполiвiспрямованого
9. S. Odoulov, M. Soskin, A. Khyzhnyak, Oscillators with на застосування цiєї методики для мультиплiкацiї (розще-
Degenerate Four-Wave Mixing (Harwood, Chur, London, плення) первинного лазерного пучка на декiлька вторин-
1991). них,керуваннямвеличиноюенергiївцихпучках,їхгрупу-
ваннямiрозгрупуваннямзгiднозпотрiбнимчасовималго-
Received03.04.15 ритмом.
308
ISSN 2071-0186. Ukr. J. Phys. 2016. Vol. 61, No. 4