Measurement and analysis of reversible transformations of vortex-free and singular light fields produced by PDLC cells
In this work, we have firstly realized and investigated reversible transformations of vortex-free and singular optical complex landscapes appearing in a He-Ne laser beam transmitted through a PDLC cell, which is controlled by an applied DC voltage. Biaxes of all micro size LC domains are oriented...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2009
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irk-123456789-1188682017-06-01T03:04:53Z Measurement and analysis of reversible transformations of vortex-free and singular light fields produced by PDLC cells Ponevchinsky, V.V. Vasil’ev, V.I. Soskin, M.S. In this work, we have firstly realized and investigated reversible transformations of vortex-free and singular optical complex landscapes appearing in a He-Ne laser beam transmitted through a PDLC cell, which is controlled by an applied DC voltage. Biaxes of all micro size LC domains are oriented approximately along the applied electric field, and vortex-free complex landscape exists at 200 V. At 160 V, biaxes orientation spreads, and the first ‘embryo’ of vortices in the form of a smooth phase step appears. The first vortex pair nucleates at 140 V. Multitude of vortex pairs is realized when electric field is switched off. Reversed evolution is realized when the applied DC voltage grows from zero value to 200 V. It was shown that the observed topological evolution is fully defined by changes in structure and localization of real and imaginary zero-intensity lines for output complex light field. The developed technique of parametric dynamics can be applied successfully to realize and investigate various types of controlled optical elements including media with nanoadditions. 2009 Article Measurement and analysis of reversible transformations of vortex-free and singular light fields produced by PDLC cells / V.V. Ponevchinsky, V.I. Vasil’ev, M.S. Soskin // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 3. — С. 234-239. — Бібліогр.: 16 назв. — англ. 1560-8034 PACS 42.25.Ja 42.30.Ms 42.25.Kb http://dspace.nbuv.gov.ua/handle/123456789/118868 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
| description |
In this work, we have firstly realized and investigated reversible
transformations of vortex-free and singular optical complex landscapes appearing in a
He-Ne laser beam transmitted through a PDLC cell, which is controlled by an applied
DC voltage. Biaxes of all micro size LC domains are oriented approximately along the
applied electric field, and vortex-free complex landscape exists at 200 V. At 160 V,
biaxes orientation spreads, and the first ‘embryo’ of vortices in the form of a smooth
phase step appears. The first vortex pair nucleates at 140 V. Multitude of vortex pairs is
realized when electric field is switched off. Reversed evolution is realized when the
applied DC voltage grows from zero value to 200 V. It was shown that the observed
topological evolution is fully defined by changes in structure and localization of real and
imaginary zero-intensity lines for output complex light field. The developed technique of
parametric dynamics can be applied successfully to realize and investigate various types
of controlled optical elements including media with nanoadditions. |
| format |
Article |
| author |
Ponevchinsky, V.V. Vasil’ev, V.I. Soskin, M.S. |
| spellingShingle |
Ponevchinsky, V.V. Vasil’ev, V.I. Soskin, M.S. Measurement and analysis of reversible transformations of vortex-free and singular light fields produced by PDLC cells Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Ponevchinsky, V.V. Vasil’ev, V.I. Soskin, M.S. |
| author_sort |
Ponevchinsky, V.V. |
| title |
Measurement and analysis of reversible transformations of vortex-free and singular light fields produced by PDLC cells |
| title_short |
Measurement and analysis of reversible transformations of vortex-free and singular light fields produced by PDLC cells |
| title_full |
Measurement and analysis of reversible transformations of vortex-free and singular light fields produced by PDLC cells |
| title_fullStr |
Measurement and analysis of reversible transformations of vortex-free and singular light fields produced by PDLC cells |
| title_full_unstemmed |
Measurement and analysis of reversible transformations of vortex-free and singular light fields produced by PDLC cells |
| title_sort |
measurement and analysis of reversible transformations of vortex-free and singular light fields produced by pdlc cells |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118868 |
| citation_txt |
Measurement and analysis of reversible transformations
of vortex-free and singular light fields produced by PDLC cells / V.V. Ponevchinsky, V.I. Vasil’ev, M.S. Soskin // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 3. — С. 234-239. — Бібліогр.: 16 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT ponevchinskyvv measurementandanalysisofreversibletransformationsofvortexfreeandsingularlightfieldsproducedbypdlccells AT vasilevvi measurementandanalysisofreversibletransformationsofvortexfreeandsingularlightfieldsproducedbypdlccells AT soskinms measurementandanalysisofreversibletransformationsofvortexfreeandsingularlightfieldsproducedbypdlccells |
| first_indexed |
2025-07-08T14:48:31Z |
| last_indexed |
2025-07-08T14:48:31Z |
| _version_ |
1837090589429989376 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 234-239.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
234
PACS 42.25.Ja 42.30.Ms 42.25.Kb
Measurement and analysis of reversible transformations
of vortex-free and singular light fields produced by PDLC cells
V.V. Ponevchinsky, V.I. Vasil’ev, M.S. Soskin
Institute of Physics, National academy of Sciences of Ukraine,
46, Prospect Nauki, 03028 Kyiv, Ukraine
Corresponding author: Phone +380445255566, Fax +380445251589,
Email: marat.soskin@gmail.com
Abstract. In this work, we have firstly realized and investigated reversible
transformations of vortex-free and singular optical complex landscapes appearing in a
He-Ne laser beam transmitted through a PDLC cell, which is controlled by an applied
DC voltage. Biaxes of all micro size LC domains are oriented approximately along the
applied electric field, and vortex-free complex landscape exists at 200 V. At 160 V,
biaxes orientation spreads, and the first ‘embryo’ of vortices in the form of a smooth
phase step appears. The first vortex pair nucleates at 140 V. Multitude of vortex pairs is
realized when electric field is switched off. Reversed evolution is realized when the
applied DC voltage grows from zero value to 200 V. It was shown that the observed
topological evolution is fully defined by changes in structure and localization of real and
imaginary zero-intensity lines for output complex light field. The developed technique of
parametric dynamics can be applied successfully to realize and investigate various types
of controlled optical elements including media with nanoadditions.
Keywords: singular optics, optical vortices, topology, PDLC cell.
Manuscript received 17.03.09; accepted for publication 14.05.09; published online 15.05.09.
1. Formulation of the problem
History of optical singularities, or wavefront dislocations,
started in 1974 by the seminal J. Nye and M. Berry paper
‘Dislocations in wave trains’ [1]. It initiated creation of
singular optics [2, 3] developing rapidly last two decades.
Generic transformation of a smooth (vortex-free) complex
landscape to a singular wavefront is the problem of
principle importance for singular optics and singular wave
physics at whole. It has not been resolved and even
formulated up to now, due to our knowledge. For the
beginning, existence of an inhomogeneous vortex-free
scalar/elliptic field (speckle patterns) has to be justified in
principle. Arbitrary complex landscape possesses the
following general form [1]:
.)],(Im[)],(Re[
),(exp),(),(
yxEiyxE
yxiyxyxE
(1)
Vortices appear at the crossing points of real
0)],(Re[ yxE and imaginary 0)],(Im[ yxE nodal
lines of this landscape where the field amplitude is exactly
zero, what causes the phase uncertainty [1-3]. In a vortex-
free complex landscape, these nodal lines have to avoid
each other. In a complex landscape with an irregular
structure, ‘percolating nodal lines meander back and forth
and it is not easy to imagine any mechanism by which
they can avoid each other’ [2]. Therefore, M. Berry has
constructed the exceptional complex landscape with a
system of smooth symmetric amplitude hills, the zero
average wavevector k and circular not intersecting system
of nodal lines 0)],(Re[ yxE and 0)],(Im[ yxE ,
which are shifted [2]:
)],(Re[)],(Im[ 2
1
2
1 yxEyxE , (2)
Such type vortex-free complex landscapes can’t be
transformed to a vortex complex landscape. Therefore,
our first task to be solved from the outset was finding of
a real controlled media with a vortex-free complex
landscape in a transmitting laser beam. Photorefractive
lithium niobate crystals used in all our investigations of
dynamic singular optics [5-9] would not do because
output scattered speckle field possesses many
singularities at the very beginning due to unavoidable
random refractive index heterogeneities. A managed
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 234-239.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
235
Fig. 1. Polymer morphology of the PDLC composite with 35 vol% of a polymer phase. (a) Scanning electron microscope
(SEM) image of the polymer phase; (b) diagram of the size distribution of liquid crystals (LC) domain voids. (Courtesy of [10]
co-authors).
nonlinear medium is suited, which allows to transform
nodal line up to their intersection needed for optical
vortices creation [5].
The plan of paper is as follows. The structure and
parameters of the used electrically controlled PDLC cell
are described in Sec. 2. Sec. 3 presents the elaborated
technique for amplitude and phase distribution
measurements in an output beam cross-section,
procedure of data processing. Sec. 4 considers evolution
of the complex landscape from vortex-free to multiple-
vortices complex landscape with diminishing value of
applied DC electric field. For understanding the
mechanism of a vortex-free complex landscape
transformation to a singular wave front, statistics of an
intensity distribution was measured as a function of the
applied electric field value. Obtained results and general
questions of topological transformation of a vortex-free
complex landscape to the singular complex landscape
and vice versa are discussed. The main findings are
summarized in Sec. 5.
2. Electrically controlled PDLC cells
We have focused on polymer-dispersed liquid crystal
(PDLC) cells with optical properties controlled by
applied DC electric field ([10] and literature therein).
The PDLC cell with 20 µm thickness and 40 vol% of
polymer (the nematic mixture E7 from Merk) was used.
Polymer matrix of such concentration possesses a
sponge-like structure (Fig. 1a) with 6 μm average size of
LC domains voids (Fig. 1b). Therefore, a propagating
beam interacts with 3 to 4 layers of LC voids. The
refractive index of the used polymer was intermediate
between the liquid crystal ordinary and extraordinary
refractive indices of nematic mixture E7 from Merk.
Biaxial axes of LC domains are directed randomly
without applied electric field. Therefore, an incident
light beam scatters strongly and cell transparency is
nearly zero [10]. Applied electric field with strong
enough DC voltage aligns biaxial axes of LC domains
along the direction of electrical field with small
deviations. Its value is specific for each PDLC cell and
was 200 V in our case. As a result, the cell transparency
grows strongly. Due to this property, PDLC cells are
used nowadays in various optical systems as an element
with controllable transparency [10]. We have
investigated firstly PDLC cells from the viewpoint of
singular optics as element suitable for controlled
parametric dynamics of light fields with various
complex landscapes. The idea was clear and simple. We
were waiting that controllable transition from light
scattering regime to transparent state of a cell controlled
by the value of applied DC voltage could be followed by
essential change of output beam singular properties. And
obtained results live up to our expectations.
3. Measurement technique and data processing
The experimental setup is shown in Fig. 2. The selected
plane of a measured fragment of an investigated
complex landscape was projected on a CCD camera with
10× magnification. Its 15-cm distance from the PDLC
cell what was enough for overlapping and interference of
scattered light components. The typical angle between
object and reference beams was ~0.01 rad to obtain
interferential patterns with ~80 μm fringes.
Interference of a speckle field with plane wave
rises to the intensity pattern I(x,y):
,)),(cos(
),(),(),(
yxykxk
yxbyxayxI
yx
(3)
where ),( yxa is an interference background component,
),( yxb is an interference signal envelope, ),( yx is a
speckle field phase distribution, xk and yk are spatial
frequencies caused by a relative tilt of interfering beams.
We use the modified method of Fourier-transform to
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 234-239.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
236
Fig. 2. Experimental setup. Beam splitters BS1, BS2 and mirrors M1, M2 form a Mach–Zehnder interferometer tuned to obtain
a finite fringe interferogram. Linearly polarized Gaussian beam of He–Ne laser is directed on the entrance plane of splitter BS1.
Interference patterns are recorded by the digital camera FINE T-392C with 720×576 pixels screen. A PDLC cell is placed into
an object arm of the interferometer. A telescope TL expands object beam up to 2 mm diameter. A spatial filter SF forms plane
wave in the reference beam. When the reference beam is shut off, the setup is used for acquisition of intensity distribution. The
lens system L projects appeared speckle field in a selected plane onto the screen of the CCD camera.
Fig. 2. Experimental setup. Beam splitters BS1, BS2 and mirrors M1, M2 form a Mach–Zehnder interferometer tuned to obtain
a finite fringe interferogram. Linearly polarized Gaussian beam of He–Ne laser is directed on the entrance plane of splitter BS1.
Interference patterns are recorded by the digital camera FINE T-392C with 720×576 pixels screen. A PDLC cell is placed into
an object arm of the interferometer. A telescope TL expands object beam up to 2 mm diameter. A spatial filter SF forms plane
wave in the reference beam. When the reference beam is shut off, the setup is used for acquisition of intensity distribution. The
lens system L projects appeared speckle field in a selected plane onto the screen of the CCD camera.
reconstruct phase distribution from the interference
pattern bitmap [11]. To correctly run the algorithm, we
need the interference fringe width to be a multiple of the
used CCD camera pixel size. For any field fragment with
optical vortex,
2),( yxd
C
(4)
The path of integration С is a boundary of a
square that is usually taken to be 2 pixels on a side.
The measured intensity distribution ),( yxI and the
reconstructed phase map ),( yx give full information
about the investigated speckle field ),( yxE with real
and imaginary parts
),(sin),()],([Im
),(cos),()],([Re
yxyxIyxE
yxyxIyxE
, (5)
Zero lines and discrete equiphase contours for the
measured fragment of an output beam complex
landscape allow to fix arrangement of all existing
singularities and embryos of potential singularities.
Indeed, the phase interval between neighbor nodal lines
0)],(Re[ yxE and 0)],(Im[ yxE is 2 with the
averaged phase gradient
rdr
d
2
(6)
where 212
21
2
21 ])()[( yyxxr is the minimal
distance between analyzed nodal lines. This phase
gradient tends to infinity when they approach.
Arrangement of all the existing vortices into topological
network [12, 13] can be established, if saddles and
traverse them equiphase lines starting and finishing on the
vortices are found from the measured interference map.
4. Results and discussion
According to the principle of PDLC cell functioning, the
control parameter is value of applied DC voltage which
tries to arrange biaxes along the electric field direction.
The full gamut of complex landscapes from vortex-free
at high enough DC voltage up to its absence when
complex landscape possesses multi-vortices generic
(natural) form was realized and measured. The applied
voltage range was 0 to 200 V. For each voltage, we have
measured crucial characteristics of a complex landscape:
phase map and contours of real )],(Re[ yxE and
imaginary )],(Im[ yxE zero lines. The experiment has
shown that it’s enough to trace equiphase contours with
16 interval to find all actual topological features of a
complex landscape. The characteristic complex
landscape structures and corresponding values of applied
voltages were chosen (Fig. 3): (a) the vortex-free
complex landscape (200 V), (b) the first nearly touch of
nodal lines, i.e. developed vortex ‘embryo’ as for
polarization singularities [6] (160 V), (c) nucleation of
the first vortex pair (140 V), and (d) initial generic field
at switched off electric field.
The evolution of an output beam complex
landscape is defined by growing random orientation of
biaxes directions resulting in speckle patterns structuring
with development of deeper intensity minima. Full
destructive interference is needed for complete
destructive interference in the points where vortices
appear [14]. In turn, this can happen for fully random
amplitude and phase distribution in the field local
structure of complex landscape around this point [6]. To
understand better the matter of heart of the complex
landscape topological evolution, we have measured
statistics of speckle patterns intensity distribution in
output speckle patterns at values strengths of the applied
field through 20 independent realizations for each
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 234-239.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
237
Fig. 3. Evolution of optical complex landscape induced by the PDLC cell. (a) Vortex-free landscape (200 V) (frame deposits
the embryo); (b) Vortex-free landscape before first vortex pair creation (160 V) (frame deposits the pre-threshold embryo); (c)
creation of the first vortex pair (140 V); (d) the initial complex landscape with vortices multitude (electric field is switched off).
Positive (negative) charged vortices are white circles with black rimes (black circles). Nodal lines of Re[E(x,y)]/Im[E(x,y)] are
shown bold/dashed.
measured point (Fig. 4). The light field statistic after a
gaussian diffuser is shown as the limited case measured
recently for speckle patterns generated by lithium
niobate crystal [9]. It possesses the negative exponential
distribution [15]:
I
I
I
Ip exp
1
)( , (7)
Let us consider now measured topological
evolution of the complex landscape structure and
corresponding statistics of the speckle pattern intensity
as a function of the applied electric field. At the strong
field (200 V) (Fig. 3a), biaxes of all LC domains are
oriented along the direction of electric field with small
deviation. Therefore, full destructive interference is
absent automatically and the complex landscape is
vortex free. Its intensity statistics differs cardinally from
gaussian diffuser statistics and has the form of low broad
curve with zero probability density at zero intensity (Fig.
4a, curve 1). It corresponds to intensity distribution of a
weak modulated speckle patterns. The phase map is also
smooth enough with few smooth phases extrema. It is
natural, that complete destructive interference is
impossible. Two real and imaginary zero lines are fully
separated and meander in approximately the same
averaged direction for our generic/natural complex
landscapes contrary to M. Berry apprehension [2].
Contrary to smoothness of intensity distribution,
there are the distinguished small areas where angular
distribution of LC domain biaxes is much broader then
in average. Namely, such situation is realized in right
upper quadrant where two nodal lines 0)],(Re[ yxE ,
0)],(Im[ yxE approach essentially with the highest
phase gradient between them among the shown phase
landscape. This corresponds to the phase fold with 2
as vortex embryo in full analogy with measured recently
azimuth step in random elliptic speckle patterns as the
embryo of C point pair nucleation [6]. Therefore, this
pair of neighbor nodal lines is a promising candidate for
vortex creation at lower voltages of electric field.
Descent of the applied field up to 160 V leads to
spread of biaxes orientation. Destructive interference
grows and amplitude minima deepen. Most of isolated
0)],(Re[ yxE loops append to 0)],(Re[ yxE
augment its meandering contrary to very small changes
of 0)],(Im[ yxE contours (Fig. 3b). This is natural
because the speckle pattern structure is mainly sensitive
to statistics of biaxes distribution. Real and imaginary
zero lines near the existing singularity embryo become
close and almost tangent, which strongly enhances the
embryo phase gradient tend to infinity, what corresponds
to the threshold value of the vertical π/2 height step and
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 234-239.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
238
Fig.4. Measured statistics of the speckle pattern intensity (arbitrary units) distribution governed by the voltage of electric field
applied to the PDLC cell: 1 – 200 V; 2 – 140 V; 3 – 100 V; 4 – 70 V; 5 – switched-off applied field; 6 – the intensity
distribution statistics of light field after a gaussian diffuser.
Fig. 5. Self-organization of nucleated vortex dipoles to the first quadruple (70 V). a - Complex landscape at 70 V
with the first vortex quadruple nucleated. The nodal lines of Re[E(x,y)]/Im[E(x,y)] are shown bold/dashed. The
positive (negative) charged vortices are white circles with black rimes (black circles). The first vortex quadruple is
shown in the black frame. b – Full phase map with saddles (black squares) and equiphase lines shown with π/16
interval. The bold equiphase lines connect the equal-charged vortices through the open saddle, that is shown by
white square. All other squares are shown by black squares.
wavefront tier. When the electric field is above 140 V
the embryo transforms to a vortex pair (Fig. 3c), which
indicates full destructive interference in vortex centers.
Two additional embryos appear simultaneously below
this vortex pair, what prepares nucleation of two new
vortex pairs. But creation of the vortex pair can’t change
essentially the p(I) curve. Indeed, it moves a little to the
lower intensities and its maximum grows slightly (Fig. 4,
curve 2).
The first quadruple of vortices appears at 70 V,
statistics curve prolongs to move to lower intensities, and
its maximum grows (Fig. 4, curve 4). Finally, multitude of
vortices exists without applied field (34 OVs in checked
field fragment), i.e. at not perturbed PDLC cell (Fig. 3d).
The p(I) curve shifts to low intensities, its half-width
diminishes and maximum grows essentially. Of course, it
differs from true Gaussian curve. It witnesses that LC
domains in a PDLC cell don’t possess full random
statistics. The careful reader will fix essential change of
topology of a generic not perturbed complex landscape.
Besides seen above crossing closed contours, there are
two separated meandering nodal lines 0)],(Re[ yxE ,
0)],(Im[ yxE that are stud with contours of other sorts.
The meander zero lines don’t intersect.
It was known that in singular vector fields two near
located C point dipoles as in Fig. 5a are self-organized
spontaneously in quadruples with both pairs of equal
sign C points connected pairwise by equiazimuth lines
through an open saddle [16]. It was natural to expect that
this property is valid for scalar optical fields, too. Our
first measurements have confirmed existence of such
quadruples in fields after a PDLC cell [9]. Investigations
undertaken this time allow to obtain a detailed structure
of there quadruples (Fig. 5b).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 234-239.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
239
Presented results show an essential difference of
real-time and parametric dynamics of random fields. The
real-time dynamics contains sequence of local creation
and annihilation events happen during field
development by chain and loop topological events [6].
Contrary, one-direction variation of the control
parameter in the parametric dynamics produces
separately nucleation and annihilation processes as we
have seen for PDLC cells. Nevertheless, all the observed
topological events are fully reversible when the applied
DC voltage diminishes instead of grow.
Topology laws are valid for all systems. Therefore,
the presented results have to be valid for all heterogeneous
non-stationary systems with topological defects. They
open wide possibilities for application of singular optics
technique for investigation of various physical, chemical,
etc. systems controlled by some parameter (temperature,
composition, concentration of special additive, etc.).
Optical vortex core is mathematical point/line in 2D/3D.
Therefore, singular optics opens unique possibilities for
investigation of nanosystems of various origins.
5. Conclusion
1. PDLC cells controlled by applied DC electric
field have shown manageable reversible transition from
a vortex-free complex landscape of a transmitted He-Ne
laser beam at high voltages to a multiple–vortices
complex landscape without applied field and vise versa.
To our knowledge, PDLC cells are the first class of
topologically controlled condensed media that provide
creation of optical singularities.
2. A vortex-free complex landscape initiated by a
PDLC cell at high applied DC electrical field transforms
to a singular complex landscape by complete destructive
interference in seldom areas where singularity pairs are
created. This happens due to transformation of LC
domains biaxes oriented along a strong enough applied
DC field to their fully disordered orientation in the
vicinity of nucleated optical vortices at lower voltages.
3. It was established a detailed scenario creation of
the first singularity pair through evolution of a created
high phase gradient structure as ‘embryo’ up to the
threshold value of a control parameter. The same
scenario is valid for creation of all the following
singularities at other values of the control parameter.
4. The developed technique of parametric dynamics
can be applied successfully for realization and
investigation of various types of controlled optical
elements including those with nanoadditions.
Acknowledgement
This work was supported by STCU Project 4687.
Authors are thankful to Drs. L.A. Dolgov, O.V. Yaro-
shchuk for provision of PDLC cells, introduction to their
physics and numerous fruitful discussions. Authors are
thankful to Prof. M. Berry (Bristol University) for
fruitful discussions.
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