Electro-optical Characteristics of a Liquid Crystal Lens with Polymer Network
We study a tunable-focus lens in which the key element is a gradientpolymer-stabilized liquid crystal (G-PSLC) structure. In this paper, we further develop the theoretical model [1, 2] that describes the dependence of the G-PSLC lens’ focal length on the applied voltage and presents a theoretical st...
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| Cite this: | Electro-optical Characteristics of a Liquid Crystal Lens with Polymer Network / S.P. Bielykh, S.L. Subota, V.Y. Reshetnyak, T. Galstian // Укр. фіз. журн. — 2010. — Т. 55, № 3. — С. 293-298. — Бібліогр.: 14 назв. — англ. |
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| author | Bielykh, S.P. Subota, S.L. Reshetnyak, V.Y. Galstian, T. |
| author_facet | Bielykh, S.P. Subota, S.L. Reshetnyak, V.Y. Galstian, T. |
| citation_txt | Electro-optical Characteristics of a Liquid Crystal Lens with Polymer Network / S.P. Bielykh, S.L. Subota, V.Y. Reshetnyak, T. Galstian // Укр. фіз. журн. — 2010. — Т. 55, № 3. — С. 293-298. — Бібліогр.: 14 назв. — англ. |
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| description | We study a tunable-focus lens in which the key element is a gradientpolymer-stabilized liquid crystal (G-PSLC) structure. In this paper, we further develop the theoretical model [1, 2] that describes the dependence of the G-PSLC lens’ focal length on the applied voltage and presents a theoretical study of lens aberrations. According to Fermat’s principle, we minimize the optical path of a test light beam and calculate the angles of a ray exiting from the cell. Using these results, the lateral and longitudinal aberrations are estimated. The obtained results can be used to optimize the G-PSLC lenses.
У данiй роботi вдосконалено теоретичну модель лiнзи [1, 2], утвореної в нематичному рiдкокристалiчному кристалi в процесi фотополiмеризацiї в неоднорiдному свiтловому полi гаусового пучка. Знайдено чисельно кут переорiєнтацiї директора нематичного рiдкого кристала та фокусну вiдстань лiнзи в залежностi вiд величини напруги прикладеної до нематичної комiрки. Використовуючи принцип Ферма, мiнiмiзовано оптичний шлях свiтлового пучка, що проходить крiзь утворену лiнзу. Отримано напрямок поширення свiтла на виходi з комiрки, що дозволило оцiнити поздовжню та поперечну аберацiї рiдкокристалiчної нематичної лiнзи. Зi збiльшенням прикладеної напруги, величина аберацiй зменшується. Отриманi в статтi результати дозволяють оптимiзувати якiсть зображення, що утворює лiнза.
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| first_indexed | 2025-12-07T18:45:41Z |
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ELECTRO-OPTICAL CHARACTERISTICS
ELECTRO-OPTICAL CHARACTERISTICS OF A LIQUID
CRYSTAL LENS WITH POLYMER NETWORK
S.P. BIELYKH,1 S.L. SUBOTA,1 V.Y. RESHETNYAK,1 T. GALSTIAN2
1Taras Shevchenko National University of Kyiv, Faculty of Physics
(2, Academician Glushkov Prosp., Kyiv 03680, Ukraine; e-mail: sveta_ pavl@ ukr. net )
2Center for Optics, Photonics and Laser, Physics department, Laval University
(Pavillon d Optique-Photonique, 2375 Rue de la Terrasse, Quebec, Canada G1V 0A6)
PACS 42.70.Df, 61.30.Gd,
42.15.Dp, 42.15.Fr
c©2010
We study a tunable-focus lens in which the key element is a gradient-
polymer-stabilized liquid crystal (G-PSLC) structure. In this pa-
per, we further develop the theoretical model [1, 2] that describes
the dependence of the G-PSLC lens’ focal length on the applied
voltage and presents a theoretical study of lens aberrations. Ac-
cording to Fermat’s principle, we minimize the optical path of a
test light beam and calculate the angles of a ray exiting from the
cell. Using these results, the lateral and longitudinal aberrations
are estimated. The obtained results can be used to optimize the
G-PSLC lenses.
1. Introduction
Adaptive imaging elements are more and more required
for a broad range of applications, from astrophysics to
security. Variable optical power is one of the key ele-
ments in such applications. In recent years, there has
been much interest in lenses with variable focal length,
based on liquid crystals [1–8]. These lenses are of various
types and are made using manifold methods. For exam-
ple, among them, there are the lenses that are created
by using electrodes with holes [3] or by non-planar elec-
trodes [4]; lenses employing Fresnel zones [5]; gradient-
polymer-stabilized liquid crystal (G-PSLC) lenses [6–8],
and others. But the operation of all these lenses is based
on the electrical control over the refractive index distri-
bution in a thin layer of Nematic Liquid Crystal (NLC).
In this paper, we present a theoretical model of the
G-PSLC lens [1] and describe its spherical aberrations.
The essence of the idea to create such a lens is the fol-
lowing [6,7]. The illumination of the mixture of a planar
pre-oriented NLC containing few percent up to 3% wt)
of a photopolymerizable monomer by a laser beam with
the Gaussian spatial intensity distribution may induce
an inhomogeneous polymer network. The electro-optical
response of this system to a uniform electric field is in-
homogeneous, but centrally symmetric. The refractive
index lateral profile is defined by the spatial distribution
of the director (the average orientation of long molecular
axes of the NLC). Such a cell represents a liquid crystal
lens. A change of the applied voltage varies the profile of
the refractive index and, hence, controls the focal length
of the lens.
The paper is organized as follows. In the first section,
we describe the cell geometry of the problem, find the
director reorientation under the action of an externally
applied voltage in the cell with a non-uniform polymer
network and the focal length of the corresponding lens.
In the second section, we study the spherical longitudinal
and lateral aberrations of the lens. Finally, we draw
some conclusions.
2. Director Reorientation in the Cell with a
Polymer Network Under the Action of an
Externally Applied Voltage
Let us consider a NLC cell of the thickness L with pla-
nar and uniform boundary conditions at each wall. The
geometry of the problem is shown in Fig. 1. We as-
sume that there is a strong director anchoring at the cell
walls. The cell is illuminated by a photopolymerizing
laser beam, the intensity distribution of which is
I(ρ) = I0 exp(−αρ2), (1)
where we denote α = 1
2$2 , and $ is a half-width of the
Gaussian beam.
We can analyze this system when the polymerization
process is over in the cell. We assume there is no signifi-
cant light attenuation (due to the absorption or scatter-
ing) through the cell during the polymerization process,
and the light profile is not changed noticeably. This as-
sumption is supported by the experimental observation
of a rather good fidelity of the phase profile due to the
obtained gradient of the polymer network and of the spa-
tial distribution of the polymerizing light intensity [7].
DC electric field may be applied across the cell (along
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3 293
S.P. BIELYKH, S.L. SUBOTA, V.Y. RESHETNYAK et al.
Fig. 1. LC cell geometry
the OZ-axis) by means of transparent electrodes, e.g.,
Indium Tin Oxide (ITO). That field would reorient the
director only in the xz-plane. The obtained refractive
index profile varies, as the field is applied and induces
a lens-like behavior (thanks to the corresponding gra-
dient of the polymer network), so the focal length and
aberrations are also field-dependent.
From the symmetry reason, the director field is given
by
n = (cos θ(ρ, z), 0, sin θ(ρ, z)). (2)
In order to investigate the director reorientation in the
electrical field, we minimize the free energy
Fel =
1
2
∫
K1(5n)2 dV +
1
2
∫
K2(5× n)2 dV+
+
1
2
∫
K3(n×5× n)2 dV−
−W
2
∫
Np(ρ)(ne)2 dS − 1
2
∫
DE dV. (3)
The first three terms of this equation represent the usual
elastic deformation contribution to the LC total free en-
ergy; in the fourth term, Np is the density of the polymer
network, W is the anchoring energy between the polymer
and a liquid crystal, and e is the direction of the easy axis
at the bottom substrate. In the last term, D is the elec-
tric displacement vector, K1, K2, and K3 are the elastic
constants of the pure LC, and Np is a term whose mi-
croscopic investigation is a rather complicated task and
requires a separate study. To obtain polymer network’s
profile, we should solve the rate equations of chemical
reactions. This task is quite complicated. To simplify
this problem, we introduce a new parameter w = WNp,
representing the local effective bulk anchoring energy per
unit volume. The magnitude of the parameter w can be
directly determined from an experiment.
We the assume that NLC is the ideal dielectric. Since
the characteristic length of the director inhomogeneity in
the z-direction is determined by the cell thickness, and
it is much less than the characteristic size of the director
inhomogeneity in the x-direction, we neglect the deriva-
tive ∂
∂ρ
in comparison with the derivative ∂
∂z
. Using the
solution of the equation ∂Dz
∂z
= 0 and combining it with
the equation 5 × E = 0 with the boundary conditions
Ex = Ey = 0 at the cell walls, we obtain the voltage U
across the nematic cell as
U =
L∫
0
E dz = Dz
L∫
0
(ε⊥ + εα sin θ(z)2)−1 dz. (4)
The thermodynamic functional then takes the form
F =
K
2
∫
[(θz)2 + (θρ)2]dV−
−W
2
∫
Np(ρ)(cos θ(ρ, z))2dV−
−1
2
∫
D2
z(ε⊥ + εα sin θ(z)2)−1dV. (5)
Here, we used the one elastic constant approximation:
K1 = K2 = K3 = K.
By minimizing functional (5), we get the Euler–
Lagrange equation with boundary conditions [1]
θ′′uu −
w(ν)L2
Kb2
sin θ cos θ+
+ D2
zL
2εa
K(ε⊥)2b2
sin θ cos θ(
1 +
εa
ε⊥
sin2 θ
)2 = 0,
θ(u = 0, ν) = 0,
θ(u = b, ν) = 0.
(6)
Here, we introduced the dimensionless parameters ν =
ρ/L and u = z
Lb, b = 200 is a scale coefficient. System
(6) was solved numerically.
294 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3
ELECTRO-OPTICAL CHARACTERISTICS
a
b
Fig. 2. Inhomogeneous director reorientation angle at dimension-
less voltages V = 1.2 (a) and V = 2.5 (b)
As mentioned already, while considering this model,
we don’t consider the polymer diffusion during the poly-
merization process. So, we suggest that the UV light
intensity profile and the polymer network’s profile are of
the same form. Thus, we use a Gaussian as the initial
trial polymer concentration profile:
w̃(ν) = w0 exp(−βL2ν2). (7)
2,5 3,0 3,5 4,0 4,5
1,00
1,05
1,10
1,15
1,20
1,25
V
1/
f,m
-1
Fig. 3. Lens power dependence upon the applied voltage
In our previous theoretical work [1], we estimated a value
of w0 v 11 using experimental data and ρ0 = 90, where
ρ0 is determined from an alternative parametrization of
the polymer concentration profile
w(ν) = w0(1− ν2
ρ20
), ν ≤ ρ0,
0, ν > ρ0,
(8)
where ν = ρ
L .
In this paper, we will study how the lens character-
istics depend upon the dimensionless NLC-polymer an-
choring interaction parameters at w0 = 33 and ρ0 = 100.
We have solved system (6) numerically using the fol-
lowing parameters for the NLC mixture E7 [9] (from
Merck): the principal components of the low frequency
dielectric tensor ε‖ = 19 and ε⊥ = 5.2, the principal op-
tical refractive indices ne = 1.738 and n0 = 1.518, elastic
constant K u 10−11 N, and a cell thickness L = 10 µm.
In Fig. 2,a and Fig. 2,b, one can see the dependences of
the director reorientation angle on the coordinates of the
nematic cell at some normalized voltages V = U
U0
, where
U0 is the Frederic’s threshold voltage for the pure NLC,
and U is the voltage which is applied to the nematic cell.
Using the director reorientation angles and the Fresnel
approximation, we obtain the lens power dependence on
the applied voltage [10] (Fig. 3). Note that the obtained
focal lengths have been based on the paraxial approxi-
mation. We have assumed that all rays are paraxial, that
is, that they are very close to the optic axis and make
very small angles with it. But this condition is never
obeyed exactly. So, in the next section, we consider the
aberrations of this lens.
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3 295
S.P. BIELYKH, S.L. SUBOTA, V.Y. RESHETNYAK et al.
ö
paraxial focal plane
F”
TSA
LSA
longitudinal spherical aberration
transverse spherical aberration
Fig. 4. Illustration of the spherical aberration
3. Aberration of G-PSLC Lens
In an ideal optical system, all rays of light from a point
in the object plane should converge to the same point
in the image plane, forming a clear image. But real op-
tical systems, such as lenses, don’t form perfect images,
and there is always some degree of aberration introduced
by the lens, which causes the image to be an imperfect
replica of the object. The influences which cause differ-
ent rays to converge to different points are called aber-
ration. There are different types of aberration that can
affect the image quality. In this paper, for the G-PSLC
lens, we consider spherical ones. In Fig. 4, we show
those spherical aberration definitions.
It appears from Fig. 4 that a spherically aberrated
lens has no well-defined focus. Further, from the optical
axis, the ray enters the lens and focuses nearer to the
lens (crosses the optical axis). The distance along the
optical axis between the intercept of the rays that are
nearly on the optical axis (paraxial rays) and the rays
that go through the edge of the lens (marginal rays) is
called longitudinal spherical aberration (LSA) [11]. The
height at which these rays intercept the paraxial focal
plane is called transverse spherical aberration (TSA).
These quantities are related by TSA=LSAtanϕ [12].
Theoretically, the simplest way to obtain LSA is to
find the beam trajectory in an inhomogeneous liquid
crystal cell. So, first we calculate the optical path length
of a ray inside the layer from its entrance point A to its
exit point B.
Using the eikonal equation [13]
(gradS)2 = n2
eff ,
O
s
r
z
ñ
õt
õt
Fig. 5. Paths of two rays and the angles formed by them with the
OZ axis
where neff is the effective refractive index given by
neff =
none√
n2
e cos2 ψ + n2
o sin2 ψ
, (9)
ψ is the angle between the director and the wave vector
inside the medium, we can write
gradS = neffs,
where s is the unit vector directed along the propagation
of the beam. Then, integrating along the beam, one can
obtain the optical path length of a ray inside the layer
from its entrance point A to its exit point B given by
the integral
S =
B∫
A
neff s dr,
where dr is an elementary path section along the ray.
Using sdr = cos(φ − ψ)dz, where φ = θ + ϑ, ϑ is the
angle between OZ and s (Fig. 5), and relation (9), we
present the last integral as
S = ne
L∫
0
√
1− α sin2 φ
cosϑ
dz, (10)
where L is the cell thickness, and α = 1−(no
ne
)2. Accord-
ing to the principle of Fermat, the actual optical path
of the ray must be minimal. This means that integral
(10) should be minimized. Using the Euler–Lagrange
equation
S′ρ −
d
dz
S′ρ′ = 0,
296 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3
ELECTRO-OPTICAL CHARACTERISTICS
Fig. 6. Longitudinal aberration versus the applied voltage
Fig. 7. Lateral aberration versus the applied voltage
where S′ρ = − α sin 2φ
2g cos 2ϑ
∂θ
∂ρ , S
′
ρ′ = 1√
1+(ρ′)2
[ρ′g − α sin 2φ
2g ],
d
dzS
′
ρ′ = −θ′′ρ tan θ cos3 θ, g =
√
1− α sin2 φ, tan θ = dρ
dz ,
we can find the equation of the actual ray [14]
ρ′′=
1
cos2 ϑ
g3
1−α
{[(
g− 1−α
g3
)
tanϑ−α sin 2φ
2g
]
∂θ
∂ρ
+
+
[
g − 1− α
g3
+
α sin 2φ
2g
tanϑ
]
∂θ
∂z
}
. (11)
After these lengthy calculations, we find the angle ϑt of
the beam propagation after the liquid crystal cell, using
the Snell law for the wave vector k, and then obtain lens
aberrations.
Fig. 8. Relative longitudinal aberration versus the applied voltage
Fig. 9. Relative lateral aberration versus the applied voltage
Figures 6 and 7 show the expected LSA (longitudinal
aberrations) and TSA (lateral aberrations) dependences
on the applied voltage for ρo = 100 and w = 33.
On the next plots, we show the dependence of relative
aberrations of the G-PSLC lens on the applied voltage
(Figs. 8 and 9).
4. Conclusions
In this paper, we present a theoretical model that de-
scribes the electro-optical characteristic of an NLC lens
based on the G-PSLC concept. We calculated the di-
rector profile of the NLC in a cell for some param-
eters of the lens, particularly for the Gaussian beam
profile of a polymerizing beam. Using the geomet-
ric optics approximation, we found the optical path
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3 297
S.P. BIELYKH, S.L. SUBOTA, V.Y. RESHETNYAK et al.
of a ray inside the NLC in the cell. According to
Fermat’s principle, we minimized the functional de-
scribing the optical path of a ray and calculated an-
gles of the ray exiting from the cell. Using these re-
sults, the lateral and longitudinal aberrations were esti-
mated. While the optical power of the lens first goes
up, the focal length and aberrations of the G-PSLC
further decrease with increase in the applied voltage
(for the given case of a Gaussian profile of the net-
work). The obtained aberration and the focal length
dependence on the applied voltage allows optimizing the
lens parameter (including the polymer network’s pro-
file) to get the best image quality, for example, the
highest optical power at the lowest aberrations. The
obtained results can be applied to develop G-PSLC
lenses that have no moving parts and allow the electro-
optical zooming of high quality. The corresponding ex-
periments are under way to validate the above predic-
tions.
We acknowledge the NATO grant
CBP.NUKR.CLG.981968. We are grateful to Timothy
J. Sluckin (Southampton, UK) for fruitful discussions.
1. S.L. Subota, V.Yu. Reshetnyak, S.P. Pavliuchenko, and
T. Sluckin, Mol. Cryst. Liq. Cryst. 489, 40 (2008).
2. V.Yu. Reshetnyak, S.L. Subota, and T.V. Galstian, Mol.
Cryst. Liq. Cryst. 454, 187/[589]-200/[602] (2006).
3. F. Naumov, G.D. Love, M.Yu. Loktev, and F.L. Vla-
dimirov, Optics Express 4, 344 (1999).
4. B. Wang, M.Ye, M. Honma, T. Nose, and S. Sato, Jpn.
J. Appl. Phys. 41, L 1232 (2002).
5. Y.-H. Fan, H. Ren, and S.-T. Wu, Optics Express 11,
3080 (2003).
6. V. Presnyakov and T. Galstian, Polymer stabilized liq-
uid crystal lens for electro-optical zoom, Centre for Op-
tics, Photonics and Lasers (Universite Laval, Quebec,
Canada, 1997).
7. V. Presnyakov and T. Galstian, in Photonics North 2004:
Optical Components and Devices, edited by J.C. Ar-
mitage, S. Favard, R.A. Lessard, G.A. Lampropoulos
(2004), p. 861.
8. V.Y. Reshetnyak, S.M. Shelestiuk, S.L. Subota, S. Pavli-
uchenko, and T.J. Sluckin, Theoretical modeling of het-
erogeneous LC systems: nano-suspensions and polymer
stabilized LC lens, 103101-1-103101-6 (2007).
9. P.S. Drzaic and A. Muller, Liq. Cryst. 5, 1467 (1989).
10. J.W. Goodman, Introduction to Fourier Optics
(McGraw-Hill, New York, 2002).
11. M. Born and E.W. Wolf, Principles of Optics (Pergamon
Press, Oxford, 1991).
12. http://www.mellesgriot.com/products/optics.
13. Yu.A. Kravtsov and Yu.I. Orlov, Geometrical Optics of
Inhomogeneous Media (Springer, Berlin, 1990).
14. J.A. Kosmopoulos and H.M. Zenginoglou, Applied Optics
26, 1714 (1987). Oxford, Pergamon Press (1991).
Received 26.01.10
ЕЛЕКТРООПТИЧНI ХАРАКТЕРИСТИКИ
РIДКОКРИСТАЛIЧНОЇ ЛIНЗИ
З ПОЛIМЕРНОЮ СIТКОЮ
С.П. Бєлих, С.Л. Субота, В.Ю. Решетняк, Т. Галстян
Р е з ю м е
У данiй роботi вдосконалено теоретичну модель лiнзи [1, 2],
утвореної в нематичному рiдкокристалiчному кристалi в про-
цесi фотополiмеризацiї в неоднорiдному свiтловому полi гау-
сового пучка. Знайдено чисельно кут переорiєнтацiї директо-
ра нематичного рiдкого кристала та фокусну вiдстань лiнзи в
залежностi вiд величини напруги прикладеної до нематичної
комiрки. Використовуючи принцип Ферма, мiнiмiзовано опти-
чний шлях свiтлового пучка, що проходить крiзь утворену лiн-
зу. Отримано напрямок поширення свiтла на виходi з комiрки,
що дозволило оцiнити поздовжню та поперечну аберацiї рiд-
кокристалiчної нематичної лiнзи. Зi збiльшенням прикладеної
напруги, величина аберацiй зменшується. Отриманi в статтi
результати дозволяють оптимiзувати якiсть зображення, що
утворює лiнза.
298 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 3
|
| id | nasplib_isofts_kiev_ua-123456789-13400 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 2071-0194 |
| language | English |
| last_indexed | 2025-12-07T18:45:41Z |
| publishDate | 2010 |
| publisher | Відділення фізики і астрономії НАН України |
| record_format | dspace |
| spelling | Bielykh, S.P. Subota, S.L. Reshetnyak, V.Y. Galstian, T. 2010-11-08T14:23:16Z 2010-11-08T14:23:16Z 2010 Electro-optical Characteristics of a Liquid Crystal Lens with Polymer Network / S.P. Bielykh, S.L. Subota, V.Y. Reshetnyak, T. Galstian // Укр. фіз. журн. — 2010. — Т. 55, № 3. — С. 293-298. — Бібліогр.: 14 назв. — англ. 2071-0194 PACS 42.70.Df, 61.30.Gd, 42.15.Dp, 42.15.Fr https://nasplib.isofts.kiev.ua/handle/123456789/13400 We study a tunable-focus lens in which the key element is a gradientpolymer-stabilized liquid crystal (G-PSLC) structure. In this paper, we further develop the theoretical model [1, 2] that describes the dependence of the G-PSLC lens’ focal length on the applied voltage and presents a theoretical study of lens aberrations. According to Fermat’s principle, we minimize the optical path of a test light beam and calculate the angles of a ray exiting from the cell. Using these results, the lateral and longitudinal aberrations are estimated. The obtained results can be used to optimize the G-PSLC lenses. У данiй роботi вдосконалено теоретичну модель лiнзи [1, 2], утвореної в нематичному рiдкокристалiчному кристалi в процесi фотополiмеризацiї в неоднорiдному свiтловому полi гаусового пучка. Знайдено чисельно кут переорiєнтацiї директора нематичного рiдкого кристала та фокусну вiдстань лiнзи в залежностi вiд величини напруги прикладеної до нематичної комiрки. Використовуючи принцип Ферма, мiнiмiзовано оптичний шлях свiтлового пучка, що проходить крiзь утворену лiнзу. Отримано напрямок поширення свiтла на виходi з комiрки, що дозволило оцiнити поздовжню та поперечну аберацiї рiдкокристалiчної нематичної лiнзи. Зi збiльшенням прикладеної напруги, величина аберацiй зменшується. Отриманi в статтi результати дозволяють оптимiзувати якiсть зображення, що утворює лiнза. We acknowledge the NATO grant CBP.NUKR.CLG.981968. We are grateful to Timothy J. Sluckin (Southampton, UK) for fruitful discussions. en Відділення фізики і астрономії НАН України М'яка речовина Electro-optical Characteristics of a Liquid Crystal Lens with Polymer Network Електрооптичні характеристики рідкокристалічної лінзи з полімерною сіткою Article published earlier |
| spellingShingle | Electro-optical Characteristics of a Liquid Crystal Lens with Polymer Network Bielykh, S.P. Subota, S.L. Reshetnyak, V.Y. Galstian, T. М'яка речовина |
| title | Electro-optical Characteristics of a Liquid Crystal Lens with Polymer Network |
| title_alt | Електрооптичні характеристики рідкокристалічної лінзи з полімерною сіткою |
| title_full | Electro-optical Characteristics of a Liquid Crystal Lens with Polymer Network |
| title_fullStr | Electro-optical Characteristics of a Liquid Crystal Lens with Polymer Network |
| title_full_unstemmed | Electro-optical Characteristics of a Liquid Crystal Lens with Polymer Network |
| title_short | Electro-optical Characteristics of a Liquid Crystal Lens with Polymer Network |
| title_sort | electro-optical characteristics of a liquid crystal lens with polymer network |
| topic | М'яка речовина |
| topic_facet | М'яка речовина |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/13400 |
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