Theoretical and Experimental Investigation of Polarization
and Spectral Properties of Light in Multilayer Cholesteric
Liquid-crystalline Systems
H. Grigoryan, H. Gharagulyan, M. Rafayelyan, A. H. Gevorgyan and R. B. Alaverdyan
Yerevan State University, 1A.Manoogian, Yerevan, Republic of Armenia
Keywords: Cholesteric Liquid Crystals, Photonic Crystals, Selective Reflection, Photonic Band Gap.
Abstract: At the present work we have studied the polarization and spectral properties of light in different cholesteric
liquid-crystalline systems, particularly in the systems prepared from mixture of right and left-handed
cholesterics and nematic liquid crystal. The following systems were also examined: a) system consisting of
right and left handed cholesterics (with the same pitch), which have selective reflection in the same range of
the visible spectrum, b) system consisting of right and left handed cholesterics, which have selective
reflection in red and green ranges of the visible spectrum and c) 4-layer system consisting of cholesterics
with different pitches. As a result of our investigations, we have verified the possibility of controlling of
polarization plane rotation of light. We propose a new device for expansion of Bragg’s reflection range.
1 INTRODUCTION
Materials with a sufficiently strong periodic
modulation of the refractive index exhibit a photonic
band gap, which means that in certain frequency
ranges light propagation is forbidden. Such optical
media are called photonic crystals (PCs).
Cholesterics liquid crystals (CLCs) are one of the
most attractive one-dimensional PCs due to their
unique optical properties. As a result of their helical
structure a circularly polarized light with the same
handedness as the CLC helix propagating along a
helical axis is selectively reflected, while the rest of
the light is transmitted, therefore a stop band appears
(De Gennes and Prost, 1993). CLCs have attracted
scientists and engineers for the past decade also
because their properties offer ways to control light
polarization. The investigation of polarization
characteristics, namely polarization plane rotation
and light polarization controlling is important from
the point of view of application in modern photonics
and optoelectronics. The essence of this
phenomenon lies in the fact that linear polarized
light passing through the cholesteric film remains
linear polarized but direction of its polarization
(electric vector) is rotated by angle in respect to
the incident light (=-2k, where k=0;1;2;3...). The
angle depends on the properties of the medium
and on the d thickness of the cell: =d, where is
the specific rotation. In cholesterics has a very big
value (Belyakov et al., 1982); (Khoo, 2007). If the
thickness of the system is increased, the rotation of
the polarization plane is decreased. The
investigations of CLCs have shown that they are
very sensitive towards external factors such as
electric, magnetic or strong light fields, UV radiation
or thermal gradient. From this point of view it is
interesting to examine the use of liquid-crystalline
mediums, if we take into account the wide
possibility to control them by an external field,
including optical (Simoni, 1997). Therefore varying
the parameters of the CLCs it becomes possible to
control its photonic band gap and other properties.
The polarization plane rotation property is widely
used in different optical devices, such as light
modulators, valves, etc. From an application point of
view, PC devices for polarization control should be
important because they do not rely on the intrinsic
properties of the constituent materials of PC. In
particular, the properties of photonic crystals are
dependent on the boundary conditions, which can be
engineered to suit a wide variety of diverse
applications. Additionally the polarization control of
light is important for optical information processing,
display and storage devices (Mochizuki et al., 2000);
(Furumi and Sakka, 2006); (O'Neill and Kelly,
111
Grigoryan H., Gharagulyan H., Rafayelyan M., Gevorgyan A. and Alaverdyan R..
Theoretical and Experimental Investigation of Polarization and Spectral Properties of Light in Multilayer Cholesteric Liquid-crystalline Systems.
DOI: 10.5220/0004339801110114
In Proceedings of the International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS-2013), pages 111-114
ISBN: 978-989-8565-44-0
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
2003); (Yeh and Gu, 1999); (Wu and Yang, 2001).
The aim of this work is to experimentally and
theoretically investigate the characteristics of the
behavior of light polarization in the liquid crystalline
medium.
2 EXPERIMENT
2.1 Sample Preparation
In order to investigate polarization plane rotation of
light we have prepared cholesteric liquid-crystalline
cell through the contact of two cholesteric liquid
crystals. For that purpose a mixture of right-handed
pelargonium, left-handed oleate and E-7 nematic
liquid crystals was prepared. These two mixtures
were one reflecting in the green range named SG,
the other reflecting in the red range, named SR. One
of the substrates was coated with Cholesteric liquid
crystal (1), which was green in colour, and other
substrate was coated with Cholesteric liquid crystal
(2), which was red in colour. Clearly between two
adjacent surfaces the diffusion process has occurred.
The inner surfaces of glass substrates were first
coated with thin polymide layer and were then
rubbed with a special material. As a result, the
orientation of CLCs director was parallel to the
surfaces, which means that the helix axis was
perpendicular to the surfaces of the cell. The mixture
was drop filled into the empty cell. The thickness of
our sample was 15m.
2.2 Experimental Set-up
In order to investigate the polarization plane rotation
of light we have assembled the experimental set-up,
depicted in Figure 1. The CLC cells were
illuminated He-Ne laser with λ=0.63m and with
λ=0.53m wavelength diode pumping
semiconductor laser radiations.
Before the investigation of the polarization plane
rotation the selective reflection bands for green and
red CLCs were observed.
In order to investigate polarization plane rotation
the primary direction was defined. The angle of
polarization plane rotation was measured every hour
in the temperature range 14-21°C, which includes
selective reflection band gaps of both green and red
CLCs. Measurements were done on the daily basis.
As a source of laser radiation both He-Ne laser and
diode pumping semiconductor laser were used. In
figure 2 dependences of polarization plane rotation
Figure 1: Scheme of experimental set-up for investigation
of polarization plane rotation of light: 1.Source of laser
radiation,2.Prism,3.Polarizer,4.Modulator,5.Microrefrigira
tor,6.CLCcell,7.Polarizer,8.Photodiode,9.Oscillograph,10.
DC source,11.Controller of temperature.
angle on temperature for different cases are
represented
. Figure 2 a) corresponds to the case,
when light from semiconductor laser first falls on a
cell substrate coated with green CLC, and figure 2 b)
corresponds to the case, when substrate of the cell,
coated with red CLC, is illuminated with light from
He-Ne laser. In Figure 2 c) and d) are shown the
following cases: c) substrate of the cell, coated with
green CLC, is illuminated with light from He-Ne
laser, d) substrate of the cell, coated with red CLC,
is illuminated with light from semiconductor laser.
As it is seen from the graphs, the polarization
plane rotation has maximum value in the cases a)
and b) and approximately equals to 35, but the
polarization plane rotates only by a few degrees in
the cases c) and d).
So the main purpose was to obtain large
polarization plane rotation with small loss.
We have also obtained the reflection spectra of
green and red CLCs for the mutual temperature
t=17C .
In order to investigate the transmission and
reflection spectra for unpolarized and linear
polarized lights (at normal incidence) we have
assembled the experimental set-up, depicted in
Figure 3. In our experiment StellarNet spectrometer
with optical resolution of 0,75 nm was used. The
reflection spectra for linear polarized light is
depicted in figure 4.
3 THEORY
3.1 Method of Analysis
The problem is solved by Ambartsumian’s layer
addition modified method. This method was earlier
developed for the solution of astrophysical problems
of multiple scattering in turbid media. It has been
PHOTOPTICS2013-InternationalConferenceonPhotonics,OpticsandLaserTechnology
112
a)
b)
c)
d)
Figure 2: Dependences of polarization plane rotation angle
on temperature for different cases: a) substrate of the cell,
coated with green CLC, is illuminated with light from
semiconductor laser, b) substrate of the cell, coated with
red CLC, is illuminated with light from He-Ne laser, c)
substrate of the cell, coated with green CLC, is illuminated
with light from He-Ne laser, d) substrate of the cell, coated
with red CLC, is illuminated with light from
semiconductor laser. The different colours correspond to
the measurements of different days.
Figure 3: Scheme of experimental set-up for investigation
of discussed system’s reflection and transmission spectra:
1.Tungsten-krypton lamp.2. CLC cell, 3.
Microrefrigerator, 4. Controller of temperature, 5.Tester,
6.Spectrometer, 7. PC.
Figure 4: Reflection spectra for linear polarized light.
developed for optical wave propagation through
inhomogeneous media. The employed method
rigorously takes into account the boundary
conditions and interface reflections of the CLC
medium. A CLC film can be treated as a bilayer
system: CLC(1)- CLC(2). Let us present the solution
of the boundary problem of light transmission
through the multi-layer system in the form:
ˆˆ
,
riti
EREETE
(1)
where the indices I, r and t denote the incident,
reflected and transmitted waves’ fields,
ˆ
R
and
T
ˆ
are the reflection and transmission matrices.
,,
,, ,, ,,
,,
,
p
irt
ps
irt irt p irt s
s
irt
E
EEnEn
E
(2)
where
p
n
and
s
n
are the unit vectors of orthogonal
linear polarizations,
p
tri
E
,,
and
s
tri
E
,,
are
corresponding amplitudes of the incident, reflected
and transmitted waves. According to
Ambartsumian’s
layer addition modified method, if
there is a
system consisting of two adjacent (from
left to right) layers, A and B, then the reflection
transmission matrices of the system, A+B , viz.
A
B
R
and
A
B
T
, are determined in terms of similar
matrices of its component layers by the matrix
equations:
TheoreticalandExperimentalInvestigationofPolarizationandSpectralPropertiesofLightinMultilayerCholesteric
Liquid-crystallineSystems
113
1
1
,
,
AB A A B A B A
AB B A B A
RRTRIRRT
TTIRRT
(3)
where the tilde denotes the corresponding reflection
and transmission matrices for the reverse direction
of light propagation, and
I
ˆ
is the unit
matrix(Wohler et al. 1991). The exact reflection and
transmission matrices for a finite CLC layer (at
normal incidence) are well known.
The ellipticity e and the azimuth
of the
transmitted light are expressed by
/
s
p
tt
EE
through the following formulas:
2
2Re
1
arctg
2
1
2
2Im
1
arcsin
2
1
etg
(4)
Due to Ambartsumian’s layer addition modified
method in our experiment the azimuth of the
transmitted light was calculated. In figure 5 the
azimuth dependence on wavelength for three
different moments of diffusion process is presented.
Figure 5: Azimuth dependence on wavelength for different
moments of diffusion process.
Let us note, that there are many methods of
solving the light propagating problem through a
system containing liquid-crystalline layer. Here it is
convenient and novel to apply Ambartsumyan's
layer addition modified method, because the exact
reflection and transmission matrices of the finite
CLC layer are known.
4 CONCLUSIONS
We have studied polarization features of light in
CLC systems consisting of right and left-handed
cholesterics and nematic liquid crystal. These
investigations provide much information on possible
new applications of photonic crystals in optics. Our
results can be used in the systems as a band optical
diode for circularly polarized incident light as well
as in sources of elliptically polarized light with
tunable ellipticity. We also showed that the
bandwidth of cholesteric reflection was broadened
.
So, the most important peculiarity of cholesteric
liquid crystals is related to control of their optical
characteristics. The investigations of the polarization
and spectral properties of light in other systems such
as: systems consisting of right and left handed
cholesterics with the same pitch and 4-layer CLC
systems with pitch gradient, are still in progress.
ACKNOWLEDGEMENTS
This work was supported by Grant 11-1c194 of State
Committee of Science of Republic of Armenia.
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Khoo, I. C, 2007. Liquid Crystals,NJ, Wiley,p. 383.
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