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Transcript
N° d’ordre : 2009telb
THÈSE
Présentée à
l’ÉCOLE NATIONALE SUPÉRIEURE DES TÉLÉCOMMUNICATIONS
DE BRETAGNE
en habilitation conjointe avec l’Université de Bretagne Sud
pour obtenir le grade de
DOCTEUR de TELECOM BRETAGNE
Mention « Science pour l’Ingénieur »
par
Alexey DENISOV
RECONFIGURABLE PHOTONIC CRYSTALS: EXTERNAL FIELD
STRUCTURING OF LIQUID CRYSTAL – POLYMER COMPOSITES
Soutenue le 10 avril 2009 devant la Commission d’Examen :
Composition du Jury
-
Rapporteurs
:
Alexander FISHMAN, Professeur, l’Université de Kazan, Russie
Marc WARENGHEM, Professeur, l'Université d'Artois
-
Examinateurs
:
Jean-Louis de BOUGRENET de la TOCNAYE,
Professeur, Directeur de la thèse, Telecom Bretagne
Jean-Pierre HUIGNARD, Docteur, THALES Research & Development
Pierre PELLAT-FINET, Professeur, l’Université de Bretagne Sud
2
Contents:
ACKNOWLEDGEMENTS: ................................................................................................... 4
LIST OF ABBREVIATIONS: ................................................................................................ 5
INTRODUCTION:................................................................................................................... 6
CHAPTER I: MATERIALS FOR TUNABLE PHOTONIC CRYSTALS. ....................... 9
I.1 PHOTONIC CRYSTALS: BACKGROUND AND DEFINITIONS. .................................................... 9
I.2 TUNABLE PHOTONIC CRYSTALS:...................................................................................... 16
I.2.1 Computer modelling of photonic crystals. ............................................................... 18
I.2.2 Particular case of 2D sine modulation. ................................................................... 19
I.3 LC – POLYMER COMPOSITES FOR PHOTONIC CRYSTALS: .................................................. 21
I.3.1 Cholesteric Liquid Crystal – 1-D photonic crystal: ................................................ 21
I.3.2 Photo-refractive effect: ............................................................................................ 22
I.4 LITERATURE FOR CHAPTER I. ........................................................................................... 23
CHAPTER II: INTRODUCTION TO LC AND LC COMPOSITES. THICK CLC
STRUCTURING. ................................................................................................................... 27
II.1 NEMATIC LIQUID CRYSTALS. .......................................................................................... 30
II.1.1 Static distortions in a nematic single crystal. ......................................................... 31
II.1.2 Optical anisotropy. ................................................................................................. 34
II.2 CHOLESTERIC LIQUID CRYSTALS. ................................................................................... 35
II.2.1 Intrinsic textures and defects in cholesterics. ......................................................... 36
II.3 POLYMER + LC. .............................................................................................................. 39
II.3.1 Polymer Dispersed Liquid Crystals. ....................................................................... 40
II.3.2 Polymer Stabilized Liquid Crystal .......................................................................... 41
II.3.3 Polymer stabilized CLC. ......................................................................................... 43
II.4 OPTICAL PROPERTIES OF CLC. ........................................................................................ 45
II.4.1 Bragg reflection. ..................................................................................................... 48
II.4.2 Numerical solution for 1-D CLC. ........................................................................... 49
II.5 THICK CLC STRUCTURING. ............................................................................................. 50
II.5.1 Basic requirements. ................................................................................................ 50
II.5.2 Cells preparation. ................................................................................................... 51
II.5.3 Mixture preparation. .............................................................................................. 51
II.5.4 The need for polymer stabilization. ........................................................................ 52
II.5.5 Homogeneous CLC structure. ................................................................................ 55
II.6 CONCLUSION: ................................................................................................................. 57
II.7 LITERATURE FOR CHAPTER II: ........................................................................................ 59
CHAPTER III: 2-D PHOTONIC CLC. ............................................................................... 61
III.1 2D PHOTONIC CLC SCALING. ........................................................................................ 61
III.2 COMPUTER MODELING OF 2D PHOTONIC CLC. .............................................................. 65
III.3 EXPERIMENTAL REALIZATION. ...................................................................................... 66
III.3.1 Electric Field structuring. ..................................................................................... 67
III.3.2 Measurement set-up. ............................................................................................. 69
3
III.3.3 Experimental results and qualitative description.................................................. 69
III.3.4 Summary of experimental observations. ............................................................... 74
III.4 POLYMER STRUCTURING................................................................................................ 75
III.5 CONCLUSION. ................................................................................................................ 77
III.6 LITERATURE FOR CHAPTER III: ..................................................................................... 79
CHAPTER IV: PHOTOREFRACTIVE LC-POLYMER COMPOSITES. ..................... 80
IV.1 INTRODUCTION TO PHOTOREFRACTIVE EFFECT IN LC-POLYMER COMPOSITES............... 80
IV.1.1 Organic Photorefractive materials........................................................................ 81
IV.1.2 Charge generation mechanism in LC. ................................................................... 83
IV.1.3 Space-charge field formation in LC. ..................................................................... 85
IV.2 POLYMER – LC COMPOSITES. ........................................................................................ 86
IV.2.1 Material choice. ..................................................................................................... 87
IV.2.2 Material description. ............................................................................................. 89
IV.3 EXPERIMENTAL RESULTS. .............................................................................................. 92
IV.3.1 Diffraction efficiency measurements. .................................................................... 92
IV.3.2 Photocurrent measurement. .................................................................................. 96
IV.3.3 Diffraction efficiency vs intensity and grating period. .......................................... 97
IV.4 EXPLANATIONS AND RESTRICTIONS............................................................................. 100
IV.4.1 Larger thickness. ................................................................................................. 101
IV.4.2 Suggestion for increase in photorefractive effect efficiency. ............................... 103
IV.4.3 Preliminary results on a new material. ............................................................... 104
IV.5 CONCLUSION AND SUGGESTIONS. ................................................................................ 104
IV.6 LITERATURE FOR CHAPTER IV. ................................................................................... 106
CHAPTER V: SOFT-MATTER MICRO-STRUCTURING. .......................................... 108
V.1 CLC STRUCTURING. ..................................................................................................... 110
V.2 PHOTOREFRACTIVE LC-POLYMER COMPOSITES. ........................................................... 111
V.2.1 Material improvements. ........................................................................................ 112
V.3 LITERATURE FOR CHAPTER V. ...................................................................................... 115
APPENDIX 1: CELLS PREPARATION. ......................................................................... 116
APPENDIX 2: MASK REPLICATION ON ITO. ............................................................ 121
APPENDIX 3: LC QD PHOTOREFRACTIVE LIGHT VALVE. ................................. 127
4
Acknowledgements:
I would thank my family, who supported me during the work on my thesis.
I also would like to thank my scientific advisor Jean-Louis de Bougrenet de la Tocnaye, for
inviting me to work on the thesis and encouraging me during my Ph.D. study.
I enjoyed working with a lot of people in Telecom Bretagne.
Especially I would like to thank people from whom I learned a lot:
Olivier, Jean – Louis, Bertrand, Loran, Tatiana.
There were also a lot of people whose company I appreciated a lot. I have told them about it
personally.
This thesis was financed by Region Bretagne under FSE convention №1860.
5
List of abbreviations:
1-D: One dimensional
2-D: Two dimensional
3-D: Three dimensional
TPC: Tunable photonic crystal
LC: Liquid Crystal
CLC: Cholesteric Liquid Crystal
PSLC: Polymer Stabilized Liquid Crystal
PSCLC: Polymer Stabilized Liquid Crystal
PDLC: Polymer dispersed Liquid Crystal
Holo-PDLC: Holographic Polymer Dispersed Liquid Crystal
QD: Quantum Dot
RCP : Right Circular polarization
LCP : Left Circular Polarization
UV: Ultraviolet
ITO: Indium Tin Oxide
FDM: Finite Difference Methods
FEM: Finite Element Methods
WDM: Wavelength Division Multiplexing
6
Introduction:
The main motivation of this work was to investigate new materials engineering for Tunable
Photonic Crystal (TPC) suitable for applications in optical communication networks. To
achieve this goal we investigate several aspects related to new material engineering, involving
composite liquid crystal media.
Photonic crystals – periodical structures with a period close to the wavelength of light, i.e.
200 nm – 10 µm, impact the propagation of light inside them in a way similar to how
semiconductor crystals impact the propagation of electrons. The solution of Maxwell
equations for such structures shows the presence of wavelengths forbidden for the light
propagation, which are called photonic band gaps. One dimensional photonic crystals have
been extensively studied in optics and have given rise to various applications, whereas 2-D
and 3-D crystals only recently entered into the research laboratories, after several promising
applications were identified.
Tunable Photonic Crystals (TPC), i.e. photonic crystals whose configuration could be
changed by an external field (light or electric filed) could find applications in several
domains, for example, as tunable filters for optical communication networks or spectroscopy
needs. Tunable photonic crystals can be made on the basis of different materials. In this work
we focus on Liquid Crystal (LC) – polymer composites. The choice was motivated by the
unique electro-optical properties of LC, which provides a possibility for electrically
controlling the TPC. Polymer network in LC increases the engineering capabilities for
material structuring.
In the present state of the theory and numerical simulations of condensed matter, such as LC
and LC-polymer composites, one cannot engineer a compound with predetermined properties.
Therefore, we choose an experimental approach relying on qualitative models and analogies,
and a simple physical scaling as guidelines for the experiment planning. The validity of our
scaling and analogies was subsequently confirmed by experiments. We carried out some
computer simulations, but it turned out to be exceedingly difficult due to the complexity of
material and provided little practice information.
Only the information on the Bragg
reflection in the 1-D case, obtained from a computer modeling, was used for our experiment
scaling.
7
In several aspects this work is a continuation of the research previously carried out in Optics
department of TELECOM Bretagne. Switchable 1-D and 2-D photonic crystals were
previously demonstrated in our laboratory. They were fabricated on polymer and then
extended to Holographic Polymer Dispersed Liquid Crystal (Holo-PDLC) [Details can be
found in PhD thesis of Jean-Luc Kaiser and S. Massenot]. These photonic crystals could be
switched between on and off states by the application of an electric field, but they could not
be reconfigured over a large range, as the periodic structure was obtained by the holographic
polymerization of Liquid Crystal (LC) and monomer mixture, which created a fixed grating
of polymer with LC droplets inside.
The direction of research was to a large extent motivated by technical facilities and research
experience on holography and soft matter structuring available in the optics department.
However, some research aspects that required advanced chemical engineering were beyond
our actual capabilities, requiring special equipments which are not presently available. These
directions could be explored in the future of this study.
Among various research directions we choose only two approaches.
The first one is based on using Cholesteric Liquid Crystals (CLC) as the basic host material.
This material is interesting as it is a natural 1-D photonic crystal and thus adding a modulation
just in one direction could be sufficient to produce a 2-D photonic crystal. In the frame of the
first approach we tried two different options: modulation by an electric field and modulation
by a fixed polymer grating. First option brought a partial success, we demonstrated the proof
of the concept, but the efficiency of the prototype was too low for applications. On the other
hand, we failed to realize the second option. The issue we had to face concerned compatibility
of mixtures. We had a problem with de-mixing, we could not solve with available time and
resources.
The second approach is based on using photorefractive effect for the same purpose of
obtaining a TPC. The photorefractive effect approach is still in its early stage of investigation
and we could demonstrate only a 1-D tunable photonic crystal, i.e. reconfigurable diffraction
grating. We choose a Polymer-LC-QD (Quantum dots) composite for this study, as it was one
of the technologically simplest approaches possible. Our work with these composites resulted
8
in the improvement of some characteristics of the photorefractive composites. However, in
our view additional improvements of several properties would be necessary, before the LCpolymer based photorefractive material could be used for successful application.
Outline of the dissertation:
Chapter I. This chapter provides an introduction to photonic crystals and their possible uses.
We also motivate the choice of polymer – LC composites for TPC.
Chapter II. First, we present a short introduction to LC, CLC and LC-polymer composites.
Second, we present experimental results on the thick CLC structuring. We discuss the
advantages of using the polymer stabilization of CLC and a way to obtain a homogenous CLC
structure, which is necessary for subsequent developments.
Chapter III. We present scaling of 2-D photonic CLC, describe the process of its fabrication
and show our experimental results. The results are qualitatively interpreted, the main limiting
factors are identified and the direction for research continuation is proposed. We also discuss
the difficulties of computer modeling of such device and propose a continuation.
Chapter IV. This chapter summarizes our work on photorefractive effect in LC-polymer
composites. First, we present an introduction to photorefractive effect in organic matter and
motivate our choice of the material for the investigations. Second, we present experimental
results and demonstrate some improvement in comparison to previous work on similar
materials. Finally, we propose some directions for future developments based on our
qualitative models of the photorefractive mechanism in these compounds.
Chapter V. We summarize the material structuring side and show how all the various
physical and chemical parameters interact in micro structuring the soft matter. In conclusion
we propose some directions for future investigations.
Appendixes.
There are three appendixes. Two appendixes concern the details of our
experiments. Third appendix concerns the light valve, which we obtained as a side result of
our experiments on the photorefractive effect.
9
Chapter I
Chapter I: Materials for Tunable Photonic Crystals.
In this chapter, we introduce briefly the concept of photonic crystals, after discussing the
theoretical background, we present some materials and their manufacturing. Then we extend
our analysis to the case of tunable photonic crystals and explain our choice of polymer-liquid
crystal composites to implement tunable photonic crystals in particular for optical
communication systems.
I.1 Photonic crystals: background and definitions.
Photonic crystals are periodic electromagnetic media (1-D, 2-D or 3-D lattices) with a
periodicity close to the wavelength of light at least along one dimension. They generally have
photonic band gaps, the frequencies and directions at which light cannot propagate through
the structure. This phenomenon is in many ways similar to the band gap, observed with
electrons in semiconductors devices.
The general theoretical approach to 1D, 2D or 3D photonic crystals should start with the
solution of the Maxwell equations, for a known dielectric tensor. This solution will determine
fundamentally the behavior of light in such a media.
10
For most cases such a solution cannot be analytically obtained. The straightforward approach
consists in solving the Maxwell equations numerically. Unfortunately, it is not possible in
most of the interesting cases and often it does not bring much value in terms of understanding
and technical insight. For example, to design a photonic crystal medium for applications, we
need some guiding principles, which would give us a rough prediction of the resulting
properties for a dedicated structure without making a calculation of all the possible designs.
An alternative approach is to consider various asymptotic cases for which Maxwell equations
could be solved or to exploit some symmetries and useful analogies. This approach allows us
developing some insight and a better general understanding of the structure. The most
important similarity that we will demonstrate later on is the analogy to the Schrodinger
equation for electrons and similarity between non-scattering propagation of electrons in
crystalline solids and absorption-less propagation of light in photonic crystals under certain
conditions.
Figure 1.1. A simple example of a photonic crystal in one, two and three directions. The
different colors signify different dielectric constants.
Electromagnetic wave propagation in periodic media was first studied by the Lord Rayleigh in
1887, but his study as well as most of the experimental work on periodic structures was
restricted to one dimensional structure. Multilayer structures exhibiting Bragg reflection and
11
endowed with an angle and a frequency dependent band gap present a prominent example of a
1-D photonic crystal.
Only in 1987 with the original papers by John and Yablonovitch [1, 2] who combined the
methods of electrodynamics with that of solid-state physics, the concept of many directional
band gap was introduced. This generalization opened a large theoretical and experimental
field as well as coined the name ‘photonic crystal’ for such structures.
Maxwell’s Equations in Periodic Media :
In macroscopic and isotropic material, without losses, Maxwell equations can be written as
[3]:
 
  
H (r , t )
  E r , t    0
0
t 
   
  
 E (r , t )
  (r ) E r , t   0   H r , t    0  (r )
0
t
  
H ( r , t )  0


(1.1)
where E, H are (vector) electric and magnetic fields, ε is the scalar dielectric tensor and ε0, μ0
are the vacuum permittivity and permeability respectively. Using the standard complex field
notation and remembering to take a real a part in the end to obtain the physical fields, we can
introduce:
 
 
H (r , t )  H (r )e it
 
 
E (r , t )  E (r )e it
(1.2)
Introducing (1.2) into (1.1) and after some algebra to eliminate E, one can get a ‘master
equation’ [3]:
  1       2  
      H r ,      H r ,  
  (r )
 c
(1.3)
Solving equation (1.3) is equivalent to solving (1) as we can reconstruct electric field with the
help of magnetic field and the scalar dielectric function.

If we define operator

as:
12
  1 


      (r)   ...
(1.4)
And also introduce a scalar product of two vector fields as:
F , G    d rF

3
*
  
(r )G (r )
(1.5)
where ‘*’ means the complex conjugate. In the new notations equation (1.3) takes form of an
eigenvalue problem:
2
 
   
 H r ,     c  H r ,  

(1.6)
Moreover, with respect to the definition of the scalar product (1.5), operator (1.4) is Hermitian
[3]. This property allows us to establish a link to the mathematical formalism of quantum
mechanics resulting in many useful facts.
Quantum Mechanics
Field
Eigenvalue problem
Hermitian operator
Electrodynamics
 
 
H (r , t )  H (r )e it
Et

 i
 ( r , t )   ( r )e 

H

H
  E


2 2
  V (r )
2m
2
 
   
 H r ,     c  H r ,  


  1 

      (r)   ...
Bloch theorem and origin of a band gap:
In a photonic crystal, its dielectric function will be a periodic function of space coordinates,


 
and can be written as  (r )   (r  Ri ) , where Ri are primitive lattice vectors. In this case
Bloch-Floquet theorem states that the solution to the eigenvalue problem (1.6) will be
 

 


periodic functions that can be chosen in the form H (r )  e ikr H n,k (r ) , where H n ,k (r )
satisfies a different eigenvalue problem:
13
 2
   1       n (k )  
 H 
  ik      ik  H n,k   
 n ,k
  (r )
  c 




(1.7)

in a finite primitive cell. The eigenvalues n (k ) form discrete ‘bands’, similar to the energy
bands in crystals, giving all possible direction and energies for electromagnetic waves
propagation in photonic crystals. The application of Bloch-Floquet theorem simplifies the
problem reducing the equation to the Brillouin zone only.
This simplification arises due to the symmetry of the crystal, as the solution for the eigenvalue
equation (1.6) should satisfy the symmetry group of the crystal, it is sufficient to find the
solution for the smallest part of the crystal, i.e. Brillouin zone, and the solution for the rest of
the crystal can be found by the application of the symmetry group transformations.
A complete photonic band gap corresponds to such ω, for which there is no solution of the
equation (1.7), and therefore light propagation is impossible. It can be rigorously shown that
any periodic variations of a dielectric function in one dimension leads to a band gap [3], this
result was first identified by Lord Rayleigh in 1887.
Though the concept of complete band gap, in two or three dimensions was proposed in 1987
(with the introduction of ‘photonic crystals’), the first real example of a three dimensional
photonic crystal, with a complete band gap, was identified only 3 years later due to
computational and experimental difficulties. In the work of Ho et al. [4] the system of
overlapping Si spheres with the diameters of 330nm exhibited a complete bang gap for
λ=1,55µm. The band gap for this system is shown on the figure 1.2, one can see that for all
the directions in the irreducible Brillouin zone the band gap is non-zero.
14
Figure 1.2. A complete photonic band gap for the photonic crystal made of overlapping Si
spheres. The irreducible Brillouin zone is shown [4], one can see that the bandgap in non zero
for all the possible k vectors.
After the identification of a first 3-D photonic crystal with a complete band gap, several
others structures were identified and there are now several families of photonic crystals with
complete band gaps. Still the design of photonic crystals remains a trail and error process, as
no rigorous guide lines where identified.
In summary, much theoretical work identified the analogy between ordinary crystals, such as
semiconductors or metals, and periodic structures with much bigger periods, i.e. ‘photonic
crystals’. The theoretical treatment shows that in some photonic crystals a photonic band gap
should be present, explains the propagation of light without scattering and predicts the
behavior of such structures in presence of defects. Line defects are particularly critical in
photonic crystals because they give rise to waveguiding and point defect results in the
appearance of resonant cavities [3].
15
Fabrication:
The characteristic length scale for a photonic crystal is equal to a half of the wavelength of
interest. If we take telecom wavelength of 1,55 µm, we would need to fabricate structures
with the periods of about 750 nm. There exist several methods that allow producing structures
with even smaller length scale, but most of such methods are very expensive and far from
applications.
A natural method for photonic crystal production would be well-developed silicon or GaAs
photolithography, which is commonly used in microprocessor technology with the resolution
of about 100 nm, but this approach requires a layer-by-layer fabrication, which in the end
proves to be quite expensive [5].
A more promising method in terms of application is the fabrication by holographic
lithography [6]. The basic principle is the same as in holography, when an interference pattern
between two or more coherent light waves is recorded in a photosensitive layer. For two beam
interference 1D photonic crystal can be obtained (simple gratings). For 3 beams interference
arrays with hexagonal symmetry can be produced. Using 4 beams, even 3D structures are
made possible, thought they require some sophistication in respect to experimental technique
[6].
There are several advantages of holographic lithography compared to semiconductor layer by
layer approach. These are big volumes production, long-range periodicity (with
semiconductor technique one can produce only a few layer thick structures), cost efficiency.
Among the disadvantages are smaller index modulation compared to semiconductor materials,
and restriction to the possible structure types that can be produced, for examples an array of
cylindrical holes can’t be produced with this method.
Other methods are currently developed which allow to produce photonic crystals in volume
such as colloids assembly [7], self-assembly [8, 9] and glancing angle deposition [10]. It is
likely that for the future applications, one of the cost efficient methods would be used, such as
holographic lithography or colloids assembly. Afterwards a cavity, a guide or other structure
of interest could be introduced inside the photonic crystal in order to take advantage of a
photonic band-gap [3].
16
I.2 Tunable Photonic Crystals:
For many applications it would be advantageous to be able to tune the photonic crystal
properties, through electro-optic effects by using simple means such as the applied voltage for
instance. One of possible application could be the routing of signals in a Wavelength Division
Multiplexing (WDM) optical communications network, by using wavelength tunable filters.
The first attempt on tunable photonic crystals implementation was based on the porous
inverse opal structure filled with liquid crystal, see Figure 1.3. In the theoretical work of one
of the pioneers of photonic crystal developments S. John [12], it was shown that such
composite structure allows regulating the size of photonic band gap, closing it completely if
needed.
Figure. 1.3. “Cross-sectional view through the inverse opal backbone (blue) resulting from
incomplete infiltration of silicon into the air voids of an artificial opal. After etching out the
template, a face-centered-cubic lattice of overlapping air spheres remains and additional air
voids appear as triangular or diamond shaped holes on the surface of the cut. A tunable
photonic bang gap is obtained by infiltrating this backbone with nematic liquid crystal
(yellow) which wets the inner surface of each sphere (only one is shown in the figure).” [12].
That theoretical work was soon followed by experimental demonstration of temperature
tuning of photonic band gap in photonic crystals structures infiltrated by liquid crystals [13,
14]. However, it proved only a partial success, as it was hard to control the degree to which
17
porous structure could be filled by liquid crystal, moreover electric field controlled tuning
would be more suitable for applications. Other means used for tuning PC were proposed later
such as mechanical tuning [15], which suffers from the same drawback as the mechanical
tuning is costly solution in practical application and quite slow.
Investigations on the possibility of tuning a passive photonic crystal by infiltrating it with an
active medium is a subject of ongoing experimental and theoretical research [16]. Another but
similar in spirit approach to the problem of tunable photonic crystal was pioneered by the
group of G. Crawford. They proposed to use Holographic Polymer Dispersed Liquid Crystal
material Holo-PDLC to form photonic crystals. When using such materials the photonic
crystal structure is created by photo-polymerization (UV curing) of liquid crystal-monomer
mixture [17], see figure 1.4. The polymerization of the mixture is then photo controlled and
allows to form various types of photonic crystals [18], using different interference geometries
(4 beams with different polarizations and amplitude).
Figure 1.4. Holo-PDLC preparation process. A homogeneous mixture of monomer and liquid
crystal is polymerized by application of an interference light pattern to obtain a polymer
network with liquid crystal droplets imbedded in it.
This approach is in essence the same as holographic lithography [6], but due to the presence
of the liquid crystal it is suitable for tunable liquid crystal fabrication.
18
Holo-PDLC approach to tunable photonic crystal fabrication has several advantages, such as
big volume production, low cost, different lattices that are possible with complex interference
patterns. The degree of tuning is controlled by electric field which makes practical
applications possible, in contrast to mechanical or temperature tuning. The main disadvantage
is the low index modulation, as the liquid crystal experiences a strong anchoring in the
droplets.
In a recent work (2006) G. Crawford’s group demonstrated the principle possibility to realize
photonic crystals in another liquid crystal based material. Doping liquid crystal with azo-dyes
they obtained surface-induced 2-D holographic polarization gratings [19] which has a higher
degree of reconfigurability in comparison to the Holographic polymer dispersed liquid
crystals, but demonstrate a much lower overall efficiency.
As we have seen most of the tunable photonic crystals are realized on the base of liquid
crystal composite materials. The main advantage of liquid crystals is their large electro-optical
effect under low applied voltages which in proper conditions allow controlling photonic
crystal properties and theoretically will enable large tuning range capabilities.
I.2.1 Computer modelling of photonic crystals.
With the lower cost of computer calculation the field of digital computing has exploded with
thousands of papers published every year. In application to photonic crystals there are many
numerical methods are currently used, the most prominent being Finite Difference Methods
and Finite Element Methods [20].
Though both of these methods bring in the end an approximate solution for Maxwell
equations, finite difference method [21] provides an approximation for the partial differential
equations, whereas the finite element method looks for the approximation of the final
solution. The most attractive feature of FEM [22] is that it can handle complex geometries, at
the same time it shows better stability and better approximation to the final solution than
FDM. On the other hand FDM is easier to implement [22].
19
There are several commercial as well as free-source programs using FDM or FEM, though to
our knowledge they are not suitable for the materials with anisotropic dielectric tensor.
I.2.2 Particular case of 2D sine modulation.
A case of 2D sinusoidal modulation was considered in the Ph.D. thesis [23] done at our
department and the resulted work was published in collaboration with another team [24].
Index modulation obtained in that work could be written as:
 2x 
 2y 
  nY cos

nx, y   n0  n X cos
 X 
 Y 
(1.8)
where the average refractive grating n0 is modulated in two directions in a sinusoidal way
with periods  X and  Y , figure 1.5 provides a qualitative graphical presentation of (1.8).
Figure 1.5. A 2-D photonic crystal with sinusoidal index variation in two dimensions. The
figure gives an idea of what a 2D periodic index modulation looks like.
The behaviour of such a structure was studied by means of computer modelling and it was
found that when the incident wavelength is chosen near the band edge of the reflection grating
formed by modulation in Y direction, the grating shows both Bragg operation and diffraction
efficiency enhancement [24]. The increase at the wavelength selectivity observed at the same
time looks promising for use in WDM network filtering.
20
The result of computer modelling [23] for the following parameters: incidence angle θ=3.45°
(in the material),  X = 4,1 µm,  Y  244 nm, n=1,52, n X  0.045 , nY  0.00015 ,
L=20µm is shown on figure 1.6. The spectral selectivity and diffraction efficiency
enhancement for the structure presented on figure 1.5 is clearly enhanced compared to a 1-D
transmission grating, which is shown on in green colour.
Figure 1.6. Computer modelling results. Transmission grating diffraction efficiency, green
line. 2-D sinusoidal grating diffraction efficiency, red line.
The incidence angle, when the diffraction enhancement was observed corresponded to the
Bragg angle for the transmission grating: sin  B 
R
2n X
, and the band edge of the
reflection grating (modulation in Y direction) was found at λ0=755nm.
In essence the amplification was observed when the maximum in transmission for the
reflection grating, located at the band edge coincided with the Bragg angle for the thin
transmission grating [24]. The results of the computer modeling where experimentally
confirmed when a 2-D sinusoidal grating was recorded in a photosensitive polymer.
21
I.3 LC – Polymer composites for photonic crystals:
In the current work, our purpose is to develop tunable photonic crystals suitable for
telecommunication applications; a natural choice of materials for this purpose, as one can see
from above is a liquid crystal based material. We decide to investigate here new technical
options and material choices. The first option that we investigated was Cholesteric Liquid
Crystal (CLC). This material presents a natural choice for us as it has intrinsic periodic 1-D
structure under given conditions, and exhibits a partial 1-D band gap. Then we tried to
combine this property with the creation of a second perpendicular grating induced by
transverse electric field or by fixed polymer network. The second option was to generate
internal space charge field in the material using liquid crystal – polymer composite doped by
fullerene, which exhibited photorefractive effect. Using this effect we demonstrated
reconfigurable Bragg gratings, i.e. 1-D tunable photonic crystal, made a proof of concept for
more complex structures recording and demonstrated a large capability for material
engineering.
I.3.1 Cholesteric Liquid Crystal – 1-D photonic crystal:
We will provide more detailed presentation of liquid crystals and in particular CLC in the next
section. At the moment we will present CLC structure from the view point of photonic crystal
approach.
In case of a planar Grandjean orientation of CLC, when taking into account only x and y
components of dielectric tensor, it can be written as [20]:
 ( z) 
 //     1 0   //     cos2qz 
2

 
0 1
2
sin 2qz  


 sin 2qz   cos2qz 
(1.8)
where q  2 p , p – being the pitch or period of the structure.
From (1.8), we see a clear periodicity of dielectric tensor (8) in a z-axis direction; therefore
following the general ideas about photonic crystals we can expect a 1-D gap. The solution of
22
Maxwell equations for dielectric tensor (8) indeed shows a presence of a gap [25], but only
for one polarization either left or right circular depending on the sign of ( //    ). . This fact
also can be understood, as in our presentation of photonic crystals we deal with a scalar
dielectric function and not an anisotropic tensor.
Next step in making a non-trivial photonic crystal would be to add a modulation in another
direction, making this way a 2-D photonic crystal. Some degree of tunability can be expected
due to the electro-optical response of Liquid Crystal. So combining an additional modulation
of dielectric tensor we can expect to demonstrate 2-D tunable photonic crystal.
The difficulty in this case was the lack for physical model. The feasibility of such an approach
was still an open question before our work, as in our case we work with a material that has
dielectric anisotropy, which escapes a general treatment for photonic crystals presented in
theoretical work such as [3].
We considered two means of adding a modulation of the dielectric tensor in a second
direction, first by a periodic electric field applied to CLC and second by adding a periodic
polymer structure. In the first case, we were able to make a proof of concept and make a
principle demonstration of polarization dependent 2-D photonic crystal effect. The second
approach proved to be too difficult for us due to a lack of large chemistry engineering
capacities.
In the mean advances have been achieved in this domain. In a recent publication [26] a
method for holographic structuring of CLC by UV laser was proposed. This approach can be
applied, in principle to our problem too, in order to realize a 2nd option of structuring CLC by
a polymer network.
I.3.2 Photo-refractive effect:
Photorefractive effect is normally observed as the altering of the refractive index of a media in
response to the light intensity. The materials which exhibit photorefractive effect are natural
candidates for tunable photonic crystals as by changing external light field one can change the
corresponding refractive index modulation in the media. For example, if the light field in the
material is created by interference of two beams resulting in an interference pattern in the
23
media, by changing the angle between the beams one can change the period of interference
pattern, which would correspond to a tunable 1-D photonic crystal.
Once again, liquid crystals seem to be natural candidates for the base material for
photorefractive effect due to their large electro-optic effect. And since the discovery of
photorefractive effect in LC [27, 28] there is an ongoing research in this domain. With our
research we focused first on the reproduction and verification of the fundamental results
published by other authors and after that on the possibility of improvements.
The basic material that we considered for our research was chosen further to the work of other
authors due partly to the ease of preparation that we could reproduce with our facilities and
rather large efficiency demonstrated in their samples [29]. The basic material is the LCpolymer mixture doped with fullerene, which serves as a charge generator.
The concentration of fullerene reported in literature was about 0.05%, which is due to the low
solubility of fullerene in organics. Whereas, the first step was the reproduction of the results
obtained by other authors, as an improvement we decided to increase the concentration of
photo-synthesizer (C60) using instead of a fullerene, its derivatives which have better
solubility in organic solvents, other than LC to improve the grating efficiency. We were able
to increase the concentration of fullerene derivatives in LC by a factor 10, which resulted in
improvement in the effects, such as response time and diffraction efficiency. We will come
back to the photorefractive effect in LC and in LC-polymer composites in the Chapter IV
where we will describe the state of the art in this domain.
Using that material we demonstrated reconfigurable diffraction grating, which period could be
changed by changed the period of modulation. This way we come back to the topic of tunable
photonic crystals, as diffraction gratings can be looked at as 1D photonic crystals. A second
step that could be realized as a continuation of this study is the development of 2-D photonic
crystals on the base of the same photorefractive material.
I.4 Literature for Chapter I.
24
[1] E. Yablonovitch "Inhibited Spontaneous Emission in Solid-State Physics and Electronics",
Phys. Rev. Lett., Vol. 58, 2059 (1987)
[2] S. John, "Strong Localization of Photons in Certain Disordered Dielectric Superlattices",
Phys. Rev. Lett. 58, 2486 (1987)
[3] John D Joannopoulos, Johnson SG, Winn JN & Meade RD (2008). “Photonic crystals:
Molding the Flow of Light”, 2nd Edition, Princeton NJ: Princeton University Press.
[4] K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic
dielectric structures” Phys. Rev. Lett. 65, 3152 (1990).
[5] Minghao Qi, Elefterios Lidorikis, Peter T. Rakich, Steven G. Johnson, J. D. Joannopoulos,
Erich P. Ippen & Henry I. Smith, “Title”Nature 429, 538-542 (3 June 2004)
[6] Campbell, M., Sharp, D. N., Harrison, M. T., Denning, R. G. & Turberfield, A. J.
”Fabrication of photonic crystals for the visible spectrum by holographic lithography”.
Nature 404, 53–56 (2000); D. N. Sharp et al., “Photonic crystals for the visible spectrum
by holographic lithography", Opt. Quant. Elec. 34, 3 (2002)
[7] N. D. Denkov, O. D. Velev, P. A. Kralchevsky, I. B. Ivanov, H. Yoshimura and K.
Nagayama, "Dynamics of Two-Dimensional Crystallization", Nature 361, 26 (1993)
[8] Vlasov, Y. A., Bo, X. Z., Sturm, J. C. & Norris, D. J. “On-chip natural assembly of silicon
photonic bandgap crystals”. Nature 414, 289–293 (2001).
[9] Blanco, A. et al. “Large-scale synthesis of a silicon photonic crystal with a complete threedimensional bandgap near 1.5 µm”. Nature 405, 437–440 (2000).
[10] Kennedy, S. R., Brett, M. J., Toader, O. & John, S. “Fabrication of tetragonal square
spiral photonic crystals”. Nano Lett. 2, 59–62 (2002)
[11] S. F. Mingaleev, M. Schillinger, D. Hermann and K. Busch, “Tunable photonic crystal
circuits: concepts and designs based on single-pore infiltration”, 2858 Optics Letters, 29,
(2004);
[12] Kurt Busch and Sajeev John, "Liquid Crystal Photonic Band Gap Materials: The Tunable
Electromagnetic Vacuum", , Physical Review Letters 83 (5), 967-970 (1999)
[13] Yoshino, Y. Shinoda, Y. Kawagishi, K. Nakayama, and M. Ozaki,” Temperature tuning
of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as
tunable photonic crystal” Appl. Phys. Lett. 75, 932 (1999).
[14] W. Leonard, J. P. Mondia, H. M. van Driel, O. Toader, S. John, K. Busch, A. Birmer, U.
Gosele, and V. Lehmann, “Tunable two-dimensional photonic crystals using liquid crystal
infiltration”, Phys. Rev. B 61, R2389 (2000).
25
[15] W. Park and J.-B. Lee, “Mechanically tunable photonic crystal structure”, Applied
Physics Letters, 4845, 85 (2004)
[16] W. Park and C. J. Summers, “Optical properties of superlattice photonic crystal
waveguides”, Appl. Phys. Lett. 84, 2013 (2004).
[17] G.P. Crawford and S. Zumer: “Liquid Crystals in Complex Geometries.” Taylor &
Frances, (1996)
[18] M. J. Escuti, J. Qi, and G. P. Crawford, “Tunable face-centered-cubic photonic crystal
formed in holographic polymer dispersed liquid crystals”, Optics Letters, 522, 28, (2003)
[19] S. Gorkhali, S. Cloutier and G. Crawford, “Two-dimensional vectorial photonic crystals
formed in azo-dye-doped liquid crystals”, 3336, 31, (2006)
[20] Kiyotoshi Yasumoto, “Electromagnetic Theory and Applications for Photonic Crystals
(Optical Science and Engineering)” , 2006, CRC Press, Taylor and Francis
[21] A. Taflove, “Computational electrodynamics: The finite difference time domain method”
, 2nd edition, Artech House, 2000. A short introduction can be found on-line, for example
at: http://en.wikipedia.org/wiki/Finite-difference_time-domain_method
[22] J. Jin, “The Finite Element Method in electromagnetics”, 2nd edition, Piscat-away, NJ:
Wiley-IEEE Press, 2002. A short introduction can be found on-line, for example at:
http://en.wikipedia.org/wiki/Finite_element_method
[23] S. Massenot, “Study, modelling and realization of diffractive components: Contribution
to the study of tunable materials and applications to holographic recordings of resonant
optical filters.” PhD, UBS ENST Bretagne, January 31, 2006. (in French)
[24] Q. He, I. Zaquine, A Maruani, S. Massenot, R. Chevallier and R. Frey, “Band-edgeinduced Bragg diffraction in 2D photonic crystals”, Optics Letters 31, 1184-1186 (2006).
[25] P.G. de Gennes and J. Prost : “The physics of Liquid Crystalls.” Clarendon Press,
Oxford, 1993.
[26] Beckel, Eric; Natarajan, Lalgudi; Tondiglia, Vincent; Sutherland, Richard; Bunning,
Timothy, “Electro-optical properties of holographically patterned polymer-stabilized
cholesteric liquid crystals“, Liquid Crystals, Volume 34, Number 10, October 2007 , pp.
1151
[27] E. V. Rudenko and A. V. Sukhov, “Photoinduced electroconductivity and
photorefraction in nematic”, JETP Lett. 59 142-146, (1994)
[28] I. C. Khoo, H. Li, and Y. Liang, "Observation of orientational photorefractive effects in
nematic liquid crystals," Opt. Lett. 19, 1723-1725 (1994)
26
[29] H. Ono and N. Kawatsuki, "Orientational photorefractive effects observed in polymerdispersed liquid crystals," Opt. Lett. 22, 1144-1146 (1997)
27
Chapter II
Chapter II: Introduction to LC and LC composites.
Thick CLC structuring.
This chapter provides a theoretical introduction to the properties of liquid crystals, polymer –
LC composites with a particular attention paid to experimental approach to structuring thick
samples cholesteric liquid crystal. Most of the well established material can be found in
review books such as [1,2], for more recent developments we provide necessary references.
Types of Liquid Crystals.
Liquid crystals are mesophases (intermediate between solid and liquid ones). In these
intermediate phases, they exhibit macroscopic behaviour similar to a liquid, as they flow
easily, and at the same time the show a certain degree of anisotropy typical to crystalline
solids. The nature of such behavior lies in the molecular structure of liquid crystals. Liquid
crystal molecules have a high degree of anisotropy. In most cases liquid crystal molecules
look like elongated rods, with a length that is much bigger that width, while a disc shaped or
even banana shaped liquid crystal molecules are known.
Let us take an example of a rod like molecule such as 5CB 4'-n-pentyl-4- cyanobiphenyl,
shown on figure 2.1.
28
Figure 2.1. Chemical formula of a typical LC molecule 5CB 4'-n-pentyl-4- cyanobiphenyl.
We know that it is a rod-like molecule from theoretical considerations as connected phenyl
groups give it rigidity, though a short C5H11 chain allows for some flexibility. Imagine now a
5CB chemical compound, the relative position of molecules in the compound will be strongly
influenced by their geometrical shape. It is clear that in a rough rod model the molecules will
have preferred orientations in one direction minimizing the steric energy, i.e. the repulsion
due to the defined geometric boundaries. On the other hand we can imagine that the
molecules can have, at the same time, some degree of mobility with respect to each other, as
the molecules of a typical liquid, see for example a typical liquid crystal – nematic, which is
shown on figure 2.2.
Figure 2.2. The orientational order of nematic phase.
If we heat a nematic liquid crystal, it results in another phase transition, into isotropic or
liquid phase. In that phase molecules loose the preferred orientation and the matter behaves as
a conventional liquid. Molecules orientation is expected to show no orientational preference
like on a figure 2.3.
29
Figure 2.3. Isotropic, or liquid phase of a liquid crystal.
Nematic phase is the simplest and less organized liquid crystal phase. Some liquid crystals
like 5CB with which we started the discussion have only one intermediate mesophase,
typically it is a nematic mesophase, whereas other liquid crystals can show a more complex
behavior according to temperature changes with 2-3 or sometimes >5 mesophases like for
recently discovered banana shaped molecules.
From theoretical point of view a liquid has short range order, but lacks long range order
meaning that density-density correlation function has a characteristic length scale of an order
of several inter-molecular distances after which all the correlations are lost. A crystalline solid
on the other hand has a long range order, meaning that the density-density correlation function
is a periodic function of the distance between the molecules. Liquid crystals are found in
between these cases, there is a liquid like order at least in one direction of space and a some
degree of anisotropy is present like in solids. In case of a nematic liquid crystal the densitydensity correlation function is anisotropic, but the position of the molecules is non correlated
after a certain length scale. There are also cases where the position of molecules have higher
correlation than in case of nematics. It is the case for instance with smectics where there is 1D positional order. Smectics structure looks like the layers of liquid stacked on each other
with a well defined spacing (see figure 2.4). In a vertical direction the arrangement on figure
2.4 looks like a 1-D crystal, while in the horizontal direction it is a 2-D liquid.
30
Figure 2.4. Smectic phase: “a set of two dimensional liquid layers, stacked on each other with
a well defined spacing”.
There is also a case where liquid crystal looks like 2-D crystal with 1D liquid direction, such
phase is displayed by discotic molecules, shown on figure 2.5.
Figure 2.5: Columnar discotic phase, and an example of discotic liquid crystal molecule.
II.1 Nematic Liquid Crystals.
As we have seen the origin of specific macroscopic properties of liquid crystals lies in the
anisotropy of its molecules. A simple road model provides a simple intuitive picture but it
does not explain many essential liquid crystal properties. For a better understanding, the
molecular composition of a liquid crystal should be taken into account.
On the other hand, for many practical purposes a simpler approach can be used. On a certain
length scale liquid crystals can be described in a frame of a continuum theory. In essence it is
a mean field theory where the liquid crystal is characterised by its order parameter. This
31
approach imposes several constraints on the length scale, temperature, applied fields. The
constraints are similar to all mean field theories; the system should be far from phase
transition temperature, the characteristic distances over which the order parameter changes
should be much bigger than molecular length scale, etc.
II.1.1 Static distortions in a nematic single crystal.
The average direction of nematic molecules is denoted as a vector n(r). This average is taken
over a macroscopic volume and in the frame of the model can vary at distances, which are
much largeer than the molecular dimension. The unit vector n(r) is called the liquid crystal
director.
The orientation of an individual molecule would be different from n(r), see figure 2.5, and
the orientation distribution can be characterized by a certain distribution function f(θ). The
more this function is peaked around the angles θ=0 and θ=π the more the liquid crystal
molecules are ordered in the direction of n, in an isotropic state, all the molecule orientations
have equal probability and we cannot even define the director.
Figure 2.5. Local director of the nematic liquid crystal.
In the framework of a mean field theory the tensor order parameter has the form :
1


Q  QT  n n     
3


(2.1)
32
Where n is the projection of the director on the α axis of the coordinate frame and QT 
reflects the temperature dependence of the order parameter. The free energy can be expanded
in powers of the order parameter as (proposed by Landau)
F  F0 
 
1
AT Q Q  O Q 3
2
(2.2)
where coefficients of the expansion depend on the temperature. The Landau relation shows
that the nematic-isotropic is the first order phase transition and makes some predictions about
measurable quantities behaviour near the phase transition temperature.
If one is interested in the static behaviour of nematics in presence of external field one can
construct a mean field theory which takes into account small distortions of the director field
by expanding the free energy around its equilibrium state in a similar way to (2.2), but in
terms of the director gradients. The important assumptions is the smallness of these additional
terms, which is possible only when the variations of director are small on the molecular scale

a n  1 . Such an expansion in presence of electric field for a small volume ΔV at a certain
point takes the form:
F  F0  FEL  FE
(2.3)
where F0 is the free energy in the absence of distortions and electric field, FEl is the elastic
term of liquid crystal and FE is the coupling energy to the electric field.
Elastic free energy depends on the gradient of the director and can be written as
2
2


1  
1 
1 


FEl  K1  div n   K 2  n curl n   K 3  n curl n 
2 
2 
2 



2
(2.4)
Where K1 is the splay constant, K2 is the twist constant and K3 is the bend constant. All the
constants are positive, so that all the distortions increase the energy of the system.
33
The coupling to electric field is due to anisotropy of the liquid crystal, i.e. the static dielectric
constants measured along (  ) or normal (   ) to nematic axis are different. This anisotropy
of a small volume of nematic can in turn be traced back to the anisotropy of liquid crystal
molecules which have different energy with respect to their orientation in the external electric
field. The resulting contribution to the free energy is:
FE  
 0 
2
E2 
 0     
n E
2 

2
(2.5)
where       can be positive or negative depending on the chemical composition of
the molecules. If is positive   0 the nematic will tend to align parallel to electric field,
wheras for negative   0 the molecules will align perpendicular to electric field. In our
work, all the liquid crystal compounds have positive dielectric anisotropy, i.e. positive 
and align in the direction of electric field.
Surface effects and anchoring.
The free energy of the whole system can be written as an integral over the whole volume of
the sample of the expression (2.3):
V
F   F   FV
(2.6)
Then the equilibrium state of a liquid crystal in the framework of mean field theory can be
determined by minimizing the free energy F, with respect to the director field. In order to
fulfil this goal we need to define boundary conditions on the surfaces. Theoretically it

amounts to defining the director field n on the boundaries, as shown on the figure 2.6. where
homeotropic (perpendicular to the surface) and planar (parallel to the surface) alignment is
shown.
Figure 2.6. Homeotropic alignment (left) and planar alignment (right) of nematic LC.
34
In practice, the surface alignment can be achieved by several means. The most common
method is to use a suitable surface treatment such as a deposition of a polyimide film or more
recently photo-alignment technique [3]. In order to achieve a planar alignment it is necessary
to rub the polyimide film with a velvet or paper after the film deposition, while for
homeotropic alignment no additional treatment is needed.
Whereas for the homeotropic alignment the origin can be understood based on the preferential
orientation of the molecules on the surfaces like in a case of hydrophobic or hydrophilic
molecules, the microscopic origin of planar alignment is less clear. One could explain the
alignment as the result of steric forces on the surface, as one can expect that after rubbing
polymer chains would be oriented in the rubbing direction creating an “easy” axis for liquid
crystal orientation, but it was recently found that some polyimide films align liquid crystals
perpendicular to the rubbing direction.
This discrepancy was explained by careful investigations and a model was proposed [4]. The
idea behind the model is quite simple; it focuses on the fact that by rubbing the anisotropy in
the orientation of polymer chains is created. Depending on the chemical composition of the
chains it can be energetically favourable for the liquid crystal molecules to orient
perpendicularly to the chain direction, on the other hand when the chemistry plays less
important role the steric effect will play a more important role orienting liquid crystal in the
rubbing direction.
II.1.2 Optical anisotropy.
Liquid crystal anisotropy shows itself in their optical properties. Nematic single crystal is a
linear birefrigent uniaxial material. The ordinary mode has a polarisation which is
perpendicular to the nematic axis, while extraordinary one is polarised in the plane formed by
the wave vector k and director n. This effect once again can be linked to the molecular
structure of a nematic liquid crystals, the cylindrical symmetry of nematics explains their
uniaxial behaviour and the anisotropy of molecules explains their different polarizational
properties when an oscillating electric field in a form of a plane wave


E  E0 exp i k r  t 


is applied to them.
(2.7)
35
Similarly to ordinary birefrigent crystals, optical properties of nematic liquid crystals can be
described by a permittivity tensor:
 nO2

  0
 0


0
nO2
0
0

0
n E2 
(2.8)
which has a diagonal form in the coordinate frame where z-axis coincides with the director of
the nematic n, nO and n E are the ordinary and extraordinary refraction indices of nematic.
The typical order of magnitude for refraction indices for visible light are nO  1.5 ,
n  n E  nO  0.1 .
II.2 Cholesteric Liquid Crystals.
If one adds into a nematic liquid crystal a chiral molecule, i.e. a molecule which cannot be
superimposed on its mirror image one would find that the structure of nematics undergoes a
helical distortion. The resulting structure can be described as a stack of thin nematics slabs
rotated by a small degree while passing from one slab to another, figure 2.7.
Figure 2.7. The molecules arrangement in the cholesteric mesophase.
The director in cholesterics varies according to the following expression:
n X
n
 Y

nZ
θ




cos θ
sin θ
0
q0 Z  const
(2.9)
36
where wave-vector q relates to the period of the structure as P 
2
, P is also called the
q0
pitch.
Pitch of cholesteric liquid crystals is inversely proportional to the chiral dopant concentration
c: Pc  const and depends on the temperature of surrounding media.
As discussed in the literature, the behaviour of cholesterics with large pitch >400 nm is
similar to that of nematics, and the continuum theory previously described is applied if one
changes the equilibrium local distribution to take into account a natural twist. In this case the
equation (2.4), is modified as:
2
2


1  
1 
1 


FEl  K1  div n   K 2  n curl n  q0   K 3  n curl n 
2 
2 
2 



2
(2.10)
If we consider the pure twist situation, when n X  cos z , nY  cos z , nZ  0 , the equation
(2.10) reduces to the
FEl 
1  q

K 2   q0 
2  z

2
(2.11)
corresponding to the equilibrium distortion of a form (2.9).
The electric and magnetic field effect is taken into account the same way as in nematics by
adding the term in equation (2.5) to the modified elastic energy (2.10).
II.2.1 Intrinsic textures and defects in cholesterics.
Similarly to ordinary crystals, liquid crystals can have defects in their structures. Generally,
the more complex is the liquid crystal structure the more different kinds of defects is possible.
In the next section we will speak about experimental protocol for obtaining a cholesteric
mono-crystal, but before that we would like to present a short description of the defects and
non-planar possible configurations in cholesterics. Though the study of defects topology in
37
cholesterics is a separated research field (see a review in [5] or recent papers [6, 7]),
according to our work objective, all the deviations from planar structure are unwanted.
Focal conics.
Let us consider a cholesteric liquid crystal between two parallel glass plates, with a planar
alignment on each of them, then the equilibrium configuration with lowest energy would be a
planar one, such as depicted on figure 2.8.
Figure 2.8. Cholesteric liquid crystal in planar configuration.
If we apply electric field between these glass plates (figure 2.9), we will find that the structure
has changed, and instead of a one helix we observe many domains in each of them CLC is
still organized in a helical fashion but the helixes in neighbouring domains are turned relative
to each other. This texture is called the focal conic texture.
Figure 2.9. Focal conic structure formed under a low applied electric field.
Taking into account expression (2.10) for elastic energy and (2.5) for the electric field
contribution one can see the cause for such a transformation. In absence of electric field the
orientation of helix is defined by the surface energy, which favours the orientation of liquid
crystal molecules parallel to the glass plates, in the bulk CLC (when the cell is thick enough >
15µm) organizes itself so that it can minimize the elastic energy (2.10), i.e. into a well defined
38
helix. If an electric field is applied, there is competition between elastics and surface energy
which favours orientation of liquid crystal molecules parallel to the glass plates and the
electric field energy which is minimized when the molecules are turned perpendicular to the
glass plates (positive anisotropy). As a compromise a focal conic texture is formed. Due to
random distribution of domains in focal conic structure, it scatters incoming light.
If one applies even higher electric field to the structure, and the energy of surface anchoring
and elastic energy become negligible compared to electric field energy and cholesteric liquid
crystal aligns homeotropically, figure 2.10.
Figure 2.10. Homeotropic alignment of cholesteric liquid crystal under a sufficiently strong
electric field.
Disclination lines.
If after application of a strong or moderate electric field one switches it off, the CLC structure
in some cases does not relax into a planar configuration shown on figure 2.9. A common case
that is observed in experiment is a structure shown on figure 2.11.
Figure 2.11. Planar oriented domains of cholesteric liquid crystal separated by the defect
lines. Photo taken between crossed polarizers.
39
Uniformly colored domains correspond to CLC in planar alignment, whereas the lines
separating them are called the disclination lines. These lines can have a quite complex
structure [1, 5], from a simple thin lambda line which separates the domains of different
colors on the figure 2.11, to the lines with a complex topology.
On the figure 2.12 the orientation of director in the neighborhood of a disclination line is
shown, we see that three half turns on the left of the defect become 4 half turns to the right,
creating a defect line in the middle. Such a defect line once created cannot easily disappear, as
the matter is found in metastable state. The stable state of such a defect line can be understood
by looking on the necessary rearrangements of liquid crystal molecules to make the line
disappear, it is easy to see that this rearrangement has a non-local character, leading to high
energy cost for it.
Figure 2.12. One of the simplest disclination lines (lambda-line) observed in cholesterics.
II.3 Polymer + LC.
Liquid crystal polymer composites show some advantages compared to the pure liquid
crystals. Depending on the preparation process, polymer network can speed up the relaxation
time, stabilize liquid crystal against mechanical stress, prevent some defect formation or even
provide a completely new mode of operating [8, 9,10].
The behaviour of polymer – liquid crystal composites is well understood on the qualitative
level, but the quantitative theory of these materials rises serious problems, as the details of
behaviour depend on the chemical properties of liquid crystal-polymer interfaces. To cite a
40
conclusion of a recent review [11]: “ However little is known concerning the required nature
of the interface between the liquid crystal and the polymer itself to obtain proper samples of
LC/polymer blends and composites of practical interest.”
In our work, we use two types of liquid crystal – polymer composites: Polymer Dispersed
Liquid Crystals (PDLC) and Polymer Stabilized Liquid Crystals (PSLC).
II.3.1 Polymer Dispersed Liquid Crystals.
For the first time, PDLC were proposed for the use in display technology [8, 9]. The principle
of operation is shown on figure 2.13. With no applied voltage the thin film scatters light due
to a mismatch between the refractive indexes of polymer and LC, the left part of the figure.
When a sufficiently strong voltage is applied the ordinary index of polymer matches the
refractive index of polymer and no scattering occurs.
There are several methods to make a PDLC, by temperature induced, solvent induced or
polymerization induced phase separation. The size of the liquid crystal droplets can be
adjusted by changing the composition or a phase separation speed.
Figure 2.13. Polymer dispersed liquid crystal composite, the principle of electro optical effect.
In all cases, one starts with a homogeneous mixture. For a temperature induced phase
separation one mixes liquid crystal and high molecular mass polymer at a higher temperature.
41
Due to the temperature dependence of the miscibility of liquid crystal and polymer a
homogeneous mixture at higher temperature starts to phase separate if cooled down. For a
solvent induced phase separation, liquid crystal and polymer are first dissolved in a common
solvent, which is evaporated afterwards. For a polymerization induced phase separation, a
mixture of liquid crystal, monomer and initiator of polymerization is prepared and the phase
separation happens during the photo-curing.
II.3.2 Polymer Stabilized Liquid Crystal
Polymer stabilized liquid crystals are prepared by dissolving a smaller amount of monomer
than for PDLC (of the order of 5%) and polymerizing it to form a polymer network in liquid
crystal matrix [9, 11]. Main interest in this composite arises from the stabilizing effect that
polymer network has on the liquid crystal phase.
If one stabilizes nematic liquid crystal in a nematic phase, the properties of the composite will
be similar to that of the pure nematic liquid crystal due to the low concentration of polymer
network, at the same time some macroscopic properties could be improved. For example, Bos
et al group [9] found that in twisted nematic cells, a significant reduction in operational can
be achieved at low polymer concentration.
Figure 2.14. Polymer stabilized nematic liquid crystal.
In the application of devices based on polymer stabilization, it is important to understand how
the polymer network is formed, what factors control its morphology and finally its role in the
properties of a composite. The study of the polymer network morphology [12, 13] showed a
strong dependence on the polymerization temperature, concentration of initiator, monomer
and liquid crystal structure.
42
As an example, we provide chemical formulas for commonly used monomer RM257 and
polymerization initiator Igracure 651, figure 2.15. The central part of RM257 has certain
rigidity and gives rise to a liquid crystalline phase. (The rigid part of a molecule which gives
rise to liquid crystalline order is commonly called a mesogen.)
The advantage of using a mesogen monomer, is that in many cases due to its liquid crystalline
properties such monomer can be added in quite high concentration to other liquid crystals
without changing a liquid crystalline phase. We found, for example, that cholesteric liquid
crystal planar configuration can be preserved with the concentration of RM257 up to 15%. On
the other hand, if one uses a non-mesogen monomer the liquid crystal phase is not preserved
for sufficiently high concentrations.
Figure 2.15. Mesogenic monomer RM257 and polymerization initiator Igracure 651.
After polymerization, a branched polymer network is formed like the one shown on figure
2.16. Details of the chemical reaction can be found in [14].
43
Figure 2.16. A branched polymer network formed by RM257, not all the connections would
be present in a real network.
II.3.3 Polymer stabilized CLC.
One of the applications of polymer stabilization which illustrates very well the effect of the
polymer network on the liquid crystal properties is the reverse and normal mode cholesteric
liquid crystal shutters [15, 16, 17].
As we have seen CLC have different textures exhibiting different behaviors with respect to
the incoming light. By using a polymer network to stabilize a desired texture one can develop
scatters as it is shown on figures 2.17 and 2.18.
In the case of a reverse mode shutter, polymer network stabilizes planar configuration of CLC
insuring that after the application of electric field liquid crystal would relax back to the initial
state. In the absence of a polymer network the texture will not relax back to the planar state
for a sufficiently thick sample. Even for a thin sample where the surface forces could be high
enough to achieve a planar state configuration, the presence of a polymer network reduces the
relaxation time by an order of magnitude.
44
Figure 2.17. Reverse mode shutter. For a large enough pitch the polymer stabilized CLC is
transparent to the incoming light, left. When electric field is applied CLC structure transforms
to scattering focal conic, making the device opaque, right.
In a normal mode the scattering state is achieved without application of external electric field,
as it is shown on figure 2.18. In this case, polymer network stabilizes the focal conic texture,
then upon application of electric field the molecules are reoriented in a homeotropic state and
relax back into a focal conic state when the field is switched off. The main role of the polymer
network is to speed up the relaxation process.
Figure 2.18. Normal mode shutter. Focal conic texture of CLC is stabilized with a polymer
network, so that when it is switched into a homeotropic state (right), it becomes transparent
and relaxes back to a scattering state when the electric field is switched off.
It was found that, the morphology of a polymer network, which is polymerized in particular
liquid crystal texture, reflects the ordering of this texture [13, 15]. So not only the polymer
network influences the properties of liquid crystals, but the liquid crystal influence the
formation and behaviour of polymer network too (see for example V-shape technique [18]).
45
Scattering of polymer stabilized CLC.
The transparent state of polymer stabilized CLC that is presented on the figures 2.18 and 2.19
is practice weakly scattering. This weak scattering is due to the mismatch between the
refractive index of polymer network and LC, and the phase separated nature of the composite.
The degree of phase separation and the morphology of the polymer network, which is formed
during the polymerization, depend on many factors, such as temperature, UV intensity, photoinitiator amount, etc. The degree of scattering will depend on the size of phase separated
regions in respect to the wavelength of scattered light. Similarly to the PDLC, where
scattering for the visible light can be considerably reduced by decreasing the size of the LC
droplets to ~100nm, the scattering of PSLC can be reduced by the appropriate change of
polymer network morphology [12, 13, 15].
The scattering of polymer stabilized CLC can be quite small, less than ~3%, if the mesogenic
monomer is used. In this case the polymer network can match the LC to a high degree,
resulting in a small size of phase separated regions and reduced degree of scattering. In our
work, we noticed some scattering of the polymer stabilized CLC in the visible range.
However, we did not undertake particular effort in the optimization of the experimental
protocol to reduce the scattering, as it was not the main obstacle for the optimization of the
photonic CLC performance in the 1,55 µm range.
Still, we would like to notice that the optimization of scattering of polymer stabilized CLC
can be important for some application such as switchable Bragg mirror, where high
reflectivity is important. The optimization can be obtained by controlling the morphology of
the polymer network and choosing the appropriate mesogenic monomer and LC to reduce the
index mismatch between LC and polymer network [12, 13, 15].
II.4 Optical properties of CLC.
So far we presented an introduction to the material properties of LC and LC-polymer
composites. Now, we will make a short introduction to the optical properties of CLC and
discuss the state of the art of computer modeling of such structures and how to obtain good
CLC structure with a large thickness
46
Optical properties of ideal helix.
Helical structure of cholesterics gives rise to a Bragg reflection in a certain bandgap; unlike an
ordinary Bragg mirrors only the waves of a certain polarization are reflected. Moreover when
the pitch of cholesteric liquid crystal is much larger than the wavelength the structure exhibits
a guiding effect (this effect is used in twisted nematic structure, but without the same modes,
here circular). The theory of optical properties of CLC was established by Mauguin, Oseen
and de Vries [1, 2].
The theory is based on the assumption of local uniaxial behaviour of CLC, i.e. a thin slab of
CLC behaves similarly to nematic with the same permittivity tensor. Based on this, in a local
coordinate frame, which is connected with the liquid crystal director the permittivity tensor
can be written as :
 ( z) 
 //     1 0   //     cos2q0 z 
2

 
0 1
2
sin 2q0 z  


 sin 2q0 z   cos2q0 z 
(2.12)
where the z axis is chosen perpendicularly to the CLC director orientation and only x and y
components of the tensor are taken into account (z component is constant). We will show the
general idea of how the solution can be obtained without going into details, that can be found
elsewhere [1, 2].
Let us consider the propagation along z-axis, of an electromagnetic wave with a frequency ω:
E X  ReE X z  exp  it 
EY  ReEY z  exp  it 
(2.13)
Maxwell equations reduce in this case to:
d 2 Ei
 
    ij E j
2
dz
c
2
The following is rather straightforward. Introducing:
i , j  x, y
(2.14)
47
    
k    //
2
c
2
2
O
(2.15)
   
k12    //
2
c
2
Equation (2.14) can be written as:
d 2 EX
 k O2 E X  k12 cos2q0 z E X  sin 2q0 z EY 
2
dz
d 2 EY

 k O2 EY  k12 sin 2q0 z E X  cos2q0 z EY 
2
dz

(2.16)
By introducing circularly polarized modes E  E X  iEY , (2.16) can be transformed into:
d 2 E
 k O2 E   k12 e i 2 q0 Z E 
2
dz
d 2 E

 k O2 E   k12 e i 2 q0 Z E 
2
dz

(2.17)
Solution for equation (2.17) is obtained in the form
E   a expil  q0 z
E   b expil  q0 z
(2.18)
Where a and b are constants defined by initial conditions, and l is the wavevector which
defines propagating mode. They satisfy the following relation, which one gets by substitution
of (2.18) into (2.17):
(l  q )  k a  k b  0
 k a  (l  q )  k b  0
2
0
2
1
2
0
2
1
2
0
2
0
(2.19)
The general solution (2.18) is analyzed for different parameter combinations and all limiting
cases are identified [1, 2].
48
II.4.1 Bragg reflection.
For the following we are interested only in the case of Bragg reflection, which corresponds to
the values of ω inside the interval:
cq0
cq
  0
nE
nO
(2.20)
or in the wavelength domain no P    nE P .
For this frequency interval equation (2.19) has nontrivial solution only for two real values for
wavevector l  l1 , other roots are imaginary l  i , where the values  l1 and  i set to
zero the determinant of (2.19). The real root corresponds to a propagating wave and the
imaginary one to an evanescent wave (with an amplitude ~ exp - z ). The reflected wave has
circular polarization with the same handedness that the cholesteric helix has. The transmitted
(propagating wave) has opposite handedness.
Figure 2.19. Reflection of a circularly polarized wave from a cholesteric and mirror. In case
of the CLC polarization remains unchanged, while it the case of a mirror it is inversed.
Another particular property of the CLC Bragg reflection is the difference with the reflection
from a metallic mirror and CLC Bragg. When a right circularly polarized wave is reflected
from cholesteric with right handed helix, the wave does not change its polarization, while
49
when the same wave is reflected from a mirror the polarization is reversed to the left circular,
Figure 2.19.
II.4.2 Numerical solution for 1-D CLC.
The analytical solution of the Maxwell equations for CLC, that we outlined, is possible only
in a case of an ideal helix, i.e. when the variation of director follows the equation (2.9), and
only in an infinite case under normal incidence. If one deviates from an ideal case one needs
to resort to numerical calculations.
A first numerical method for the case of non-sinusoidal pitch variation and the oblique
incidence case was developed by Berreman [19]. Though this method handles well the
solution of Maxwell equations for anisotropic media, it does not generalize well into a 2-D
case, so in order to solve the problem in such cases other methods are used.
Figure 2. 20. Establishment of the Bragg reflection for cholesterics depending on the number
of layers. Result of numerical modelling by FEM for a 1D structure with several layers.
Modelling parameters: P=1µm; n  1.5 ; n  0.2 .
50
As we already discussed in the first chapter the most widely used methods for solving
Maxwell equations in general case are Finite Difference Time Domain and Finite Element
Method. These methods only recently were applied to the CLC, calculating the Bragg in nonideal case. Among many facts, the dependence on the central wavelength for a Bragg
reflection in the case of oblique incidence was established as [20, 21]:
  n P0 cos
where n
2

(2.21)

 n E2  2nO2 3 is the average refractive index.
Another fact which is of importance for our work is the establishment of the Bragg reflection
depending on the number of layers in the CLC, shown in figure 2.21. To obtain this figure we
numerically solved the Maxwell equations using FEM for CLC with different number of
layers. The important facts for us were the number of layers necessary for the establishment
of the Bragg reflection and the dependence of the width of the side lobs on the number of
CLC layers. One can see that the width of the lobes decreases when the number of CLC
pitches increases.
Though the numerical solution in 1D case allowed a better understanding of optic properties
of CLC, the 2-D and 3-D case are still not well investigated. The problem arises due to
anisotropy of dielectric tensor, which makes the algorithm more complex and requires more
computational resources than the case of an isotropic dielectric tensor.
The only work to date that approaches the computer modelling of 2D CLC structure was
issued in 2006, and uses FDTD method to solve the problem [22].
II.5 Thick CLC structuring.
II.5.1 Basic requirements.
On the first stage of the photonic CLC preparation we had to develop an experimental
protocol for making thick homogeneous CLC cells. The samples should be thick in order to
obtain a high efficiency Bragg reflection, which is a first essential requirement for photonic
crystal development. A second requirement is a high homogeneity of a sample, because the
51
effect that we try to demonstrate depends on the presence of a well-defined band-edge for a
reflection grating (see discussion in the first Chapter), if the sample is a polydomain one the
band edge would be ill defined and we would not see any effect. The last requirement is the
stability of the sample under application of electric field, which leads to the need for a
polymer stabilization and the development of a corresponding protocol.
High requirements for the sample thickness and homogeneity are specific for our work, as in
most of the applications such as reflective displays only a basic reflective shape of CLC is
important. Therefore the requirements for the thickness and homogeneity are not as strict as in
our case. On the other hand the polymer stabilization is a well-developed technique and
commercially available mesogenic monomers are very suitable for this task.
II.5.2 Cells preparation.
The empty cells were prepared following the standard protocol of LC industry. The basic
technological process was shown to me by a Ph.D. student of optics department B. Caillaud,
and it is described in his thesis [23]. I have adapted the process to the specific requirements of
cholesteric liquid crystals. The details of the empty cell preparation can be found in the
appendix.
A schema of an empty cell is shown on figure 2.21. The main adaptations consisted in putting
the spacers to the side of the cell, to avoid defects generation, and precise control of the cell
thickness to avoid the disclination lines.
Glass plate
ITO Layer
Alignement
Layer
Spacer
Figure 2.21. An assembled cell. Side view.
II.5.3 Mixture preparation.
To prepare a CLC sample we purchased from Merck two liquid crystals: MDA-00-1444 –
nematic, and MDA-00-1445 – cholesteric mixture. Their exact composition is not available.
52
We can assume, though, that MDA-00-1445 is the same liquid crystal as MDA-00-1444 with
a chiral dopant, or MDA-00-1445 has a similar chemical structure to MDA-00-1444 with a
chiral group that induces CLC structure. In both cases the two LC are easily mixable and by
changing their corresponding concentrations one can change the position of the reflection
peak. The other data that we received from Merck are their ordinary refraction index of 1.5
and an extraordinary of 1.68 (values for the visible wavelength), we also received the data that
the mixture of 79% MDA-00-1445 + 21% MDA-00-1444 has a reflection peak at 0.6
µm. With this value one can calculate the mixture composition to put the reflection peak at
other wavelengths.
II.5.4 The need for polymer stabilization.
As we already discussed, under the application of electric field CLC in planar configuration
transforms into a focal conic texture. We observed it in experiment, when we have measured
transmission spectrum for thick CLC sample figure 2.22, after the application of electric field
the sample became scattering and has not relaxed back into a planar state in the following
hours. In our opinion the structure did not come back to planar state due to its large thickness.
Figure 2.22: 30 µm CLC sample, P=1µm. Spectrum measured in a planar configuration
before applying voltage, and after the relaxation into a focal conic state. The bottom curve
corresponds to the focal conic state, with reduced transmission due to scattering.
53
This effect should be avoided, as we later would like to introduce modulation by electric field
and the sample should stay stable. Therefore we had to use polymer stabilization. We chose to
work with a mesogenic monomer RM257, as it shows good results in the previous work
carried out in our department [23]. It also proved to be soluble with concentrations up to 15%
in the CLC mixture. We also added a small concentration of photo-initiator Igracure 651 and
polymerized the mixture after filling. We observed a slight dependence of the resulting
structure on the UV intensity for polymerization for the UV intensity between 2 and
20mW/cm2.
We checked several concentrations of monomer. The concentrations below 5% does not have
a good stabilizing effect and if electric field of more then 2V/µm is applied the CLC structure
does not relax into original planar state. On the other have with the increase of the monomer
concentration the effect of electric field decreases and liquid crystal molecules do not turn
under the electric field. It can be seen on the figures 2.23 and 2.24, where the transmission for
the visible light depending on the applied electric field is shown. (The measurements were
carried out with the use of He-Ne laser, and intensity of the transmitted light was monitored
by photodiode connected to the oscillograph.)
Figure 2.23: Measurement of the response time and dynamic behavior of polymer stabilized
CLC (top curve). Polymer concentration is equal to 15%. The bottom grey curve is the
applied voltage.
54
The CLC samples for these tests were prepared with a pitch of 1 µm and reflection band at
about 1,5 µm. Without applied field they are transparent to the visible light, with a small
degree of scattering due to mismatch of the refractive index of polymer network and CLC.
When the electric field applied to the sample part of the CLC in the bulk turns into focal conic
state and sample scatters light. One can see that for high polymer concentration 15% the
transmission of the cell changes much less than for the case of low polymer concentration 5%.
This means that for 15% the stabilization effect is too high, and lower concentrations are
preferred.
Figure 2.24: Measurement of the response time and dynamic behavior of polymer stabilized
CLC (top curve). Polymer concentration is equal to 5%. The bottom grey curve is the applied
voltage.
Finally, the lowest concentration of monomer that guarantees the relaxation of the sample into
planar configuration and at the same time allows for a deep index modulation equals 5% and
this value was used for all our samples.
The values for relaxation and switching time that we observed, ~400 µs for the switching to
scattering focal conic state and relaxation into a planar configuration are consistent with the
values in the literature [24].
55
II.5.5 Homogeneous CLC structure.
Another big obstacle that we faced was homogeneity for thick samples, i.e. >10 µm with a
pitch P=1 µm. (The value of pitch corresponded to the reflection band at about 1,5 µm, at
which we planed to do the measurements.)
For 10 µm thick sample, a good homogeneous structure was obtained by surface alignment
and no additional steps were necessary. For thicker samples, some defects appeared during the
filling of the cell, and did not relax with time. One of the solutions to the problem of defects
in CLC cells is proposed in the literature [1, 2] and is done by slightly displacing one of the
glasses. In this case the glue that holds the glasses together should not be polymerized.
This approach allows to get rid of the defects, but with this method it is difficult to obtain a
good planarity of the cell. Another disadvantage of this method is the difficulty of its
implementation on the industrial scale; it is not compatible with the common method of liquid
crystal industry.
We found another method that produced a good homogeneous structure. We noticed that most
of the defects appear at the entrance of the cell, during the filling process, and by reducing the
speed of filling it is possible to greatly reduce the number of defects in the CLC structure. We
reduced the speed by decreasing the entrance size, by polymerizing some UV glue near the
entrance. On the next step we left the filled cell for a period of 24 hours at the room
temperature (20°), which relaxed even more defect lines. Finally, we applied ‘thermal
treatment’, by heating the samples up to 60° and leaving at this temperature for a period of 36 hours.
After this procedure the samples had very few defect lines with the typical domain size of
3mm by 3 mm, which was good enough for all experimental purposes. Having obtained a
homogeneous sample, we exposed it to for polymer stabilization.
Quality control.
During the preparation stage, the quality of the samples was controlled by verifying the
homogeneity of the structure through a microscope. The defects lines and different domains
56
were clearly visible under the crossed polarisers examination. Good quality samples had big
domains with the typical size of 3 mm by 3 mm.
With the polymerized samples we made two more tests to verify their quality.
First, we measured the polarization dependence of the transmission for our CLC samples; it is
a way to measure the quality of the samples. After a polarizer we put a quarterwave plate for
  n P that could be rotated to an arbitrary angle, during the rotation the polarization of
light is changed from right circularly polarized to left circularly polarized. In the ideal case, at
the wavelength of the Bragg reflection   n P , one circularly polarized mode is completely
reflected, while the other one is completely transmitted (we consider normal incidence case).
In the whole range of quarterwave plate positions the transmission should depend on the angle
as cos2θ, which was indeed observed figure 2.25. This experiment verified that behaviour of
our samples is close to the behaviour of ideal CLC, which confirms the high quality of the
planar structure of CLC in our samples.
Figure 2.25: Transmission responses of the PSCLC (Polymer Stabilized CLC) as a function of
the polarization. Each sector corresponds to 10°.
57
The second test of samples quality is the observation of the band edge oscillation. For the
good quality samples, these oscillations are clearly visible in transmission spectra for the light
with the circular polarization that corresponds to the CLC helix handedness. One of the
transmission spectrums for a good quality sample is presented on the figure 2.26.
Figure 2.26: Circularly polarized light transmission for a 30 m CLC sample. Band edge
oscillations are clearly visible.
Experimental observation of the band edge oscillation is an important sign of the quality of
the sample. For low quality samples, with the domains of a small size, the oscillations are
poorly resolved. From the theoretical view, in poly-domain samples the band edge oscillations
are non existent, as the central reflection wavelength is different for each domain and the
superposition of each domain oscillation leads to a smooth shape of the reflection band
without oscillations.
II.6 Conclusion:
In this chapter we gave an introduction to the basic properties of material that are used in our
experimental work: LC, CLC, LC - polymer composites. After that introduction we presented
our experimental results on the structuring of thick polymer stabilized CLC.
Requirements for the CLC material were based on its utilization for the 2-D photonic crystal
development. We needed a many layer planar CLC with the number of pitches greater than 15
to have a well defined reflection band edge. We also needed to stabilize it by polymer in order
to avoid defect grow under application of electric field. And finally the structure had to be
58
very homogeneous, essentially we needed a sample with large domains, to avoid the
smoothening of the band edge oscillations.
During the experimental work we found that mesogenic monomer RM257 (Merck) was
compatible with the CLC and provided a good stabilization at the concentration of 5%. With
the PSCLC we elaborated an experimental protocol which resulted in a sample with large
domains. In the process we tried to suppress the creation of defects and defect lines and found
a way to relax the defects that appeared. From a theoretical view point the lowest energy state
for CLC sample with the planar alignment on both surface correspond to the monodomain
planar structure. All the defect lines can be considered as the metastable higher energy state.
The experimental protocol can be summarized as follows. First, we tried to make as clean
samples as possible, because the dust in the cell generated defects. Second, we found that by
filling the cell with a small speed, it was possible to suppress the defect generation. It is likely
that during the slow filling resulted in a lower energy state of the system, similarly to the slow
growing of ordinary crystals, that results in a smaller number of defects. Third, the defects can
be relaxed through the treatment, i.e. controlled heating of the sample. Heating gives the
energy to the system to go over the potential barrier that separates a metastable defect state
and the ground monodomain state.
In conclusion, we elaborated an experimental protocol for homogeneous thick polymer
stabilized CLC samples fabrication. The fabricated samples had a well-defined band-edge,
which is necessary for the photonic CLC fabrication that will be described in the next section.
59
II.7 Literature for Chapter II:
[1] P.G. de Gennes and J. Prost : ‘The physics of Liquid Crystals’. Clarendon Press, Oxford,
1993.
[2] P. Oswald and P. Pieranski : ‘Nematic and Cholesteric Liquid Crystals: Concepts and
Physical Properties Illustrated by Experiments (Liquid Crystals Series)’ , CRC press,
Taylor and Francis, 2005.
[3] V. Chigrinov, V. Kozenkov and H.-S. Kwok, ‘Photoalignment of Liquid Crystalline
Materials: Physics and Applications’, John Wiley and Sons Ltd, 2008.
[4] J. Stohr, et al , “Microscopic Origin of Liquid Crystal Alignment on Rubbed Polymer
Surfaces”, Macromolecules, 31, 1942-1946, (1998)
[5] Chirality in Liquid Crystals, Springer-Verlag New York, Inc. See Chapter 5, ‘Cholesteric
Liquid Crystals: Defects and Topology’, by O. Lavrentovich and M. Kleman,(2001)
[6] J.F. Stromer, et al. ‘Electric-field-induced disclination migration in a Grandjean-Cano
wedge’ J. Appl. Phys. 99, 064911 (2006);
[7] A. Dequidt and P. Oswald, ‘Zigzag instability of a χ disclination line in a cholesteric liquid
crystal’, Eur. Phys. J. E 19, 489 (2006)
[8] F. Simoni, ‘Nonlinear optical properties of liquid crystals and polymer dispersed liquid
crystals’, World Scientific, New Jersey, (1997).
[9] Crawford and Zumer eds, “Liquid crystals in complex geometries” , Taylor&Francis
(1996)
[10] L. Bouteiller and P. Le Barny, ‘Polymer-dispersed liquid crystals: Preparation, operation
and application.’, Liq. Cryst. 21, 157 (1996)
[11] M.Mucha, “Polymer as an important component of blends and composites with liquid
crystal,” Progress in Polymer Science, vol. 28, pp. 837–873, (2003).
[12] C. V. Rajaram, S. D. Hudson, L. C. Chien, "Effect of Polymerization Temperature on the
Morphology and Electro-Optic Properties of Polymer Stabilized Liquid Crystals,", Chem.
Mater. 8, 2451 (1996).
[13] D. S. Muzic, C. V. Rajaram, L. C. Chien, S. D. Hudson, "Morphology of Polymer
Networks Polymerized in Highly-Ordered Liquid Crystalline Phases,", Polym. Adv. Tech.
7, 737 (1996).
[14] C. Decker, K. Zahouily et A.Valet, “Curing and photostabilization of thermoset and
photoset acrylate polymers,” Macromolecular Materials and Engineering, vol. 286, pp. 5–
16, (2001).
60
[15] G.P. Crawford and S. Zumer, “Polymer-stabilized Cholesteric Textures: Materials and
Applications, “D.-K. Yang, L.-C. Chien, Y.K. Fung, in Liquid Crystals in Complex
Geometries, eds., Ch. 5, 103-142, Taylor and Francis: London (1996).
[16] J. L. West, R. B. Akins, J. Francl et J. W. Doane, “Cholesteric/polymer dispersed light
shutters,” Applied Physics Letters, vol. 63, pp. 1471–1473, (1993).
[17] H. Ren et S.-T. Wu, “Reflective reversed-mode polymer stabilized cholesteric texture
light switches,” Journal of applied physics, vol. 92 (2), pp. 797–800, (2002).
[18] Shikada, Y. Tanaka, et al. "Novel mesogenic polymer stabilized FLC display device
exhibiting V-shape electro-optic charachtersitics”, Journal of Applied Physics, vol. 40, pp.
5008-5010, (2001)
[19] Berreman D.W. “Optics in Stratified and Anisotropic Media: 4 × 4-Matrix Formulation”
J. Opt. Soc. Am. 62, 502-510, (1972)
[20] Hong Q; Wu T.X.; Wu S-T. “Optical wave propagation in a cholesteric liquid crystal
using the finite element method “ , Liquid Crystals, Volume 30, pp. 367, (2003)
[21] S.T. Wu and D. K. Yang, “Reflective Liquid Crystal Display”, Wiley, New York (2001).
[22] Chi-Lun Ting Tsung-Hsien Lin, Chi-Chang Liao,Andy Y. G. Fuh, “Optical simulation of
cholesteric liquid crystal displays using the finite-difference time-domain method” 2006,
Vol. 14, No. 12 , Optics Express 5594
[23] B. Caillaud "Structuring of the Liquid crystal phases by polymer network. Applications."
PhD, UBS ENST Bretagne, April 20., 2007. (in french)
[24] V. Sergan, Y. Reznikov, J. Anderson, P. Watson, J. Ruth, and P. Bos, “Mechanism of
relaxation from electric field induced homeotropic to planar texture in cholesteric liquid
crystals”, Molecular Crystal Liquid Crystal 330, 1339-1344 (1999).
61
Chapter III
Chapter III: 2-D photonic CLC.
In this chapter we provide the operating mode description and the scaling of 2-D photonic
CLC, taking into consideration the material structuring part that was discussed in the second
chapter and photonic crystal aspects discussed in the first chapter. We continue with the
experimental aspects of the realisation of the 2-D photonic CLC. Finally we show the
experimental results that validate the concept, propose qualitative explanations of
experimental results and discuss the possible improvements.
III.1 2D photonic CLC scaling.
As we have seen from previous discussion CLC, under certain conditions, is a natural 1-D
photonic crystal. The main idea of the first part of this thesis is to exploit its natural properties
in order to produce a reconfigurable 2-D photonic crystal. More particularly we would like to
make a device which would operate in a similar way as the photonic crystal made by two
sinusoidal gratings described in the first section. It was demonstrated that such structure has
wavelength filtering properties which could be used for practical applications. In order to
make such 2-D photonic crystal based on CLC, we need to structure it so that additional
modulation is introduced and will enter into resonance with the intrinsic one. We considered
two ways of such a structuring: by the electric field and by a polymer network.
62
Electric field structuring.
Under the application of an electric field, the liquid crystal with a positive dielectric
anisotropy reorients into the direction of the field. This effect provides a possibility to make a
2-D photonic CLC.
Figure 3.1. Principle of the CLC structuring by an electric field.
A schematic view is shown on the figure 3.1, CLC in planar configuration is confined
between two glass plates with a thickness L, on one glass plates parallel electrodes with a
certain period
X
are etched, the conductive layer on the other glass plate acts as a large
counter electrode. When the electric field is applied between the electrodes, CLC is reoriented
in the direction of the electric field providing additional modulation to the structure.
This device is switchable and has some potential for reconfiguration by changing the
electrodes geometry, i.e. applying electric field to every second electrode increasing the
period of modulation by a factor of 2, or by changing the value of the applied electric field
which also could change the device characteristics.
Polymer structuring.
Another possibility is to structure CLC with the help of a polymer chain or network, as it is
shown on the figure 3.2. If one can produce regions in a planar CLC structure with different
63
polymer concentration, then due to the difference in refractive index between CLC and
polymer one can produce a modulation similar to the modulation by an electric field.
Figure 3.2. CLC structured by polymer.
One way to do this would be to dissolve some monomer in a CLC, then after obtaining a
planar configuration, monomer can be photo-polymerized by an inhomogeneous light field,
then in the illuminated regions the density of polymer chains would be larger than in the dark
regions, as the chemical reaction is initiated by light.
Scaling of 2D photonic CLC.
As we have seen in the Chapter I, in order to obtain the resonance peak in diffraction and
spectral selectivity for the case of 2-D photonic crystal with sine modulation several
conditions should be fulfilled.
The wavelength of interest and the incidence angle should be positioned at the band edge of
the reflection grating, where the structure is transparent. The period and index modulation of
the transmission grating are chosen so that the transmission grating operates in the Bragg
regime for the chosen wavelength and incidence angles.
The filtering effect is qualitatively explained by the enhancement of the diffraction efficiency
by the structure when the incident light is at the photonic band-edge. On the qualitative level
similar situation is possible with the band edge which originates due to the cholesteric liquid
crystal bandgap. In the case of CLC the situation is somewhat complicated due to polarization
dependence of the reflected wavelength, and overall anisotropic nature of CLC and
64
transmission grating modulation. Still we assume that the principal effect should stay the
same and we validate the principle experimentally in this chapter.
The analogy to the case of 2D sinusoidal modulation can be seen, if we consider only Right
Circularly Polarized (RCP) light. Due to the CLC Bragg structure RCP light would ‘see’ a
bandgap similarly to the case of 1-D sinusoidal reflection grating. For the transmission grating
RCP light would also ‘see’ it similarly to the sinusoidal modulation case. When both gratings
are superimposed RCP would ‘see’ an effect similar to the 2-D sinusoidal for a linearly
polarized light.
In order to realise an experimental device, we need to make an estimate of the relevant
parameters, similarly to the case of sine gratings. The wavelength λR , which corresponds to
the location of the band-edge for the reflection grating should satisfy the Bragg condition for
the transmission grating.
We choose λR to be in the wavelength range 1500nm – 1610 nm, as we have a tuneable laser
source for this wavelength range. The period of transmission grating is determined by the
available technology and fixes the incidence Bragg angle through :
sin  B 
R
2n X
(3.1)
The location of a cholesteric band-edge is found at no P   R  nE P and can be adjusted by
changing the cholesteric pitch through chemical composition of the mixture. So for a given
wavelength λR and the transmission grating period
X,
we can adjust the location of the band-
edge of CLC by changing its chemical composition and observe the band edge induced Bragg
diffraction for an angle given by equation (3.1).
One needs to keep in mind that, even under the above assumption, the concept that worked in
the case of 2D sinusoidal modulation should be experimentally validated for the considered
case. Despite the qualitative similarities, the presence of anisotropy of the CLC, a non
sinusoidal form of the modulation for the transmission grating could lead to a quite different
behaviour of the device.
65
III.2 Computer modeling of 2D photonic CLC.
Before investing time and effort into experimental validations of the 2-D photonic CLC
concept we investigated the possibility of a computer modelling of the device structure.
A computer simulation can be divided into an optical and material parts. In the material part
of the computer modeling one finds the director distribution which serves as an input for the
modeling of optical properties.
Material part.
In a material part one needs to calculate the director field dependence on the applied voltage.
In the case of an ideal nematic this requires minimizing the free energy integral (2.6), for a
given distribution of the electric field generated by electrodes, where the elastic energy
contribution has a form of (2.10) and the electric field contribution (2.5). The planar
alignment on the surfaces as a boundary condition should be taken into account. This field
computation is quite well-developed and even commercial solutions exist that operate even
for CLC case, see for example [2, 3].
In practice the numerical solution, in case of a pure liquid crystal, is not sufficient, as
experiments are carried out on a polymer composite material, because a polymer stabilization
is required to obtain CLC Grandjean structure on thick samples. Therefore the equation (2.10)
should be modified to take into account the presence of the polymer network, which
according to our knowledge, is not a simple task by itself due to the complexity of LC to
polymer interaction.
Optical part.
The director distribution field which in principle can be calculated by the solution of ‘material
part’ differential equations, provides an input for an all optical calculation. Knowing the
director field distribution would allow us to specify the permittivity tensor (2.8) in any point
of the media, it will require the specification of the angles between the global coordinate
system and a local one which is given by the director orientation.
66
Afterwards one can fulfill the program described in the Chapter I, by numerically solving the
Maxwell equations with a known permittivity tensor. As we already pointed out in Chapter I,
this solution is difficult even for isotropic photonic crystals. In our case, we deal with
anisotropic case, which further complicates the situation.
Whereas, there is commercially available software for isotropic photonic crystals, to our
knowledge, this is not the case for anisotropic case. The only attempt to handle the optical
part for 2-D CLC is very recent [1]. It considers some aspects of the 2-D modelling. The
application of that method to modelling 2-D photonic crystal based on CLC would result in
substantial increase in computation requirements, as one would need to model thick cell and
several grating periods in order to observe the resonance. In other words, computer modelling
of the optical part could be a subject of a full separate research.
Feasibility of computer modeling of 2-D CLC.
As a conclusion, we were not sure if we would be able to realize a reliable computer modeling
of the proposed 2-D CLC photonic crystal. The modeling of both material and optical part is
on the boundary of the state of the art and was never tried by any team. So, in our view, the
experimental approach greatly outweighs the computer modeling approach in terms of time
and resource investments.
III.3 Experimental realization.
According to the chosen approach we tried to realize 2-D photonic CLC experimentally by
structuring it by an electric field and by a polymer network. Electric field structuring led us to
a partial success. We observed the increased transmission at the band-edge of CLC similarly
to the 2D sine modulation described in the first chapter. The approach also showed its
limitations, we discuss at the end of this chapter. In contrast, we failed to structure CLC by a
polymer network, as it is shown on the figure 3.2. We follow up this chapter with the
description of the experimental protocol and the obtained results. The results on electric field
structuring were published in [4, 5].
67
III.3.1 Electric Field structuring.
Mask scaling.
The performance of the 2-D photonic CLC, similarly to that of 2-D grating with sinusoidal
index modulation, can be expected to depend on the thickness to period ratio. Therefore, we
choose to investigate several grating periods.
The grating periods that we could obtain were limited by the available technology within the
Optics Department. The technological process for the mask fabrication by the photoplotter
available in the department determined the resolution for the electrode size to more than 3
µm. The distance between electrodes should exceed this value; otherwise the electric field
produced by electrodes would overlap too much in the bulk of the sample as a function of the
thickness.
With these constrains, we have chosen to study three successive gratings with different
periods ( ΛX = 8µm, 15µm,
30µm). For periods much smaller than the thickness, we
expected that electric fields created by each stripes overlap, distorting the planar structure and
resulting in weaker index modulation depth. As the period increases the overlap decreases and
the index modulation in the bulk is closer to the ideal case (i.e. a square wave). All three
gratings were realized in one chromium mask, as shown on figure 3.3
8µm
15µm
30µm
Figure 3.3. The mask with three different periods realized at our department. Three different
periods are shown; the electrode thickness is always 3 µm.
Mask replication on ITO.
The mask was replicated on ITO, using the standard process, described in more details in
Appendix 2. The substrates with the etched ITO had a replica of chromium mask such as
68
shown on figure 3.3. The cell was made with one substrate which had a grating of etched
electrodes, whereas another had a whole counter-electrode, as it is shown on figure 3.1.
Band edge adjustment.
The cells with one etched side were prepared using the protocol described in chapter II. They
were filled with a polymer stabilized CLC, with 5% concentration of polymer. The location of
the band-edge was finely tuned by changing the composition of the CLC mixture.
The pitch of a cholesteric depends on the amount of chiral dopant as
1
   C . Taking into
P
account that the position of the reflection band of a CLC is proportional to the pitch
0  n P and the reflection bandwidth is also proportional to the pitch   nP we come
to the conclusion that the location of the band-edge will be proportional to the concentration
of chiral dopant
1
 BE
   C , where  

n  n
. The α coefficient, ordinary and
2
extraordinary refractive indexes were provided to us by the LC supplier, so we could calculate
the location of the band-edge and make a mixture of necessary composition. However this
formula does not take into account the presence of a polymer added for stabilization. The
monomer RM257 that we add for stabilization is a liquid crystal monomer, which exhibits
nematic phase at 67 to 127 °C, so when we add this monomer, the effective concentration of
chiral dopant changes and the location of the band-edge is no longer at the same place.
The location of band edge was finely tuned by changing the concentration of dopant, and
measuring the transmission spectrum of polymer stabilized mixture. Finally, we found that the
mixture with concentration of MDA-00-1445 of 29%
(cholesteric mixture) and the
concentration of MDA-00-1444 of 71% (nematic host) stabilized with 5% of RM257 had a
band-edge in region of 1500nm – 1620 nm. This wavelength region was chosen because of
the possibility of measurements with the tuneable laser, with a tuning range corresponding to
that region.
69
III.3.2 Measurement set-up.
The experimental set-up (Figure 3,5) allows measurements at different incidence angles and
arbitrary incident light polarizations. We could find a spectral response at arbitrary angles, i.e.
,  and input polarization are free parameters. More specifically, we use a tuneable laser
Tunics-BT with a tuning range of 1500-1620 nm. Polarizer and analyzer are made up of broad
band polarizer and quarter-wave plate which are achromatic in the considered range. Quarter
wave plates can rotate providing various input polarizations, and selecting via the output
analyzer various output polarization states. The spot size of the incoming light is about 1 mm,
which was smaller than the average domain size of the sample ~ 3 mm.
Figure 3.5. Schematic of the measurement setup.
III.3.3 Experimental results and qualitative description.
Several series of samples were prepared according to the experimental protocol described in
Chapter II and beginning of the Chapter III. The results were similar for all the samples,
though the sharpness of the experimental curves depended on the samples quality. The
thickness of all samples was 30 µm. We studied the behavior of gratings with three different
periods (8 µm, 15 µm, 30 µm) under different incident polarization and different applied
voltages. In the following, we summarize experimental results and provide a qualitative
explanation of our observations.
Main observation:
We observed the effect of the spectral selectivity and amplification in diffraction efficiency
near the band-edge of CLC, as it is shown on figure 3.6. One can see the sharp peak in
70
diffraction efficiency of -1 diffraction order, which is near the band-edge. In contrast to the
observation in a case of sinusoidal modulation, discussed in the first chapter, in our samples
we observed two peaks corresponding to the first two transmission maxima of CLC side
lobes. Moreover the diffraction efficiency for the second peak was in many case higher than
the intensity of the first peak.
Figure 3.6: Resonance diffraction spectra for a 30 µm period grating, -1 diffraction maximum.
Voltage and angle chosen for a larger intensity in the 1st or 2nd peak. D1: 0.5 V/µm, 10°
incidence angle. D2: 0.2 V/µm, 6° incidence angle.
Polarization dependence.
We observed high polarization dependence for the diffraction efficiency and spectral
selectivity. For Left Circular Polarization (LCP) of incoming light, when the CLC Bragg
mirror does not operate we do not observe any spectral selectivity or improvement of
diffraction efficiency near the band-edge, see figure 3.7 and figure 3.8. The effect similar to
the effect of 2-D photonic crystal with sinusoidal modulation is observed only for the case of
Right Circular Polarization (RCP) of incoming light.
71
This can be expected since for the LCP the CLC Bragg does not operate and only the
diffraction on 1-D grating occurs. For RCP we turn to the case of 2-D photonic crystal and all
the corresponding effects are observed.
Figure 3.7: Diffracted order polarization dependence for a 30 µm period grating: Grey curve
(–1), black (+1). Input polarizations vary from RCP (sector 2) to a LCP (sector 6) (maximum
efficiency is observed for RCP). Each sector corresponds to 20°.
Polarization dependence should be coupled with the dependence on applied external electric
field. As it can be seen on figure 3.8, for the low applied electric field we observe the increase
in diffraction efficiency for the RCP near the band-edge with respect to the LCP, bottom two
curves. Whereas for the high applied electric field we observe the spectral selectivity for RCP,
but no increase of diffraction efficiency in comparison to LCP. This is probably due to the
distortions of the CLC structure which are increasing with the increase in the external electric
field.
72
Figure 3.8: 1st diffracted order spectrum (30 µm grating period). Bottom 2 curves for low
applied voltages: 0.25 V/µm and orthogonal polarizations RCP and LCP (no change in
intensity for LCP). Top 2 curves for larger applied voltage 2 V/µm, and orthogonal
polarizations RCP and LCP (once again for LCP, no visible wavelength dependence, apart
from the random noise.)
Dependence on the applied electric field:
Diffraction efficiency increased with the increase in the applied electric field till the applied
field reaches 3 V/µm, after it decreases due to distortions of the CLC structure, figure 3.9. We
also observe the disappearance of the first peak and the slight shift of the second peak with a
voltage increase. The shape of the diffraction spectrum is also changing, indicating increasing
distortions of the structure at larger applied electric field values. The observed effect can be
qualitatively explained by a simultaneous increase of the modulation depth of a transmission
grating and distortions of the CLC structure. The increase in modulation depth leads to larger
diffraction efficiency, where as the distortions of the CLC structure change the shape of the
curves. After a certain value the distortions of CLC become too high and the spectral
selectivity, which is due to CLC Bragg disappears.
73
Figure 3.9: 3D representation of resonant diffraction spectra for a 30 µm grating, -1
diffraction order. Axis Z corresponds to intensity in arbitrary units, axis Y to the wavelength,
axis X to the applied voltage. The curve profiles are marked by the corresponding voltage:
V1: 0.25 V/µm; V2: 0.5 V/µm; V3: 1 V/µm; V4: 3 V/µm; V5: 5 V/µm;
Dependence on the grating period.
The result presented so far corresponded to the grating period equal to 30 µm. For the 15 µm
and 8 µm we observed a low efficiency effect as well, as it is shown on figure 3.10. We
explain the low value of spectral selectivity for gratings with smaller period by stronger
distortions of the CLC structure.
74
Figure 3.10:. Diffracted order spectra, for PCLC with different grating periods and the same
applied voltage (0.25 V/µm). Thin black curve (first sharp peak is not fully shown)
corresponds to 30 µm grating, thick black curve to the 15 µm and thick grey curve
corresponds to the 8 µm grating.
III.3.4 Summary of experimental observations.
Experimental observations confirm the feasibility of 2-D photonic crystals based on CLC.
There is even some improvements in efficiency compared to the 2-D photonic crystals with a
sinusoidal modulation. The efficiency for the wavelength peak in case of 2-D CLC was in the
range of 3-10%, whereas in the original publication [6] only 0,1% of diffraction efficiency
was obtained. (It should be noted that they used a different material in their experiment.) The
existence of strong polarization dependence for 2-D photonic CLC is in good agreement with
the nature of the material and can provide an efficient control parameter for the future
applications. Dependence of the diffraction wavelength peak on the applied voltage provides a
possibility for an electrical tuning of such photonic crystals.
With this demonstration of proof of concept we pointed out some restrictions in the
realization of photonic CLC, with electric field modulations. The main problem is the
distortions in the 1-D CLC Bragg structure which are introduced by the electric field. When
75
the index modulation depth for transmission gratings is increasing, the distortions in the CLC
reflection grating (intrinsic Bragg) lead to a smoothening of the diffraction peak. The effect of
distortions restricts the possible addressable grating periods to values comparable to the
sample thickness, which excludes high efficiency diffraction regimes (thick grattings).
Modulation by an electric field can be implemented also with the use of etched counter
electrodes. It raises additional technological difficulties, due to the need for an accurate
alignment of the top and bottom gratings. Another possible approach is the thick electrodes
design shown on the figure 3.11.
However, in our view, the main problem is the inhomogeneous index modulation by electric
field. Homogenous periodic modulation can be obtained only for small inter-electrode
distances, which would lead us to the thin grating regime and low diffraction efficiency, in all
electrodes configurations. Therefore, in order to obtain a more regular and homogeneous
modulation profile another approach should be used, such as holographic structuring. In such
case a more regular index modulation can be expected.
Figure 3.11. Thick electrode design for the modulation of CLC bulk.
III.4 Polymer structuring.
As we have already discussed in the first chapter liquid crystal can be structured by polymer
in such way as to produce the periodic regions of polymer rich and polymer poor areas, see
figures 1.4 and 3.2. This method is based on the holography structuring (see review [7]), and
produces switchable holographic polymer dispersed liquid crystals (Holo-PDLC). By
76
producing periodic modulation of polymer density during the photo-polymerisation process 1D switchable gratings and even 2-D switchable photonic crystals [8] can be made. This
photonic crystal can be switched on and off by application of an electric field, due to the
reorientation of LC. On the other hand they cannot be tuned to a desired wavelength, because
of the rigidity of the polymer network. In the optics department we have experimented with
holo-PDLC materials, within the frame of a collaboration with G. Crawford group [9, 10].
In order to structure CLC with polymer as it is shown on figure 3.2, one needs to introduce
into a CLC a monomer which would be compatible with CLC and polymerize it using a
periodic interference pattern. It should be noted that the process is different from commonly
used, as one needs to preserve CLC planar structure during polymerization.
In the laboratory we had a monomer “Ebecryl” and initiator ‘Rose Bengal’ that were used for
holographic-PDLC development using argon laser at 514 nm [9, 10]. We have made several
tests mixing this monomer with the CLC in different concentrations, all the tests failed as the
mixtures phase separated. We did not have a choice of other monomers and initiators in order
to form a mixture that could exhibit cholesteric phase.
A natural choice of the monomer for holographic structuring is the RM257 that is used for
polymer stabilization, as it is compatible with CLC and one can form a planar CLC structure
with a significant concentration of this monomer. In order to initiate polymerization one
needs to use the initiator ‘Igracure’ which does not absorb at 514nm. It does absorb at 350nm
and the structuring could have been achieved with the use of a UV laser. We have thought
about that possibility, but we lacked the necessary equipment: powerful UV laser.
Recently another group demonstrated the feasibility of holographic structuring of CLC in
[11]. In that work their prime concern was the switching and tuning effect for the CLC. It was
shown that by using a certain combination of LC, monomers and holographically structuring
the mixture, the size of LC domains increased in the direction parallel to the polymer network
stripes. Holographically structured CLC showed improvement in switching characteristics. In
relation to our work, the process that they used can be well adapted to our needs, as they use a
very similar process: dissolving the monomer, structuring CLC in a planar configuration,
polymerising in a patterned way.
77
Holographic structuring by UV laser could be a natural continuation of electric field
structuring. However, we have to face some particular issues in this approach that can be
resolved only by experiments. As the concentration of monomer cannot be too high, with the
risk to disrupt the CLC structure, the index modulation that would be obtained in the end of
the process would be limited due to the low polymer content. Another possible problem is the
distortions in the CLC structure due to the polymer walls formed during the polymerization.
Still, with the clearly visible limits of electric field structuring, holographic structuring
presents the only possible way for improvement of the photonic CLC design.
III.5 Conclusion.
We have demonstrated the proof of concept and the feasibility of a 2-D photonic crystal based
on CLC. We demonstrated grating resonances and in particular the improvement of the
wavelength selectivity of a thin diffraction grating. We have shown some degree of tunability
provided by the voltage modulation and the specific interest of photonic CLC due to the use
of polarization as a control parameter to switch from 1-D to 2-D photonic crystal behaviour.
The future improvements on the functionality of 2-D photonic crystal lies, in our view, on
holographic structuring approach. It is theoretically possible to generate a 1-D transmission
grating by polymerization of a suitable monomer with a periodic interference pattern (two
beam interferences). Such a composite would have a certain degree of tunability through the
application of electric field and the polarization dependence would provide another control
possibility, however the recorded grating will be fixed and the photonic crystal would be only
partially reconfigurable, compared to the first option with electric field control.
The main issue in CLC holographic structuring is the CLC mixture engineering, as the
monomer that one would use should be compatible with the chemical structure of the
cholesteric liquid crystal. The rate of polymerization should be finely controlled in order to
avoid the distortions of the CLC planar structure. The investigations and attempts that we
performed with available materials we own, failed due to the incompatibility of CLC with the
monomer and the initiator necessary for polymerization.
In a recent work published in October 2007 [11] , the feasibility of holographic structuring of
CLC was demonstrated with the use of UV laser, the monomer RM257 and initiator Igracure
78
651. The same monomer is compatible with CLC that we used for our studies and the
experimental protocol suggested in the article can be adapted to our needs too. The main
requirement is the UV laser suitable for holography, which is not available presently in the
optics laboratory.
The issue of the homogeneity of grating modulation can be solved in principle by using
photorefractive effect. One can imagine that the second modulation in CLC is induced by the
charge-space field due to the photorefractive effect. However, in our view the technical
difficulties for practical application of photorefractive effect even in pure LC or LC – polymer
composites. The use of CLC for photorefractive material would add more technical problems,
such as chemical compatibility, problems with application of electric field, etc. In other
words, at this stage it is unclear if photorefractive effect in CLC can be observed and can have
a practical application.
79
III.6 Literature for Chapter III:
[1] Chi-Lun Ting Tsung-Hsien Lin, Chi-Chang Liao,Andy Y. G. Fuh, “Optical simulation of
cholesteric liquid crystal displays using the finite-difference time-domain method”, 2006,
Vol. 14, No. 12 , OPTICS EXPRESS 5594
[2] Z. Ge, et al. Comprehensive Three-Dimensional Dynamic Modeling of Liquid Crystal
Devices Using Finite Element Method, Journal of display technolgies, vol 1., No2,
December 2005
[3]
http://www.autronic-melchers.com/index.php?product=3
AUTRONIC-MELCHERS
GmbH's (online), Modeling tool for Chiral Nematic (Cholesteric) Liquid Crystalline
medium with anisotropic elastic, dielectric and optical properties.
[4]
A. Denisov and J.- L. de Bougrenet de la Tocnaye, "Resonant gratings in planar
Grandjean cholesteric composite liquid crystals", Applied Optics, 46, 6680, (2007)
[5] A. Denisov and J.- L. de Bougrenet de la Tocnaye, “Photonic crystals based on
Cholesteric Liquid Crystals”. Molecular Crystals and Liquid Crystals, 494(01), pp. 179 –
186 (2008), Proceedings of the 9th European Conference on Liquid Crystals.
[6] Q. He, I. Zaquine, A Maruani, S. Massenot, R. Chevallier and R. Frey, “Band-edgeinduced Bragg diffraction in 2D photonic crystals”, Optics Letters 31, 1184-1186 (2006).
[7] R. T. Pogue, R. L. Sutherland, M. G. Schmitt, L. V. Natarajan, S. A. Siwecki, V. P .
Tondiglia, and T. J. Bunning, "Electrically Switchable Bragg Gratings from Liquid
Crystal/Polymer Composites," Appl. Spectrosc. 54, 12A-28A (2000)
[8] R. Sutherland, V. Tondiglia, L. Natarajan, S. Chandra, D. Tomlin, and T. Bunning,
"Switchable orthorhombic F photonic crystals formed by holographic polymerizationinduced phase separation of liquid crystal," Opt. Express 10, 1074-1082 (2002)
[9] J-L. Kaiser, R. Chevallier, J.-L. de Bougrenet de la Tocnaye, H. Xianyu, and G. P.
Crawford, "Chirped Switchable Reflection Grating in Holographic Polymer-Dispersed
Liquid Crystal for Spectral Flattening in Free-Space Optical Communication Systems,"
Appl. Opt. 43, 5996-6000 (2004)
[10] J.-L. Kaiser, “Study of the polymer - liquid crystal composite materials: applications for
the devices for optical telecommunications and switchable holography. ” PhD, University
of Rennes and ENST Bretagne, May 11 , 2004. (in French)
[11] E. Beckel; L. Natarajan; V. Tondiglia; R. Sutherland; T. Bunning, “Electro-optical
properties of holographically patterned polymer-stabilized cholesteric liquid crystals“,
Liquid Crystals, 34, 1151-1158, (2007)
80
Chapter IV
Chapter IV: Photorefractive LC-polymer
composites.
IV.1 Introduction to photorefractive effect in LC-polymer
composites.
The photorefractive effect in inorganic matter was first observed in the mid-60s [1], since then
there were extensive studies on these crystalline materials such as LiNbO3, LiTaO3 BSO (see
the review [2]). The main disadvantage of these materials was the low index modulation and
as a result a low magnitude of the effect obtained under large applied electric fields..
Another topical domain on photorefractive researches opened with the discovery of the
photorefractive effect in organic materials. It was observed in polymers in 1991 [3] and later
in liquid crystals in 1994 [4, 5]. The magnitude of the effect was larger in both cases
compared to the inorganic matter. In 1997 LC- polymer composites were introduced [6, 7].
The mechanism of photorefractive effect involves in all these materials three phenomena:
1. Charge generation under the illumination and charge migration.
2. Local photo induced charge field generation.
3. Change of optical properties due to electro-optical effect or molecular reorientation.
81
Figure 4.1. The charges are generated, so that the local electric field is shifted w.r. to the light
field. Application of an external electric field in most cases is necessary to amplify the effect.
The physics on each of these three stages is different for all three types of materials: inorganic
crystals, conductive polymers and LC. The difference results in the different photorefractive
responses and different limitations for possible applications. For each particular application, a
material should be chosen, depending on the application requirements.
IV.1.1 Organic Photorefractive materials.
Organic photorefractive materials are highly promising for future applications. Since their
discovery, the properties of such materials were greatly improved [8-21] (see the review
[17]). However a lot of work is needed before they would be suitable for a commercial
application. Currently, several groups are improving the properties of organic photorefractive
materials, trying to lower the requirement for the laser beam intensity which is used for the
experiments, increase the index modulation, lower the applied electric field, etc.
Organic photorefractive materials can be separated into two main groups on the basis of the
mechanism of the charge generation. In the first group, there are liquid crystal based
materials, where the charge separation process goes through the complex formation between
the photosynthesizing molecules and solvent [4, 9]. In the second group, there are conducting
polymer based materials, where the charge separation is due to the interaction between the
photosynthesizing molecules and the conducting polymer [3, 8].
82
Liquid crystal based materials have the advantage of a large index modulation under low
applied voltages. Diffraction efficiency of 10-30% was observed for applied voltages of ~0,1
V/µm and writing beam intensities of ~1 mW/cm2. Unfortunately such materials show high
diffraction efficiency (~30%) only in a thin grating regime, when the grating period  X  2L
is two times larger than the cell thickness [9, 10, 13, 14].
Polymer based materials, require application of large external field ~20-50 V/µm in order to
obtain high diffraction efficiency. The advantage of such materials is the possibility of writing
thick gratings with the periods of ~1 µm and high diffraction efficiency [3, 21].
The properties of each type of materials can be improved in some respect by making a
polymer-LC composite. The properties of LC based materials are improved by adding the
inert polymer network, which does not change the charge generating mechanism, whereas
improving the resolution or endowding the material with memory [6, 15, 18-20]. The
properties of polymer based materials can be improved by adding to them some LC. In this
approach LC is used to increase the effective index modulation as it reorients readily under
applied electric field, whereas the charge generation mechanism is not impacted by the
presence of LC droplets or domains [7, 16]. These photorefractive polymer-LC composites
show some advantages in comparison to ‘parent’ materials, but they have also drawbacks. In
many cases they are more difficult to manufacture; they also exhibit unwanted side effects,
such as an increase in scattering.
Presently, it is hard to say which direction in material development would lead to a successful
application. For our research, we have chosen a material which was close to our domain of
expertise: namely polymer – LC composite with the charge generation mechanism of the first
type, i.e. due to the interaction between the photosensitive molecules and LC. Polymer
network in this case is an inert one. This direction started with the work of H. Ono and N.
Kawatsuki [6], and continued in their subsequent contributions [15, 18, 19].
Tuneable photonic crystals based on photorefractive effect.
On the basis of photorefractive media, one can develop tuneable photonic crystals. One
dimensional tuneable photonic crystal can be made, simply by changing the period of
83
interference pattern. This would results in a different period of space-charge field modulation
and different period of 1-D index modulation.
Two dimensional photonic crystals can be made similarly to the methods described in Chapter
I, by using several beams interference, leading to 2-D space-charge field. Another way is to
make 2-D photonic crystal in two step process. On the first stage, a one dimensional fixed
grating is made in holographic PDLC. On the second stage, due to the presence of a
photorefractive mechanism, a second grating is induced, with a period that can be tuned by an
external light field.
Even with existing photorefractive materials, some of these approaches can be realised in
principle. The main problem is to develop a tuneable photonic crystal suitable for application,
and this task requires a lot of material engineering research in organic photorefractive
compounds. The requirements for the successful application such as low cost, reliability, high
efficiency are still not reached for the organic photorefractive materials.
In the following sections, we present a study of one particular polymer-LC composite, which
exhibits photorefractive effect. We show how its properties can be improved and we propose
a direction for the future work, which can lead, in our view, to substantial improvements in
material properties.
IV.1.2 Charge generation mechanism in LC.
As we mentioned previously, photorefractive effect in LC can be observed with a low applied
electric field. In the particular case of a Methyl Red dye [15], the photorefractive effect is
observed without application of external dc field. It means that the charge separation process
does not require application of large electric fields.
Direct photo-ionization of the media by visible light is impossible and requires much higher
energies, the energy of the photon at 515 nm is ~2,4 eV and the first ionization potential for
typical organic molecules are ~10 eV or higher. An indirect process which results in the
generation of ions was proposed in [4], goes through the formation of a chemical complex,
that can dissociate into two neutral molecules, or into two ions. Later this mechanism was
confirmed in [10], where a complex was formed between electron donor and acceptor
molecules added to LC.
84
For the observation of photorefractive effect, low molecular mass nematic LC is doped with
the photo-synthesizer molecules such as TNF, fullerene or laser dyes such as Methyl Red,
Rhodamine 6G. A common feature of all these molecules is the existence of a long living
excited state, such as a triplete state in case of a fullerene:
h
1
3
C 60 
C 60
 C 60
(4.1)
3
The excited molecule AT* (in the case of fullerene AT*  C 60
), during its lifetime can interact
with many molecules of the solvant and form a chemical complex, which can dissociate in
two channels as it is illustrated by (4.2):

A 
A*  AT*


AT*  S  A S   A S    f
*
(4.2)
A  S  A S   A  S 
where S – molecule of the solvent, and A is the photo-synthesizer. The probabilities of each
channel depend on the specific properties of the molecules and intermolecular interaction in
the mixture. Dissociation of the A  S  complex has a lower probability for ion channel, which
can be estimated as [4] :
W A
where R and
2
 Ec 
, Ec  e
 exp  
WA
 0 R
 k BT 
(4.3)
Ec are equilibrium distance and energy between the ions, W A ,WA- –
probabilities of complex dissociation in ionic and neutral channel. If we assume that the
concentration of ions is much smaller than the concentration non-ionized molecules
: n   n   n 0 , we can write the equation for the ion generation and recombination balance
as:
n 
 I  n  n 
t
(4.4)
where α and γ are constants, that depend on the details of the charge generation and
recombination process, and I is the light intensity. The equilibrium solution for (4.4) is
n   I , which gives the square of intensity proportionality for the conductivity [4]:

2D  e 2 
n  I
k BT
(4.5)
85
D  is the average diffusion constants for positive and negative ions.
The square root dependence of the conductivity on the light field intensity was observed in
original publication [4].
IV.1.3 Space-charge field formation in LC.
If one applies to a LC doped with charge-generating molecules a periodically modulated light
field:
I  I 0 1  m sin qx 
(4.6)
where q is the grating wave-vector q  2  X , m and I 0 are constants, it can be shown [4]
that a space-charge field appears, that can be written under some approximations as:
 mk T

0
E ph  E ph
cosqx    B qv
   D
 2e

 cosqx 

(4.7)
where k B is the Boltzman constant,  the photo-conductivity,  D the dark state

conductivity, v  D   D 
 D



 D  , with D , D

diffusion speeds of negative and
positive ions and q the grating wave vector. It should be noted that the local electric field is
shifted by π/2 with respect to the light field.
One can expect that, periodical local space-charge field (4.7) would result in the reorientation
of LC directors and corresponding to the modulation of the refraction index of the media. The
real picture is more complex. First, a larger value of the effect is observed under the
application of an external dc electric field in a slanted geometry as it is shown on figure 4.2.
This amplification is explained in [4], as the combined effect of the external field and the
space-charge field. Second, it was shown by I.C. Khoo [9] that there are other contributions
to the nematic reorientation other than (4.7). Namely, the space-charge field arising from the
dc conductivity anisotropy (Carr-Helfrich effect [22].). It was also shown that a permanent
component appears, which is “due to a large and irreversible perturbation of the surface
director axis alignment by the current and nematic f lows under the prolonged application of
the dc fields” [9].
86
Figure 4.2. Periodic light field is created inside a LC cell by the interference of the two
coherent beams I1 and I2. A constant electric field Vdc is applied to the cell. The cell normal
makes an angle α with respect to the bisector of the beams I1 and I2.
More recent investigations introduced some doubts on the description proposed by previous
authors, as it was shown [12] that to a large degree, the nematic reorientation is caused by the
surface reorientation. It means that the photorefractive grating that appears in LC is probably
mainly due to changes in surface alignment.
In summary, we understand qualitatively the main steps of the photorefractive effect in LC:
ion production through the chemical complex formation, charge separation under applied
electric field and reorientation of the nematic directors. On the other hand a quantitative
description is lacking. Overall, in my opinion, the question is not completely solved, but it is
likely that several mechanisms overlap and small volume effects are masked by a strong
surface one, due to the nematic surface distortions.
IV.2 Polymer – LC composites.
In comparison to LC, where experimental and theoretical works provided a qualitative
description of the phenomenon, the polymer – LC composites, with an inert polymer matrix,
87
are much less developed both from experimental and theoretical points of view. This is due to
a higher complexity of the involved phenomenon, as it is hard to describe the interaction
between the polymer matrix, LC and ions forming the space charge.
It is assumed, in general, that due to the inert nature of the polymer network, the charge
generation process is governed by the same mechanism as in pure LC. In our view, it can be
valid only as a first approximation, because in such composites larger electric fields ~10
V/µm can be used, and it can impact the charge generation process, as the ionic channel for
dissociation (see (4,2)) can become more favourable, due to a gain in Coulomb energy in
external electric field. The space-charge formation theory for LC is not valid at all, and the
expression (4.7) should be modified to take into account the influence of the polymer
network, as it would change strongly the diffusion of ions. Such effects were observed in the
early work [6], where strong memory effect was observed and later in [15], where the general
behaviour was different from pure LC. As for the reorientation of LC in polymer-LC
composites, one can expect a very different behaviour from the one observed in LC. Nematic
flows would be absent due to the effect of the polymer network, and the formation of
photorefractive grating has to be considered in a new way.
Whereas there is a lack of experimental evidence and theoretical modelling for a good
understanding of the photorefractive effect in LC-polymer composites, there were some
experimental indications that the presence of the polymer network can bring important
improvements in the characteristics of such composites. For example, a memory effect can be
important for some applications, and some improvement in resolution was observed [6, 15,
17-19].
The possibility of improvement in material properties in comparison to LC as well as our
previous experience in polymer-LC composites motivated our choice of the material for
photorefractive effect studies. A relative ease in sample preparation in comparison to some
advanced chemistry such as described in [16] has influenced our choice too.
IV.2.1 Material choice.
As the basic material for our studies we took the LC-Polymer composite previously studied
by the Japanese group lead by H. Ono and N. Kawatsuki [6, 15]. Actually, one of the first
88
observations of photorefractive effect in Polymer Stabilized Liquid Crystal (PSLC) was
reported by this group in [6]. The material they used contained low molecular mass LC E44 in
[6] and E7 in [15], Polymethyl Methacrylate (PMMA) polymer and was doped with a small
amount of fullerene C60. It is comparatively easy to prepare this composite, as all the
compounds can be mixed into a homogeneous solution at higher temperatures. This LCpolymer composite corresponds to the composites with inert polymer network, as PMMA is a
non-conducting polymer.
For the first time the observation of photorefractive effect in PSLC (or PDLC) was reported in
[6] and later the effect of different concentrations of polymer and different droplet or domain
sizes formed during the phase separation was investigated in [15]. The concentration of
fullerene was not changed and always stayed at ~0.05%. This is due to the low solubility of
the C60 in organic solvents.
On the other hand the amount of charge generating molecules is an important parameter for
the photorefractive response. It is clear, from the theoretical view point, that an increase in
charge generating molecules will increase the absorption and result in a larger production of
ions. It is also confirmed experimentally in pure LC. High diffraction efficiency under low
external light fields observed in Methyl Red doped LC in [14] was attributed to the increase in
charge generator concentration.
We found that, for the use in organic electronics, specific molecules based on fullerenes were
synthesized [20]. These are so called, functionalized fullerenes such as Phenyl–C61-Butyric–
Acid–Methyl–Ester ([60]PCBM ), see figure 4.3 for its chemical formula. This functionalized
fullerene was developed for greater solubility in organic solvents, whereas preserving
electronic and optical properties of the parent compound C60.
89
Figure 4.3. Chemical formulas of the chemicals used in our studies, [60]PCBM, PMMA, E7.
The functionalized fullerenes were not used as photosynthesizing molecules in LC before our
studies and it was not clear if we would observe the increase in solubility. There was a high
probability, that it can be dissolved in higher concentration than C60 in LC and LC-polymer
composites, judging by its higher (2 orders of magnitude) solubility in organic solvents such
as toluene.
On the basis of our understanding of the photorefractive effect in LC-polymer composites and
our expectation of the improved performance of functionalized fullerene as a charge
generator, we purchased the following chemicals: E7 liquid crystal from Merck; PMMA with
different molecular weight of 15,000, 120,000 and 300,000 from Sigma Aldrich; different
fullerenes C60, C70 , [60]PCBM and [70]PCBM from Nano-C.
IV.2.2 Material description.
We tested various compositions of LC, PMMA and nano-particles. The solubility studies we
made in two steps. On the first step, we observed the behaviour of the mixture during several
days after mixing to check, if phase separation appeared. On the second stage we filled 20µm
cells with the mixtures and observed the cells under the microscope.
The cells for polymer-LC composite had no surface treatments, whereas the cells for LC
doped with fullerenes had a surface treatment with an homeotropic alignment. It was obtained
90
by spin-coating of a commercial ZLI PA 334 (Merck) with spin-coating parameters: t=30s,
V=3000rpm, a=3500rot/rpm. Homeotropic alignment for the LC based mixtures allowed us to
make a direct comparison with the previous works [4, 5, 9, 14], where the same LC alignment
was used.
PMMA + E7.
PMMA can be mixed with LC to form a homogeneous solution at temperature ~150°C for all
molecular masses that were available to us, for a polymer concentration lower than 20%.
After cooling down to room temperature ~20°C LC and polymer phase separate, forming a
Polymer Stabilized Liquid Crystal (PSLC). The mixture is transparent at high temperature,
whereas it becomes scattering after the phase separation due to the mismatch between the
refractive index of E7 and PMMA.
The E7 – PMMA mixtures can be filled into 20 µm cells by capillarity at high temperatures
~150°C. For the PMMA with molecular mass of 300,000 the filling by capillarity had to be
carried out at temperature ~180°C for a concentration of 10% (by mass), and the process
slowed down noticeably after filling to about 7mm. Afterwards the LC evaporated faster than
the filling is completed. Due to such a difficulty it results in additional doubts about the
reproducibility of the process. Therefore, we preferred working with lower molecular mass
polymer, where the filling process proceeded easier.
The size of the LC domains, we observed after cooling the filled cells depended on the
molecular mass. For the PMMA with low molecular mass of 15,000, the LC domain size, as
observed under the polarizing microscope, approached ~20 µm. For the PMMA with
molecular mass of 120,000 the domains were significantly smaller ~2 µm and we choose to
continue working with the latter.
The size of domains depends also on the cooling process, for the slow cooling process, the
domains were larger than for the faster one, similarly to the description given the previous
studies [15].
Solubility.
We studied solubility of fullerene derivatives in pure E7 and in E7 – PMMA mixture.
91
The fullerene derivatives [60]PCBM and [70]PCBM could be dissolved in E7 in higher
concentration than C60. Especially high concentration ~1% could be obtained, when the
mixture was heated to ~100 °C, during stirring. Unfortunately, these high concentrations were
not stable and resulted in the aggregation of nano-particles after cooling the solution. Stable
concentrations, with no aggregation of fullerenes were observed corresponding to the values
of ~0.3-0,4 %, which is an order of magnitude larger than the maximum possible
concentration for C60 ~0.05 %.
In contrast to pure E7, the mixture of E7+PMMA allowed us to obtain higher concentrations
of fullerenes without aggregation. We observed no aggregation with a concentration of ~2%
of [60]PCBM in the mixture of 88% of E7 + 10 % of PMMA + 2% of [60]PCBM. We explain
these high concentrations by the phase separated morphology which restricts clustering of
[60]PCBM.
In the following section, we present the summary of our experimental observations for three
mixtures: M1, M2, M3. Mixture M1 made up of E7 : PMMA : [60]PCBM. For a direct
comparison, we prepared a mixture M2 made up of E7: PMMA : C60 (proportions are given in
table 1). The C60 concentration was not controlled and corresponded to the maximum
solubility achievable at 150 °C. To compare with a pure LC case we prepared a mixture M3,
made up of low molecular mass nematic LC and fullerene. The highest diffraction efficiency
among the pure LC mixtures that we prepared was observed for a mixture M3, made up of E7
: [60]PCBM : C70 (concentrations given in table 1).
Table 4.1. Mixtures composition.
LC content
Polymer content
Fullerene content
M1
88%
of E7
10% of PMMA
2%
of [60]PCBM
M2
90%
of E7
10% of PMMA
0,05% of C60
M3
99,6% of E7
0%
0,4% of (C70 +[60]PCBM)
92
Comparisons between M1 and M2 show the effect of the high concentration of fullerene for
the same concentration of polymer and LC. Comparisons between M1 and M3 show the effect
of the polymer network.
It should be noticed that the mixtures similar in composition to M2 were excessively studied
in [6, 15], which gave us a good basis for the investigation of photorefractive effect and the
possibility of direct comparison. Mixtures similar to M3 were studied in [4, 9, 12, 14] and our
observations fit well with the previously reported results. The main purpose of displaying the
results for pure LC mixture M3 is the possibility of a direct comparison which has not been
done previously due to differences in experimental conditions of the previously reported
observations.
IV.3 Experimental results.
Overall our experimental results are in accordance with what has been published in the
literature. New behaviour appears only for the M1 mixture and is attributed to the increased
concentration of fullerene and the effect of the polymer network, which was not observed
previously at lower concentration of charge generators.
IV.3.1 Diffraction efficiency measurements.
Photorefractive gratings were recorded with an Ar+ laser at 514 nm, the linearly polarized
beam was enlarged to a diameter size of 8 mm and split into two beams of equal intensity.
Diffraction efficiency was measured with a linearly polarized beam of He-Ne laser (632.8
nm). The intensity of 0.5 mW on a 1 mm diameter was lowered so that it cannot influence the
grating formation. Relatively large writing beams simplify greatly the experimental set-up as
it became easier to have a large recording surface. The measurement geometry is shown on
figures 4.4 – 4.6. Figure 4.4 shows the sample, which makes an angle α between normal and
93
the bisector of writing beams I1 and I2. Angle β between the beams defines the grating period,
according to
X 
G

 G
2 sin    
(4.8)
 2
where G =514 nm is the writing wavelength of the Ar+ laser. Angle γ gives the incidence
angle of the He-Ne laser onto the grating. Intensity of the first diffraction order of He-Ne laser
was measured with photo detector “Newport”.
Figure 4.4 Scheme of the measurement geometry. The diffraction of the He-Ne (red) beam on
the photorefractive grating is measured. Angles α, β and γ can be changed over a wide range.
In practice, α=45°, γ~5°.
The photograph of the actual optical set-up is shown on the figure 4.5. By changing the
position and orientation of the sample on the table, as well as the positions of the mirrors, the
angles α, β and γ can be chosen over a wide range according to our needs.
94
Figure 4.5. View of the measurement set-up. The cell holder can be moved on the bench,
adjusted in height, and rotated so that the angle α (defined on figure 4.4) can be controlled
with an accuracy of ~1°. The position of the mirrors and beam splitter cubes can also be
adjusted so that angles β and γ can have predefined values.
The accessible periods with our set-up shown on figure 4.5. are mainly restricted by the
values of β. In the actual geometry, with the restrictions of the bench length and the distance
between the beam splitter and the mirror, the angle β cannot be made smaller than β ~1/20
radians, for a period ΛX~10 µm.
For the smaller angles β the set-up was modified, by adding an additional beam splitter and a
mirror, as it is shown on figure 4.6. In this geometry very small angles β between the writing
beams were possible. For the maximum size, the restrictions were at about ~1/15 radians,
ΛX~8 µm, so using one of these set-ups we could make the measurements over the range of
periods 1 µm< ΛX <100 µm.
95
Figure 4.6. The geometry shown on figure 4.5, and the scheme depicted on the right is not
suitable for the small angle interferences (less than β~1/20 radians, or ΛX~10 µm). For
smaller angles a modified set-up (Mach-Zehnder like) is used, depicted on the left.
The intensities of the writing beams were measured before they reached the sample. The high
intensity power of the Ar+ laser available in the laboratory (~2.6 Watt in a single-mode
regime) allowed us to change the writing beam intensity over a wide range.
For the periods ΛX>5µm, diffraction for the He-Ne is in the Raman-Nath regime, as it can be
estimated from the value of
Q
2L
n2X
(4.9)
which characterizes the transition from thin to thick gratings [23]. The thick grating
corresponds to Q>10, and for the cell thickness L=20 µm, is possible only for ΛX<2 µm. For
the grating period ΛX>5 µm, which correspond to the case of a thin grating, the diffraction
efficiency depends weakly on the variation of γ, near the Bragg angle. For the measurements
with the small grating periods: 2.5 µm and 1µm, γ was adjusted for the maximum diffraction

efficiency, which, according to theory, is at the Bragg incidence angle: sin   R
where R =633 nm is the reading wavelength, and     
2
2 X
,
is the incidence angle. In such
experimental condition, we measured the maximum diffraction efficiency for the He-Ne laser.
M3 sample absorption at 514 nm and 633 nm was 36% and 9% respectively. Samples were
set-up so that the angle between the sample normal and bisector of the recording beams was
96
45° (angle α on the figure 4.4). The diffraction efficiency for He-Ne laser depends on the
polarization, reaching a maximum value when oriented parallel to the grating and decreasing
to 0 when perpendicular to it. No diffraction occurred in absence of applied dc electric field,
or when angles between the bisector of writing beams and sample normal approached 0.
These observations are consistent with the orientational photorefractive effect and pure index
gratings observed in [4, 6, 9, 15].
IV.3.2 Photocurrent measurement.
Photoconductivity was measured (dc current) by a pico-Ampere-meter from Keithley (model
485). The dark photocurrent was measured under no illumination and the photocurrent
measured by illuminating the sample with an Ar+ laser at 514 nm, with a 8 mm beam
diameter. Results for M1 and M3 are displayed Figure 4.7, where the photocurrent /dark
current ratio for the same sample is displayed. Conductivity under constant electric field is
proportional to the photocurrent density J  E , therefore the photocurrent/dark current ratio
is  /  D , where  is the photo-conductivity and  D the dark state conductivity.
Photocurrent and diffraction efficiency measurements were performed for M1 with an applied
field of 10 V/µm. Dark current value at the same applied voltage and for the surface of 50
mm2 was equal to 3 µA. Photocurrent for M2 was difficult to measure due to its low value
and the high dark current value, probably due to the presence of impurities in commercial
products. High photocurrent values compared to M1 indicates an increase in charge
generation due to higher fullerene concentration. Dark current and photocurrent for M3 were
measured with an applied electric field of 0.2 V/µm. Dark photocurrent for a surface of 50
mm2 equals 40 nA. Photocurrent increases with an intensity increase, roughly in proportion to
the intensity square root  /  D  I (Figure 4.7), in accordance to previous observations
[4] and theoretical expectations (equation (4.5)) of
the equilibrium between quadratic
recombination of the charges and their generation, through the formation of a complex
between the excited photosensitive molecules and the solvent molecules [4].
97
Figure 4.7. Photocurrent dependence on light intensity, normalized to the dark current value.
M1 (square), applied field 10 V/µm, dark current 3 µA. M3 (circle), applied field 0.2 V/µm,
dark current density 20 nA/cm2. Continuous line is a fit  /  D  I . Cell thickness equals
20 µm for both mixtures.
IV.3.3 Diffraction efficiency vs intensity and grating period.
Diffraction efficiency is defined as the ratio of the first order diffraction beam and the


incoming beam intensities   I 1 I , where scattering and absorption losses have not been
subtracted from the incoming intensity. We estimated them to be about 30% by measuring the
ratio of the beam probe intensity before and after the sample, in absence of writing beams
under the applied dc field. Figure 4.8 shows a typical dependence of the diffraction efficiency
on the writing beam intensity for all mixtures. The diffraction intensity reaches saturation for
M1, whereas for M2 it is far from saturation for the used writing intensities. It should be
noticed that in [6, 15] a He-Ne laser was used for writing the gratings, with intensities of 4-5
W/cm2 and similar diffraction efficiencies, whereas for M1 the saturation was obtained for
writing intensities of about 20-30 mW/cm2, corresponding to a two order of magnitude
98
improvement. For thin gratings, the index modulation can be estimated from   nL   ,
2
where L is the grating thickness. Estimates from Figure 4.8 give values of n  3,5  10 3 ,
which fits well with the maximum index modulation reported in [15] n  3  10 3 . For M3,
we observe a linear increase in diffraction efficiency. Beam intensities used to record the
grating are lower than in [9], but an order of magnitude larger than in [14]. The diffraction
efficiency for M1 reaches the saturation before  /  D approaches unity (as it can be seen
on figure 4.7) , in contrast to M3, indicating some influence of the polymer network.
Figure 4.8. Probe beam diffraction efficiency dependence on the writing beam intensity sum.
M1 (square), (M2) triangle, (M3) circle. Grating periods: M1 = M2 = 8 µm, M3 = 20 µm,
applied field 10 V/µm for M1, M2, 0.2 V/µm for M3. Cell thickness = 20 µm. (M3 diffraction
efficiency at low grating period was too low for accurate measurements.)
We also measured the diffraction efficiency dependence on the grating period (Figure 4.9).
The 50 mW/cm2 writing beam intensity used for that measurement is larger than the
saturation value for the diffraction efficiency of M1 shown on Figure 4.8. For M3 at
intensities larger than 50 mW/cm2 higher diffraction efficiencies are observed, but the cut-off
grating period remains the same, which is enough to compare with M1. For M1 we observe a
99
diffraction efficiency plateau from 7µm to 40µm. For M2, the plateau is from 10 µm to 30
µm, similar to [15]. For M3 we observe a diffraction efficiency peak at  X  40µm with a
sharp cut-off at low grating periods and a smother one at larger periods, which fits well to the
theory and experiments [4, 5, 9, 10, 14]. The observed diffraction efficiency dependence on
grating period for M1 varies from what has been observed earlier for PSLC [6, 15], it also
differs from observations on pure LC. We clearly observe an improvement in diffraction
efficiency at low grating periods, which we attribute to the polymer network.
Figure 4.9. Probe beam diffraction efficiency dependence on grating period for a 20 µm
sample. Writing beam intensity 50 mW/cm2. Squares for M1, triangles for M2 and circles for
M3.
Our observation can be summarized as follows:
1. Qualitatively, our experimental results fit well to the previous work on LC and
polymer - LC composites.
2. We observe the effect of the larger concentration of fullerene, in larger index
modulation achieved at lower writing intensities. This fits well to the theoretical
100
expectations and is explained by the increased charge generation due to larger
solubility of [60]PCBM.
3. We observe the effect of polymer network in higher diffraction efficiency at small
grating periods, in comparison to pure LC.
IV.4 Explanations and restrictions.
The effect of polymer network can be observed as well in the increase of writing and
relaxation times: writing times to ~20s and relaxation times of about ~60s for M1. These
values should be compared to recording and relaxation times (in absence of writing beams)
which are typically observed in pure LC ~1s [4, 9, 14] (existence of fast ~1s components was
reported in PSLC too [15] ). This behaviour indicates the existence of a charge trapping
mechanism either on the interfaces separating LC domains or in the polymer network.
Comparison of photocurrent dependence on light intensity and diffraction efficiency (Figure
4.7 and 4.8) also show the polymer network influence, as the saturation in diffraction
efficiency occurred a long time before the photocurrent reaches the dark current value.
As we have seen previously (equation (4.7)) in the absence of a polymer network, the
electric field caused by charge separation can be written as:
 mk T

0
E ph  E ph
cosq    B qv
   D
 2e

 cosq 

k B is the Boltzman constant,  the photo-conductivity,  D the dark state conductivity,

v  D  D
 D



 D  , with D , D

diffusion speeds of negative and positive ions and
q the grating wave vector. For PSLC, the liquid crystal is reoriented under the combined
effect of external dc electric field and periodic electric field E ph . The higher the E ph , the
larger the LC director deviation from the external field direction. As noticed previously, the
writing intensity for which the diffraction efficiency saturation occurs for M1 (as shown
Figure 4.8, ~30 mW/cm2) is much lower than the intensity at which   d ~1 ~300 mW/cm2.
This means the maximum of the effective reorienting space-charge field is obtained at lower
photocurrent than it would be the case for electric fields given by (1). Such a discrepancy
101
confirms the existence of a trapping mechanism, due to the polymer network presence. We
can take into account this trapping mechanism, in a phenomenological way, by modifying:
qv




  qv
 CTR t ,  , q 
   d      d 

(4.10)
where CTR t ,  , q corresponds to the trapped charges and depends on the history, similar to
memory effects observed in liquids and polymers. We may rightfully think that the first term
reaches a steady state value much faster than the second. The amount of trapped charges
increases with time during the writing process to reach a saturation value, depending on the
specific interaction chemistry between LC, polymer and fullerenes and in lower degree to the
photocurrent  and grating period  X  1/ q . When the saturated value of CTR t ,  , q
does not depend on  , q , it corresponds to the approximation CTR t,  , q  CTR t  . If we
introduce this approximation into (4.7) assuming that CTR   qv    d  :
 mk T

mk BT

E ph   B qv
 CTR  cosq  
CTR  cosq 
   D
2e
 2e

(4.11)
one would observe a diffraction efficiency plateau, as shown on Figures 4.8 and 4.9. The
introduction of the memory function CTR t ,  , q enables us to explain a part of our
experimental observations. Accurate computations of the memory function CTR t ,  , q is
extremely difficult, even for simple cases of dense liquids requires numerical approach or
introduction of uncontrolled approximations.
IV.4.1 Larger thickness.
We have made some preliminary experiments with thicker cells. In case of M1 mixture we
observed an additional effect of the decrease in transmitted beam intensity with time. For the
first time we observed it, during the measurements of the diffraction efficiency, but later we
found the same effect with only one beam.
The simplest experiment that exhibits such an effect went as follows. A single beam from Ar+
laser is normally incident on the sample, with a thickness of 50 µm, with the M1 mixture,
102
with a 10 V/µm dc applied electric field. The intensity of the transmitted beam decreases,
with a time decay with an order of magnitude of about ~60sec.
Currently, we do not fully understand the origin of this phenomenon. A possible explanation
could be an accumulation of charges in the cell bulk, which creates a depolarizing electric
field. The effective electric field that aligns the LC domains decreases due to the depolarizing
field resulting in increased scattering. Due to the increased scattering the sample looses
transparency.
A possible solution to this problem, can be the use of a transparent PSLC material which does
not require the application of a large external dc field. If the LC domains, in the PSLC are
oriented in one direction, the accumulation of charges in the bulk would not result in
scattering and decreased transmission. Such tranparent materials have already been reported
in [18, 19], where specially designed polymers with mesogenic groups have been used to
form a transprent polymer-LC composite.
Direct picture recording.
In the large thickness samples we were able to record pictures in cells filled with M1 mixture
with a normal incidence of incoming light. The picture was projected on the sample of 50 µm
thickness with Ar+ laser and then ‘read’ with the He-Ne one. We also observed similar effect
in 20 µm samples, but it was more difficult to reproduce. Recorded pictures can be found in
the appendix on the light valve.
These experiments are on a preliminary stage, we observed the effect but we have not
investigated it in many details as it lied outside of the scope of this Ph.D. There are two
possible explanations of the observed phenomena. First possibility, the pictures are recorded
due to accumulation of charges in the illuminated areas and the larger scattering in these
areas. Second possibility, we assume that charges accumulated in the illuminated areas induce
depolarising field, which results in a smaller index modulation. If the sample is viewed under
crossed polarisers, one would observe different intensities of transmitted light in different
regions.
103
The determination of the precise mechanism of this effect would require additional
experiments. However, there is no doubt that this effect provides another proof of the memory
effect due to charge trapping by polymer network.
IV.4.2 Suggestion for increase in photorefractive effect efficiency.
Charge trapping mechanism offers a new insight for another way of using photorefractive
effect in PSLC. First, the external electric dc field is applied to PSLC and charges are trapped.
Second, the external field is removed and only the space-charge field operates. In such a case
LC would be reoriented more efficiently and the index modulation would be larger (Figure
4.10). In addition, this improves greatly the PSLC resolution, approaching the resolution of
photorefractive polymers, with the benefit of smaller applied voltages.
Figure 4.10. Phenomenological model for the diffraction efficiency increase mechanism via
charge trapping. Increase in refractive index modulation due to higher LC reorientation in
absence of external dc field (bottom figure). The local field is due to charges trapped in the
polymer network.
As one can see on Figure 4.9, we have recorded a grating with a ~1µm period with a
noticeable diffraction efficiency of ~2%. For transparent PSLC, without external dc field,
we could expect a higher diffraction efficiency when dc field is switched off. The proposed
approach requires the use of a transparent PSLC, because in the phase separated morphology
observed for M1 and M2, the composite highly scatters in absence of external electric field.
Such transparent PSLC can be made by using a technique described in [18,19] where the
polymer, used for stabilization, has a mesogenic side chain. Therefore, polymer and LC can
104
form an oriented transparent phase. Another possibility is to use a mesogenic monomer and
polymerize it in a nematic LC phase.
IV.4.3 Preliminary results on a new material.
As we have seen the transparent PSLC material can improve the performance of
photorefractive material in many ways. It will probably solve the issue related to the thickness
increase. It would require lower applied dc voltages. And finally it can operate in a new way
increasing the efficiency of diffraction in the absence of strong external dc field.
In our first attempt, we realized a transparent PSLC by mixing a nematic LC 5CB, a
mesogenic monomer RM257, a photo-initiator Igracure 651 and a photo-synthesizer
[60]PCBM with proportions 89.4%:10%:0,5%:0.1%. The mixture was filled into a 20 µm cell
and UV cured at 50°C with 10 mW/cm2 intensity. RM257 is a mesogenic diacrylate, which
we previously used for the stabilization of CLC. Charge generation process remains the same
as for M1 and is due to the interaction between LC and fullerene. Other ways in preparing
transparent PSLC are possible, such as described in [18, 19]. The important point is the
presence of the charge trapping mechanism in the material bulk due to the presence of the
polymer network.
In order to confirm the presence of the memory effect in this compound, we recorded a
grating at a ΛX=2.5 µm period under a 5 V/µm applied electric field, and a writing power of
50 mW/cm2. During the recording no diffraction of the He-Ne probe beam was observed.
After 30 s we removed the writing beam and the applied dc field. We observed a slowly
decaying grating with 4% efficiency. It confirmed the proposed operating way and the
existence of trapping mechanism in some PSLC. This mechanism operates differently in this
mixture, as we do not observe a noticeable diffraction during the writing stage. Additional
experiments are necessary for the optimization of this compound and establishing a working
model.
IV.5 Conclusion and suggestions.
We found a fullerene derivative [60]PCBM soluble in high concentration in Polymer-LC
composite, made of PMMA and E7. Solubility up to 0.5% was observed in pure LC as well.
Increase in fullerene concentration, operating as an efficient charge generator, resulted in an
105
increase in diffraction efficiency. We obtained PSLC efficiency improvements with respect to
previous work by a factor 10-100 depending on the writing intensity and grating periods. High
diffraction efficiency improvements have been observed in particular at small grating periods
with respect both to LC and similar polymer–LC composites investigated previously. A part
of the improvement could be attributed to an increase in charge generation, similar to what
has been observed earlier in pure LC [14]. Another part was attributed to the trapping
mechanism due to polymer network. On this basis, a new approach for designing high
efficiency Polymer-LC composites has been proposed and is currently investigated. The idea
is to record the grating by trapping the charges in the bulk, via the polymer network, in
presence of an external electric field and to read it without external applied field. In absence
of external electric fields, the media exhibits a higher index modulation, resulting in a higher
diffraction efficiency, especially at small grating periods.
The need for a transparent polymer – LC composite was also emphasized by the effect of the
attenuation observed at the thickness of 50µm for PSLC composites with phase separated
morphology and randomly oriented LC domains. We attributed the attenuation of the incident
laser beams to the formation of depolarizing electric field in the bulk, which increases the
scattering and reduces the transmission of the incident beam.
The practical application such as 1D and 2D photonic crystal would require additional
improvement in material properties. In our view, the use of transparent PSLC and optimizing
the memory effect can provide a material suitable for application. The advantage of this
solution is a better resolution than for pure LC materials and lower applied voltages in
comparison to conducting polymer based materials. According to this point, high diffraction
efficiency could be obtained, if the issue related to the thickness increase would be solved.
Another possibility for practical applications, which uses memory effect in investigated
composites, is the realisation of light valve. The principle demonstration is presented in the
Appendix 3. The operating mechanism is yet to be determined. The understanding of the
mode of operating and improvement in the recording time, contrast, etc would require a
separate study.
106
IV.6 Literature for Chapter IV.
[1] A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and
K. Nassau, "Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,"
Appl. Phys. Lett. 9, 72–74 (1966).
[2] P. Gunter and J. – P. Huignard. “Photorefractive materials and their application”,
(Springer - Verlag, Berlin, 1989), Vol. I. and II.
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Effect in a Polymer” Phys. Rev. Lett. 66, 1846, (1991)
[4] E. V. Rudenko and A. V. Sukhov, “Photoinduced electroconductivity and photorefraction
in nematic”, JETP Lett. 59 , 142-146, (1994)
[5] I. C. Khoo, H. Li and Y. Liang, “Observation of orientational photorefractive effects in
nematic liquid crystals” Opt. Lett. 19, 1723, (1994)
[6] H. Ono, N. Kawatsuki, “Orientational photorefractive effects observed in polymerdispersed liquid crystals," Opt. Lett. 22, 1144-1146 (1997).
[7] A. Golemme, B.L. Volodin, B. Kippelen, N. Peyghambarian, "Photorefractive polymerdispersed liquid crystals," Opt. Lett. 22, 1226-1228 (1997)
[8] J. S. Schildkraut and A. V. Buettner, "Theory and simulation of the formation and erasure
of space-charge gratings in photoconductive polymers," J. Appl. Phys. 72, 1888-1893
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[9] I. C. Khoo, "Holographic grating formation in dye- and fullerene C60-doped nematic
liquid-crystal film," Opt. Lett. 20, 2137-2139 (1995)
[10] G.P. Wiederrecht, B.A. Yoon, M.R. Wasielewski, “High Photorefractive Gain in
Nematic Liquid Crystals Doped with Electron Donor and Acceptor Molecules”, Science
270, 1794-1797 (1995).
[11] P. Pagliusi and G. Cipparrone, “Surface-induced photorefractive-like effect in pure liquid
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[13] W. Lee and C.-S. Chiu, "Observation of self-diffraction by gratings in nematic liquid
crystals doped with carbon nanotubes," Opt. Lett. 26, 521-523 (2001)
107
[14] I. C. Khoo, S. Slussarenko, B. D. Guenther, Min-Yi Shih, P. Chen, and W. V. Wood,
"Optically induced space-charge fields, dc voltage, and extraordinarily large nonlinearity in
dye-doped nematic liquid crystals," Opt. Lett. 23, 253-255 (1998)
[15] H. Ono, H. Shimokawaa, A. Emotoa, N. Kawatsukib, “Effects of droplet size on
photorefractive properties of polymer dispersed liquid crystals”, Polymer, 44, 7971–7978,
(2003)
[16] J. G. Winiarz and P. N. Prasad, "Photorefractive inorganic organic polymer-dispersed
liquid-crystal nanocomposite photosensitized with cadmium sulfide quantum dots," Opt.
Lett. 27, 1330-1332 (2002)
[17] Wiederrecht GP, “Photorefractive Liquid Crystals”, Annual Revue of Materials
Research, 31, 139-169, (2001)
[18] H. Ono, A. Hanazawa, T. Kawamura, H. Norisada, N. Kawatsuki, “Response
characteristics of high-performance photorefractive mesogenic composites”, Journal of
Applied Physics, 86, 1785-1790, (1999)
[19] N. Kawatsuki, H. Norisada, T. Yamamoto, H. Ono and A. Emoto, “Photorefractivity in
polymer dissolved liquid crystal composites composed of low-molecular-weight nematic
liquid crystals and copolymer comprising mesogenic side groups”, Science and
Technology of Advanced Materials, 6, 158-164 (2005).
[20] J.C. Hummelen, G. Yu., J. Gao, F. Wudl, A.J. Heeger, “Polymer Photovoltaic Cells:
Enhanced Efficiencies via a Network of Internal Donor-Acceptor Heterojunctions”,
Science, 270, 1789-1791, (1995).
[21] M. Elarp, J. Thomas, G. Li, S. Tay, A. Schulzgen, R.A. Norwood and N. Peyghambarian,
M. Yamomoto, “Photrefractive polymer device with video-rate response time operating at
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108
Chapter V
Chapter V: Soft-matter micro-structuring.
Most of the original contributions of this work focused finally on micro-structuring of soft
matter, using liquid crystals as reconfigurable medium. The use of liquid crystals as the base
material is interesting due to their large electro-optic effect under low voltages. However, we
have seen that their micro-structuring, over large sizes and thickness is a complex topic,
involving several technological, chemical and physical aspects. We will rapidly discuss in this
chapter how all these parameters interact in practice and indicate possible research trends for
future works. Before that we will emphasize the role of some critical features in soft matter
structuring:
1. Mixture compatibility and solubility:
.
In most cases only qualitative guidelines are available for material structuring. This is a
general problem in condensed matter research, which is due to high complexity of a many
body problem is statistical physics. The corresponding equations cannot be solved
analytically, and require the use of numerical methods, such as molecular dynamic simulation.
Such a simulation, at the present stage, can be performed only for a small numbers of simple
molecules, such as it is the case for simple liquids, or for a single big molecule, for example in
a protein folding problem.
109
Even in relatively simple cases, such as the solubility of one compound in another, it cannot
be treated from the first principle and require experimental approach. The only choice in this
situation is to proceed by analogies. In our work for instance, we assumed that fullerene
derivatives would have a higher solubility in liquid crystal as they can be dissolved in higher
concentration in organic solvent, in comparison to C60.
The actual situation with the mixture compatibilities is far from being satisfying, and a more
methodological approach would be of high interest for future researches. If one could design a
composite with an analytical approach, a lot of experimental resources could have been saved.
At present, in my view, mixture engineering looks like a trial and error approach with a very
few guidelines.
2. Chemistry engineering.
We have not done any original chemical engineering in our work. We used the chemicals
synthesized and used by other people. However, a chemical engineering is necessary for a
successful material development. Synthesize molecules with specific properties could add a
lot of flexibility for soft matter structuring.
For instance in our work, we used RM257+ Igracure 651 as an initiator to stabilize the CLC.
We were fortunate that the monomer was compatible with the liquid crystal. Unfortunately,
the polymerization can be initiated only by UV-light, which required a UV laser for
holographic structuring. If an initiator of polymerization sensible to visible light would be
available, we could make that structuring at 514 nm, using the equipment available in the
laboratory. The synthesis of other initiators or other mesogenic monomers could have been
very useful in the future research, increasing the structuring possibilities.
Another possibility for a chemical engineering are the functionalized fullerenes. It is probably
possible to make functionalized fullerenes with a mesogenic side chain, which would be even
more compatible with LC. Once again it requires a complete molecular engineering.
110
3. Solve a combinatory issue:
A general issue in structuring soft matter research is the choice of a direction for experiments.
In most cases, there are a lot of parameters that can be changed and one needs to decide which
are the most critical according to some targeted optical properties to find the right
combination of them which produces the best result. It cannot be done by checking all
possible options, due to the huge combinatory. Therefore, a guideline is necessary, one needs
a qualitative model, which identifies the most important factors and their interactions.
Another possible approach is to search for specific phenomenon, which is qualitatively
possible. For example, polymer network can be used for a stabilization of a specific phase, so
that the properties of one phase can be extended into another. In our work, for instance, we
wanted first to investigate how to structure CLC Grandjean planar structure to take advantage
of this intrinsic phase to make photonics crystals, second we would investigate the effect of
charge generator (fullerene) increase on the photorefractive effect in LC- polymer composite.
From these two directions we derive the following research trends.
V.1 CLC structuring.
As a continuation of the work on PSCLC, I can see only holographic structuring as a possible
promising direction for future researches. It can be done in one of the following directions:
A. It is likely that there exists a way to initiate the polymerization of RM257 with a visible
light. This requires a specific molecule to initiate the reaction or may be several molecules,
i.e. initiator and co-initiator. A specific investigation of chemical literature could give
probably some hints or interaction with chemical scientists.
B. It is possible that other mesogenic monomers exist, for which polymerization could be
initiated in the visible light. Once again it requires some chemistry expertise.
C. Using a UV laser with RM257 and Igracure. It would require the modification of the Ar+
laser for the UV part of the spectrum and purchasing specific optics for UV light.
111
V.2 Photorefractive LC-polymer composites.
This is a relatively new research domain and a lot of possibilities are not explored yet by the
scientific community. It is also a promising material for various applications. In this case, the
micro-structuring becomes more complex. This is why, for the optimization of the material
we used a three level scheme to describe the interaction and cross-linking between different
parameters. This scheme enables to emphasize on some of the most important parameters of
an overall device engineering.
QD
choice
Thickness
Material
Stability and
Reliability
Scattering
Efficiency
&
memory
Charge
Transfert
Voltage
Index
modulation
Trapping
Sites
Concentration
and composition
of polymer vs
LC
The goals of optimization
Material properties influenced
by external parameters.
External parameters which can
be optimized.
Figure 5.1. Interaction flow of the various physical parameters which can be used to engineer
LC-polymer composites.
In the red central area we find the parameters we want to optimize such as the diffraction (or
index modulation) efficiency and the switching time, or long and short time memory,
depending on the selected application. In addition, it is required to have a stable material and
reproducible fabrication process.
112
These target parameters are influenced by second level parameters (green area), related on
material properties that cannot be influenced directly, but which will impact other external
parameters. For example, the scattering depends on the cell thickness and on the concentration
of LC and polymer; it depends on the applied voltage as well.
On the third level, there are parameters that can be directly influenced by external technical
choices such as the thickness, choices of LC type, polymer and Quantum Dots (fullerene in
our case). The third level of parameters can have simultaneously positive and negative
influence (with respect to the goals), in this case a certain trade-off need to be found. For
example, an increase in voltage reduces the scattering, but simultaneously decreases the index
modulation with an impact on the material stability resulting, for instance in current leakages
and short-circuits.
V.2.1 Material improvements.
Our experiments presented in the fourth chapter identified the most critical factors for a future
improvement of material properties, with respect to the photorefractive effect.
A. Scattering.
We have identified that scattering, due to the presence of a polymer network, is one of the
main obstacles in photorefractive matter micro-structuring, as it does not allow us to increase
the thickness. An immediate solution to this issue is to design, for instance, transparent PSLC.
It can be done by extending our preliminary work with RM257 or by using other suitably
designed polymers. The stabilization with RM257 can be done in various conditions. For
example, one can polymerize it at different temperatures and under the applied electric field.
B. Charge separation.
We used a simple method for increasing the charge separation by increasing the QD
concentration. It leads to an increase in the absorption of the media, which is unwanted for
many applications. Another approach could involve an increase in the charge generation due
to a different mechanism of charge separation, which can lower the absorption. For instance,
113
one can use ready solutions from the field of organic photovoltaic. The fundamental
mechanism for the charge separation in photovoltaic is the same as in photorefractive effect,
therefore the solutions developed in this field could be readily transferable here.
There are a lot of investments from the industry in this field involving intensive chemical
engineering on organic photovoltaic materials. The current state of the art on the charge
separation process in photovoltaic materials overlaps the existing state of the art of
photorefractive effect in LC. Moreover, we have demonstrated already that a part of the
solutions found in that field (soluble fullerenes) can be used in LC. It is likely that other
combinations would work as well.
C. Holo-PDLC and photorefractive effect.
It is likely that photorefractive effect can be observed in holo-PDLC. To our knowledge there
are no publications on this topic yet. This approach can be used for designing tunable 2-D
photonic crystals. A fixed 1-D grating can be recorded during photo-polymerization and the
tunable 1-D grating is generated by photorefractive effect.
It is obvious that this approach would require smaller resolution for the photorefractive
material.
The resolution of the polymer – LC composites is limited to the values of about ~3 µm as it
can be seen from our experiments and the experiments of other authors [1-3]. There are also
theoretical estimations that the charge separation mechanism in LC [4] imposes restrictions on
the charge separation distance of ~ 5µm. Experimental work in photorefractive polymers
show that the charge separation distances and grating periods as small as ~0.5µm can be
obtained [5]. This is due to a different mechanism of charge separation, when the charge
separate occurs due to the interaction between hole-conducting polymer and the photosynthesizer molecules such as TNF or fullerene [5, 6]. Thus, for a smaller resolution in
phorefractive holo-PDLC it could be necessary to use a conducting polymer in LC-Polymer
composite.
In conclusion, as one can notice, we only graze here these two topics (structuring CLC and
photorefractive effect in PSLC). In this chapter we tried to present and discuss the role of the
114
most important factors in the material development and propose some possibilities for future
researches. We explain why the theoretical approach is difficult in soft matter structuring and
emphasize the importance of the qualitative models and guidelines, as well as the role of
chemical engineering in particular for solubility and photo-polymerization.
115
V.3 Literature for Chapter V.
[1] H. Ono, A. Hanazawa, T. Kawamura, H. Norisada, N. Kawatsuki, “Response
characteristics of high-performance photorefractive mesogenic composites”, Journal of
Applied Physics, 86, 1785-1790, (1999)
[2] N. Kawatsuki, H. Norisada, T. Yamamoto, H. Ono and A. Emoto, “Photorefractivity in
polymer dissolved liquid crystal composites composed of low-molecular-weight nematic
liquid crystals and copolymer comprising mesogenic side groups”, Science and Technology
of Advanced Materials, 6, 158-164 (2005).
[3] A. Denisov and J.L. de Bougrenet de la Tocnaye, "Soluble fullerene derivative in polymer
liquid crystal composites and their impact on photorefractive gratings efficiency and
resolution.”, submitted to Applied Optics.
[4] E. V. Rudenko and A. V. Sukhov, “Photoinduced electroconductivity and photorefraction
in nematic”, JETP Lett. 59 , 142-146, (1994)
[5] W.E. Moerner, A. Grunnet-Jepsen and C.L. Thompson, “Photorefractive Polymers”,
Review of Materials Science, 27, 585-623, (1997)
[6] J. S. Schildkraut and A. V. Buettner, "Theory and simulation of the formation and erasure
of space-charge gratings in photoconductive polymers," J. Appl. Phys. 72, 1888-1893
(1992).
116
Appendix 1
Appendix 1: Cells preparation.
The basic technology for the samples preparation as it is used in LC industry was shown to
me by a Ph.D. student of optics department B. Caillaud, and it is described in his thesis. The
whole protocol takes two days of work in a clean room to prepare 10 empty cells.
We start with the glass plates coated by a transparent conducting layer of Indium Tin Oxide.
The thickness of the layer was 25nm, and the resistivity 80 ohms/square. The large glass
plates bought from manufacturers were cut into smaller plates of an appropriate dimension.
The experimental protocol described here was first used for the glass plates of 20 mm by 20
mm, while in the experiments described in the Chapter III we used larger glass plates 35 mm
by 35mm.
The cell preparation process is carried out in a class 100 clean room available at our
department. Class 100 corresponds to a clean environment where there are less than 100
particles of the 0.5 µm size in a pied cube, and where water and other chemicals are of
appropriate purity too.
1. Cleaning.
We start the process in the clean room with cleaning of the glass slides. The glass plates are
put into a deionised water solution of commercial cleaning liquid “DECON”, with
117
concentration of 4%. Then they are put into an ultrasonic bath with heated water (~80°) for 30
minutes. After this time the beaker with the slides is put under the current of deionised water,
till the disappearance of bubbles. Then the beaker is put once again into an ultrasonic bath for
30 minutes to wash away the rest of “DECON” which rest on the slides. Afterwards the slides
are rinsed once again in deionised water.
The quality of cleaning is verified by a point light source (a light pen), which allows to see if
there is any dust left, as it scatters the light. If the slide is clean it is put into the oven at 200°
to remove the residual liquid.
This procedure was developed with the cooperation of other Ph.D. students and is different
from the previously used. The results of the cleaning are good enough in most cases for the
subsequent steps.
2. Alignment layer deposition.
The alignment by a surface layer deposition and subsequent rubbing is the standard method in
LC industry. For our work we used commercial polymer alignment material (Polyimide 410
from Nissan) diluted in proportion 50:50 by a commercial solvent. This layer was deposited
by spin coating onto the clean slides. The spin-coating parameters were: Time 40s, Speed
3500 turns/min, Acceleration 3500 turn/min/s. During spin-coating a thin film of monomer is
deposited onto a glass plate and then it is polymerized, when the slides are put into an oven
heated at 180° for 2 hours.
After this procedure the polyimide film has to be rubbed to provide a planar alignment. (As
we had discussed in chapter II it works due to symmetry breaking during rubbing.) The
rubbing force could be regulated with the facilities available in the clean room and we
empirically adjusted it, by changing the distance between a glass plate and the velvet cylinder
to obtain the best alignment. The quality of alignment was judged in the end of the process by
examining the quality of the cells.
118
3. Cell assembly.
The glass slides with alignment layer obtained after the previous step were assembled in a socalled ‘anti-parallel’ orientation, when the rubbing direction in the opposite slides goes
opposite way figure A.1. It is necessary due to existence of a pretilt angle, which is an angle
between a liquid crystal molecule and the aligning surface. In the polyimide that we used it is
small and is equal to 3-4°. Nevertheless, the anti-parallel assembly has advantage as it applies
less stress on the structure. This observation holds true in the CLC case too.
Figure A1.1. A cell filled with nematic LC, with an anti-parallel orientation of the rubbing
direction for surface alignment. Nematic LC is oriented with a small angle towards the surface
due to existence of a pretilt.
The distance between glass plates was fixed by spacers, that were put on the sides and the
slides were kept together due to the presence of glue joint. We used a glue UVS-91, which is
polymerized by the UV light.
4. Filling.
After the cell is assembled (figure A.2), it can be filled with a liquid crystal, or LC – monomer
mixture by capillarity, to do this a small drop is put on the side and then it enter by itself.
119
Glass plate
ITO Layer
Alignement
Layer
Spacer
Figure A1.2. An assembled cell. Side view.
After the cell is filled with a chosen mixture the entrance can be closed with glue and
electrodes are connected on the sides for the convenient use. The glass plates are shifted one
relative to another during assembly to have a space for electrode contact.
Planarity control.
In a standard LC displays technological protocol spacers of a certain size are dispersed over
the whole surface of one glass plate and the glass plates are pressed under vacuum in order to
control the thickness of the cell. After pressing the glass plates and polymerizing the glue the
cell gap is equal to the spacer diameter. This method provides a good control over the cell
thickness.
In our case this method of controlling the cell thickness proved to be unsatisfactory, due to
generation of a large amount of defect lines which were fixed on the spacers. That is why we
had to use spacers located on the sides of the cell. Unfortunately the planarity of the cell was
not satisfactory. We observed several interference line per millimetre, on the surface of the
cell.
For a CLC pitch of P=1µm, the half turn corresponds to 500 nm, and if the difference of the
cell thickness between two points will be more or equal to this value a disclination line
separating two domains will appear, such as the one shown on figure 2.13. Therefore in order
to have a good homogeneity of the sample on the scale of 1mm one needs to have a gradient
in height of less than 500 nm per millimetre length.
120
The film spacers that we used were of a non uniform thickness which added additional
obstacle to obtain a good planar cell. We solved these problems by using a simple machine
that allowed us to manually regulate the pressure applied to the sides of the cell. At the same
time we controlled the degree of planarity by monitoring the interference pattern produced by
a thin film of the air between the slides.
With this approach we made cells with a difference of thickness of less than 500 nm per 10
mm, which is largely sufficient for our experiments. In practice it meant a single interference
fringe over 1cm distance.
121
Appendix 2
Appendix 2: Mask replication on ITO.
The master mask was replicated on ITO using a standard photolithography protocol, which
will be outlined here. The whole process took place in the photolithography class 1000 clean
room of the optics department. The process requires clean environment, because the defects
which can appear at different stages can cut the connection of electrode stripes with the main
electrode making the substrate unusable.
The whole process is shown schematically on the figure A2.1. First, the glass plate with ITO
is coated with photoresist and is brought into contact with the nontransparent mask. Second,
the photoresist is exposed to UV through the mask. Third, the photoresist is developed and
only the parts protected by mask areas are left untouched. Fourth, ITO is etched by acid where
it is not protected by the photoresist. Fifth, the photoresist is dissolved by acetone.
In more details the experimental protocol is the following:
Photoresist deposition:
1. Glass plates with ITO coating are cleaned according to the protocol described in
Chapter II.
2. Clean plates are spin coated with photoresist “Microposit S1818”. Spin-coating
parameters: speed 2700 turn/min, time 45 sec, acceleration 2500 turn/min/min.
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3. The cells with a thin layer of photoresist were dried on a hot plate at T=100 °C.
UV exposure:
1. Mask was brought in contact with the photoresist coated glass plate using mask
aligner, which allowed us to orient the mask parallel to the edges of the glass plate.
2. Photoresist was exposed for 8 sec to UV light. The time of exposure was optimized for
the best result.
123
1. Mask is brought in
contact to the
photoresist.
UV
2. Photoresist is exposed
to UV light.
3. After development
exposed to UV areas of
photoresist are dissolved.
4. The areas of ITO not
protected by photoresist
are etched in the acid.
5. Photoresist dissolved in
acetone.
Figure A2. 1. Chrome mask reproduction on the ITO coated glass.
124
Development of the photoresist:
1. The glass plate was let for about 60 sec into a developer prepared as a solution of
Photoposit Shipley MF 160 with deionized water in proportion 1:4.
2. The developer was then washed with water.
3. The water was dried with the air. This stage was rather critical; the stripes of
photoresist could fly away if the pressure of air was too high.
4. Quality of the photoresist stripes was verified under the microscope, if necessary the
development time or exposure time was increased.
5. The plate was put on the glass plate at 120 °C to fix the stripes before the next stage.
ITO etching.
1. The hydrochloric acid (HCL) was dissolved in proportion 1:1 with deionized water.
2. The acid was heated to 60° C.
3. The glass plates were put for 45sec to dissolve ITO. The time necessary for the
dissolution can be varied depending on the thickness of ITO.
Photoresist removal.
1. Photoresist was dissolved by acetone.
2. Before acetone evaporated, the plate was wet by ethanol and dried by air.
A production of 8 etched glass plate takes one and a half day. Normally only about 5 of them
were of a good quality. The process is complicated and could fail at any stages. For example,
if the quality of the cleaning was not good enough, on the final stage of ITO dissolving, ITO
was dissolved under the photoresist too, due to a low adherence.
The cells with etched ITO were used for the cell preparation as described in chapter II.
On the figures A2.2. and A2.3. one can see the pictures of our samples taken under the
microscope. The contrast of the electrodes is higher on the figure A2.2, due to irreversible
change in CLC structure. In effect we see the electrodes and the perturbation of the CLC
structure. The sample on the figure A2.3. has a better quality, there is almost no defect lines.
125
Figure A2.2. Picture of a sample taken under microscope in reflection mode. The electrodes
on the left side have a period of 15 µm, on the right side 8 µm. This sample was not good
enough for the measurements, as it has a lot of defect lines which were discussed in the
Chapter II. One can see also the electrode cuts, which appeared during the mask replication
process.
126
Figure A2.3. Picture of a sample take under a microscope in reflection mode. The electrodes
on the left side have a period of 15 µm, on the right side 8 µm. This is one of our best samples
and there are not many defect lines and domains. One can see the isolated defects, which are
not connected by the defect lines and do not give rise to domains.
127
Appendix 3
Appendix 3: LC QD photorefractive light valve.
Optically addressed light valve.
Optically addressed spatial light modulators, or light valves, can be used for various
applications in adaptive optics and optical processing [1-3]. The optically addressed light
valve is capable of accepting a low intensity, white or monochromatic light input image, and
converting it into an output image with light from the same or another light source.
A conventional liquid crystal light valve is shown on figure A3.1.
128
Figure A3.1. Cross-sectional schematic of the liquid crystal light valve [1]. The dielectric
mirror is optional (only used when the same wavelength are used for both reading and
writing).
There are two key elements: photosensitive layer and liquid crystal layer. Photosensitive layer
responds to the incoming light, forming a spatial charge pattern corresponding to the writing
light intensity. Liquid crystal layer is modulated due to the different voltage at different space
regions following the pattern established by photosensitive layer. The index modulation of LC
can be transferred into the modulation of reading beam using polarized light.
These two
functions (writing and reading) are generally separated.
As a photosensitive medium a photorefractive crystal can be used [4] and the light valve can
operate in an optimized transmission mode, because photosensitive and modulating layers are
no longer separated. In that case, the light valve can operate in a full transmission mode, and
the absorption of photosensitive layer can be reduced.
129
Photorefractive light valve.
In our experiments, we used a photorefractive sample with a thickness of 50 µm, filled by the
M1 mixture. In the case of photorefractive polymer stabilized LC, we combine photosensitive
layer and modulating layer into one unique layer, which performs these two functions. A
corresponding scheme is shown on the figure A3.2. The writing light has a normal incidence
onto the sample and the dc applied electric field is used to assist the charge separation.
Figure A3.2. Cross sectional schematic of the light valve based on photorefractive PSLC.
The picture which was projected onto the sample with Ar+ laser at 514 nm, was subsequently
read with a He-Ne laser at 633 nm, the experimental geometry is shown on the figure A3.3.
Both beams were enlarged to the diameter of 8mm. The read beam was projected onto the
screen and the photograph were taken.
130
Ar+, 514 nm
Target
Lens
Sample
He-Ne, 633 nm
Polarizers
Screen
Figure A3.3. Scheme of the measurement set-up.
The pictures on gifure A3.4 show the reference target and its projection onto the sample with
the green laser. One can see that the central region is well reproduced on the sample.
Figure A3.4. Picture and its projection onto the sample.
Four pictures on figure A3.5 show the projection of the writen images onto the screen. One
can see as the projected image is formed on the sample, the pcitures are taken with the time
inerval of a few seconds. If one turns one of the polarizers by 90° degrees, the negative of
theses images can be obseved.
131
Figure A3.5. Projection on the screen of the written images.
These manifestation of the photorefractive effect lies a little outside of the scope of this thesis,
that is why we have not investigated it in details. We also have not undertaken any effort in
the effect optimization. The mechanism of the oberved phenomenon is due to the charge
formation in the photrefractive media. However, the recording of the image in a normal
incedence of writing beam requirs another explanation of the index modulation formation.
In our opinion, our observation can be explained by formation of the depolarizing electric
field due to the charge separation in the illuminated regions. The LC in dark regions is
oriented in the direction of applied dc field ( field value ~10 V/µm), in the illuminated regions
the LC is reoriented in a smaller degree due to the depolarizing field. Thus the variation of
intensity of a projected image is transfered into an index variation, which can be read out by
using polarized light.
It is likely that the observed effect can be optimized for a better contrast and smaller response
time. It can be also a topic of a future research work.
132
Literature:
[1] Casasent D., “Coherent light valves”, Applied Optics and Optical Engeneering, R.
Kingslake Ed. 6, New York, Academic, 143-200, (1979)
[2] Efron Y, “The silicon liquid crystal light valve”, Journalm of Applied Physics 57, 13561368, (1985)
[3] L. Dupont, Z.Y. Wu, P. Cambon and J.L. de Bougrenet de la Tocnaye, “Smectic A and C*
liquid crystal light valves”, J. Phys. III France 3, 1381-1399, (1993)
[4] P. Aubourg, J. P. Huignard, M. Hareng, and R. A. Mullen, "Liquid crystal light valve
using bulk monocrystalline Bi12SiO20 as the photoconductive material," Appl. Opt. 21,
3706-3712, (1982)
133
Reconfigurable photonic crystals: external field structuring of Liquid
Crystals - Polymer composites.
In this dissertation we present the study of composite Liquid Crystal (LC) – polymer
materials. Our goal was to design and realize photonic crystals, whose structure makes them
reconfigurable by external electric or light fields. Our first realization is based on the use of a
polymer stabilized Cholesteric Liquid Crystals (CLC). CLC have an inherent periodic Bragg
structure, making them a natural 1-D photonic crystal. We realised 2-D photonic crystals by
inducing an electric field to produce a periodic modulation of the CLC structure. This
structure allowed us to make a principle demonstration of a band-edge effect in 2D photonic
crystals based on CLC as well as the possibility of tuning the resonance by changing the
applied electric field. In a second approach we use the photorefractive effect in a composite
liquid crystal material doped by quantum dots (fullerene C60). We studied the 1-D
reconfigurable photo-induced gratings in these composites. To improve the recording
efficiency and resolution of the photorefractive effect observed in such composites we
investigated the impact of the concentration of fullerene, using for this purpose fullerene
derivatives C70 and [60]PCBM. We observed the improvement in resolution due to the
combined effect of an increased fullerene concentration and the trapping mechanism due to
the polymer network. We proposed a new way of operating for photorefractive effect in LCpolymer composites, which can substantially improve diffraction efficiency of a new material,
approaching the requirements for practical applications.
Key words: photonic crystals, liquid crystals, cholesteric liquid crystals, photorefractive
effect, fullerenes.
Cristaux photoniques reconfigurables : structuration des mélanges cristaux
liquides / polymère par un champ externe
Cette thèse concerne l’étude des composites cristaux liquides (CL) / polymère. Notre but est
de concevoir et de fabriquer des cristaux photoniques dont la structure soit reconfigurable par
l’action d’un champ appliqué, électrique ou lumineux. Notre première réalisation se base sur
l’utilisation de cristaux liquides cholestériques (CLC) stabilisés par un polymère. Les CLC
présentent naturellement une structure hélicoïdale périodique, et sont donc des cristaux
photoniques à une dimension pour certaines longueurs d’ondes. Pour former un cristal
photonique bidimensionnel, nous avons induit une modulation périodique de la structure CLC
dans une seconde direction en appliquant un champ électrique. Cette structure a permis de
montrer expérimentalement un effet de bord de bande et la possibilité d’ajuster la résonance
en modifiant le champ appliqué. Notre deuxième approche se base sur l’effet photoréfractif
dans les composites cristaux liquides / polymères dopés par des fullerènes. Dans ces
matériaux, nous avons photo-inscrit des réseaux unidimensionnels reconfigurables. Pour
améliorer l’efficacité et la résolution, nous avons étudié l’influence de la concentration du
dopant, utilisant le fullerène C70 ou le dérivé PCBM-60. Nous avons observé une amélioration
de la résolution due à l’effet conjoint d’une augmentation de la concentration en dopant et du
mécanisme de piégeage des charges dans le réseau polymère. Nous présentons également une
nouvelle façon expérimentale d'exploiter l'effet photoréfractif dans des composites cristaux
liquides / polymère, permettant d'améliorer l'efficacité de diffraction, pour mieux satisfaire à
des besoins d’applications pratiques.
Mots clés : cristaux photoniques, cristaux liquides, cristaux liquides cholestériques, effet
photoréfractif, fullerènes.