# Holographic Polymer-Dispersed Liquid Crystals:  Materials, Formation, and Applications

Authors: Y. J. Liu; X. W. Sun
Journal: Advances in OptoElectronics
 (2008)

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## Abstract

By combining polymer-dispersed liquid crystal (PDLC) and holography, holographic PDLC (H-PDLC) has emerged as a new composite material for switchable or tunable optical devices. Generally, H-PDLC structures are created in a liquid crystal cell filled with polymer-dispersed liquid crystal materials by recording the interference pattern generated by two or more coherent laser beams which is a fast and single-step fabrication. With a relatively ideal phase separation between liquid crystals and polymers, periodic refractive index profile is formed in the cell and thus light can be diffracted. Under a suitable electric field, the light diffraction behavior disappears due to the index matching between liquid crystals and polymers. H-PDLCs show a fast switching time due to the small size of the liquid crystal droplets. So far, H-PDLCs have been applied in many promising applications in photonics, such as flat panel displays, switchable gratings, switchable lasers, switchable microlenses, and switchable photonic crystals. In this paper, we review the current state-of-the-art of H-PDLCs including the materials used to date, the grating formation dynamics and simulations, the optimization of electro-optical properties, the photonic applications, and the issues existed in H-PDLCs.


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## Body

## 1. Introduction

### 1.1. Polymer and Photopolymerization

The discovery  of polymers has much contributed to the change of
day-to-day life. In fact, the use of polymers in human history dates back as
early as   Egyptian mummies. Before the mummies were wrapped, the cloth was
soaked in a  solution of oil lavender. When the cloth was dried by exposure to
the sunlight, the oil was converted into a protective polymer. This was a
typical application of photopolymerization. Polymers are involved in almost all
aspects of our lives. Some examples include their use in textile, automotive
and electronic industries, and as building and packing materials.Monomers are the building blocks or structural units of the polymers. For
polymer formation, the monomer must be able to link two or more other monomers,
that is, the functionality of the monomer is not less than 2. Depending on the
functionalities of the monomer, different morphologies of polymer networks can
be formed [1]. If the polymer is constructed from difunctional
monomers, it is a linear chain
(Figure 1(a)). If higher functional monomers are used, a
branched polymer will be formed
(Figure 1(b)). The presence of the branches limits the motion
of chains, thus strengthening the polymer. If the functionality is even higher,
the branches start to connect to one another in three dimensions. The polymer
becomes a cross-linked network
(Figure 1(c)). This cross-linked network enables the polymer to
be much stronger, but also much more brittle.Different polymer
structures. (a) A linear polymer chain.  (b)
A branched chain. (c) A cross-linked network.
(a)(b)(c)The most widely used and simple method of polymer formation
is radical-chain addition polymerization. Polymerization involves initiation,
propagation, transfer, and termination steps. Initiation is the step where
initiating radicals are formed by external stimulations such as light, heat,
gamma-radiation, and redox processes. Light-induced photopolymerization has
several advantages over other methods. The fabrication temperature is low,
usually room temperature, and controllability can be realized by selecting
different irradiation wavelength and light intensity. Moreover, light can be
focused on a particular site, thus polymer can be formed where it is desired.Photopolymerization is a very flexible process and can be
used in various technological applications such as photoresists in modern
electronics. In this process, a film of monomer mixture is placed on the
surface of a silicon wafer and is illuminated through a photomask. After
polymerization, the unpolymerized material can be washed away, leaving the
polymer intact. The polymer-covered areas on the silicon wafer are then used to
resist chemical etching, resulting in integrated circuit formation or printed
circuit board construction. This technology has allowed billions of transistors
to be placed on a single integrated circuit.


### 1.2. Liquid Crystal and Polymer Composites

In the past decade, liquid crystal/polymer composites
have attracted great attention due to their special dynamic characteristics. Liquid
crystal/polymer composites could appear in the form of network or droplet
depending on the polymer and its concentration. In the low-concentration regime
(1–2 wt%) [2, 3], the response time can be much improved, however,
the associated light scattering is quite strong in the visible range. As the
polymer concentration increases to 3–8 wt%, the
polymer-stabilized liquid crystal (PSLC, also known as gel) is formed in a
homogeneous or homeotropic cell [4, 5]. These PSLC cells exhibit an anisotropic light
scattering behavior and have potential for reflective display and telecom
applications [6, 7]. As the polymer concentration increases to
30–40 wt%, the
polymer-dispersed liquid crystal (PDLC) is formed [8, 9]. No surface alignment layers in the PDLC cell are
needed. Micron-sized LC droplets are buried in the polymer matrix. In this
case, visible light is strongly scattered and this scattering is independent of
polarization. In the high polymer concentration regime
(60–70 wt%),
nanoscale holographic PDLC (H-PDLC) droplets are formed [10, 11]. Since the droplet size is much smaller than the
visible wavelength, H-PDLC film is free of light scattering and its response
time is fast (30–200 μs).
However, to reorient LC molecules in these small droplets, a relatively high switching
electric field (15–20 V/μm)
is required. In this approach, no surface alignment is required.


### 1.3. Holography and H-PDLC

Holography is the
process of recording the complete information of the electric field in both
amplitude and relative phase, and consequently a real three-dimensional image
can be reconstructed [12, 13]. Since most of recording materials are only
sensitive to the intensity of the light, interference is a very convenient way
to convert the phase information to the amplitude information. Transmission and
reflection holograms are two common types whose images can be reconstructed by
appropriate use of optics, such as prisms, lenses, and mirrors. The most
attractive and unique property of a hologram is the wavelength and angle
sensitivity, and the ability to manipulate the light that is either reflected
or diffracted. To date, holographic optical elements (HOEs) have found numerous
important roles in photonics.Photopolymers are
one of the holographic materials that have been widely used in the fabrication
of HOEs. Thin volume gratings can be obtained by holographic interference
patterning and subsequent modulation of the refractive index in photopolymer
materials.  They can be classified into
two categories, active and passive devices, depending on their optical
function. An element that can change its refractive index dynamically with
applied external stimulus, such as electric field, optical strength, forces, is
called an active optical element, while an element with a fixed modulation of
the refractive index is called a passive optical element.The marriage
of holography and PDLC materials [14] has produced a number of photonic applications
in information and display systems, electro-optic filters, free-space optical
switches, and wavelength division multiplexer. For a typical PDLC, LCs are
randomly distributed in the polymer matrix and the droplets are randomly
orientated, while in H-PDLC system, the interference of two beams generates
periodic dark and bright fringes in the photopolymer film. In the photopolymer
system, the polymerization rate is higher in the bright region and lower in the
dark region. During the holographic recording process, the monomer diffuses
into the bright region to form polymer and at the same time LCs diffuse into
dark regions. The main advantage of this technique is the fast and single-step
ability to fabricate large area grating structures.


#### 1.3.1. Transmission and Reflection Gratings

Depending on the writing geometries, H-PDLC gratings can
be divided into two different modes according to the holography recording
configuration, transmission, and reflection. For transmission H-PDLC, the recording two beams are in the same side of
the medium, as shown in Figure2(a). In transmission H-PDLC, the recorded fringes are perpendicular to the
substrates.  This   type of H-PDLC is very
sensitive to the incident angle of light beam. On the contrary, for
reflecting H-PDLC, the recording light beams are in
the two sides of the recording medium, indicated as
Figure 2(b). In reflection H-PDLC,
the recorded fringes are parallel to the substrates. This type of H-PDLC is
very sensitive to the wavelength. Therefore, we can design the grating pitch to
reflect red, green, or blue light, which makes it potentially useful in
displays. Here, for both reflection and transmission H-PDLCs, the recording light beams are all symmetrical,
and therefore the fringes are parallel or perpendicular to the substrates. If
the recording beams are not symmetrical, slant fringes will be obtained in
H-PDLC.Schematic
holographic recording for (a) transmission and (b) reflection gratings,
respectively.
(a)(b)


#### 1.3.2. Raman-Nath and Bragg Gratings

Generally, two
types of diffraction
are distinguished by defining a dimensionless Cook-Klein parameterQ:(1)Q=2πλdnΛ2, where d is the thickness of
the grating, Λ is the grating period, n is the
spatially averaged refractive index of the recording medium, and λ is the incident wavelength.A 		“thick” or
volume grating (Q≥10) corresponds to the Bragg diffraction and
provides the diffraction when incident angle satisfies the phase matching
conditions. Such structures exhibit only two diffraction orders (zeroth and first order) and a strong dependency of
the diffraction efficiency on the angle and wavelength of the incident light.
The diffraction efficiency of the transmission volume phase grating in Bragg
conditions is   described by(2)ηvol=sin2(Δδvol2)=sin2(πn1dλcosθ0), where n1 is the amplitude of refractive index
modulation of the material, θ0 is the Bragg angle of the incident light
within the material.On the other hand, “thin” gratings (Q≤1) correspond to the Raman-Nath regime of the
optical diffraction. In this regime, many orders of the diffraction can be
observed. The efficiency of the first-order Raman-Nath diffraction for the
grating with a sinusoidal modulation of refractive index is given by(3)ηsurf=J12(Δδsurf2)=J12(2πh(nI−nII)λ), where J12(Δδsurf/2) is the first-order Bessel function of the
first kind, h is the depth of the gratings grooves, nI and nII                                                                                                                            are the refractive indices of the adjacent
areas of the grating.


### 1.4. POLICRYPS

Recently, a new kind of holographic grating made of
polymer slices alternated to films of regularly aligned nematic liquid crystals,
so-called POLICRYPS, an acronym of Polymer Liquid Crystal Polymer Slices, was
demonstrated by an Italian research group
[15–18]. This kind of grating was fabricated at an elevated
temperature, which is higher than the nematic-isotropic transition temperature,
thus avoiding the appearance of the nematic phase during the curing process.
After cooling, these structures present a sharp and uniform morphology, without
those optical inhomogeneities which are due to the NLC droplets in usual H-PDLC
samples. As a result, the scattering losses were reduced and the diffraction
efficiency was increased accordingly. The diffraction efficiency of POLYCRYPS
was reported to be as high as 98% [18]. The big difference between H-PDLC and POLYCRYPS
gratings was shown in
Figure 3. Based on POLYCRYPS gratings, Asquini et al. developed a switchable optical
add-drop multiplexer [19]. This designed switchable add-drop multiplexer using
a POLICRYPS grating performs with a cross-talk of −22 dB and with just
0.8 nm
wavelength spacing as used in DWDM optical communication systems. However,
compared to most H-PDLCs, the POLICRYPS grating shows more sensitivity to the
polarization and slower response times including rising time and falling time
[20].Field dependence of transmission curve (squares), first-order diffraction curve
(circles), and total transmission curve (triangles) for (a) a POLICRYPS grating,
(b) a PDLC grating. The insets show typical (a) POLICRYPS, (b) PDLC grating
morphology with the same period, observed under a polarizing optical microscope
[18].
(a)(b)


### 1.5. H-PDFLCs

Ferroelectric liquid crystals (FLCs)
have been demonstrated as excellent candidates for fast electro-optic switching
applications such as displays [21] and optical switches [22]. However, limited device commercialization is available,
partly due to the lack of achieving suitable alignment layers that are both
stable and robust for homogeneous alignment of the FLC. Over the past decade,
researchers have shown different techniques to aid in the alignment of
ferroelectric liquid crystals by combining FLCs and polymer dispersions with
shearing forces [23]. Recently, some researchers investigated the holographic polymer-dispersed
ferroelectric liquid crystals (H-PDFLCs)
[24–26]. In H-PDFLCs, different alignment states of FLCs can
be created by changing the weight ratio of FLCs and monomer.
Figures 4(a)
and 4(b) show the droplet-like and channel-like
morphologies in the FLC-rich regions for H-PDFLC samples with a 50:50 weight ratio
mixture of FLC and monomer and a 40:60 weight ratio mixture, respectively,
which show different polarization properties. The droplet-like samples produced
polarization insensitive while the channel-like ones produced polarization
sensitive electro-optical properties, which indicated different alignments of
FLCs in these two different kinds of samples. In the droplet-like samples, the
FLCs are not well aligned, inducing the lack of grating contrast under a
polarized optical microscope, as shown in
Figure 5. While in the channel-like samples, the FLCs are well
aligned, which produces a sharp grating contrast under the polarized optical
microscope, as shown in
Figure 6. Woltman and his coworkers developed a
phenomenological model to describe the channel-like morphology of the
homogeneously aligned FLCs between the polymer walls [26]. The FLC alignment is parallel to the polymer walls,
which is different   with the nematic-based H-PDLCs, where the nematic LC alignment
is orthogonal to the polymer walls
[27]. The H-PDFLCs studies are still in early stage and
the results are   preliminary. A big advantage   of H-PDFLCs is the faster   response
time. Rapid switching between 20 and 50 μs
[27] has been observed for the H-PDFLCs above a threshold
voltage.H-PDFLC samples constructed from (a) a 50:50 weight
mixture of FLC and monomer, and from (b) a 40:60 weight mixture, respectively [24].
(a)(b)Optical polarizing microscopy of a polarization insensitive FLC H-PDLC grating
(a)90° between crossed
polarizers, (b) 45° between crossed polarizers [25].
(a)(b)Optical polarizing microscopy of a polarization insensitive FLC H-PDLC grating
(a)90°
between crossed polarizers, (b) 45° between crossed polarizers
[25].
(a)(b)


### 1.6. Azo Dye Doped H-PDLC

In some cases, polarization sensitive gratings are
useful as a polarized or unpolarized beam splitter, depending on the
polarization of the incident light. Adding a small amount of azo dye into the
PDLC materials, polarization sensitive gratings can be obtained by holography
[28]. The formation of the polarization gratings is
attributed to the anisotropic adsorption of the azo dyes on the surfaces of
polymer walls, inducing the reorientation of the liquid crystal molecules
[29].
Figure 7
shows a sharp grating contrast under an optical
microscope with a polarizer parallel and perpendicular to the direction of the
stripe in the grating, respectively. Woo et
al., also investigated the
effect of the azo dye on the diffraction efficiency, gratings morphologies, and
electro-optic properties [30]. As the concentration of dye molecules increased,
the liquid crystal droplets became small due to the slow rate of polymerization,
as shown in
Figure 8. In addition, azo dye molecules strongly reorient LC
molecules perpendicular to the grating, giving rise to enhanced diffraction
efficiency and short response times.Grating images observed under an
optical microscope with a polarizer placed in front of the sample. The
transmission axis of the polarizer is (a) parallel and (b) perpendicular to the direction of the stripes in the
grating [29].
(a)(b)SEM micrographs for a transmission HPDLC prepared (a) without and with (b)
0.5%, (c) 1% azo dye
[30].
(a)(b)(c)


### 1.7. Nematic Director Configurations in PDLCs

A typical example
of PDLCs is the light valve configuration presented in
Figure9. The PDLC light valve is fabricated by sandwiching
PDLC material between transparent conducting electrodes with a 10–25 μm spacer. In the
“off” state, the liquid
crystal droplets with positive dielectric anisotropy are randomly oriented in
the film and the size of the droplets is comparable to or larger than an
optical wavelength, usually 2–5 μm. In the translucent state, the film has a
white opaque appearance due to the scattering properties of the film.  Once an electric field is applied, the liquid
crystal molecules in each droplet will align in the direction parallel to the
field direction as shown in
Figure 9
(“on” state). If the ordinary refractive index, no, (perpendicular to the
nematic director) approximately matches the refractive index, np, of the surrounding
polymer matrix, the film will be transparent. Upon removal of the field, the
droplets will return to their random orientation and the film reverts back to
its opaque state. Therefore, the PDLCs are switched between the scattering
state and transmission state.Illustration of the principle behind the operation of a PDLC display. The
material has a white translucent appearance in the “off” state. Application of
a voltage to the transparent conducting electrodes reorients the symmetry axis
of the bipolar droplets parallel to the electric field direction
(“on” state)
and the material becomes transparent if the ordinary refractive index of the
liquid crystal matches that of the polymer matrix.
(a)(b)The
PDLC structure formation through photopolymerization is a complicated process
including physical changes and chemical reactions. Usually, the droplets of a
nearly uniform size are formed during the phase separation. The average droplet
size varies from submicron up to several tens of microns depending on the conditions
during the formation process. The nematic structure inside a droplet is the
result of the interplay between elastic, surface, and external field
interactions. The minimization of the phenomenological free energy is usually
used to determine the stable structure of a chosen system at constant
temperature and volume. It is convenient to divide the free-energy density into
elasticfe, interfacial  fs, and field  ff parts.The
nematic free-energy densityfe can be expressed as (4)fe=12[k11(∇⋅n)2+k22(n⋅∇×n)2+k33(n×∇×n)2−k24∇⋅(n(∇⋅n)+n×∇×n)], where k11, k22,
and k33 are the splay,
twist, and bend elastic constants, respectively, and n is the director axis.The
interaction of the liquid crystal with the surrounding medium is described by a
simple contact interaction(5)fs=(1−(n⋅er)2)W02δ(r−R) characterized by er,
the preferred anchoring direction on the droplet surface and the anchoring
strength W0. The vector R in (5) defines points on the droplet surface.The
interaction with an external magnetic fieldB is described by (6)ff=−μ02Δχ(B⋅n)2, where μ0 is the permeability of free space, B is the external magnetic field,
and Δχ is the difference between the principal values
of the susceptibility tensor corresponding to the directions parallel and
perpendicular to n.The
minimization of the total free energy(7)F=∫(fe+fs+ff)d3r is achieved by
solving the Euler-Lagrange differential equations, which lead to the prediction
of equilibrium structures. With very few exceptions, the solutions are obtained
numerically using relaxation methods
[31, 32].The director field
configurations of some equilibrium structures are schematically illustrated in
Figure10 for spherical and ellipsoid shaped cavities.
Figures 10(a)
and 10(c) are two of the most commonly observed
nematic director configurations resulted from parallel and perpendicular
boundary conditions, respectively. The effect of an
electric field on the bipolar configuration is to
align the symmetry axis parallel to the field with little distortion of the
director configuration within the droplet, as shown in
Figure 10(b). The effect of the electric field on the radial
configuration is to induce a configuration transition to the axial
configuration shown in
Figure 10(d). Particularly in large droplets, metastable
structures are relatively diverse.
Figures 10(e)–10(h) have also
been reported in some special cases [33, 34]. The nematic director configurations in
the liquid crystal droplets in PDLCs help to understand the similar things in
H-PDLCs, although the droplets in H-PDLCs are usually much smaller (less than
100 nm) than those in PDLCs.Schematic illustration of nematic director configurations in
spherical cavities: (a) the bipolar configuration, (b) the bipolar
configuration aligned by an electric field, (c) the radial configuration, (d) the
axial configuration in an applied field, and (e) the toroidal configuration.
The corresponding (f) bipolar, (g) radial,
and (h) axial configurations in elongated
droplets.
(a)(b)(c)(d)(e)(f)(g)(h)In the following
parts of this review article, we will concentrate on the H-PDLCs. H-PDLCs have
wide range applications for displays [35], switchable gratings
[14, 36–38], photonic crystals
[39–41],
lasers
[42–45], microlenses
[46, 47], and so forth. A vitally important method used to
construct H-PDLC devices is photopolymerization induced phase separation (PIPS)
by either UV or visible lasers, depending on the materials used. Different from
the working mechanism of PDLC, H-PDLC works between the diffraction state and
transmission state, as shown in
Figure 11. By applying a proper electric field, the grating can
be switched between “on” and “off” states. The working principle of such a
switch is fairly straightforward. A linearly polarized light beam incident on
the switch will see the phase grating formed by the LC-polymer materials with
different refractive index, and thus be diffracted. When an electric field is
applied, the LC molecular director is reoriented, changing the refractive index
seen by the incoming light. If properly designed, with a suitable voltage
applied, nLC=npolymer can be achieved, and
the Bragg grating disappears. If and when the condition is met, the beam is no
more diffracted.Schematic of an H-PDLC transmission grating.
(a)(b)


## 1.1. Polymer and Photopolymerization

The discovery  of polymers has much contributed to the change of
day-to-day life. In fact, the use of polymers in human history dates back as
early as   Egyptian mummies. Before the mummies were wrapped, the cloth was
soaked in a  solution of oil lavender. When the cloth was dried by exposure to
the sunlight, the oil was converted into a protective polymer. This was a
typical application of photopolymerization. Polymers are involved in almost all
aspects of our lives. Some examples include their use in textile, automotive
and electronic industries, and as building and packing materials.Monomers are the building blocks or structural units of the polymers. For
polymer formation, the monomer must be able to link two or more other monomers,
that is, the functionality of the monomer is not less than 2. Depending on the
functionalities of the monomer, different morphologies of polymer networks can
be formed [1]. If the polymer is constructed from difunctional
monomers, it is a linear chain
(Figure 1(a)). If higher functional monomers are used, a
branched polymer will be formed
(Figure 1(b)). The presence of the branches limits the motion
of chains, thus strengthening the polymer. If the functionality is even higher,
the branches start to connect to one another in three dimensions. The polymer
becomes a cross-linked network
(Figure 1(c)). This cross-linked network enables the polymer to
be much stronger, but also much more brittle.Different polymer
structures. (a) A linear polymer chain.  (b)
A branched chain. (c) A cross-linked network.
(a)(b)(c)The most widely used and simple method of polymer formation
is radical-chain addition polymerization. Polymerization involves initiation,
propagation, transfer, and termination steps. Initiation is the step where
initiating radicals are formed by external stimulations such as light, heat,
gamma-radiation, and redox processes. Light-induced photopolymerization has
several advantages over other methods. The fabrication temperature is low,
usually room temperature, and controllability can be realized by selecting
different irradiation wavelength and light intensity. Moreover, light can be
focused on a particular site, thus polymer can be formed where it is desired.Photopolymerization is a very flexible process and can be
used in various technological applications such as photoresists in modern
electronics. In this process, a film of monomer mixture is placed on the
surface of a silicon wafer and is illuminated through a photomask. After
polymerization, the unpolymerized material can be washed away, leaving the
polymer intact. The polymer-covered areas on the silicon wafer are then used to
resist chemical etching, resulting in integrated circuit formation or printed
circuit board construction. This technology has allowed billions of transistors
to be placed on a single integrated circuit.


## 1.2. Liquid Crystal and Polymer Composites

In the past decade, liquid crystal/polymer composites
have attracted great attention due to their special dynamic characteristics. Liquid
crystal/polymer composites could appear in the form of network or droplet
depending on the polymer and its concentration. In the low-concentration regime
(1–2 wt%) [2, 3], the response time can be much improved, however,
the associated light scattering is quite strong in the visible range. As the
polymer concentration increases to 3–8 wt%, the
polymer-stabilized liquid crystal (PSLC, also known as gel) is formed in a
homogeneous or homeotropic cell [4, 5]. These PSLC cells exhibit an anisotropic light
scattering behavior and have potential for reflective display and telecom
applications [6, 7]. As the polymer concentration increases to
30–40 wt%, the
polymer-dispersed liquid crystal (PDLC) is formed [8, 9]. No surface alignment layers in the PDLC cell are
needed. Micron-sized LC droplets are buried in the polymer matrix. In this
case, visible light is strongly scattered and this scattering is independent of
polarization. In the high polymer concentration regime
(60–70 wt%),
nanoscale holographic PDLC (H-PDLC) droplets are formed [10, 11]. Since the droplet size is much smaller than the
visible wavelength, H-PDLC film is free of light scattering and its response
time is fast (30–200 μs).
However, to reorient LC molecules in these small droplets, a relatively high switching
electric field (15–20 V/μm)
is required. In this approach, no surface alignment is required.


## 1.3. Holography and H-PDLC

Holography is the
process of recording the complete information of the electric field in both
amplitude and relative phase, and consequently a real three-dimensional image
can be reconstructed [12, 13]. Since most of recording materials are only
sensitive to the intensity of the light, interference is a very convenient way
to convert the phase information to the amplitude information. Transmission and
reflection holograms are two common types whose images can be reconstructed by
appropriate use of optics, such as prisms, lenses, and mirrors. The most
attractive and unique property of a hologram is the wavelength and angle
sensitivity, and the ability to manipulate the light that is either reflected
or diffracted. To date, holographic optical elements (HOEs) have found numerous
important roles in photonics.Photopolymers are
one of the holographic materials that have been widely used in the fabrication
of HOEs. Thin volume gratings can be obtained by holographic interference
patterning and subsequent modulation of the refractive index in photopolymer
materials.  They can be classified into
two categories, active and passive devices, depending on their optical
function. An element that can change its refractive index dynamically with
applied external stimulus, such as electric field, optical strength, forces, is
called an active optical element, while an element with a fixed modulation of
the refractive index is called a passive optical element.The marriage
of holography and PDLC materials [14] has produced a number of photonic applications
in information and display systems, electro-optic filters, free-space optical
switches, and wavelength division multiplexer. For a typical PDLC, LCs are
randomly distributed in the polymer matrix and the droplets are randomly
orientated, while in H-PDLC system, the interference of two beams generates
periodic dark and bright fringes in the photopolymer film. In the photopolymer
system, the polymerization rate is higher in the bright region and lower in the
dark region. During the holographic recording process, the monomer diffuses
into the bright region to form polymer and at the same time LCs diffuse into
dark regions. The main advantage of this technique is the fast and single-step
ability to fabricate large area grating structures.


### 1.3.1. Transmission and Reflection Gratings

Depending on the writing geometries, H-PDLC gratings can
be divided into two different modes according to the holography recording
configuration, transmission, and reflection. For transmission H-PDLC, the recording two beams are in the same side of
the medium, as shown in Figure2(a). In transmission H-PDLC, the recorded fringes are perpendicular to the
substrates.  This   type of H-PDLC is very
sensitive to the incident angle of light beam. On the contrary, for
reflecting H-PDLC, the recording light beams are in
the two sides of the recording medium, indicated as
Figure 2(b). In reflection H-PDLC,
the recorded fringes are parallel to the substrates. This type of H-PDLC is
very sensitive to the wavelength. Therefore, we can design the grating pitch to
reflect red, green, or blue light, which makes it potentially useful in
displays. Here, for both reflection and transmission H-PDLCs, the recording light beams are all symmetrical,
and therefore the fringes are parallel or perpendicular to the substrates. If
the recording beams are not symmetrical, slant fringes will be obtained in
H-PDLC.Schematic
holographic recording for (a) transmission and (b) reflection gratings,
respectively.
(a)(b)


### 1.3.2. Raman-Nath and Bragg Gratings

Generally, two
types of diffraction
are distinguished by defining a dimensionless Cook-Klein parameterQ:(1)Q=2πλdnΛ2, where d is the thickness of
the grating, Λ is the grating period, n is the
spatially averaged refractive index of the recording medium, and λ is the incident wavelength.A 		“thick” or
volume grating (Q≥10) corresponds to the Bragg diffraction and
provides the diffraction when incident angle satisfies the phase matching
conditions. Such structures exhibit only two diffraction orders (zeroth and first order) and a strong dependency of
the diffraction efficiency on the angle and wavelength of the incident light.
The diffraction efficiency of the transmission volume phase grating in Bragg
conditions is   described by(2)ηvol=sin2(Δδvol2)=sin2(πn1dλcosθ0), where n1 is the amplitude of refractive index
modulation of the material, θ0 is the Bragg angle of the incident light
within the material.On the other hand, “thin” gratings (Q≤1) correspond to the Raman-Nath regime of the
optical diffraction. In this regime, many orders of the diffraction can be
observed. The efficiency of the first-order Raman-Nath diffraction for the
grating with a sinusoidal modulation of refractive index is given by(3)ηsurf=J12(Δδsurf2)=J12(2πh(nI−nII)λ), where J12(Δδsurf/2) is the first-order Bessel function of the
first kind, h is the depth of the gratings grooves, nI and nII                                                                                                                            are the refractive indices of the adjacent
areas of the grating.


## 1.3.1. Transmission and Reflection Gratings

Depending on the writing geometries, H-PDLC gratings can
be divided into two different modes according to the holography recording
configuration, transmission, and reflection. For transmission H-PDLC, the recording two beams are in the same side of
the medium, as shown in Figure2(a). In transmission H-PDLC, the recorded fringes are perpendicular to the
substrates.  This   type of H-PDLC is very
sensitive to the incident angle of light beam. On the contrary, for
reflecting H-PDLC, the recording light beams are in
the two sides of the recording medium, indicated as
Figure 2(b). In reflection H-PDLC,
the recorded fringes are parallel to the substrates. This type of H-PDLC is
very sensitive to the wavelength. Therefore, we can design the grating pitch to
reflect red, green, or blue light, which makes it potentially useful in
displays. Here, for both reflection and transmission H-PDLCs, the recording light beams are all symmetrical,
and therefore the fringes are parallel or perpendicular to the substrates. If
the recording beams are not symmetrical, slant fringes will be obtained in
H-PDLC.Schematic
holographic recording for (a) transmission and (b) reflection gratings,
respectively.
(a)(b)


## 1.3.2. Raman-Nath and Bragg Gratings

Generally, two
types of diffraction
are distinguished by defining a dimensionless Cook-Klein parameterQ:(1)Q=2πλdnΛ2, where d is the thickness of
the grating, Λ is the grating period, n is the
spatially averaged refractive index of the recording medium, and λ is the incident wavelength.A 		“thick” or
volume grating (Q≥10) corresponds to the Bragg diffraction and
provides the diffraction when incident angle satisfies the phase matching
conditions. Such structures exhibit only two diffraction orders (zeroth and first order) and a strong dependency of
the diffraction efficiency on the angle and wavelength of the incident light.
The diffraction efficiency of the transmission volume phase grating in Bragg
conditions is   described by(2)ηvol=sin2(Δδvol2)=sin2(πn1dλcosθ0), where n1 is the amplitude of refractive index
modulation of the material, θ0 is the Bragg angle of the incident light
within the material.On the other hand, “thin” gratings (Q≤1) correspond to the Raman-Nath regime of the
optical diffraction. In this regime, many orders of the diffraction can be
observed. The efficiency of the first-order Raman-Nath diffraction for the
grating with a sinusoidal modulation of refractive index is given by(3)ηsurf=J12(Δδsurf2)=J12(2πh(nI−nII)λ), where J12(Δδsurf/2) is the first-order Bessel function of the
first kind, h is the depth of the gratings grooves, nI and nII                                                                                                                            are the refractive indices of the adjacent
areas of the grating.


## 1.4. POLICRYPS

Recently, a new kind of holographic grating made of
polymer slices alternated to films of regularly aligned nematic liquid crystals,
so-called POLICRYPS, an acronym of Polymer Liquid Crystal Polymer Slices, was
demonstrated by an Italian research group
[15–18]. This kind of grating was fabricated at an elevated
temperature, which is higher than the nematic-isotropic transition temperature,
thus avoiding the appearance of the nematic phase during the curing process.
After cooling, these structures present a sharp and uniform morphology, without
those optical inhomogeneities which are due to the NLC droplets in usual H-PDLC
samples. As a result, the scattering losses were reduced and the diffraction
efficiency was increased accordingly. The diffraction efficiency of POLYCRYPS
was reported to be as high as 98% [18]. The big difference between H-PDLC and POLYCRYPS
gratings was shown in
Figure 3. Based on POLYCRYPS gratings, Asquini et al. developed a switchable optical
add-drop multiplexer [19]. This designed switchable add-drop multiplexer using
a POLICRYPS grating performs with a cross-talk of −22 dB and with just
0.8 nm
wavelength spacing as used in DWDM optical communication systems. However,
compared to most H-PDLCs, the POLICRYPS grating shows more sensitivity to the
polarization and slower response times including rising time and falling time
[20].Field dependence of transmission curve (squares), first-order diffraction curve
(circles), and total transmission curve (triangles) for (a) a POLICRYPS grating,
(b) a PDLC grating. The insets show typical (a) POLICRYPS, (b) PDLC grating
morphology with the same period, observed under a polarizing optical microscope
[18].
(a)(b)


## 1.5. H-PDFLCs

Ferroelectric liquid crystals (FLCs)
have been demonstrated as excellent candidates for fast electro-optic switching
applications such as displays [21] and optical switches [22]. However, limited device commercialization is available,
partly due to the lack of achieving suitable alignment layers that are both
stable and robust for homogeneous alignment of the FLC. Over the past decade,
researchers have shown different techniques to aid in the alignment of
ferroelectric liquid crystals by combining FLCs and polymer dispersions with
shearing forces [23]. Recently, some researchers investigated the holographic polymer-dispersed
ferroelectric liquid crystals (H-PDFLCs)
[24–26]. In H-PDFLCs, different alignment states of FLCs can
be created by changing the weight ratio of FLCs and monomer.
Figures 4(a)
and 4(b) show the droplet-like and channel-like
morphologies in the FLC-rich regions for H-PDFLC samples with a 50:50 weight ratio
mixture of FLC and monomer and a 40:60 weight ratio mixture, respectively,
which show different polarization properties. The droplet-like samples produced
polarization insensitive while the channel-like ones produced polarization
sensitive electro-optical properties, which indicated different alignments of
FLCs in these two different kinds of samples. In the droplet-like samples, the
FLCs are not well aligned, inducing the lack of grating contrast under a
polarized optical microscope, as shown in
Figure 5. While in the channel-like samples, the FLCs are well
aligned, which produces a sharp grating contrast under the polarized optical
microscope, as shown in
Figure 6. Woltman and his coworkers developed a
phenomenological model to describe the channel-like morphology of the
homogeneously aligned FLCs between the polymer walls [26]. The FLC alignment is parallel to the polymer walls,
which is different   with the nematic-based H-PDLCs, where the nematic LC alignment
is orthogonal to the polymer walls
[27]. The H-PDFLCs studies are still in early stage and
the results are   preliminary. A big advantage   of H-PDFLCs is the faster   response
time. Rapid switching between 20 and 50 μs
[27] has been observed for the H-PDFLCs above a threshold
voltage.H-PDFLC samples constructed from (a) a 50:50 weight
mixture of FLC and monomer, and from (b) a 40:60 weight mixture, respectively [24].
(a)(b)Optical polarizing microscopy of a polarization insensitive FLC H-PDLC grating
(a)90° between crossed
polarizers, (b) 45° between crossed polarizers [25].
(a)(b)Optical polarizing microscopy of a polarization insensitive FLC H-PDLC grating
(a)90°
between crossed polarizers, (b) 45° between crossed polarizers
[25].
(a)(b)


## 1.6. Azo Dye Doped H-PDLC

In some cases, polarization sensitive gratings are
useful as a polarized or unpolarized beam splitter, depending on the
polarization of the incident light. Adding a small amount of azo dye into the
PDLC materials, polarization sensitive gratings can be obtained by holography
[28]. The formation of the polarization gratings is
attributed to the anisotropic adsorption of the azo dyes on the surfaces of
polymer walls, inducing the reorientation of the liquid crystal molecules
[29].
Figure 7
shows a sharp grating contrast under an optical
microscope with a polarizer parallel and perpendicular to the direction of the
stripe in the grating, respectively. Woo et
al., also investigated the
effect of the azo dye on the diffraction efficiency, gratings morphologies, and
electro-optic properties [30]. As the concentration of dye molecules increased,
the liquid crystal droplets became small due to the slow rate of polymerization,
as shown in
Figure 8. In addition, azo dye molecules strongly reorient LC
molecules perpendicular to the grating, giving rise to enhanced diffraction
efficiency and short response times.Grating images observed under an
optical microscope with a polarizer placed in front of the sample. The
transmission axis of the polarizer is (a) parallel and (b) perpendicular to the direction of the stripes in the
grating [29].
(a)(b)SEM micrographs for a transmission HPDLC prepared (a) without and with (b)
0.5%, (c) 1% azo dye
[30].
(a)(b)(c)


## 1.7. Nematic Director Configurations in PDLCs

A typical example
of PDLCs is the light valve configuration presented in
Figure9. The PDLC light valve is fabricated by sandwiching
PDLC material between transparent conducting electrodes with a 10–25 μm spacer. In the
“off” state, the liquid
crystal droplets with positive dielectric anisotropy are randomly oriented in
the film and the size of the droplets is comparable to or larger than an
optical wavelength, usually 2–5 μm. In the translucent state, the film has a
white opaque appearance due to the scattering properties of the film.  Once an electric field is applied, the liquid
crystal molecules in each droplet will align in the direction parallel to the
field direction as shown in
Figure 9
(“on” state). If the ordinary refractive index, no, (perpendicular to the
nematic director) approximately matches the refractive index, np, of the surrounding
polymer matrix, the film will be transparent. Upon removal of the field, the
droplets will return to their random orientation and the film reverts back to
its opaque state. Therefore, the PDLCs are switched between the scattering
state and transmission state.Illustration of the principle behind the operation of a PDLC display. The
material has a white translucent appearance in the “off” state. Application of
a voltage to the transparent conducting electrodes reorients the symmetry axis
of the bipolar droplets parallel to the electric field direction
(“on” state)
and the material becomes transparent if the ordinary refractive index of the
liquid crystal matches that of the polymer matrix.
(a)(b)The
PDLC structure formation through photopolymerization is a complicated process
including physical changes and chemical reactions. Usually, the droplets of a
nearly uniform size are formed during the phase separation. The average droplet
size varies from submicron up to several tens of microns depending on the conditions
during the formation process. The nematic structure inside a droplet is the
result of the interplay between elastic, surface, and external field
interactions. The minimization of the phenomenological free energy is usually
used to determine the stable structure of a chosen system at constant
temperature and volume. It is convenient to divide the free-energy density into
elasticfe, interfacial  fs, and field  ff parts.The
nematic free-energy densityfe can be expressed as (4)fe=12[k11(∇⋅n)2+k22(n⋅∇×n)2+k33(n×∇×n)2−k24∇⋅(n(∇⋅n)+n×∇×n)], where k11, k22,
and k33 are the splay,
twist, and bend elastic constants, respectively, and n is the director axis.The
interaction of the liquid crystal with the surrounding medium is described by a
simple contact interaction(5)fs=(1−(n⋅er)2)W02δ(r−R) characterized by er,
the preferred anchoring direction on the droplet surface and the anchoring
strength W0. The vector R in (5) defines points on the droplet surface.The
interaction with an external magnetic fieldB is described by (6)ff=−μ02Δχ(B⋅n)2, where μ0 is the permeability of free space, B is the external magnetic field,
and Δχ is the difference between the principal values
of the susceptibility tensor corresponding to the directions parallel and
perpendicular to n.The
minimization of the total free energy(7)F=∫(fe+fs+ff)d3r is achieved by
solving the Euler-Lagrange differential equations, which lead to the prediction
of equilibrium structures. With very few exceptions, the solutions are obtained
numerically using relaxation methods
[31, 32].The director field
configurations of some equilibrium structures are schematically illustrated in
Figure10 for spherical and ellipsoid shaped cavities.
Figures 10(a)
and 10(c) are two of the most commonly observed
nematic director configurations resulted from parallel and perpendicular
boundary conditions, respectively. The effect of an
electric field on the bipolar configuration is to
align the symmetry axis parallel to the field with little distortion of the
director configuration within the droplet, as shown in
Figure 10(b). The effect of the electric field on the radial
configuration is to induce a configuration transition to the axial
configuration shown in
Figure 10(d). Particularly in large droplets, metastable
structures are relatively diverse.
Figures 10(e)–10(h) have also
been reported in some special cases [33, 34]. The nematic director configurations in
the liquid crystal droplets in PDLCs help to understand the similar things in
H-PDLCs, although the droplets in H-PDLCs are usually much smaller (less than
100 nm) than those in PDLCs.Schematic illustration of nematic director configurations in
spherical cavities: (a) the bipolar configuration, (b) the bipolar
configuration aligned by an electric field, (c) the radial configuration, (d) the
axial configuration in an applied field, and (e) the toroidal configuration.
The corresponding (f) bipolar, (g) radial,
and (h) axial configurations in elongated
droplets.
(a)(b)(c)(d)(e)(f)(g)(h)In the following
parts of this review article, we will concentrate on the H-PDLCs. H-PDLCs have
wide range applications for displays [35], switchable gratings
[14, 36–38], photonic crystals
[39–41],
lasers
[42–45], microlenses
[46, 47], and so forth. A vitally important method used to
construct H-PDLC devices is photopolymerization induced phase separation (PIPS)
by either UV or visible lasers, depending on the materials used. Different from
the working mechanism of PDLC, H-PDLC works between the diffraction state and
transmission state, as shown in
Figure 11. By applying a proper electric field, the grating can
be switched between “on” and “off” states. The working principle of such a
switch is fairly straightforward. A linearly polarized light beam incident on
the switch will see the phase grating formed by the LC-polymer materials with
different refractive index, and thus be diffracted. When an electric field is
applied, the LC molecular director is reoriented, changing the refractive index
seen by the incoming light. If properly designed, with a suitable voltage
applied, nLC=npolymer can be achieved, and
the Bragg grating disappears. If and when the condition is met, the beam is no
more diffracted.Schematic of an H-PDLC transmission grating.
(a)(b)


## 2. H-PDLC Materials

One of the fundamentals of research
on H-PDLCs is to develop new formulations of materials. All formulations have
two underlying components: monomer and liquid crystal. In addition, to improve
the performance of H-PDLCs, some other components may be added into the
material set, such as photoinitiator dye, coinitiator, surfactant, and so on. Both the
ratios of these components and the components themselves will determine the
performance of H-PDLC.


### 2.1. Ultraviolet (UV) Curing

The general
material  formulation for a UV-curing prepolymer mixture consists of the
thiol-ene photopolymers, NOA series (Norland Inc.), and photoinitiator,
Irgacure 1173, which is developed by Natarajan and his coworkers, specially for
the wavelength of 363 nm from Ar+ laser
[48]. NOA 65 is the most common one in NOA series,
which is widely   used in photonics for adhesion of optical components. Although
the commercial NOA 65 has a proprietary UV initiator, the addition of Irgacure
1173 UV initiator will greatly enhance the diffraction
efficiency.The advantages of
such kind of material system compared to the acrylate system are smaller
shrinkage, more stable electro-optical properties, and long-term stability. The
droplets of LC are bigger than those in acrylate system, leading to a decreased
driving voltage. However, the response time is relatively long, in the order of
milliseconds.


### 2.2. Visible (Blue and Green) Curing

The above NOA series
materials can be also polymerized under visible light exposure if another kind
of photoinitiator is doped into these materials. The reflection mode H-PDLC
grating was made using NOA 81 doped Rose Bengal (RB) under a 532 nm laser
exposure by Wu and Fuh [49].
However, generally, for
such kind of materials, high exposure intensity is needed to ensure a good
structure grating formation.In the visible
range, the acrylate material system is the most common one used to
date, which
cures at 488/514.5 nm produced by Ar+ laser or 532 nm produced by a
frequency-doubled Nd:YAG laser. Sutherland et al., firstly fabricated the Bragg grating using acrylate
materials [14].The most common
recipe of the H-PDLC for the visible curing generally contains a
multifunctional monomer, chain extender N-vinyl pyrrolidinone (NVP),
photoinitiator RB, coinitiator N-phenylglycine (NPG), surfactant, and nematic
liquid crystal. Different monomers with different functionalities were tried in
this kind of formulation, such as Dipentaerythritol penta-/hexa-acrylate
(DPPHA), pentaerythritol triacrylate (PETA), trimethylolpropane triacrylate (TMPTA),
pentaerythritol tetraacrylate [PET(etra)A], and Tri(propylene glycol)
diacrylate (TPGDA). Their chemical structures were shown in
Figure12. The chemical structures of RB, NPG, and NVP are
shown in Figure 13. The advantages of the
photoinitiator (RB) chosen are that it has a broad absorption
spectrum in the
region of 470–550 nm (as
indicated in
Figure 14) and it is very
suitable for excitation with argon ion laser wavelengths as well as
frequency-doubled Nd-YAG (532 nm) [50].Figure 12
Chemical structures of the five
monomers.Figure 13
Chemical structures of H-PDLC
components.Figure 14
Absorption spectrum of the
photoinitiator dye RB.


### 2.3. Visible (Red) Curing

Given the abundance and low
cost of He-Ne lasers and red diode lasers, the feasibility investigation of
recording a H-PDLC grating by utilizing 633 nm wavelength of an He-Ne laser is
hence motivated. Ramsey and Sharma firstly reported H-PDLC grating fabrication
using He-Ne laser
[51, 52]. The big significance is
to make H-PDLC to be fabricated using a very small power laser and lower the
cost of the fabrication.The material system for
He-Ne laser curing is composed of monofunctional acrylic oligomer, CN135, cross-linker,
SR295, and initiator (photo-oxidant dye), methylene blue and coinitiator,
p-toluenesulfonic acid.


### 2.4. Near Infrared (NIR) Curing

The development of
H-PDLC material systems for NIR curing also attracts much attention without
exception. Pilot et al.
developed the material system under NIR range in 1999
[53]. The materials used include monomer,
Di-penta-erithrithol-penta-acrylate (DPEPA) doped with 2-ethoxy-ethoxy-ethyl
acrylate ester (2EEEA), Cyanine dye, IR-140, initiator, ethyl-di-methyl-amino-benzoate
(EDMABzt), and electron donor, CBr4. An 834 or 850 nm laser diode was used to
illuminate the material. The material can achieve good resolution (2500
lines/mm) and shows excellent long-term chemical stability. However, same as
the acrylate system, the switching voltage is still relatively high.


## 2.1. Ultraviolet (UV) Curing

The general
material  formulation for a UV-curing prepolymer mixture consists of the
thiol-ene photopolymers, NOA series (Norland Inc.), and photoinitiator,
Irgacure 1173, which is developed by Natarajan and his coworkers, specially for
the wavelength of 363 nm from Ar+ laser
[48]. NOA 65 is the most common one in NOA series,
which is widely   used in photonics for adhesion of optical components. Although
the commercial NOA 65 has a proprietary UV initiator, the addition of Irgacure
1173 UV initiator will greatly enhance the diffraction
efficiency.The advantages of
such kind of material system compared to the acrylate system are smaller
shrinkage, more stable electro-optical properties, and long-term stability. The
droplets of LC are bigger than those in acrylate system, leading to a decreased
driving voltage. However, the response time is relatively long, in the order of
milliseconds.


## 2.2. Visible (Blue and Green) Curing

The above NOA series
materials can be also polymerized under visible light exposure if another kind
of photoinitiator is doped into these materials. The reflection mode H-PDLC
grating was made using NOA 81 doped Rose Bengal (RB) under a 532 nm laser
exposure by Wu and Fuh [49].
However, generally, for
such kind of materials, high exposure intensity is needed to ensure a good
structure grating formation.In the visible
range, the acrylate material system is the most common one used to
date, which
cures at 488/514.5 nm produced by Ar+ laser or 532 nm produced by a
frequency-doubled Nd:YAG laser. Sutherland et al., firstly fabricated the Bragg grating using acrylate
materials [14].The most common
recipe of the H-PDLC for the visible curing generally contains a
multifunctional monomer, chain extender N-vinyl pyrrolidinone (NVP),
photoinitiator RB, coinitiator N-phenylglycine (NPG), surfactant, and nematic
liquid crystal. Different monomers with different functionalities were tried in
this kind of formulation, such as Dipentaerythritol penta-/hexa-acrylate
(DPPHA), pentaerythritol triacrylate (PETA), trimethylolpropane triacrylate (TMPTA),
pentaerythritol tetraacrylate [PET(etra)A], and Tri(propylene glycol)
diacrylate (TPGDA). Their chemical structures were shown in
Figure12. The chemical structures of RB, NPG, and NVP are
shown in Figure 13. The advantages of the
photoinitiator (RB) chosen are that it has a broad absorption
spectrum in the
region of 470–550 nm (as
indicated in
Figure 14) and it is very
suitable for excitation with argon ion laser wavelengths as well as
frequency-doubled Nd-YAG (532 nm) [50].Figure 12
Chemical structures of the five
monomers.Figure 13
Chemical structures of H-PDLC
components.Figure 14
Absorption spectrum of the
photoinitiator dye RB.


## 2.3. Visible (Red) Curing

Given the abundance and low
cost of He-Ne lasers and red diode lasers, the feasibility investigation of
recording a H-PDLC grating by utilizing 633 nm wavelength of an He-Ne laser is
hence motivated. Ramsey and Sharma firstly reported H-PDLC grating fabrication
using He-Ne laser
[51, 52]. The big significance is
to make H-PDLC to be fabricated using a very small power laser and lower the
cost of the fabrication.The material system for
He-Ne laser curing is composed of monofunctional acrylic oligomer, CN135, cross-linker,
SR295, and initiator (photo-oxidant dye), methylene blue and coinitiator,
p-toluenesulfonic acid.


## 2.4. Near Infrared (NIR) Curing

The development of
H-PDLC material systems for NIR curing also attracts much attention without
exception. Pilot et al.
developed the material system under NIR range in 1999
[53]. The materials used include monomer,
Di-penta-erithrithol-penta-acrylate (DPEPA) doped with 2-ethoxy-ethoxy-ethyl
acrylate ester (2EEEA), Cyanine dye, IR-140, initiator, ethyl-di-methyl-amino-benzoate
(EDMABzt), and electron donor, CBr4. An 834 or 850 nm laser diode was used to
illuminate the material. The material can achieve good resolution (2500
lines/mm) and shows excellent long-term chemical stability. However, same as
the acrylate system, the switching voltage is still relatively high.


## 3. Fabrication

The
prepolymer and LC were mechanically blended according to the appropriate weight
ratio and stirred in an ultrasonic cleaner at a temperature higher than the
clearing point of the liquid crystal for at least 2 hours to form a homogeneous
mixture in dark. After that, the mixture was injected in a cell by capillary
effect or in vacuum, which was formed by two pieces of indium-tin-oxide (ITO)
coated glass, and then subjected to laser exposure. The cell thickness can be
controlled by the bead spacers between the two pieces of ITO glass. During
exposure, the pattern formed by two interfering beams was recorded in the LC
cell. After exposure, the samples were further cured for 15 minutes by mercury
lamp to ensure the complete polymerization of prepolymer.Depending on the writing geometries,
transmission and reflection mode gratings can be fabricated, respectively. In
the case of writing transmission gratings, the writing beams are coincident on
the same side of the sample with an angle between the two writing beams and the
resulting grating vector is parallel to the substrates. In reflection gratings,
the writing beams are counter propagating and the resulting grating vector is
perpendicular to the substrates.
Figure15
shows the specially designed setups to fabricate the
transmission and reflection gratings, respectively. The use of single prism in
the fabrication setups decreases the complexity of the optics. More importantly,
the setups are self-adaptive, that is, the effect of the external vibration
during the fabrication process is minimized. The LC cells filled with prepolymer mixture stick
onto the hypotenuse of the prism using the index matching liquid.Experimental setups of holographic (a) transmission and (b) reflection grating
recording, respectively.
(a)(b)


## 4. Characterization

### 4.1. Structures

For
morphology analysis, the samples were fractured first by sinking them in liquid
nitrogen. Then the samples with one-side ITO glass removed are soaked in
ethanol for more than 12 hours in order to completely remove the LC. After
drying, the morphologies can be investigated by high-resolution optical
microscope, atomic force microscopy (AFM), or scanning electron microscope
(SEM).AFM
(Dimension 3000 Scanning Probe Microscope, Digital Instruments) is used to
measure the surface morphology of the films. The root mean square (RMS)
roughness is obtained from the digital image-processing package of the AFM
system.Field
emission gun scanning electron microscopy (FEG-SEM) (JEOL JSM 6700F) is used to
observe the surface morphology of the films. Since the H-PDLC films are
nonconductive polymers, a thin layer of gold or platinum is coated on the
H-PDLC surface by a JEOL JFC-1200 fine coater in order to eliminate the charging
effect.


### 4.2. Electro-Optical Properties

(i) Diffraction Efficiency
For the switchable volume gratings, diffraction efficiency is a very important
parameter. It is defined as the diffracted power in the first order divided by
the incident power. All samples were measured with polarized He-Ne laser (λ=633nm) at room temperature. The
diffraction efficiency for p- and s-polarized light was measured and
compared, respectively.(ii) Response Time
Figure16 shows the measurement setup of the response time.
Polarized light from a He-Ne laser was used for the diffraction/transmittance
properties and the response time studies. The laser beam was incident on the
sample with the exact Bragg angle, and the diffraction was measured by a
photomultiplier. In the measurements, the H-PDLC Bragg grating was driven by an
AC signal with various frequencies. In our measurement, a high-voltage
amplifier/function generator (Trek, Model: 609E-6-FG) is used to generate the
AC signal with different  waveforms  and frequencies. For the response time measurements, the photodetector signal
was fed into one input channel of an oscilloscope (Agilent, Model: 54641A). The
voltage signal, which was used to trigger the oscilloscope, was fed into
another input channel of the oscilloscope. From the waveforms captured by the oscilloscope,
the rising and falling times can be subtracted.
The turn-on time is the time required for the
transmitted intensity to change from 10% to 90% upon application of the voltage,
and the turn-off time is the time required for the transmitted intensity to
decrease from 90% to 10% after removal of the voltage. The switching time is
the sum of the turn-on and turn-off times. Typically, the turn-on time is
inversely proportional to the applied voltage and is limited by the viscosity
of the liquid crystal. The turn-off time is typically inversely proportional to
droplet size, and is governed by the relaxation processes.
The switching voltage depends on the droplet
morphology and the electrical properties of the liquid crystal and the polymer
matrix. Typically, the switching voltage is inversely proportional to the
droplet size. Small droplets enhance the liquid crystal’s elastic deformation
energy, and thus larger voltages are required to reorient the liquid crystal
molecules confined to the droplets and thus to switch on a PDLC. The enhanced
elastic deformation energy associated with small droplets also leads to shorter
turn-off times. The switching voltage also depends on the resistive properties
of the liquid crystal droplets and surrounding polymer. For example, higher
applied voltages are required if the resistive properties reduce the electric
field experienced by the droplets.Figure 16
Measurement setup of the response time.


## 4.1. Structures

For
morphology analysis, the samples were fractured first by sinking them in liquid
nitrogen. Then the samples with one-side ITO glass removed are soaked in
ethanol for more than 12 hours in order to completely remove the LC. After
drying, the morphologies can be investigated by high-resolution optical
microscope, atomic force microscopy (AFM), or scanning electron microscope
(SEM).AFM
(Dimension 3000 Scanning Probe Microscope, Digital Instruments) is used to
measure the surface morphology of the films. The root mean square (RMS)
roughness is obtained from the digital image-processing package of the AFM
system.Field
emission gun scanning electron microscopy (FEG-SEM) (JEOL JSM 6700F) is used to
observe the surface morphology of the films. Since the H-PDLC films are
nonconductive polymers, a thin layer of gold or platinum is coated on the
H-PDLC surface by a JEOL JFC-1200 fine coater in order to eliminate the charging
effect.


## 4.2. Electro-Optical Properties

(i) Diffraction Efficiency
For the switchable volume gratings, diffraction efficiency is a very important
parameter. It is defined as the diffracted power in the first order divided by
the incident power. All samples were measured with polarized He-Ne laser (λ=633nm) at room temperature. The
diffraction efficiency for p- and s-polarized light was measured and
compared, respectively.(ii) Response Time
Figure16 shows the measurement setup of the response time.
Polarized light from a He-Ne laser was used for the diffraction/transmittance
properties and the response time studies. The laser beam was incident on the
sample with the exact Bragg angle, and the diffraction was measured by a
photomultiplier. In the measurements, the H-PDLC Bragg grating was driven by an
AC signal with various frequencies. In our measurement, a high-voltage
amplifier/function generator (Trek, Model: 609E-6-FG) is used to generate the
AC signal with different  waveforms  and frequencies. For the response time measurements, the photodetector signal
was fed into one input channel of an oscilloscope (Agilent, Model: 54641A). The
voltage signal, which was used to trigger the oscilloscope, was fed into
another input channel of the oscilloscope. From the waveforms captured by the oscilloscope,
the rising and falling times can be subtracted.
The turn-on time is the time required for the
transmitted intensity to change from 10% to 90% upon application of the voltage,
and the turn-off time is the time required for the transmitted intensity to
decrease from 90% to 10% after removal of the voltage. The switching time is
the sum of the turn-on and turn-off times. Typically, the turn-on time is
inversely proportional to the applied voltage and is limited by the viscosity
of the liquid crystal. The turn-off time is typically inversely proportional to
droplet size, and is governed by the relaxation processes.
The switching voltage depends on the droplet
morphology and the electrical properties of the liquid crystal and the polymer
matrix. Typically, the switching voltage is inversely proportional to the
droplet size. Small droplets enhance the liquid crystal’s elastic deformation
energy, and thus larger voltages are required to reorient the liquid crystal
molecules confined to the droplets and thus to switch on a PDLC. The enhanced
elastic deformation energy associated with small droplets also leads to shorter
turn-off times. The switching voltage also depends on the resistive properties
of the liquid crystal droplets and surrounding polymer. For example, higher
applied voltages are required if the resistive properties reduce the electric
field experienced by the droplets.Figure 16
Measurement setup of the response time.


## 5. Phase Separation Kinetics

### 5.1. Formation Kinetics of H-PDLCs

The
grating formation process is schemed in
Figure17. Grating formation ensues when the material is
irradiated with a sinusoidal intensity pattern. In the bright regions,
absorption by the photoinitiator results in a highly reactive triplet state.
The coinitiator undergoes an electron-transfer reaction with this triplet state
to create a free radical. Free-radical polymerization is then initiated. The
presence of the chain-extender promotes cross-linking of the polymer chains
produced. The result is a rapid consumption of monomers and polymer growth in
the bright regions of the intensity pattern.Figure 17
Schematic formation process of H-PDLC gratings. (a) Homogeneous mixture before exposure.
(b) The exposure intensity distribution is sinusoidal. In the bright region, the monomer polymerizes first.
The liquid crystal diffuses to the dark region. (c) Finally, alternate polymer-rich and liquid crystal region formed.
The refractive index is modulated alongx-axis direction.Ignoring interactions between
various components, the chemical potential for theith component of the mixture may be approximated by (8)μi=μi0+kBTln(Ni∑jNj), where μi0 is the chemical potential of
the pure ith component, Ni is the number of molecules of the ith
component, kB is Boltzmann's constant, and T is the
absolute temperature. Under thermodynamic equilibrium, the sum μi is a constant. A gradient in
the light intensity preferentially initiates photopolymerization in the high-intensity
regions. Since the mixture is dominated by
monomer and LC components initially, we see that the chemical potential of the
monomer decreases while that of the LC increases in the bright regions. In the
neighboring dark regions, at least for early times, the chemical potentials are
all equal to their initial equilibrium values. Hence, spatial gradients in the
chemical potential are established which produces a diffusion of monomers (and
other reactants) into the bright regions, and a counter-diffusion of LC into
the dark regions. This process continues until a new equilibrium chemical
potential is established.As
the growing polymer network propagates outward into the dark regions, gelation
of the system ensues. Fluctuations in the free energy of the system result in
local minima where a distinct LC phase begins to form. Similar to the
discussion of the droplet formation in PDLCs in
Section1.7, the total droplet
energy is minimized at a critical droplet radius, Rc, which is
proportional to the surface tension of the droplet, σ. A droplet of this size will be stable and
can grow if more LC molecules are available for incorporation or if coalescence
with a nearby droplet is feasible. Growth will eventually terminate when the
surrounding polymer rigidly locks the droplet in place and prevents further LC
diffusion.A big disadvantage of free-radical photopolymerization is
its susceptibility to oxygen inhibition. This inhibition is particularly
problematic in thin film and coating applications where oxygen diffusion plays
a significant role in increasing cure times, which often results in incomplete conversion
[54, 55]. When oxygen, which is
essentially a biradical in its electronic ground state, reacts with a free radical,
it forms a peroxy radical, which is much less reactive.As
a result, the kinetic reactions of photo-induced free-radical polymerization
can be summarized by the following four steps.Initiation:   (9)I→hνR•R•+Mn→kiMn•.Propagation:(10)Mn•+M→kpMn+1•.Termination:(11)Mn•+Mm•→ktcMn+mMn•+Mm•→ktdMn+Mm.Inhibition by Oxygen:(12)M•+O2→M−O−O•M−O−O•+M→NoReaction.


### 5.2. One-Dimensional Diffusion Model

Physically, the formation of the H-PDLC
gratings can be well simulated using one-dimensional (1D) diffusion model.
Assuming the monomers are free to diffuse in the materials, a 1D diffusion
equation can be written for the monomer concentration as follows [56, 57]:(13)dϕ(x,t)dt=−F(x,t)ϕ(x,t)+ddx(D(x,t)dϕ(x,t)dx), where ϕ(x,t) is the monomer concentration, F(x,t) is the
polymerization rate, and D(x,t) is the diffusion rate.When
monomers react and bind with the growing polymer radical, free volume is
generated since the covalent single carbon bond in the polymer is as much as
50% shorter than the Van der Waals bond in the liquid monomer state. The
mechanical response of the medium to reduce this free volume leads to physical
shrinkage of the system. Assuming the volume shrinkage rate isz, which denotes
that the monomers convert into 1/(1+z)
polymer in unit volume. Therefore, the concentration of the polymer can be written
as (14)ψ(x,t)=∫0t11+zF(x,t′)ϕ(x,t′)dt′, the concentration of liquid crystal can be
written as (15)η(x,t)=∫0t[z1+zF(x,t′)ϕ(x,t′)−ddx(D(x,t′)dϕ(x,t′)dx)]dt′. In
the whole system, ψ, ϕ,
and η are satisfying the equation ψ+ϕ+η=1.
So there are only two independent parameters in this system.Consider
a holographic grating formed by the interference of two plane waves in liquid
crystal-polymer composites. The spatial distribution of optical intensities is(16)I(x,t)=I0[1+Vcos(kx)], where I0 is the average intensities, V is the fringe visibility, k=2π/Λ,
and Λ is the grating pitch. We assume the
polymerization rate to be proportional to the exposure intensities, so we may
write (17)F(x,t)=F0[1+Vcos(kx)], where F0=κI0,
and κ is a constant.For our case, the monomer concentration will
also be periodic and an even function ofx.
Thus, we can write ϕ(x,t), ψ(x,t),
and η(x,t) as Fourier series: (18)ϕ(x,t)=∑i=0∞ϕi(t)cos(ikx),(19)ψ(x,t)=∑i=0∞ψi(t)cos(ikx),(20)η(x,t)=∑i=0∞ηi(t)cos(ikx).Substituting (18)–(20) into
(13)–(15)
and assuming the amplitude of the harmonics of order
greater   than 3 can be ignored, we obtain a set of coupled differential
equations  as follows: (21)dϕ0(ξ)dξ=−ϕ0(ξ)−12Vϕ1(ξ),(22)dϕ1(ξ)dξ=−Vϕ0(ξ)−[1+Rexp(−αξ)cosh(αVξ)]ϕ1(ξ)−[12V−Rexp(−αξ)sinh(αVξ)]ϕ2(ξ),(23)dϕ2(ξ)dξ=−[12V−Rexp(−αξ)sinh(αVξ)]ϕ1(ξ)−[1+4Rexp(−αξ)cosh(αVξ)]ϕ2(ξ)−[12V−3Rexp(−αξ)sinh(αVξ)]ϕ3(ξ),(24)dϕ3(ξ)dξ=−[12V−Rexp(−αξ)sinh(αVξ)]ϕ2(ξ)−[1+9Rexp(−αξ)sinh(αVξ)]ϕ3(ξ), where R=Dak2/F0, ξ=F0t=κI0t. We can also
treat ψ, η with the  same method.  Finally, the equations are dependent on
four parameters: the ratio of diffusion rate to
polymerization rate, R, the constant
that characterizes the rate of decrease of the diffusion coefficients, α,
the shrinkage rate when the monomers polymerize, z, and the fringe visibility, V.
We solved the equations numerically using different parameters and got some useful
results.For our case, the ratio of monomer and liquid
crystal is 7:3. However, (21)–(24)
are solved numerically using MATLAB. The amplitude of
the first four harmonics of monomer concentration distribution, polymer
concentration distribution, and liquid crystal concentration distribution are
plotted as a function of exposure ξ,
with R=0.5, V=1, z=0.05,
and α=0.1.
Figure 18(a)
shows that all the harmonics of monomer
concentration finally diminish with the time increment. This means the monomers
are all polymerized. The corresponding harmonics of polymer concentration and
liquid crystal concentration will saturate when the monomer are totally
exhausted. Because of the shrinkage of polymer, we also can see that the
polymer concentration does not reach the maximum 0.7 and the liquid crystal
concentration will also have a small increment to fill with the interspace
induced by the polymerization.The harmonics of (a) monomer,
(b)  polymer, and (c) liquid crystal concentration
as a function of time,
respectively.
(a)(b)(c)The
ratio of diffusion rate to polymerization rateR is a very important parameter
that controls the formation of H-PDLC gratings.
Figure 19
shows the amplitude of each harmonic of polymer
concentration as a function of exposure ξ for different R, with  V=1,  z=0.05,
and  α=0.1.
In general, the polymer concentration increases with the exposure and will
reach a saturation value. We can see that the saturation depends strongly on R. Great R results in large saturation values. However, for R≫1,
there is almost no difference about the saturation for the zero harmonic. From
Figure 19(a), we can see the zero harmonics are almost the same
for R=5 and R=50.
From Figure 19(c), we can see the smaller the R, the stronger the second
harmonic. When R≫1,
the harmonics whose order more than one can be ignored because the zero and
first-order harmonics dominate absolutely.The amplitude of each harmonic of polymer concentration as a
function of exposureξ for
different R with V=1, z=0.05, and α=0.1.
(a)(b)(c)(d)Figure20 shows the relationship between the saturation of the
first and second harmonics and the fringe visibility V for different R. We can
see that the larger the R, the more linear the saturation of the harmonics. For R=50,
the saturation of the harmonics are completely linear.  We also can see that the second harmonic is
almost zero when R=50,
which means no influence for the polymerization for the second harmonic.The relationship between the
saturation of the first and second harmonics
and the fringe visibilityV
for different R.
(a)(b)Figure21 shows the relationship between the saturation of the
first and second harmonics and α.
We can see that αdoes not affect the grating formation
strongly.The relationship between the saturation of
the first and second harmonics andα.
(a)(b)Figure22
shows the polymer distribution profile for different R.
The profile is purely sinusoidal for
large R. When the R decreases, the higher harmonics will
be obtained. So a large R can produce
a good grating structure.Figure 22
The polymer distribution profile for differentR.Many researchers studied the H-PDLC grating
formation using this simple model
[58–60]. Kyu
et al. gave a 2D simulation using time-dependent Ginzburg-Landau equations (TDGL model C) [61].


## 5.1. Formation Kinetics of H-PDLCs

The
grating formation process is schemed in
Figure17. Grating formation ensues when the material is
irradiated with a sinusoidal intensity pattern. In the bright regions,
absorption by the photoinitiator results in a highly reactive triplet state.
The coinitiator undergoes an electron-transfer reaction with this triplet state
to create a free radical. Free-radical polymerization is then initiated. The
presence of the chain-extender promotes cross-linking of the polymer chains
produced. The result is a rapid consumption of monomers and polymer growth in
the bright regions of the intensity pattern.Figure 17
Schematic formation process of H-PDLC gratings. (a) Homogeneous mixture before exposure.
(b) The exposure intensity distribution is sinusoidal. In the bright region, the monomer polymerizes first.
The liquid crystal diffuses to the dark region. (c) Finally, alternate polymer-rich and liquid crystal region formed.
The refractive index is modulated alongx-axis direction.Ignoring interactions between
various components, the chemical potential for theith component of the mixture may be approximated by (8)μi=μi0+kBTln(Ni∑jNj), where μi0 is the chemical potential of
the pure ith component, Ni is the number of molecules of the ith
component, kB is Boltzmann's constant, and T is the
absolute temperature. Under thermodynamic equilibrium, the sum μi is a constant. A gradient in
the light intensity preferentially initiates photopolymerization in the high-intensity
regions. Since the mixture is dominated by
monomer and LC components initially, we see that the chemical potential of the
monomer decreases while that of the LC increases in the bright regions. In the
neighboring dark regions, at least for early times, the chemical potentials are
all equal to their initial equilibrium values. Hence, spatial gradients in the
chemical potential are established which produces a diffusion of monomers (and
other reactants) into the bright regions, and a counter-diffusion of LC into
the dark regions. This process continues until a new equilibrium chemical
potential is established.As
the growing polymer network propagates outward into the dark regions, gelation
of the system ensues. Fluctuations in the free energy of the system result in
local minima where a distinct LC phase begins to form. Similar to the
discussion of the droplet formation in PDLCs in
Section1.7, the total droplet
energy is minimized at a critical droplet radius, Rc, which is
proportional to the surface tension of the droplet, σ. A droplet of this size will be stable and
can grow if more LC molecules are available for incorporation or if coalescence
with a nearby droplet is feasible. Growth will eventually terminate when the
surrounding polymer rigidly locks the droplet in place and prevents further LC
diffusion.A big disadvantage of free-radical photopolymerization is
its susceptibility to oxygen inhibition. This inhibition is particularly
problematic in thin film and coating applications where oxygen diffusion plays
a significant role in increasing cure times, which often results in incomplete conversion
[54, 55]. When oxygen, which is
essentially a biradical in its electronic ground state, reacts with a free radical,
it forms a peroxy radical, which is much less reactive.As
a result, the kinetic reactions of photo-induced free-radical polymerization
can be summarized by the following four steps.Initiation:   (9)I→hνR•R•+Mn→kiMn•.Propagation:(10)Mn•+M→kpMn+1•.Termination:(11)Mn•+Mm•→ktcMn+mMn•+Mm•→ktdMn+Mm.Inhibition by Oxygen:(12)M•+O2→M−O−O•M−O−O•+M→NoReaction.


## 5.2. One-Dimensional Diffusion Model

Physically, the formation of the H-PDLC
gratings can be well simulated using one-dimensional (1D) diffusion model.
Assuming the monomers are free to diffuse in the materials, a 1D diffusion
equation can be written for the monomer concentration as follows [56, 57]:(13)dϕ(x,t)dt=−F(x,t)ϕ(x,t)+ddx(D(x,t)dϕ(x,t)dx), where ϕ(x,t) is the monomer concentration, F(x,t) is the
polymerization rate, and D(x,t) is the diffusion rate.When
monomers react and bind with the growing polymer radical, free volume is
generated since the covalent single carbon bond in the polymer is as much as
50% shorter than the Van der Waals bond in the liquid monomer state. The
mechanical response of the medium to reduce this free volume leads to physical
shrinkage of the system. Assuming the volume shrinkage rate isz, which denotes
that the monomers convert into 1/(1+z)
polymer in unit volume. Therefore, the concentration of the polymer can be written
as (14)ψ(x,t)=∫0t11+zF(x,t′)ϕ(x,t′)dt′, the concentration of liquid crystal can be
written as (15)η(x,t)=∫0t[z1+zF(x,t′)ϕ(x,t′)−ddx(D(x,t′)dϕ(x,t′)dx)]dt′. In
the whole system, ψ, ϕ,
and η are satisfying the equation ψ+ϕ+η=1.
So there are only two independent parameters in this system.Consider
a holographic grating formed by the interference of two plane waves in liquid
crystal-polymer composites. The spatial distribution of optical intensities is(16)I(x,t)=I0[1+Vcos(kx)], where I0 is the average intensities, V is the fringe visibility, k=2π/Λ,
and Λ is the grating pitch. We assume the
polymerization rate to be proportional to the exposure intensities, so we may
write (17)F(x,t)=F0[1+Vcos(kx)], where F0=κI0,
and κ is a constant.For our case, the monomer concentration will
also be periodic and an even function ofx.
Thus, we can write ϕ(x,t), ψ(x,t),
and η(x,t) as Fourier series: (18)ϕ(x,t)=∑i=0∞ϕi(t)cos(ikx),(19)ψ(x,t)=∑i=0∞ψi(t)cos(ikx),(20)η(x,t)=∑i=0∞ηi(t)cos(ikx).Substituting (18)–(20) into
(13)–(15)
and assuming the amplitude of the harmonics of order
greater   than 3 can be ignored, we obtain a set of coupled differential
equations  as follows: (21)dϕ0(ξ)dξ=−ϕ0(ξ)−12Vϕ1(ξ),(22)dϕ1(ξ)dξ=−Vϕ0(ξ)−[1+Rexp(−αξ)cosh(αVξ)]ϕ1(ξ)−[12V−Rexp(−αξ)sinh(αVξ)]ϕ2(ξ),(23)dϕ2(ξ)dξ=−[12V−Rexp(−αξ)sinh(αVξ)]ϕ1(ξ)−[1+4Rexp(−αξ)cosh(αVξ)]ϕ2(ξ)−[12V−3Rexp(−αξ)sinh(αVξ)]ϕ3(ξ),(24)dϕ3(ξ)dξ=−[12V−Rexp(−αξ)sinh(αVξ)]ϕ2(ξ)−[1+9Rexp(−αξ)sinh(αVξ)]ϕ3(ξ), where R=Dak2/F0, ξ=F0t=κI0t. We can also
treat ψ, η with the  same method.  Finally, the equations are dependent on
four parameters: the ratio of diffusion rate to
polymerization rate, R, the constant
that characterizes the rate of decrease of the diffusion coefficients, α,
the shrinkage rate when the monomers polymerize, z, and the fringe visibility, V.
We solved the equations numerically using different parameters and got some useful
results.For our case, the ratio of monomer and liquid
crystal is 7:3. However, (21)–(24)
are solved numerically using MATLAB. The amplitude of
the first four harmonics of monomer concentration distribution, polymer
concentration distribution, and liquid crystal concentration distribution are
plotted as a function of exposure ξ,
with R=0.5, V=1, z=0.05,
and α=0.1.
Figure 18(a)
shows that all the harmonics of monomer
concentration finally diminish with the time increment. This means the monomers
are all polymerized. The corresponding harmonics of polymer concentration and
liquid crystal concentration will saturate when the monomer are totally
exhausted. Because of the shrinkage of polymer, we also can see that the
polymer concentration does not reach the maximum 0.7 and the liquid crystal
concentration will also have a small increment to fill with the interspace
induced by the polymerization.The harmonics of (a) monomer,
(b)  polymer, and (c) liquid crystal concentration
as a function of time,
respectively.
(a)(b)(c)The
ratio of diffusion rate to polymerization rateR is a very important parameter
that controls the formation of H-PDLC gratings.
Figure 19
shows the amplitude of each harmonic of polymer
concentration as a function of exposure ξ for different R, with  V=1,  z=0.05,
and  α=0.1.
In general, the polymer concentration increases with the exposure and will
reach a saturation value. We can see that the saturation depends strongly on R. Great R results in large saturation values. However, for R≫1,
there is almost no difference about the saturation for the zero harmonic. From
Figure 19(a), we can see the zero harmonics are almost the same
for R=5 and R=50.
From Figure 19(c), we can see the smaller the R, the stronger the second
harmonic. When R≫1,
the harmonics whose order more than one can be ignored because the zero and
first-order harmonics dominate absolutely.The amplitude of each harmonic of polymer concentration as a
function of exposureξ for
different R with V=1, z=0.05, and α=0.1.
(a)(b)(c)(d)Figure20 shows the relationship between the saturation of the
first and second harmonics and the fringe visibility V for different R. We can
see that the larger the R, the more linear the saturation of the harmonics. For R=50,
the saturation of the harmonics are completely linear.  We also can see that the second harmonic is
almost zero when R=50,
which means no influence for the polymerization for the second harmonic.The relationship between the
saturation of the first and second harmonics
and the fringe visibilityV
for different R.
(a)(b)Figure21 shows the relationship between the saturation of the
first and second harmonics and α.
We can see that αdoes not affect the grating formation
strongly.The relationship between the saturation of
the first and second harmonics andα.
(a)(b)Figure22
shows the polymer distribution profile for different R.
The profile is purely sinusoidal for
large R. When the R decreases, the higher harmonics will
be obtained. So a large R can produce
a good grating structure.Figure 22
The polymer distribution profile for differentR.Many researchers studied the H-PDLC grating
formation using this simple model
[58–60]. Kyu
et al. gave a 2D simulation using time-dependent Ginzburg-Landau equations (TDGL model C) [61].


## 6. Coupled-Wave Theory

### 6.1. Theory

Different
theories can be used to study holographic gratings
[62, 63]. Coupled-wave theory is widely used to describe
thick, isotropic gratings
[64]. However, an extension of the theory to optically
anisotropic materials is needed when dealing with samples showing a
polarization dependent behavior
[65–69]. Sutherland et
al. gave a detailed discussion about the diffraction efficiency of
H-PDLCs using coupled-wave theory [70]. The basic interaction
geometry of the incident light with the holographic film, LC droplets, and
applied field is shown in
Figure 23. The grating is described by grating vector K,
which is perpendicular to the grating planes. Generally, the grating vector
makes an angle φ with respect to the film normal. Light is
incident on the film at an angle θ, as measured in the medium. For
simplicity, we assume that the holographic film is sandwiched between index
matching windows. Light polarized perpendicular to the plane of incidence
(defined by the incident wave vector and the film normal, which are coplanar)
is said to be s-polarized. Light
polarized in the plane of incidence is said to be p-polarized. Each LC droplet is taken to be a uniaxial domain, with
its axis of symmetry along the applied electric field. The applied electric
field is normal to the film. Here, we defined a vector N as the droplet director. In the absence of an electric field, N  preferentially coincides
with the droplet-symmetry axis, which is also the major axis of the elongated
droplet.Figure 23
Geometry of H-PDLC grating.Considering
the pattern formed by the interference of two plane waves. The spatial
distribution of irradiance is(25)I(r⇀)=I0[1+Vcos(K⇀⋅r⇀)], where I0 is the average irradiance, V is the
fringe visibility, |K⇀|=2π/Λ, and Λ is the fringe spacing.The
refraction index distribution generally follows the pattern of the interfering
laser beams, so the expression for the index of refraction can be written
as(26)n(r⇀)=n0+n1cos(K⇀⋅r⇀), where n0 is the matrix index, n1 is
the index modulation amplitude.To
apply Kogelnik’s theory
[64], we must operate in the regime of grating known as
optically thick. The criteria for this are established with reference to two
parameters, namely (27)Q=2πλLn0Λ2, where λ is the optical wavelength and L is
the physical thickness of the grating. To be in the thick grating regime, we
must have Q≫1.
Typical gratings used in the visible spectrum have n0 ~ 1.5 and Λ ~ 0.2–1.0 μm. Thus, the
applicable thickness for the visible spectrum is in the range L≫1 μm.In
coupled-wave theory, the two waves that interact in the medium are called
incident and diffracted waves, or reference and signal waves, respectively.
They are coupled by the periodic index modulation, with a coupling strength
given by(28)νs=πn1sLλcR|cI| for s-polarization
and (29)νp=πn1pLλcR|cI|cos2(θ−ϕ) for p-polarization. The quantities (30)cR=cosθ,cI=cR−λn0Λcosϕ are called the obliquity factors. The angle
of incidence may vary slightly about the principal angle, which we designate as
the Bragg angle θB. At this angle of incidence, the wavelength
of maximum coupling is called the Bragg wavelength λB  and is
defined by (31)λB=2n0Λcos(ϕ−θB). Here, the LC droplets are assumed to be
uniaxial domains, the index modulation will be different for each polarization.
It will also depend on the direction of wave propagation. For a slanted
grating, the reference and signal waves will, thus, see a different index
modulation. In this case, the index modulation amplitude is an effective value
given by (32)n1j=χn1j,R+(1−χ)n1j,S, where χis an
adjustable parameter, j is the polarization (s or p) and the subscript
R(S) signifies that the value of n1j depends on the
propagation direction of the reference (signal) wave.We
defined a complex detuning parameter(33)ξ=ξ′−iξ′′, where ξ′ is due to a loss mechanism and ξ′′ is due to a dephasing caused by angular and
spectral departures from the Bragg condition. We have (34)ξ′′=π(θB−θ)LcSΛsin(ϕ−θ)+π(λ−λB)L2n0cSΛ2.We
assume that loss is entirely due to random scattering from the LC droplets,
although there may be additional scattering losses due to material
imperfections across gratings, and so forth. This loss mechanism is due to the
fact that each PDLC slab contains a random distribution of LC droplets, and the
corresponding positions of droplets in different slabs are uncorrelated. Thus,
in addition to the coherent Bragg scattering from average droplet sites, there
is a background of diffused incoherent scattering due to uncorrelated droplet
positions. We treat this scattering as a single-particle scattering in the
Rayleigh-Gans approximation
[71]. Thus, we define (35)ξ′=αscL4(1cR−1cS), where (36)αsc=πa2(ndn0−1)2Φ(ka) is the Rayleigh-Gans scattering coefficient
for a spherical particle of radius a,
with (37)Φs(x)=49x4∫0πG2(2xsinθ2)sinθdθ for s-polarization, (38)Φp(x)=49x4∫0πG2(2xsinθ2)cos2θsinθdθ for p-polarization,
and (39)G(u)=3u3(sinu−ucosu).We
further define a scattering transmission factor given by(40)τT=exp[−αscL2(1cR+1cS)] for
transmission gratings.We
now recognize that because the terms that involve scattering depend on polarization,τ and ξ should carry the subscript j(j=s,p) to signify the
appropriate polarization, and all of the preceding equations apply, with
(37)
used for s-polarization
and (38) used for p-polarization.We
are now in a position to give expressions for diffraction efficiency. First,
consider transmission gratings. In this case, only the first-order diffracted
beam is of interest, and we can write(41)ηj=τTjSjSj* for the diffraction efficiency of a
transmission grating, where the asterisk (*) signifies complex conjugate and(42)Sj=νjsinνj2−ξj2νj2−ξj2.For
the case when scattering loss can be ignored and the angle of incidence is the
Bragg angle, (41)
reduces to the familiar form for transmission
gratings (43)ηj=sin2νj.


### 6.2. Numerical Results

For
the case of  an unslanted grating, the diffraction efficiency is solved
numerically using Mathcad.
Figure24
gives four typical examples of diffraction efficiency
as a function of the incident angle (also called angular sensitivity plots). We
can see that with the increase of the index modulation (the refractive index
difference between the LC-rich lamellae and the polymer-rich lamellae), the
diffraction efficiency increases. The angular dependence of H-PDLCs was
detailed investigated by Vita et al.
[72]. Generally, to achieve a volume Bragg grating with
high diffraction efficiency, a relatively large index modulation is needed.Angular dependence of diffraction
efficiency for a transmission H-PDLC grating.
Key parameters:θb=π/6 (external), φ=π/2, L = 10 μm,
λ0 = 633 nm,
a = 0.020, (a)
n1 = 0.015, (b)
n1 = 0.025, (c)
n1 = 0.040, and (d)
n1 = 0.050.
(a)(b)(c)(d)However,
it is worth noting that, for the H-PDLC transmission grating, it may be
overmodulated in some cases. That is, the diffraction efficiency first passed
through a maximum (generally less than 100%) and then decreased. An obvious
feature of overmodulation in the angle sensitivity plot is the relatively large
side slobes. Figure25 showed both normal and
overmodulated cases. We can see that the largest side lobe of the overmodulated
grating is ~23%, whereas for the normal grating, the largest side
lobe is ~10%. In addition, the angular bandwidth of overmodulated
is slightly narrower than that of normal. This can be easily understood by the
conservation of energy.Angular dependence of diffraction
efficiency for a transmission H-PDLC grating, illustrating (a) normal and (b)
overmodulated cases. Key parameters:θb=π/6 (external), φ=π/2, L = 10 μm,
λ0 = 633 nm, and
a = 0.020, (a) n1 = 0.040, (b) n1 = 0.070.
(a)(b)The
film thickness,L, and the index
modulation amplitude, n1,
are reciprocal parameters, which decide the angular properties of the H-PDLC
gratings. Generally, a small index modulation and a large thickness will
produce a narrow angular sensitivity. The series of plots in
Figure 26
showed the trend of prediction. Therefore, we can
choose the parameters (i.e., film thickness and LC) according to the practical
applications. For examples, for H-PDLC displays which need large view angles, a
smaller thickness should be chosen.Angular dependence of diffraction
efficiency for a transmission H-PDLC grating, illustrating angular bandwidth
for variousL and n1. Key parameters: θb=π/6 (external), φ=π/2, λ0 = 633 nm, a  = 0.020,
(a) L = 20 μm, n1 = 0.026, (b) L =16 μm,
n1 = 0.034, (c)
L = 10 μm, n1 = 0.052,
and (d) L = 6 μm,
n1 = 0.088.
(a)(b)(c)(d)Actually,
scattering reduces the peak diffraction efficiency, preventing it from its
theoretical maximum of 100%. However, the droplet sizes in H-PDLC samples are ~20 nm
on average, which are very small with comparison to the visible wavelength. So
the scattering loss is relatively small, as indicated in
Figure27. In fact, larger scattering losses result from not
only the phase-separated LC droplets but also some other reasons such as the index
mismatch at the interfaces and imperfection of the polymer film.Figure 27
Peak diffraction efficiency of a transmission H-PDLC grating as a function of
droplet radiusa, illustrating the effects of scattering. Key parameters: θb=π/6 (external), φ=π/2, L = 10 μm, and λ0 = 633 nm.Generally,
the diffraction efficiency of H-PDLC gratings has polarization dependence more
or less because of the anisotropy of LC.
Figure28
illustrates this effect. In general, p-polarization is always greater. In our
experiment, we indeed observed this phenomenon. This is not favorable for some
applications such as optical switching which needs to be polarization
insensitive. It primarily results from the shrinkage of the polymer during the
formation of gratings.Figure 28
Angular dependence of a transmission H-PDLC grating, illustrating the
dependence on polarization. Key parameters:θb=π/6 (external), φ=π/2, L = 10 μm, λ0 = 633 nm, a  = 0.020, n1 = 0.050
(p-polarization),
and n1 = 0.016
(s-polarization).For
the switchable H-PDLC gratings, due to the various material formations and
fabrication conditions, the polarization and electro-optical properties can be
very different. Sutherland et al.,
further developed a theoretical model to elucidate the angle- and
polarization-dependent switching behavior observed in the experiments, which combines
anisotropic coupled wave theory with an elongated LC droplet switching model
and includes the effects of a statistical orientational distribution of
droplet-symmetry axes
[73, 74]. Near infrared characterization and modeling of
H-PDLCs were also done
[75], which showed H-PDLCs potentially useful in telecom
field.


## 6.1. Theory

Different
theories can be used to study holographic gratings
[62, 63]. Coupled-wave theory is widely used to describe
thick, isotropic gratings
[64]. However, an extension of the theory to optically
anisotropic materials is needed when dealing with samples showing a
polarization dependent behavior
[65–69]. Sutherland et
al. gave a detailed discussion about the diffraction efficiency of
H-PDLCs using coupled-wave theory [70]. The basic interaction
geometry of the incident light with the holographic film, LC droplets, and
applied field is shown in
Figure 23. The grating is described by grating vector K,
which is perpendicular to the grating planes. Generally, the grating vector
makes an angle φ with respect to the film normal. Light is
incident on the film at an angle θ, as measured in the medium. For
simplicity, we assume that the holographic film is sandwiched between index
matching windows. Light polarized perpendicular to the plane of incidence
(defined by the incident wave vector and the film normal, which are coplanar)
is said to be s-polarized. Light
polarized in the plane of incidence is said to be p-polarized. Each LC droplet is taken to be a uniaxial domain, with
its axis of symmetry along the applied electric field. The applied electric
field is normal to the film. Here, we defined a vector N as the droplet director. In the absence of an electric field, N  preferentially coincides
with the droplet-symmetry axis, which is also the major axis of the elongated
droplet.Figure 23
Geometry of H-PDLC grating.Considering
the pattern formed by the interference of two plane waves. The spatial
distribution of irradiance is(25)I(r⇀)=I0[1+Vcos(K⇀⋅r⇀)], where I0 is the average irradiance, V is the
fringe visibility, |K⇀|=2π/Λ, and Λ is the fringe spacing.The
refraction index distribution generally follows the pattern of the interfering
laser beams, so the expression for the index of refraction can be written
as(26)n(r⇀)=n0+n1cos(K⇀⋅r⇀), where n0 is the matrix index, n1 is
the index modulation amplitude.To
apply Kogelnik’s theory
[64], we must operate in the regime of grating known as
optically thick. The criteria for this are established with reference to two
parameters, namely (27)Q=2πλLn0Λ2, where λ is the optical wavelength and L is
the physical thickness of the grating. To be in the thick grating regime, we
must have Q≫1.
Typical gratings used in the visible spectrum have n0 ~ 1.5 and Λ ~ 0.2–1.0 μm. Thus, the
applicable thickness for the visible spectrum is in the range L≫1 μm.In
coupled-wave theory, the two waves that interact in the medium are called
incident and diffracted waves, or reference and signal waves, respectively.
They are coupled by the periodic index modulation, with a coupling strength
given by(28)νs=πn1sLλcR|cI| for s-polarization
and (29)νp=πn1pLλcR|cI|cos2(θ−ϕ) for p-polarization. The quantities (30)cR=cosθ,cI=cR−λn0Λcosϕ are called the obliquity factors. The angle
of incidence may vary slightly about the principal angle, which we designate as
the Bragg angle θB. At this angle of incidence, the wavelength
of maximum coupling is called the Bragg wavelength λB  and is
defined by (31)λB=2n0Λcos(ϕ−θB). Here, the LC droplets are assumed to be
uniaxial domains, the index modulation will be different for each polarization.
It will also depend on the direction of wave propagation. For a slanted
grating, the reference and signal waves will, thus, see a different index
modulation. In this case, the index modulation amplitude is an effective value
given by (32)n1j=χn1j,R+(1−χ)n1j,S, where χis an
adjustable parameter, j is the polarization (s or p) and the subscript
R(S) signifies that the value of n1j depends on the
propagation direction of the reference (signal) wave.We
defined a complex detuning parameter(33)ξ=ξ′−iξ′′, where ξ′ is due to a loss mechanism and ξ′′ is due to a dephasing caused by angular and
spectral departures from the Bragg condition. We have (34)ξ′′=π(θB−θ)LcSΛsin(ϕ−θ)+π(λ−λB)L2n0cSΛ2.We
assume that loss is entirely due to random scattering from the LC droplets,
although there may be additional scattering losses due to material
imperfections across gratings, and so forth. This loss mechanism is due to the
fact that each PDLC slab contains a random distribution of LC droplets, and the
corresponding positions of droplets in different slabs are uncorrelated. Thus,
in addition to the coherent Bragg scattering from average droplet sites, there
is a background of diffused incoherent scattering due to uncorrelated droplet
positions. We treat this scattering as a single-particle scattering in the
Rayleigh-Gans approximation
[71]. Thus, we define (35)ξ′=αscL4(1cR−1cS), where (36)αsc=πa2(ndn0−1)2Φ(ka) is the Rayleigh-Gans scattering coefficient
for a spherical particle of radius a,
with (37)Φs(x)=49x4∫0πG2(2xsinθ2)sinθdθ for s-polarization, (38)Φp(x)=49x4∫0πG2(2xsinθ2)cos2θsinθdθ for p-polarization,
and (39)G(u)=3u3(sinu−ucosu).We
further define a scattering transmission factor given by(40)τT=exp[−αscL2(1cR+1cS)] for
transmission gratings.We
now recognize that because the terms that involve scattering depend on polarization,τ and ξ should carry the subscript j(j=s,p) to signify the
appropriate polarization, and all of the preceding equations apply, with
(37)
used for s-polarization
and (38) used for p-polarization.We
are now in a position to give expressions for diffraction efficiency. First,
consider transmission gratings. In this case, only the first-order diffracted
beam is of interest, and we can write(41)ηj=τTjSjSj* for the diffraction efficiency of a
transmission grating, where the asterisk (*) signifies complex conjugate and(42)Sj=νjsinνj2−ξj2νj2−ξj2.For
the case when scattering loss can be ignored and the angle of incidence is the
Bragg angle, (41)
reduces to the familiar form for transmission
gratings (43)ηj=sin2νj.


## 6.2. Numerical Results

For
the case of  an unslanted grating, the diffraction efficiency is solved
numerically using Mathcad.
Figure24
gives four typical examples of diffraction efficiency
as a function of the incident angle (also called angular sensitivity plots). We
can see that with the increase of the index modulation (the refractive index
difference between the LC-rich lamellae and the polymer-rich lamellae), the
diffraction efficiency increases. The angular dependence of H-PDLCs was
detailed investigated by Vita et al.
[72]. Generally, to achieve a volume Bragg grating with
high diffraction efficiency, a relatively large index modulation is needed.Angular dependence of diffraction
efficiency for a transmission H-PDLC grating.
Key parameters:θb=π/6 (external), φ=π/2, L = 10 μm,
λ0 = 633 nm,
a = 0.020, (a)
n1 = 0.015, (b)
n1 = 0.025, (c)
n1 = 0.040, and (d)
n1 = 0.050.
(a)(b)(c)(d)However,
it is worth noting that, for the H-PDLC transmission grating, it may be
overmodulated in some cases. That is, the diffraction efficiency first passed
through a maximum (generally less than 100%) and then decreased. An obvious
feature of overmodulation in the angle sensitivity plot is the relatively large
side slobes. Figure25 showed both normal and
overmodulated cases. We can see that the largest side lobe of the overmodulated
grating is ~23%, whereas for the normal grating, the largest side
lobe is ~10%. In addition, the angular bandwidth of overmodulated
is slightly narrower than that of normal. This can be easily understood by the
conservation of energy.Angular dependence of diffraction
efficiency for a transmission H-PDLC grating, illustrating (a) normal and (b)
overmodulated cases. Key parameters:θb=π/6 (external), φ=π/2, L = 10 μm,
λ0 = 633 nm, and
a = 0.020, (a) n1 = 0.040, (b) n1 = 0.070.
(a)(b)The
film thickness,L, and the index
modulation amplitude, n1,
are reciprocal parameters, which decide the angular properties of the H-PDLC
gratings. Generally, a small index modulation and a large thickness will
produce a narrow angular sensitivity. The series of plots in
Figure 26
showed the trend of prediction. Therefore, we can
choose the parameters (i.e., film thickness and LC) according to the practical
applications. For examples, for H-PDLC displays which need large view angles, a
smaller thickness should be chosen.Angular dependence of diffraction
efficiency for a transmission H-PDLC grating, illustrating angular bandwidth
for variousL and n1. Key parameters: θb=π/6 (external), φ=π/2, λ0 = 633 nm, a  = 0.020,
(a) L = 20 μm, n1 = 0.026, (b) L =16 μm,
n1 = 0.034, (c)
L = 10 μm, n1 = 0.052,
and (d) L = 6 μm,
n1 = 0.088.
(a)(b)(c)(d)Actually,
scattering reduces the peak diffraction efficiency, preventing it from its
theoretical maximum of 100%. However, the droplet sizes in H-PDLC samples are ~20 nm
on average, which are very small with comparison to the visible wavelength. So
the scattering loss is relatively small, as indicated in
Figure27. In fact, larger scattering losses result from not
only the phase-separated LC droplets but also some other reasons such as the index
mismatch at the interfaces and imperfection of the polymer film.Figure 27
Peak diffraction efficiency of a transmission H-PDLC grating as a function of
droplet radiusa, illustrating the effects of scattering. Key parameters: θb=π/6 (external), φ=π/2, L = 10 μm, and λ0 = 633 nm.Generally,
the diffraction efficiency of H-PDLC gratings has polarization dependence more
or less because of the anisotropy of LC.
Figure28
illustrates this effect. In general, p-polarization is always greater. In our
experiment, we indeed observed this phenomenon. This is not favorable for some
applications such as optical switching which needs to be polarization
insensitive. It primarily results from the shrinkage of the polymer during the
formation of gratings.Figure 28
Angular dependence of a transmission H-PDLC grating, illustrating the
dependence on polarization. Key parameters:θb=π/6 (external), φ=π/2, L = 10 μm, λ0 = 633 nm, a  = 0.020, n1 = 0.050
(p-polarization),
and n1 = 0.016
(s-polarization).For
the switchable H-PDLC gratings, due to the various material formations and
fabrication conditions, the polarization and electro-optical properties can be
very different. Sutherland et al.,
further developed a theoretical model to elucidate the angle- and
polarization-dependent switching behavior observed in the experiments, which combines
anisotropic coupled wave theory with an elongated LC droplet switching model
and includes the effects of a statistical orientational distribution of
droplet-symmetry axes
[73, 74]. Near infrared characterization and modeling of
H-PDLCs were also done
[75], which showed H-PDLCs potentially useful in telecom
field.


## 7. Performance Optimization

Many
researchers have explored different material recipes to achieve high
diffraction efficiency, fast response time, and low drive voltage. In this
article, we focused on the material recipe for visible (blue and green)
curing, which is discussed in all the following parts. For this kind of
material recipe, due to many different components for various purposes, many
works contribute to the performance improvement of H-PDLC gratings. A clear
grating morphology is desired to achieve the high performance. The morphology
can be controlled by the following parts.


### 7.1. Exposure Conditions

#### 7.1.1. Effect of Exposure Intensity

The exposure intensity decides the rate of gelation, diffusion, and nucleation, which determines the
degree of phase separation and morphology of the droplets, and hence the
diffraction efficiency. Bunning
et al. speculated on the
extreme morphologies possible given the relative rates of diffusion,
nucleation, and gelation as shown in
Figure29
[76]. In case (a) shown in
Figure 29, if the time to diffuse across Λ/2
is fast compared to the time for droplets to nucleate and nucleation occurs
much faster than gelation, a “perfect” grating is formed. If the rates of
nucleation and gelation are on the same order, but diffusion of LC can still
take place over a distance Λ/2 during the polymerization and before
nucleation, then little growth of the LC domains would be expected once
discrete LC-rich domains are formed. These small LC domains would be spatially
segregated on a length scale commensurate with Λ as shown schematically in case (b). If the LC domains
separate out before the LC molecules can diffuse parallel to the grating vector
a distance of Λ/2, one would obtain cases (c) and (d) which at
their extremes approximate conventional floodlit samples. One can effectively
increase the time needed for diffusion of LC by increasing Λ.
In the infinite case, one has a conventionally floodlit LC composite system.
The size of the droplets and their distribution in sizes is again controlled by
the relative rates between nucleation and gelation. If gelation is slow (case
(d), then considerable coalescence of the droplets can be expected which
increases the size distribution. If gelation is fast (case (c) once droplets are
nucleated, then small individual LC domains would be formed.Figure 29
Pictorial representation of the timeline for H-PDLC grating formation. The
cases (a), (b), (c), and (d) show extreme morphologies possible based on the
relative time scales for the events listed on the timeline.tN, tG, and tD are nucleation time, gelation time, and diffusion time to Λ/2,
respectively. Λ is
the grating period
[76].Macroscopically, if the intensity is too weak, the induced energy will not be enough, leading to a slower polymerization rate and longer LC droplets growth time. Finally, the size of LC droplets will be larger and the scattering will be increased and diffraction efficiency will be lowered. On the contrary, too strong intensity will promote the rate of polymerization. The liquid crystal droplets do not have sufficient time to grow and diffuse because of the rapid cross-linking of monomers, so many droplets were trapped in the polymerized regions. The buried droplets will act as scatterers, lowering diffraction efficiency. So exposure intensity is critical to make the rate of polymerization and diffusion approximately equal and then form a clear and smooth grating structure.A representative plot of the data as a function of time is given in Figure30 [11], which shows three regions characterizing the formation
of holographic gratings in photopolymers: (a) a short induction period
during which no polymerization takes place until all inhibitors, for example,
oxygen or those added by the manufacturer to prevent accidental polymerization,
have been reacted; (b) a period of rapid polymerization and
photobleaching of the initiator dye with a concomitant rise in diffraction
efficiency; (c) a plateau region where most of the dye molecules are
irreversibly bleached. The induction period is actually quite short; measurable
diffraction efficiency is noted as early as 250 μs
after exposure [14]. The time of rapid rise in diffraction efficiency is
most certainly involved with the growth and final development of periodic LC
domains. This is consistent with the final morphology revealed by SEM and by
the fact that samples cured with no or a low concentration of LC have much
lower diffraction efficiency.Figure 30
Diffraction efficiency as a function of
time in an H-PDLC grating recording
[11].According to the previous reports
[14, 77, 78], the laser intensity is varied between 0.1 and 100 mW/cm2, with typical exposure
time of 30–120 seconds,
which strongly depends on the properties of the materials used and the
component ratio in the mixture. In our experiments, we obtained the peak diffraction
efficiency with the conditions of I =
10 mW/cm2 and t = 120 s with
the TMPTA monomer and prepolymer/LC = 70/30.


#### 7.1.2. Effect of Exposure Temperature

Another
important factor to affect the structure is the exposure temperature. The
temperature has a big effect on the viscosity
of the materials, which is believed to affect the structure morphologies significantly.
In general, at low temperatures, the diffusion rates of LCs and monomers are
low due to the high viscosity of both LCs and monomers. In this case, during
the exposure, some LC molecules (monomers) have not enough time to diffuse into
the dark (bright) regions. As a result, many LC molecules (monomers) are
trapped in the polymer-rich (LC-rich) regions, inducing an incomplete phase
separation, and thus a poor grating structure is formed. At high temperatures, the LC and monomer
viscosities decrease much and diffusion rates are much faster. As a result, a
better separated LC and polymer structure will be formed. To obtain a complete
phase separation between LC and polymer, a suitable temperature is needed.
Figure31
shows the effect of the exposure temperature on the
diffraction efficiency of a transmission H-PDLC grating. At the temperature
range of 40–50°C,
the diffraction efficiency reaches the maximum, which indicates the best phase
separation between LCs and polymer. It is worth mentioning that at a higher
temperature the prepolymer/LC mixture may polymerize rapidly so that the
grating structure is not formed at all. In this case, the temperature induced
phase separation (TIPS) plays a dominant role over the photopolymerization.
Thus, a PDLC-like structure is formed.Figure 31
Effect of exposure temperature on the diffraction efficiency of a transmission
H-PDLC grating.


### 7.2. Effect of Monomer Functionality

In H-PDLC material recipe, the monomer
generally has the largest concentration. Upon the light exposure, the monomer
polymerizes to form a cross-linking polymer matrix. The functionality of the
monomer plays a very important role in determining the degree of cross-linking
in the polymer matrix, which is then anticipated to contribute to the degree of
the phase separation between the polymer and liquid crystals, producing a
dramatic effect on the performance of H-PDLCs. Generally, larger-functional
monomer yields a highly cross-linking density, while smaller-functional monomer
yields a low or even zero cross-linking density. Fontecchio et al. investigated the monomer
functionality effect on the performance of H-PDLCs by examining the switching
properties and reflection efficiencies
[79]. They combined monomers with functionality 2, 3, and
6 to make integer and half-integer functionalities in the range from 2 to 6. By
measuring the reflection efficiency, switching properties, and SEM observation,
the optimal monomer functionality exists for the H-PDLC polymer binder. The
optimum values for the functionality to obtain the best performance are 4–4.5. Pogue et al.
studied the monomer functionality effects on H-PDLCs
[80], in particular, on the formation the anisotropic LC
domains. The experimental results demonstrated that the local volume fraction
and the LC domain size decreased substantially as the monomer functionality were
decreased. The image analysis showed that a much stronger tendency to form
anisotropically-shaped domains was observed for the higher functional syrups.
These domain anisotropy differences are correlated with the number of reactive
double bonds per monomer and are suggestive of local environmental differences
exerted at the time of the domain formation.De Sarkar and coworkers also studied the
effect of monomer functionality on H-PDLCs
[81].
Figure 32
shows the rate of  polymerization against the  monomer
conversion for mixtures with different average functionalities. In general, the
maximum rate of polymerization and the maximum conversion are inversely
proportional to the functionality. The exception to this trend is the mixture
with an average functionality of 1.3, whose maximum rate of polymerization and
extent of monomer conversion are less than the values for mixture with average
functionality of 1.5 but greater than the values for average functionality of
2.0.Figure 32
Rate of polymerization versus conversion of prepolymer solutions with different
average functionalities
[81].Figure33
shows the effect of average functionality on the
phase separated morphology of the H-PDLC gratings. The SEM observations
indicate a decrease in nematic domain size in the grating morphology with
decrease in average functionality of the prepolymer syrup. H-PDLC cells
prepared from monomer mixtures with higher average functionality exhibit more
variability in the shape and size of the LC domains. By measuring the
diffraction efficiency, an increase in diffraction efficiency was observed and
a decrease in LC domain size as the average functionality of the constituent
monomer mixture decreases. The smaller size of LC domains can reduce the
residual scattering and therefore increase the diffraction efficiency. The
increase in diffraction efficiency with decrease in functionality can also be
attributed to the increase in refractive index modulation. On the other hand, the
switching performance of H-PDLC gratings deteriorates with decrease in
functionality. The experimental results showed that an optimum average
functionality (Feff≈2.0–2.5) exists to
obtain the optimized performance of H-PDLCs below which the LC domains become
negligibly small. The similar trend was also demonstrated by other researchers
[82].SEM micrographs for transmission gratings prepared using monomer mixtures with
average functionalities of (a) 3.5, (b) 3.0,
(c) 2.4, (d) 2.0, and (e) 1.5
[81].
(a)(b)(c)(d)(e)


### 7.3. Effect of LC Concentration

LC concentration is generally the second
largest concentration in the H-PDLC material recipe, which has a dramatic effect
on the diffraction efficiency. In the pure polymer gratings, the peak diffraction
efficiency was typically ~1%. With different LC concentration of 20–40 wt%, diffraction
efficiency was very different.
Figure34
showed the effect of different LC concentrations on diffraction
efficiency. The peak diffraction efficiency was obtained with the concentration
of 28 wt%. The morphology of the samples was shown in
Figure 35. From Figure 35, we can see that if the LC concentration is higher,
the volume fraction of LC lamella throughout the bulk of the film increases and
the size of droplet is larger, thus increasing the scattering and lowering the
diffraction efficiency. However, if the concentration is lower, the volume
fraction of LC decreases, and the size of droplets becomes smaller. Within the
LC-rich lamellae, a large amount of polymer exists, which lowers the index
modulation and decreases the diffraction efficiency accordingly. Therefore, a
suitable LC concentration is needed in order to obtain both a good grating
structure and high diffraction efficiency. In most references
[11, 37], the LC concentration of ~30 wt% is the best choice
to achieve high diffraction efficiency. The diffraction efficiency can reach
more than 90%.Figure 34
Effect of LC concentration on diffraction
efficiency.The same magnification SEM photographs of the surface of H-PDLC Bragg grating
of different LC contents: (a) 20 wt%, (b) 30 wt%,
(c) 40 wt%, and (d) 28 wt%.
(a)(b)(c)(d)


### 7.4. Effect of NVP Concentration

NVP is known to be a critical component in
improving acrylate-based H-PDLC grating diffraction efficiency by reducing LC
droplet size
[83, 84]. As is the case in many acrylate systems, NVP
causes an increase in the rate of polymerization with increasing concentration
in H-PDLC formulations. This increase in the rate of polymerization occurs
through the incorporation of NVP into the H-PDLC polymer matrix. To understand
the dependence of HPDLC polymerization kinetics on NVP, the influence of NVP
concentration on the rate of polymerization has also been examined using photo-differential
scanning calorimetry (PDSC).
Figure 36(a)
shows the rate of polymerization versus double
bond conversion for HPDLC formulations containing increasing concentrations of
NVP. For comparison, the polymerization of DPPHA with increasing NVP
concentration was studied, as shown in Figure 36(b). H-PDLC formulations containing up to 15 wt% NVP
demonstrate complete NVP conversion. Examination of double bond conversion
evolution in H-PDLC formulations reveals that NVP and monomer conversion are
codependent at relatively low double bond conversions. This dependence results
from the reaction of NVP double bonds with trapped acrylate radical species.
The NVP radicals can then react with other trapped pendant acrylate double
bonds. Therefore, significant rate increases and increased acrylate conversion
result with NVP addition. The preferential reactivity of NVP with acrylate also
serves to delay the onset of the reaction diffusion termination mechanism while
also extending its predominance into higher double bond conversion.Rate of polymerization versus double bond conversion for (a) HPDLC formulations
with 0 (),
5 (),
10 (),
and 15 (•) wt% NVP and (b) DPPHA:NVP formulations with 0 (),
5 (),
10 (),
and 15 (•) wt% NVP.
(a)(b)NVP also has a major influence on LC phase
separation in the formation of H-PDLCs and ultimate polymer morphology. Study
of the appearance of the nematic phase, an indirect examination of phase
separation, shows that samples containing NVP or the chemically similar but nonreactive
moleculen-ethyl-2-pyrrolidinone (NEP),
exhibit a slower appearance of the nematic phase when compared to an H-PDLC
formulation without NVP (or NEP). In general, increasing NVP concentration
extends the homogeneity of the polymer/LC mixture into higher double bond conversions—slowing the LC
phase separation process and the appearance of the nematic phase. Further, the
kinetic influence of NVP coupled with its solubility reduces the amount of LC
phase separation, which subsequently reduces the overall amount of nematic LC.
These effects are also evident in the polymer/LC morphology. With NVP
incorporation droplet size is much smaller than that observed when incorporating
the nonreactive analogue NEP. The rate of polymerization for the H-PDLC formulation
containing NVP is much greater than that containing NEP.
This behavior, in turn, is the
cause of the significant reduction in LC droplet size and improved H-PDLC
performance with NVP inclusion.
Figure 37
shows obviously different surface morphologies
of H-PDLC transmission gratings prepared with 4 wt% and 15 wt% NVP,
respectively. It can be seen that increasing the amount of NVP leads to smaller
droplets and decreases the   anisotropy of the LC droplets.SEM images of H-PDLC transmission gratings with (a) 4 wt% and (b) 15 wt% NVP.
Scale bars represent 600 nm
[83].
(a)(b)


### 7.5. Decreasing Driving Voltage

For H-PDLC gratings, the LC droplets are
small and the anchoring energy is high, which results in a high driving
voltage. According to Mormile et al., the threshold voltage of PDLC can be written
as [85] (44)Vth≈dr[K(ℓ2−1)ε0Δε]1/2, where d is the HPDLC film thickness, r is the droplet radius, K is the effective elastic constant, ε0 is the vacuum dielectric constant, Δε is the LC dielectric anisotropy, ℓ=a/b is the droplet aspect ratio, with a and b the length of the major and minor axis of the ellipsoid-shaped
droplet, respectively. Equation (44)
was deduced by balancing the elastic and field
torques to the equilibrium orientation at the presence of a voltage applied to
a shaped  droplet [86], that is, Γd+Γe=0, where Γd is the elastic torque per unit volume and Γe is the electric torque on the droplet director per unit volume. This can be
regarded as the shape contribution to the threshold voltage of a normal PDLC.The
LC droplets of conventional PDLC are about 1 ~ 5μm in size. However, the size of HPDLC droplets
is about 0.01 ~ 0.1 μm.
The size effect on the threshold voltage can be understood by the following
comparisons. Using our experimental parameters, the cell thickness, d,
is 20 μm,
the elastic constant, K, is 1.71 × 10−11 N, the dielectric anisotropy, Δε,
is 6.49, and assuming an aspect ratio of 1.1, for LC droplets with r = 2 μm
and 0.02 μm,
the corresponding threshold voltage Vth
calculated is 2.5 V
and 250 V, respectively. It can be seen that with the reduction in dimension,
the threshold voltage increases linearly. In general, the threshold voltage of
nano-PDLC produced by holography is about one or two orders higher than that of
normal PDLC.For
practical application of HPDLC, it is desired to reduce the driving voltage.
Colegrove et al. reported that by adding a high dielectric anisotropy
material (Δε = 65), the threshold voltage of
HPDLC can be reduced significantly
[87]. In addition, adding a small portion of surfactant
to the prepolymer/LC syrup also helps to reduce the threshold voltage
[88–91]. Fluorination of the polymer matrix also has
significant effects on decreasing the driving voltage of H-PDLC
[92, 93]. In the following, the effects of surfactants and
polymer fluorination will be discussed.


#### 7.5.1. Surfactant Effect

The
role of surfactant is supposed to be a lubricant between polymer matrix and
liquid crystals. When phase separation occurs in the homogenous mixture, the
surfactant will form an intermediate layer between the polymer and the LC. The
anchoring energy at the interface of the LC and the surfactant becomes weaker
than that at the interface of the LC and polymer without surfactant. As a
result, the liquid crystal molecules could be easily reorientated under an
electric field. Therefore, the decrease in anchoring strength may effectively
lower the driving voltage.Figure38 shows the diffraction efficiency as a function of
driving electric field for three different surfactants. The H-PDLC without
surfactant is also shown for comparison. It can be seen from
Figure 38
that, the surfactant is effective in reducing the
driving voltage. The conductivity of samples with surfactants number 1 and number
3 was so high that the voltage could not be increased further before they were
completely switched. Sample number 2 can
both keep the high diffraction efficiency and reduce the driving voltage
effectively. It reduces the threshold voltage from 13 V/μm to about 2.5 V/μm.Figure 38
Diffraction efficiency versus the electric field curves for Bragg gratings made
of liquid crystal E7 with three different kinds of surfactants, octanoic acid (no. 1),
S-271 POE sorbitan monooleate (no. 2), and Tergital Min-Foam 1X (no. 3),
respectively. The diffraction efficiency without surfactant is also shown for
comparison.The
surfactant also has a significant effect on the morphologies of H-PDLC
gratings.
Figures39(a)
and 39(b) show the SEM morphologies of the HPDLC
gratings, which contain 8 wt% and 15 wt% of surfactant, respectively. From
Figure 39, it can be seen that the surfactant affects the
grating significantly. With more surfactant, the polymer regions contain more
LC droplets. Thus the surfactant affects the LC movement during polymerization.
Figure 39(a) has a clearer grating structure than
Figure 39(b), which indicates that the grating in
Figure 39(a) has better diffraction properties. In our
experiment, when the surfactant content was around 8 wt%, the HPDLC Bragg
gratings could both keep high diffraction efficiency and have excellent
electro-optical properties.SEM images of the HPDLC Bragg gratings consisting 8 wt% (a) and 15 wt% (b) of
surfactant no. 2. The monomer and liquid
crystal used are no. 3 in Figure12 and E7,
respectively.
(a)(b)Figure40 shows the diffraction efficiency as a function of the
surfactant content for samples containing number 2 surfactant. With the
increase of the content, the diffraction efficiency reduces. Generally, when
the surfactant content was less than 8 wt%, the HPDLC Bragg gratings could
still keep higher diffraction efficiency.Figure 40
Diffraction efficiency as a function of the
surfactant content for surfactant no.
2. The monomer and liquid crystal used are no.
3 in Figure12 and E7, respectively.


#### 7.5.2. Fluorination Effect

Another
way to reduce the driving voltage is to modify the monomers. The experimental
results have shown the partial fluorination of the polymer matrix has
significant effects on the morphology and electro-optical performance of H-PDLC
[92, 93]. The morphology of the fluorinated transmission
gratings displayed an enhanced phase separation as manifested in a significant
increase in nematic domain size and the LC volume fraction, as shown in
Figures 41
and 42. The incorporation of fluorinated monomers in the
standard UV H-PDLC formulation reduces the switching voltage considerably. However,
the tradeoff is that the relaxation time also increases with fluorination. The
experimental results strongly indicate that significant amount of fluorine
atoms resides at the polymer–LC interface. The
presence of fluorine atoms at the interface can manipulate the surface
anchoring strength and alignment, causing a reorientation of the original
configuration of the LC droplet directors.LVHRSEM photomicrographs of (a) standard formulation, (b) 13.2 mol% MA, and (c)
11.7 mol% HFIPA holographic PDLC films
[92].
(a)(b)(c)SEM micrographs of HPDLC transmission gratings prepared (a) from control
monomer mixture and substituting it with, (b) 10 wt%, (c) 20 wt%, (d) 25 wt%,
(e) 30 wt%, (f) 35 wt%, and (g) 40 wt% of
HFIPA [93].
(a)(b)(c)(d)(e)(f)(g)From
the above experimental results, both surfactant and fluorination has a
significant effect in decreasing the driving voltage. However, there are
side-effects. For example, the grating morphology was changed and the
diffraction efficiency was decreased more or less with addition of surfactants.
The polymer fluorination seems better to decrease the driving voltage compared
to the surfactant, but the longer relaxation time is not desired.


### 7.6. Index Matching Effect

The
index matching between the polymer matrix and liquid crystal plays an important
role in the performance optimization of H-PDLCs. In our configuration, the
polymer refractive index,np,
is chosen to be as close as possible to the ordinary refractive index, no, of LC. This helps to
reduce the diffraction loss in the transparent state. Moreover, the
birefringence of LC, Δn, is chosen to be as large as possible
in order to improve the diffraction efficiency. We experimentally optimized the
material recipe according to the refractive index match. In our experiment,
five kinds of acrylate monomers were selected and their refractive indices are
1.490 for DPPHA (no. 1), 1.484 for PETA (no. 2), 1.474 for TMPTA (no. 3), 1.487
for PET(etra)A (no. 4) and 1.450 for TPGDA (no. 5), respectively. The chemical
structures of these five monomers are shown in
Figure 12 and their corresponding functionalities are 5-6, 3, 3, 4, and
2, respectively.  Because the prepolymer
syrup includes other chemicals such as photoinitiator and coinitiator, moreover,
the refractive index changes during polymerization. In general, the refractive
index will be different from the above values for the mixture after
polymerization. Two different LCs, E7, and BL038, were chosen to match the
refractive index of polymer matrices and their physical properties were listed
in Table 1.Table 1
Basic physical properties of LC E7 and BL038.
Physical propertiesE7BL038Clearing
point (C°)+58.0+100.0Flow
viscosity
(mm2s−1)20C°39720C°145—–20C°1200—–30C°6400—Optical
anisotropy
+20C°, 589.3 nmΔn0.22530.2720ne1.74641.7990no1.52111.5270Dielectric
anisotropy
+20C°, 1.0 kHzΔε+13.8+16.9ε⊥5.26.1ε∥19.023.0The
refractive indices of the monomers are from Sigma-Aldrich. Because other
chemicals are mixed into the monomer, the refractive index of the prepolymer
syrup   changes accordingly. The prepolymer syrup refractive indices were
measured by Abbe
refractometer. Then the syrup was cured on a SiO2 substrate to form a polymer thin film, the refractive index, np, of which was measured by
m-line method [94].
Figure 43
shows the setup of refractive index measurement using
m-line method. The results are tabulated in
Table 2.Table 2
Refractive index and corresponding diffraction efficiency for various monomers
used.
No.12345Monomer1.4901.4841.4741.4871.450Prepolymer syrup1.5011.4961.4891.4981.471Cured film1.5291.5281.5221.5301.502DE for E741.2%56.4%65.0%41.6%32.2%DE for BL03861.8%68.4%40.2%51.6%34.2%Figure 43
Measurement setup of the refractive indexnp.From
the table, we can see that the refractive indexnp of the cured film was larger than that of the
corresponding monomer, with the increment of 0.03 ~ 0.05 on the average. In our
experiment, the no of LC
E7 is 1.521. The number 3 monomer was the nearest to 1.521 and the experimental
results proved that diffraction efficiency was the highest with the number 3
monomer. Similarly, for BL038, no is 1.527. Only the number 2 monomer was the nearest to 1.528 and the
experimental result proved that diffraction efficiency was the highest with the
number 2 monomer. According to our selection principle, the number 3 and number
2 monomers match with E7 and BL038 liquid crystals, respectively.


### 7.7. Effect of Nanoparticle Doping

To extend H-PDLC applications, it is
desirable to obtain higher index contrast. Doping nanoparticles with high
refractive index into PDLC materials may be an easy and effective way to
realize the higher index contrast. Some researchers have successfully
demonstrated nanoparticle patterning, that is, holographic gratings, in
nanoparticle-dispersed photopolymers using holography technique
[95–99]. In the nanoparticle-doped PDLC materials, the
nanoparticles are anticipated to diffuse into the LC-rich regions during the
phase separation between the polymer and LC. Therefore, the index contrast can
be increased by this way.Jakubiak
et al. studied the ZnO
nanoparticles (125 nm in diameter) doped H-PDLC gratings
[100].
Figure 44
shows the SEM images of a transmission grating
fabricated from 1% ZnO and 36% LC with a grating period of about 500 nm. The
SEM images show rougher surface in the fractured cross
section compared to the
conventional H-PDLC gratings without nanoparticle doping. As evidenced by the
structural and performance characteristics of the nanoparticle/LC gratings, the
particles are predominately located in the LC phase. The experimental results
showed that the diffraction efficiency can be greatly enhanced for gratings
containing 1% by weight of ZnO nanoparticles.SEM micrographs of the (a) top and side and (b) side of a Bragg transmission
grating. Note in (b) the cross grating appearing as horizontal lines. The scale
bar corresponds to 1μm
for both panels
[100].
(a)(b)Kim et
al. studied the nanosized silicas doped H-PDLCs
[101]. The experimental results showed that the nanosized
silicas doped H-PDLCs provide enhanced elasticity, dimensional stability, and
diffraction efficiency.
Figures 45(a)
and 45(b) show the typical grating morphologies
without and with silica filled, respectively. From the SEM images, the
shrinkage volume is significantly decreased with the addition of filler. With
decreased shrinkage, the LC-rich phase more or less keeps its width as grated.
This implies that the rigidity of the resin phase holds the dimension of the
grating close to the Bragg’s spacings. This, together with an increased phase separation,
should give high diffraction efficiency.Grating morphology (oligomer/EHA = 3:1,
35 wt.-% LC): (a) without silica,d = 1.35 μm, and h = 0.58 μm,
(b) with Aerosil 200, d = 1.47 μm
and h = 0.76 μm
[101].
(a)(b)


## 7.1. Exposure Conditions

### 7.1.1. Effect of Exposure Intensity

The exposure intensity decides the rate of gelation, diffusion, and nucleation, which determines the
degree of phase separation and morphology of the droplets, and hence the
diffraction efficiency. Bunning
et al. speculated on the
extreme morphologies possible given the relative rates of diffusion,
nucleation, and gelation as shown in
Figure29
[76]. In case (a) shown in
Figure 29, if the time to diffuse across Λ/2
is fast compared to the time for droplets to nucleate and nucleation occurs
much faster than gelation, a “perfect” grating is formed. If the rates of
nucleation and gelation are on the same order, but diffusion of LC can still
take place over a distance Λ/2 during the polymerization and before
nucleation, then little growth of the LC domains would be expected once
discrete LC-rich domains are formed. These small LC domains would be spatially
segregated on a length scale commensurate with Λ as shown schematically in case (b). If the LC domains
separate out before the LC molecules can diffuse parallel to the grating vector
a distance of Λ/2, one would obtain cases (c) and (d) which at
their extremes approximate conventional floodlit samples. One can effectively
increase the time needed for diffusion of LC by increasing Λ.
In the infinite case, one has a conventionally floodlit LC composite system.
The size of the droplets and their distribution in sizes is again controlled by
the relative rates between nucleation and gelation. If gelation is slow (case
(d), then considerable coalescence of the droplets can be expected which
increases the size distribution. If gelation is fast (case (c) once droplets are
nucleated, then small individual LC domains would be formed.Figure 29
Pictorial representation of the timeline for H-PDLC grating formation. The
cases (a), (b), (c), and (d) show extreme morphologies possible based on the
relative time scales for the events listed on the timeline.tN, tG, and tD are nucleation time, gelation time, and diffusion time to Λ/2,
respectively. Λ is
the grating period
[76].Macroscopically, if the intensity is too weak, the induced energy will not be enough, leading to a slower polymerization rate and longer LC droplets growth time. Finally, the size of LC droplets will be larger and the scattering will be increased and diffraction efficiency will be lowered. On the contrary, too strong intensity will promote the rate of polymerization. The liquid crystal droplets do not have sufficient time to grow and diffuse because of the rapid cross-linking of monomers, so many droplets were trapped in the polymerized regions. The buried droplets will act as scatterers, lowering diffraction efficiency. So exposure intensity is critical to make the rate of polymerization and diffusion approximately equal and then form a clear and smooth grating structure.A representative plot of the data as a function of time is given in Figure30 [11], which shows three regions characterizing the formation
of holographic gratings in photopolymers: (a) a short induction period
during which no polymerization takes place until all inhibitors, for example,
oxygen or those added by the manufacturer to prevent accidental polymerization,
have been reacted; (b) a period of rapid polymerization and
photobleaching of the initiator dye with a concomitant rise in diffraction
efficiency; (c) a plateau region where most of the dye molecules are
irreversibly bleached. The induction period is actually quite short; measurable
diffraction efficiency is noted as early as 250 μs
after exposure [14]. The time of rapid rise in diffraction efficiency is
most certainly involved with the growth and final development of periodic LC
domains. This is consistent with the final morphology revealed by SEM and by
the fact that samples cured with no or a low concentration of LC have much
lower diffraction efficiency.Figure 30
Diffraction efficiency as a function of
time in an H-PDLC grating recording
[11].According to the previous reports
[14, 77, 78], the laser intensity is varied between 0.1 and 100 mW/cm2, with typical exposure
time of 30–120 seconds,
which strongly depends on the properties of the materials used and the
component ratio in the mixture. In our experiments, we obtained the peak diffraction
efficiency with the conditions of I =
10 mW/cm2 and t = 120 s with
the TMPTA monomer and prepolymer/LC = 70/30.


### 7.1.2. Effect of Exposure Temperature

Another
important factor to affect the structure is the exposure temperature. The
temperature has a big effect on the viscosity
of the materials, which is believed to affect the structure morphologies significantly.
In general, at low temperatures, the diffusion rates of LCs and monomers are
low due to the high viscosity of both LCs and monomers. In this case, during
the exposure, some LC molecules (monomers) have not enough time to diffuse into
the dark (bright) regions. As a result, many LC molecules (monomers) are
trapped in the polymer-rich (LC-rich) regions, inducing an incomplete phase
separation, and thus a poor grating structure is formed. At high temperatures, the LC and monomer
viscosities decrease much and diffusion rates are much faster. As a result, a
better separated LC and polymer structure will be formed. To obtain a complete
phase separation between LC and polymer, a suitable temperature is needed.
Figure31
shows the effect of the exposure temperature on the
diffraction efficiency of a transmission H-PDLC grating. At the temperature
range of 40–50°C,
the diffraction efficiency reaches the maximum, which indicates the best phase
separation between LCs and polymer. It is worth mentioning that at a higher
temperature the prepolymer/LC mixture may polymerize rapidly so that the
grating structure is not formed at all. In this case, the temperature induced
phase separation (TIPS) plays a dominant role over the photopolymerization.
Thus, a PDLC-like structure is formed.Figure 31
Effect of exposure temperature on the diffraction efficiency of a transmission
H-PDLC grating.


## 7.1.1. Effect of Exposure Intensity

The exposure intensity decides the rate of gelation, diffusion, and nucleation, which determines the
degree of phase separation and morphology of the droplets, and hence the
diffraction efficiency. Bunning
et al. speculated on the
extreme morphologies possible given the relative rates of diffusion,
nucleation, and gelation as shown in
Figure29
[76]. In case (a) shown in
Figure 29, if the time to diffuse across Λ/2
is fast compared to the time for droplets to nucleate and nucleation occurs
much faster than gelation, a “perfect” grating is formed. If the rates of
nucleation and gelation are on the same order, but diffusion of LC can still
take place over a distance Λ/2 during the polymerization and before
nucleation, then little growth of the LC domains would be expected once
discrete LC-rich domains are formed. These small LC domains would be spatially
segregated on a length scale commensurate with Λ as shown schematically in case (b). If the LC domains
separate out before the LC molecules can diffuse parallel to the grating vector
a distance of Λ/2, one would obtain cases (c) and (d) which at
their extremes approximate conventional floodlit samples. One can effectively
increase the time needed for diffusion of LC by increasing Λ.
In the infinite case, one has a conventionally floodlit LC composite system.
The size of the droplets and their distribution in sizes is again controlled by
the relative rates between nucleation and gelation. If gelation is slow (case
(d), then considerable coalescence of the droplets can be expected which
increases the size distribution. If gelation is fast (case (c) once droplets are
nucleated, then small individual LC domains would be formed.Figure 29
Pictorial representation of the timeline for H-PDLC grating formation. The
cases (a), (b), (c), and (d) show extreme morphologies possible based on the
relative time scales for the events listed on the timeline.tN, tG, and tD are nucleation time, gelation time, and diffusion time to Λ/2,
respectively. Λ is
the grating period
[76].Macroscopically, if the intensity is too weak, the induced energy will not be enough, leading to a slower polymerization rate and longer LC droplets growth time. Finally, the size of LC droplets will be larger and the scattering will be increased and diffraction efficiency will be lowered. On the contrary, too strong intensity will promote the rate of polymerization. The liquid crystal droplets do not have sufficient time to grow and diffuse because of the rapid cross-linking of monomers, so many droplets were trapped in the polymerized regions. The buried droplets will act as scatterers, lowering diffraction efficiency. So exposure intensity is critical to make the rate of polymerization and diffusion approximately equal and then form a clear and smooth grating structure.A representative plot of the data as a function of time is given in Figure30 [11], which shows three regions characterizing the formation
of holographic gratings in photopolymers: (a) a short induction period
during which no polymerization takes place until all inhibitors, for example,
oxygen or those added by the manufacturer to prevent accidental polymerization,
have been reacted; (b) a period of rapid polymerization and
photobleaching of the initiator dye with a concomitant rise in diffraction
efficiency; (c) a plateau region where most of the dye molecules are
irreversibly bleached. The induction period is actually quite short; measurable
diffraction efficiency is noted as early as 250 μs
after exposure [14]. The time of rapid rise in diffraction efficiency is
most certainly involved with the growth and final development of periodic LC
domains. This is consistent with the final morphology revealed by SEM and by
the fact that samples cured with no or a low concentration of LC have much
lower diffraction efficiency.Figure 30
Diffraction efficiency as a function of
time in an H-PDLC grating recording
[11].According to the previous reports
[14, 77, 78], the laser intensity is varied between 0.1 and 100 mW/cm2, with typical exposure
time of 30–120 seconds,
which strongly depends on the properties of the materials used and the
component ratio in the mixture. In our experiments, we obtained the peak diffraction
efficiency with the conditions of I =
10 mW/cm2 and t = 120 s with
the TMPTA monomer and prepolymer/LC = 70/30.


## 7.1.2. Effect of Exposure Temperature

Another
important factor to affect the structure is the exposure temperature. The
temperature has a big effect on the viscosity
of the materials, which is believed to affect the structure morphologies significantly.
In general, at low temperatures, the diffusion rates of LCs and monomers are
low due to the high viscosity of both LCs and monomers. In this case, during
the exposure, some LC molecules (monomers) have not enough time to diffuse into
the dark (bright) regions. As a result, many LC molecules (monomers) are
trapped in the polymer-rich (LC-rich) regions, inducing an incomplete phase
separation, and thus a poor grating structure is formed. At high temperatures, the LC and monomer
viscosities decrease much and diffusion rates are much faster. As a result, a
better separated LC and polymer structure will be formed. To obtain a complete
phase separation between LC and polymer, a suitable temperature is needed.
Figure31
shows the effect of the exposure temperature on the
diffraction efficiency of a transmission H-PDLC grating. At the temperature
range of 40–50°C,
the diffraction efficiency reaches the maximum, which indicates the best phase
separation between LCs and polymer. It is worth mentioning that at a higher
temperature the prepolymer/LC mixture may polymerize rapidly so that the
grating structure is not formed at all. In this case, the temperature induced
phase separation (TIPS) plays a dominant role over the photopolymerization.
Thus, a PDLC-like structure is formed.Figure 31
Effect of exposure temperature on the diffraction efficiency of a transmission
H-PDLC grating.


## 7.2. Effect of Monomer Functionality

In H-PDLC material recipe, the monomer
generally has the largest concentration. Upon the light exposure, the monomer
polymerizes to form a cross-linking polymer matrix. The functionality of the
monomer plays a very important role in determining the degree of cross-linking
in the polymer matrix, which is then anticipated to contribute to the degree of
the phase separation between the polymer and liquid crystals, producing a
dramatic effect on the performance of H-PDLCs. Generally, larger-functional
monomer yields a highly cross-linking density, while smaller-functional monomer
yields a low or even zero cross-linking density. Fontecchio et al. investigated the monomer
functionality effect on the performance of H-PDLCs by examining the switching
properties and reflection efficiencies
[79]. They combined monomers with functionality 2, 3, and
6 to make integer and half-integer functionalities in the range from 2 to 6. By
measuring the reflection efficiency, switching properties, and SEM observation,
the optimal monomer functionality exists for the H-PDLC polymer binder. The
optimum values for the functionality to obtain the best performance are 4–4.5. Pogue et al.
studied the monomer functionality effects on H-PDLCs
[80], in particular, on the formation the anisotropic LC
domains. The experimental results demonstrated that the local volume fraction
and the LC domain size decreased substantially as the monomer functionality were
decreased. The image analysis showed that a much stronger tendency to form
anisotropically-shaped domains was observed for the higher functional syrups.
These domain anisotropy differences are correlated with the number of reactive
double bonds per monomer and are suggestive of local environmental differences
exerted at the time of the domain formation.De Sarkar and coworkers also studied the
effect of monomer functionality on H-PDLCs
[81].
Figure 32
shows the rate of  polymerization against the  monomer
conversion for mixtures with different average functionalities. In general, the
maximum rate of polymerization and the maximum conversion are inversely
proportional to the functionality. The exception to this trend is the mixture
with an average functionality of 1.3, whose maximum rate of polymerization and
extent of monomer conversion are less than the values for mixture with average
functionality of 1.5 but greater than the values for average functionality of
2.0.Figure 32
Rate of polymerization versus conversion of prepolymer solutions with different
average functionalities
[81].Figure33
shows the effect of average functionality on the
phase separated morphology of the H-PDLC gratings. The SEM observations
indicate a decrease in nematic domain size in the grating morphology with
decrease in average functionality of the prepolymer syrup. H-PDLC cells
prepared from monomer mixtures with higher average functionality exhibit more
variability in the shape and size of the LC domains. By measuring the
diffraction efficiency, an increase in diffraction efficiency was observed and
a decrease in LC domain size as the average functionality of the constituent
monomer mixture decreases. The smaller size of LC domains can reduce the
residual scattering and therefore increase the diffraction efficiency. The
increase in diffraction efficiency with decrease in functionality can also be
attributed to the increase in refractive index modulation. On the other hand, the
switching performance of H-PDLC gratings deteriorates with decrease in
functionality. The experimental results showed that an optimum average
functionality (Feff≈2.0–2.5) exists to
obtain the optimized performance of H-PDLCs below which the LC domains become
negligibly small. The similar trend was also demonstrated by other researchers
[82].SEM micrographs for transmission gratings prepared using monomer mixtures with
average functionalities of (a) 3.5, (b) 3.0,
(c) 2.4, (d) 2.0, and (e) 1.5
[81].
(a)(b)(c)(d)(e)


## 7.3. Effect of LC Concentration

LC concentration is generally the second
largest concentration in the H-PDLC material recipe, which has a dramatic effect
on the diffraction efficiency. In the pure polymer gratings, the peak diffraction
efficiency was typically ~1%. With different LC concentration of 20–40 wt%, diffraction
efficiency was very different.
Figure34
showed the effect of different LC concentrations on diffraction
efficiency. The peak diffraction efficiency was obtained with the concentration
of 28 wt%. The morphology of the samples was shown in
Figure 35. From Figure 35, we can see that if the LC concentration is higher,
the volume fraction of LC lamella throughout the bulk of the film increases and
the size of droplet is larger, thus increasing the scattering and lowering the
diffraction efficiency. However, if the concentration is lower, the volume
fraction of LC decreases, and the size of droplets becomes smaller. Within the
LC-rich lamellae, a large amount of polymer exists, which lowers the index
modulation and decreases the diffraction efficiency accordingly. Therefore, a
suitable LC concentration is needed in order to obtain both a good grating
structure and high diffraction efficiency. In most references
[11, 37], the LC concentration of ~30 wt% is the best choice
to achieve high diffraction efficiency. The diffraction efficiency can reach
more than 90%.Figure 34
Effect of LC concentration on diffraction
efficiency.The same magnification SEM photographs of the surface of H-PDLC Bragg grating
of different LC contents: (a) 20 wt%, (b) 30 wt%,
(c) 40 wt%, and (d) 28 wt%.
(a)(b)(c)(d)


## 7.4. Effect of NVP Concentration

NVP is known to be a critical component in
improving acrylate-based H-PDLC grating diffraction efficiency by reducing LC
droplet size
[83, 84]. As is the case in many acrylate systems, NVP
causes an increase in the rate of polymerization with increasing concentration
in H-PDLC formulations. This increase in the rate of polymerization occurs
through the incorporation of NVP into the H-PDLC polymer matrix. To understand
the dependence of HPDLC polymerization kinetics on NVP, the influence of NVP
concentration on the rate of polymerization has also been examined using photo-differential
scanning calorimetry (PDSC).
Figure 36(a)
shows the rate of polymerization versus double
bond conversion for HPDLC formulations containing increasing concentrations of
NVP. For comparison, the polymerization of DPPHA with increasing NVP
concentration was studied, as shown in Figure 36(b). H-PDLC formulations containing up to 15 wt% NVP
demonstrate complete NVP conversion. Examination of double bond conversion
evolution in H-PDLC formulations reveals that NVP and monomer conversion are
codependent at relatively low double bond conversions. This dependence results
from the reaction of NVP double bonds with trapped acrylate radical species.
The NVP radicals can then react with other trapped pendant acrylate double
bonds. Therefore, significant rate increases and increased acrylate conversion
result with NVP addition. The preferential reactivity of NVP with acrylate also
serves to delay the onset of the reaction diffusion termination mechanism while
also extending its predominance into higher double bond conversion.Rate of polymerization versus double bond conversion for (a) HPDLC formulations
with 0 (),
5 (),
10 (),
and 15 (•) wt% NVP and (b) DPPHA:NVP formulations with 0 (),
5 (),
10 (),
and 15 (•) wt% NVP.
(a)(b)NVP also has a major influence on LC phase
separation in the formation of H-PDLCs and ultimate polymer morphology. Study
of the appearance of the nematic phase, an indirect examination of phase
separation, shows that samples containing NVP or the chemically similar but nonreactive
moleculen-ethyl-2-pyrrolidinone (NEP),
exhibit a slower appearance of the nematic phase when compared to an H-PDLC
formulation without NVP (or NEP). In general, increasing NVP concentration
extends the homogeneity of the polymer/LC mixture into higher double bond conversions—slowing the LC
phase separation process and the appearance of the nematic phase. Further, the
kinetic influence of NVP coupled with its solubility reduces the amount of LC
phase separation, which subsequently reduces the overall amount of nematic LC.
These effects are also evident in the polymer/LC morphology. With NVP
incorporation droplet size is much smaller than that observed when incorporating
the nonreactive analogue NEP. The rate of polymerization for the H-PDLC formulation
containing NVP is much greater than that containing NEP.
This behavior, in turn, is the
cause of the significant reduction in LC droplet size and improved H-PDLC
performance with NVP inclusion.
Figure 37
shows obviously different surface morphologies
of H-PDLC transmission gratings prepared with 4 wt% and 15 wt% NVP,
respectively. It can be seen that increasing the amount of NVP leads to smaller
droplets and decreases the   anisotropy of the LC droplets.SEM images of H-PDLC transmission gratings with (a) 4 wt% and (b) 15 wt% NVP.
Scale bars represent 600 nm
[83].
(a)(b)


## 7.5. Decreasing Driving Voltage

For H-PDLC gratings, the LC droplets are
small and the anchoring energy is high, which results in a high driving
voltage. According to Mormile et al., the threshold voltage of PDLC can be written
as [85] (44)Vth≈dr[K(ℓ2−1)ε0Δε]1/2, where d is the HPDLC film thickness, r is the droplet radius, K is the effective elastic constant, ε0 is the vacuum dielectric constant, Δε is the LC dielectric anisotropy, ℓ=a/b is the droplet aspect ratio, with a and b the length of the major and minor axis of the ellipsoid-shaped
droplet, respectively. Equation (44)
was deduced by balancing the elastic and field
torques to the equilibrium orientation at the presence of a voltage applied to
a shaped  droplet [86], that is, Γd+Γe=0, where Γd is the elastic torque per unit volume and Γe is the electric torque on the droplet director per unit volume. This can be
regarded as the shape contribution to the threshold voltage of a normal PDLC.The
LC droplets of conventional PDLC are about 1 ~ 5μm in size. However, the size of HPDLC droplets
is about 0.01 ~ 0.1 μm.
The size effect on the threshold voltage can be understood by the following
comparisons. Using our experimental parameters, the cell thickness, d,
is 20 μm,
the elastic constant, K, is 1.71 × 10−11 N, the dielectric anisotropy, Δε,
is 6.49, and assuming an aspect ratio of 1.1, for LC droplets with r = 2 μm
and 0.02 μm,
the corresponding threshold voltage Vth
calculated is 2.5 V
and 250 V, respectively. It can be seen that with the reduction in dimension,
the threshold voltage increases linearly. In general, the threshold voltage of
nano-PDLC produced by holography is about one or two orders higher than that of
normal PDLC.For
practical application of HPDLC, it is desired to reduce the driving voltage.
Colegrove et al. reported that by adding a high dielectric anisotropy
material (Δε = 65), the threshold voltage of
HPDLC can be reduced significantly
[87]. In addition, adding a small portion of surfactant
to the prepolymer/LC syrup also helps to reduce the threshold voltage
[88–91]. Fluorination of the polymer matrix also has
significant effects on decreasing the driving voltage of H-PDLC
[92, 93]. In the following, the effects of surfactants and
polymer fluorination will be discussed.


### 7.5.1. Surfactant Effect

The
role of surfactant is supposed to be a lubricant between polymer matrix and
liquid crystals. When phase separation occurs in the homogenous mixture, the
surfactant will form an intermediate layer between the polymer and the LC. The
anchoring energy at the interface of the LC and the surfactant becomes weaker
than that at the interface of the LC and polymer without surfactant. As a
result, the liquid crystal molecules could be easily reorientated under an
electric field. Therefore, the decrease in anchoring strength may effectively
lower the driving voltage.Figure38 shows the diffraction efficiency as a function of
driving electric field for three different surfactants. The H-PDLC without
surfactant is also shown for comparison. It can be seen from
Figure 38
that, the surfactant is effective in reducing the
driving voltage. The conductivity of samples with surfactants number 1 and number
3 was so high that the voltage could not be increased further before they were
completely switched. Sample number 2 can
both keep the high diffraction efficiency and reduce the driving voltage
effectively. It reduces the threshold voltage from 13 V/μm to about 2.5 V/μm.Figure 38
Diffraction efficiency versus the electric field curves for Bragg gratings made
of liquid crystal E7 with three different kinds of surfactants, octanoic acid (no. 1),
S-271 POE sorbitan monooleate (no. 2), and Tergital Min-Foam 1X (no. 3),
respectively. The diffraction efficiency without surfactant is also shown for
comparison.The
surfactant also has a significant effect on the morphologies of H-PDLC
gratings.
Figures39(a)
and 39(b) show the SEM morphologies of the HPDLC
gratings, which contain 8 wt% and 15 wt% of surfactant, respectively. From
Figure 39, it can be seen that the surfactant affects the
grating significantly. With more surfactant, the polymer regions contain more
LC droplets. Thus the surfactant affects the LC movement during polymerization.
Figure 39(a) has a clearer grating structure than
Figure 39(b), which indicates that the grating in
Figure 39(a) has better diffraction properties. In our
experiment, when the surfactant content was around 8 wt%, the HPDLC Bragg
gratings could both keep high diffraction efficiency and have excellent
electro-optical properties.SEM images of the HPDLC Bragg gratings consisting 8 wt% (a) and 15 wt% (b) of
surfactant no. 2. The monomer and liquid
crystal used are no. 3 in Figure12 and E7,
respectively.
(a)(b)Figure40 shows the diffraction efficiency as a function of the
surfactant content for samples containing number 2 surfactant. With the
increase of the content, the diffraction efficiency reduces. Generally, when
the surfactant content was less than 8 wt%, the HPDLC Bragg gratings could
still keep higher diffraction efficiency.Figure 40
Diffraction efficiency as a function of the
surfactant content for surfactant no.
2. The monomer and liquid crystal used are no.
3 in Figure12 and E7, respectively.


### 7.5.2. Fluorination Effect

Another
way to reduce the driving voltage is to modify the monomers. The experimental
results have shown the partial fluorination of the polymer matrix has
significant effects on the morphology and electro-optical performance of H-PDLC
[92, 93]. The morphology of the fluorinated transmission
gratings displayed an enhanced phase separation as manifested in a significant
increase in nematic domain size and the LC volume fraction, as shown in
Figures 41
and 42. The incorporation of fluorinated monomers in the
standard UV H-PDLC formulation reduces the switching voltage considerably. However,
the tradeoff is that the relaxation time also increases with fluorination. The
experimental results strongly indicate that significant amount of fluorine
atoms resides at the polymer–LC interface. The
presence of fluorine atoms at the interface can manipulate the surface
anchoring strength and alignment, causing a reorientation of the original
configuration of the LC droplet directors.LVHRSEM photomicrographs of (a) standard formulation, (b) 13.2 mol% MA, and (c)
11.7 mol% HFIPA holographic PDLC films
[92].
(a)(b)(c)SEM micrographs of HPDLC transmission gratings prepared (a) from control
monomer mixture and substituting it with, (b) 10 wt%, (c) 20 wt%, (d) 25 wt%,
(e) 30 wt%, (f) 35 wt%, and (g) 40 wt% of
HFIPA [93].
(a)(b)(c)(d)(e)(f)(g)From
the above experimental results, both surfactant and fluorination has a
significant effect in decreasing the driving voltage. However, there are
side-effects. For example, the grating morphology was changed and the
diffraction efficiency was decreased more or less with addition of surfactants.
The polymer fluorination seems better to decrease the driving voltage compared
to the surfactant, but the longer relaxation time is not desired.


## 7.5.1. Surfactant Effect

The
role of surfactant is supposed to be a lubricant between polymer matrix and
liquid crystals. When phase separation occurs in the homogenous mixture, the
surfactant will form an intermediate layer between the polymer and the LC. The
anchoring energy at the interface of the LC and the surfactant becomes weaker
than that at the interface of the LC and polymer without surfactant. As a
result, the liquid crystal molecules could be easily reorientated under an
electric field. Therefore, the decrease in anchoring strength may effectively
lower the driving voltage.Figure38 shows the diffraction efficiency as a function of
driving electric field for three different surfactants. The H-PDLC without
surfactant is also shown for comparison. It can be seen from
Figure 38
that, the surfactant is effective in reducing the
driving voltage. The conductivity of samples with surfactants number 1 and number
3 was so high that the voltage could not be increased further before they were
completely switched. Sample number 2 can
both keep the high diffraction efficiency and reduce the driving voltage
effectively. It reduces the threshold voltage from 13 V/μm to about 2.5 V/μm.Figure 38
Diffraction efficiency versus the electric field curves for Bragg gratings made
of liquid crystal E7 with three different kinds of surfactants, octanoic acid (no. 1),
S-271 POE sorbitan monooleate (no. 2), and Tergital Min-Foam 1X (no. 3),
respectively. The diffraction efficiency without surfactant is also shown for
comparison.The
surfactant also has a significant effect on the morphologies of H-PDLC
gratings.
Figures39(a)
and 39(b) show the SEM morphologies of the HPDLC
gratings, which contain 8 wt% and 15 wt% of surfactant, respectively. From
Figure 39, it can be seen that the surfactant affects the
grating significantly. With more surfactant, the polymer regions contain more
LC droplets. Thus the surfactant affects the LC movement during polymerization.
Figure 39(a) has a clearer grating structure than
Figure 39(b), which indicates that the grating in
Figure 39(a) has better diffraction properties. In our
experiment, when the surfactant content was around 8 wt%, the HPDLC Bragg
gratings could both keep high diffraction efficiency and have excellent
electro-optical properties.SEM images of the HPDLC Bragg gratings consisting 8 wt% (a) and 15 wt% (b) of
surfactant no. 2. The monomer and liquid
crystal used are no. 3 in Figure12 and E7,
respectively.
(a)(b)Figure40 shows the diffraction efficiency as a function of the
surfactant content for samples containing number 2 surfactant. With the
increase of the content, the diffraction efficiency reduces. Generally, when
the surfactant content was less than 8 wt%, the HPDLC Bragg gratings could
still keep higher diffraction efficiency.Figure 40
Diffraction efficiency as a function of the
surfactant content for surfactant no.
2. The monomer and liquid crystal used are no.
3 in Figure12 and E7, respectively.


## 7.5.2. Fluorination Effect

Another
way to reduce the driving voltage is to modify the monomers. The experimental
results have shown the partial fluorination of the polymer matrix has
significant effects on the morphology and electro-optical performance of H-PDLC
[92, 93]. The morphology of the fluorinated transmission
gratings displayed an enhanced phase separation as manifested in a significant
increase in nematic domain size and the LC volume fraction, as shown in
Figures 41
and 42. The incorporation of fluorinated monomers in the
standard UV H-PDLC formulation reduces the switching voltage considerably. However,
the tradeoff is that the relaxation time also increases with fluorination. The
experimental results strongly indicate that significant amount of fluorine
atoms resides at the polymer–LC interface. The
presence of fluorine atoms at the interface can manipulate the surface
anchoring strength and alignment, causing a reorientation of the original
configuration of the LC droplet directors.LVHRSEM photomicrographs of (a) standard formulation, (b) 13.2 mol% MA, and (c)
11.7 mol% HFIPA holographic PDLC films
[92].
(a)(b)(c)SEM micrographs of HPDLC transmission gratings prepared (a) from control
monomer mixture and substituting it with, (b) 10 wt%, (c) 20 wt%, (d) 25 wt%,
(e) 30 wt%, (f) 35 wt%, and (g) 40 wt% of
HFIPA [93].
(a)(b)(c)(d)(e)(f)(g)From
the above experimental results, both surfactant and fluorination has a
significant effect in decreasing the driving voltage. However, there are
side-effects. For example, the grating morphology was changed and the
diffraction efficiency was decreased more or less with addition of surfactants.
The polymer fluorination seems better to decrease the driving voltage compared
to the surfactant, but the longer relaxation time is not desired.


## 7.6. Index Matching Effect

The
index matching between the polymer matrix and liquid crystal plays an important
role in the performance optimization of H-PDLCs. In our configuration, the
polymer refractive index,np,
is chosen to be as close as possible to the ordinary refractive index, no, of LC. This helps to
reduce the diffraction loss in the transparent state. Moreover, the
birefringence of LC, Δn, is chosen to be as large as possible
in order to improve the diffraction efficiency. We experimentally optimized the
material recipe according to the refractive index match. In our experiment,
five kinds of acrylate monomers were selected and their refractive indices are
1.490 for DPPHA (no. 1), 1.484 for PETA (no. 2), 1.474 for TMPTA (no. 3), 1.487
for PET(etra)A (no. 4) and 1.450 for TPGDA (no. 5), respectively. The chemical
structures of these five monomers are shown in
Figure 12 and their corresponding functionalities are 5-6, 3, 3, 4, and
2, respectively.  Because the prepolymer
syrup includes other chemicals such as photoinitiator and coinitiator, moreover,
the refractive index changes during polymerization. In general, the refractive
index will be different from the above values for the mixture after
polymerization. Two different LCs, E7, and BL038, were chosen to match the
refractive index of polymer matrices and their physical properties were listed
in Table 1.Table 1
Basic physical properties of LC E7 and BL038.
Physical propertiesE7BL038Clearing
point (C°)+58.0+100.0Flow
viscosity
(mm2s−1)20C°39720C°145—–20C°1200—–30C°6400—Optical
anisotropy
+20C°, 589.3 nmΔn0.22530.2720ne1.74641.7990no1.52111.5270Dielectric
anisotropy
+20C°, 1.0 kHzΔε+13.8+16.9ε⊥5.26.1ε∥19.023.0The
refractive indices of the monomers are from Sigma-Aldrich. Because other
chemicals are mixed into the monomer, the refractive index of the prepolymer
syrup   changes accordingly. The prepolymer syrup refractive indices were
measured by Abbe
refractometer. Then the syrup was cured on a SiO2 substrate to form a polymer thin film, the refractive index, np, of which was measured by
m-line method [94].
Figure 43
shows the setup of refractive index measurement using
m-line method. The results are tabulated in
Table 2.Table 2
Refractive index and corresponding diffraction efficiency for various monomers
used.
No.12345Monomer1.4901.4841.4741.4871.450Prepolymer syrup1.5011.4961.4891.4981.471Cured film1.5291.5281.5221.5301.502DE for E741.2%56.4%65.0%41.6%32.2%DE for BL03861.8%68.4%40.2%51.6%34.2%Figure 43
Measurement setup of the refractive indexnp.From
the table, we can see that the refractive indexnp of the cured film was larger than that of the
corresponding monomer, with the increment of 0.03 ~ 0.05 on the average. In our
experiment, the no of LC
E7 is 1.521. The number 3 monomer was the nearest to 1.521 and the experimental
results proved that diffraction efficiency was the highest with the number 3
monomer. Similarly, for BL038, no is 1.527. Only the number 2 monomer was the nearest to 1.528 and the
experimental result proved that diffraction efficiency was the highest with the
number 2 monomer. According to our selection principle, the number 3 and number
2 monomers match with E7 and BL038 liquid crystals, respectively.


## 7.7. Effect of Nanoparticle Doping

To extend H-PDLC applications, it is
desirable to obtain higher index contrast. Doping nanoparticles with high
refractive index into PDLC materials may be an easy and effective way to
realize the higher index contrast. Some researchers have successfully
demonstrated nanoparticle patterning, that is, holographic gratings, in
nanoparticle-dispersed photopolymers using holography technique
[95–99]. In the nanoparticle-doped PDLC materials, the
nanoparticles are anticipated to diffuse into the LC-rich regions during the
phase separation between the polymer and LC. Therefore, the index contrast can
be increased by this way.Jakubiak
et al. studied the ZnO
nanoparticles (125 nm in diameter) doped H-PDLC gratings
[100].
Figure 44
shows the SEM images of a transmission grating
fabricated from 1% ZnO and 36% LC with a grating period of about 500 nm. The
SEM images show rougher surface in the fractured cross
section compared to the
conventional H-PDLC gratings without nanoparticle doping. As evidenced by the
structural and performance characteristics of the nanoparticle/LC gratings, the
particles are predominately located in the LC phase. The experimental results
showed that the diffraction efficiency can be greatly enhanced for gratings
containing 1% by weight of ZnO nanoparticles.SEM micrographs of the (a) top and side and (b) side of a Bragg transmission
grating. Note in (b) the cross grating appearing as horizontal lines. The scale
bar corresponds to 1μm
for both panels
[100].
(a)(b)Kim et
al. studied the nanosized silicas doped H-PDLCs
[101]. The experimental results showed that the nanosized
silicas doped H-PDLCs provide enhanced elasticity, dimensional stability, and
diffraction efficiency.
Figures 45(a)
and 45(b) show the typical grating morphologies
without and with silica filled, respectively. From the SEM images, the
shrinkage volume is significantly decreased with the addition of filler. With
decreased shrinkage, the LC-rich phase more or less keeps its width as grated.
This implies that the rigidity of the resin phase holds the dimension of the
grating close to the Bragg’s spacings. This, together with an increased phase separation,
should give high diffraction efficiency.Grating morphology (oligomer/EHA = 3:1,
35 wt.-% LC): (a) without silica,d = 1.35 μm, and h = 0.58 μm,
(b) with Aerosil 200, d = 1.47 μm
and h = 0.76 μm
[101].
(a)(b)


## 8. Electro-Optical Properties

### 8.1. Field-Dependent Diffraction

For H-PDLC-based devices, the most
interesting thing is that they can be dynamically tuned or switched. Applying
an electric field on H-PDLC is a very common way to control it. For H-PDLC
gratings, in normal mode operation, the diffraction efficiency is high when the
applied field is low and decreases with increasing field strength. Of course,
there is an abnormal case when the polymer concentration is small (3–8 wt%), so-called
reversed mode
[102, 103]. The “reversed mode” means that the incident light
goes through the film without applied voltage and is diffracted with voltage
applied. Figure 46
shows an example of reversed mode holographic
polymer-stabilized liquid crystal (H-PSLC) grating.Figure 46
Diffraction efficiency as a function of applied
voltage [103].Figure47 shows
the diffraction efficiency and transmission efficiency as a function  of the
applied electric field for a normal mode H-PDLC transmission grating. In
Figure 47, the sum of the diffraction efficiency and transmission
efficiency is also plotted. It can be seen that, the sum increases slightly
with the electric field, which indicates a decrease in the random scattering.
When the diffraction efficiency is reduced to the minimum, the transmission
efficiency reaches the maximum. Reported
switching fields vary widely from 20 V/μm
[53] to 6 V/μm
[104], depending mostly on the materials system used to
form the hologram. Lowering this value is of importance for practical
applications and is a subject of continuing research.Figure 47
Diffraction and transmission efficiency as a function of applied electric field.
The sum refers to the sum of diffraction and
transmission efficiencies.In
some cases, with the increase of applied voltage, the diffraction efficiency
firstly increases and then decreases, as shown in
Figure48
for the curve with TPGDA monomer. Optical clearing,
originating from droplet size distribution, may be the possible reason for the
initial increase in diffraction efficiency. In H-PDLC gratings, large liquid
crystal droplets tend to scatter more light, producing a haze effect. When an
electric field is applied on the sample, these large droplets will align
firstly due to the larger volume to surface area ratio, and the haze will
disappear, thus, resulting in the diffraction efficiency increase initially.
When the electric field continues to increase, the smaller droplets start to
align, and the index modulation decreases. As a result, the diffraction
efficiency will decrease. The similar
behavior was also observed in H-PDLC PhCs in the following
section. Above the switching electric field, with
further increase in electric field, the diffraction efficiency increases again,
as shown in
Figure 49. From Figure 49, an increase of diffraction efficiency can be clearly
observed when the electric field is above 27.3 V/μm.Figure 48
Diffraction efficiency as a function of
applied electric field.Figure 49
Diffraction efficiency as a function of the electric field. The threshold field
and switching field are indicated.The
general dynamic behavior for the diffraction efficiency under an external
electric field can be explained in the following. Assuming the LC droplets in
H-PDLCs are bipolar configuration, the LC droplets have an axis of symmetry
along the long axis of the droplet, which can be then considered as a uniaxial
domain with an angle-dependent extraordinary refractive index.
Figure50
shows the case when the LC droplets under an electric
field, where θB is the Bragg angle and θ(E)  is the angle between the LC director
direction and the electric field direction, which is a function of electric
field and can be expressed as (45)θ(E)=12tan−1[sin2θ0cos2θ0+(E/Ec)2], where θ0 is the angle between the symmetry axis of LC droplets and the Bragg plane
without voltage applied and   Ec
is a critical field for switching which depends on properties of the LC droplet
and surrounding polymer, (46)Ec=13a(σLCσp+2)[k33(ℓ2−1)Δε]1/2, where σLC
and σp are the electrical
conductivities of the LC and polymer, respectively, k33 is the elastic bend force constant,
and Δε is the dielectric
anisotropy of the LC.Figure 50
LC droplets under an external electric field.Initially,
without voltage applied, the LC director statistically aligns along the grating
vector director [83]. The p-polarized
incident light with exact Bragg angle sees the largest refractive index
difference between the polymer-rich lamellae and the LC-rich lamellae and thus
highest diffraction efficiency is obtained. When a voltage is applied on the
sample, the LC director will start to change its direction along the electric
field direction at a voltage, so-called threshold voltage. The incident light
then sees the decreased index difference and hence the diffraction efficiency
starts to decrease. With the increase of the voltage, when θ(E)=θB, the incident light only sees the ordinary refractive
index of the LCs, which is closest to the refractive index of polymer matrix.
As a result, the incident light sees the smallest index difference between the
polymer-rich lamellae and the LC-rich lamellae and the diffraction efficiency
decreases to the minimum value. With the further increase of the voltage, the
LC director continues to align along the electric field direction with a
smaller θ(E)
and an index mismatch appears again. As a result, the incident light sees a
larger index difference value again and the diffraction efficiency increases
again.It is
worth mentioning that an H-PDLC grating itself is 2 ×2
optical switch [38]. With an optimized ratio of various materials, the
highest  diffraction efficiency achieved at 632.8 nm was 85.7%. The
corresponding contrast ratio (CR) and   signal-noise
ratio (SNR) were about 23.4 dB and 15.1 dB,
respectively, where CR and SNR can be defined as (47)CR=10log(DEmaxDEmin)orCR=10log(TEmaxTEmin),SNR=10log(DEmaxTEmin)orSNR=10log(TEmaxDEmin), where DEmax is the highest diffraction efficiency, DEmin is the lowest diffraction efficiency, TEmax is the highest transmission efficiency, and TEmin is the lowest transmission efficiency.The
index difference plays a vital role in determining the performance of the
optical switch. We can optimize the performance of the optical switch according
to the following considerations.(1) Decreasing The Residual Diffraction
This
demands us to choose suitable liquid crystal and polymer, which makes the
ordinary refractive index of liquid crystal and the refractive index of polymer
as close as possible. Theoretically, only when the ordinary refractive index of
liquid crystal strictly equals to the refractive index of polymer, there is no
residual diffraction. In fact, it is impossible to eliminate the residual
diffraction. However, it is still possible to decrease the residual
diffraction. As known, it is difficult to modify the refractive index of
polymer. However, it is quite flexible to modify the refractive index of liquid
crystals. An easy way is to mix different liquid crystals to achieve the
ordinary refractive index with a value closer to the refractive index of
polymer.(2) Controlling The Phase Separation
It is impossible to obtain an
ideally perfect phase separation in H-PDLCs. In fact, during the process of
phase separation, many LC molecules (polymers) are trapped in the polymer-rich
lamellae (LC-rich lamellae) when the counter diffusion happens, which decreases
the index difference between polymer-rich lamellae and LC-rich lamellae and
thus the diffraction efficiency.(3) Controlling The Size of Lc Droplets
The
size of LC droplets also plays an important role to improve the diffraction
efficiency. Some LC droplets in polymer-rich lamellae act as scatterers and
thus decrease the diffraction efficiency. Smaller size of LC droplets can
reduce the residual scattering and therefore increase the diffraction
efficiency.


### 8.2. Response Time

The
on time,τon,
is the time required for an H-PDLC to switch diffraction between orders in
response to a step electric field. This corresponds to a decrease in
diffraction in a normal mode operation, an increase in diffraction in a reverse
mode operation, or a lowering of the frequency when using frequency addressed H-PDLC.
Conversely, the off time, τoff,
is the time required for an H-PDLC to change diffraction in response to a
sudden removal of an electric field. A typical time response for an H-PDLC
Bragg grating is shown in
Figure 51. The τon,
measured from the rising edge of the voltage pulse, is about 36 μs.
The τoff,
measured from the fall edge of the voltage pulse, is about 160 μs.Variation of diffracted light intensity
corresponding to (a) a square driving voltage,
(b) the magnified rising edge, and (c) the
falling edge of (a).
(a)(b)(c)Another interesting thing to note is that, in
Figure51(b), an optical bounce is clearly observed immediately
after the electric field is applied. It is probably due to the backflow effect
of liquid crystals
[105, 106]. Backflow effect is a consequence of flow close to
the LC cell walls induced by the rapidly relaxing alignment following the
removal of the electric field, which generally exists in the TN cells. This
flow essentially creates a shear flow in the center of the cell, which causes a
temporary reversal of the relaxation in that region, before the alignment
finally relaxes as one anticipates. As a result, an optical bounce in
transmission curve is experimentally observed when the light is normally
incident on the cell, which is induced by the backflow effect. In our
experiments, this phenomenon was only observed at the
edge of “on” state. We
speculate the reason as follows. In H-PDLCs, the nematic configurations in most
LC droplets are generally bipolar, as shown in
Figure 10(a). When an external electric field is applied on
H-PDLCs, the nematic director realigns along the electric field direction. At
the same time, an internal electric field is induced due to the impurities
(mobile ions) in H-PDLCs, which thus decreases the external electric field.
Then due to the balance between the elastic torque and the electric torque in
the LC droplets, and the delay between the external electric field and the
induced ion field, an optical bounce in transmission curve was observed at the
edge of “on” state. After the removal of the external electric field, the
nematic director configurations gradually revert to the original status due to
the elastic torque, where the optical bounce would be difficult to be observed
at the edge of “off” state.For
acrylate-based H-PDLCs, reported values ofτon vary from 25 μs
[107] to 750 μs
[35] and the reported τoff values are slightly longer,
ranging from 44
[107, 108] to 1000 μs
[109]. For the thoil-ene-based H-PDLCs, the reported
values of τon vary from 550 μs to 6.7 ms and the reported τoff values vary from 1.2 milliseconds
to 2.2 milliseconds
[48, 110, 111], which are generally much longer than those of the
acrylate-based H-PDLCs. This is expected from Wu’s model
[86] since there is no field to drive the LC back to the
zero field state. They expressed τoff and τon as (48)τoff=γ1a2k33(ℓ2−1),(49)τon=γ1ΔεE2+k33(ℓ2−1)/a2, where γ1 is the rotational viscosity coefficient of LC.As
can be seen from (48), the off time is mainly controlled by elastic forces
for most PDLC-based devices. Most experimental results show that the off time
is generally much slower than the on time. To improve the off time, Kitzerow
developed dual frequency H-PDLCs, which were electrically driven at both an on
and off state [113]. Using a dual-frequency LC where an electric field
is employed to turn the grating off, the switching times can be much improved
to a few milliseconds. Compared to conventional nematic-positive dielectric LCs
where the 100 ms was typically obtained when turning off the voltage, this off
speed is faster. Due to the large period the gratings where large LC droplets
existed, these speeds are slow compared to those of conventional Bragg gratings.
However, it showed a good method to improve the response time.


## 8.1. Field-Dependent Diffraction

For H-PDLC-based devices, the most
interesting thing is that they can be dynamically tuned or switched. Applying
an electric field on H-PDLC is a very common way to control it. For H-PDLC
gratings, in normal mode operation, the diffraction efficiency is high when the
applied field is low and decreases with increasing field strength. Of course,
there is an abnormal case when the polymer concentration is small (3–8 wt%), so-called
reversed mode
[102, 103]. The “reversed mode” means that the incident light
goes through the film without applied voltage and is diffracted with voltage
applied. Figure 46
shows an example of reversed mode holographic
polymer-stabilized liquid crystal (H-PSLC) grating.Figure 46
Diffraction efficiency as a function of applied
voltage [103].Figure47 shows
the diffraction efficiency and transmission efficiency as a function  of the
applied electric field for a normal mode H-PDLC transmission grating. In
Figure 47, the sum of the diffraction efficiency and transmission
efficiency is also plotted. It can be seen that, the sum increases slightly
with the electric field, which indicates a decrease in the random scattering.
When the diffraction efficiency is reduced to the minimum, the transmission
efficiency reaches the maximum. Reported
switching fields vary widely from 20 V/μm
[53] to 6 V/μm
[104], depending mostly on the materials system used to
form the hologram. Lowering this value is of importance for practical
applications and is a subject of continuing research.Figure 47
Diffraction and transmission efficiency as a function of applied electric field.
The sum refers to the sum of diffraction and
transmission efficiencies.In
some cases, with the increase of applied voltage, the diffraction efficiency
firstly increases and then decreases, as shown in
Figure48
for the curve with TPGDA monomer. Optical clearing,
originating from droplet size distribution, may be the possible reason for the
initial increase in diffraction efficiency. In H-PDLC gratings, large liquid
crystal droplets tend to scatter more light, producing a haze effect. When an
electric field is applied on the sample, these large droplets will align
firstly due to the larger volume to surface area ratio, and the haze will
disappear, thus, resulting in the diffraction efficiency increase initially.
When the electric field continues to increase, the smaller droplets start to
align, and the index modulation decreases. As a result, the diffraction
efficiency will decrease. The similar
behavior was also observed in H-PDLC PhCs in the following
section. Above the switching electric field, with
further increase in electric field, the diffraction efficiency increases again,
as shown in
Figure 49. From Figure 49, an increase of diffraction efficiency can be clearly
observed when the electric field is above 27.3 V/μm.Figure 48
Diffraction efficiency as a function of
applied electric field.Figure 49
Diffraction efficiency as a function of the electric field. The threshold field
and switching field are indicated.The
general dynamic behavior for the diffraction efficiency under an external
electric field can be explained in the following. Assuming the LC droplets in
H-PDLCs are bipolar configuration, the LC droplets have an axis of symmetry
along the long axis of the droplet, which can be then considered as a uniaxial
domain with an angle-dependent extraordinary refractive index.
Figure50
shows the case when the LC droplets under an electric
field, where θB is the Bragg angle and θ(E)  is the angle between the LC director
direction and the electric field direction, which is a function of electric
field and can be expressed as (45)θ(E)=12tan−1[sin2θ0cos2θ0+(E/Ec)2], where θ0 is the angle between the symmetry axis of LC droplets and the Bragg plane
without voltage applied and   Ec
is a critical field for switching which depends on properties of the LC droplet
and surrounding polymer, (46)Ec=13a(σLCσp+2)[k33(ℓ2−1)Δε]1/2, where σLC
and σp are the electrical
conductivities of the LC and polymer, respectively, k33 is the elastic bend force constant,
and Δε is the dielectric
anisotropy of the LC.Figure 50
LC droplets under an external electric field.Initially,
without voltage applied, the LC director statistically aligns along the grating
vector director [83]. The p-polarized
incident light with exact Bragg angle sees the largest refractive index
difference between the polymer-rich lamellae and the LC-rich lamellae and thus
highest diffraction efficiency is obtained. When a voltage is applied on the
sample, the LC director will start to change its direction along the electric
field direction at a voltage, so-called threshold voltage. The incident light
then sees the decreased index difference and hence the diffraction efficiency
starts to decrease. With the increase of the voltage, when θ(E)=θB, the incident light only sees the ordinary refractive
index of the LCs, which is closest to the refractive index of polymer matrix.
As a result, the incident light sees the smallest index difference between the
polymer-rich lamellae and the LC-rich lamellae and the diffraction efficiency
decreases to the minimum value. With the further increase of the voltage, the
LC director continues to align along the electric field direction with a
smaller θ(E)
and an index mismatch appears again. As a result, the incident light sees a
larger index difference value again and the diffraction efficiency increases
again.It is
worth mentioning that an H-PDLC grating itself is 2 ×2
optical switch [38]. With an optimized ratio of various materials, the
highest  diffraction efficiency achieved at 632.8 nm was 85.7%. The
corresponding contrast ratio (CR) and   signal-noise
ratio (SNR) were about 23.4 dB and 15.1 dB,
respectively, where CR and SNR can be defined as (47)CR=10log(DEmaxDEmin)orCR=10log(TEmaxTEmin),SNR=10log(DEmaxTEmin)orSNR=10log(TEmaxDEmin), where DEmax is the highest diffraction efficiency, DEmin is the lowest diffraction efficiency, TEmax is the highest transmission efficiency, and TEmin is the lowest transmission efficiency.The
index difference plays a vital role in determining the performance of the
optical switch. We can optimize the performance of the optical switch according
to the following considerations.(1) Decreasing The Residual Diffraction
This
demands us to choose suitable liquid crystal and polymer, which makes the
ordinary refractive index of liquid crystal and the refractive index of polymer
as close as possible. Theoretically, only when the ordinary refractive index of
liquid crystal strictly equals to the refractive index of polymer, there is no
residual diffraction. In fact, it is impossible to eliminate the residual
diffraction. However, it is still possible to decrease the residual
diffraction. As known, it is difficult to modify the refractive index of
polymer. However, it is quite flexible to modify the refractive index of liquid
crystals. An easy way is to mix different liquid crystals to achieve the
ordinary refractive index with a value closer to the refractive index of
polymer.(2) Controlling The Phase Separation
It is impossible to obtain an
ideally perfect phase separation in H-PDLCs. In fact, during the process of
phase separation, many LC molecules (polymers) are trapped in the polymer-rich
lamellae (LC-rich lamellae) when the counter diffusion happens, which decreases
the index difference between polymer-rich lamellae and LC-rich lamellae and
thus the diffraction efficiency.(3) Controlling The Size of Lc Droplets
The
size of LC droplets also plays an important role to improve the diffraction
efficiency. Some LC droplets in polymer-rich lamellae act as scatterers and
thus decrease the diffraction efficiency. Smaller size of LC droplets can
reduce the residual scattering and therefore increase the diffraction
efficiency.


## 8.2. Response Time

The
on time,τon,
is the time required for an H-PDLC to switch diffraction between orders in
response to a step electric field. This corresponds to a decrease in
diffraction in a normal mode operation, an increase in diffraction in a reverse
mode operation, or a lowering of the frequency when using frequency addressed H-PDLC.
Conversely, the off time, τoff,
is the time required for an H-PDLC to change diffraction in response to a
sudden removal of an electric field. A typical time response for an H-PDLC
Bragg grating is shown in
Figure 51. The τon,
measured from the rising edge of the voltage pulse, is about 36 μs.
The τoff,
measured from the fall edge of the voltage pulse, is about 160 μs.Variation of diffracted light intensity
corresponding to (a) a square driving voltage,
(b) the magnified rising edge, and (c) the
falling edge of (a).
(a)(b)(c)Another interesting thing to note is that, in
Figure51(b), an optical bounce is clearly observed immediately
after the electric field is applied. It is probably due to the backflow effect
of liquid crystals
[105, 106]. Backflow effect is a consequence of flow close to
the LC cell walls induced by the rapidly relaxing alignment following the
removal of the electric field, which generally exists in the TN cells. This
flow essentially creates a shear flow in the center of the cell, which causes a
temporary reversal of the relaxation in that region, before the alignment
finally relaxes as one anticipates. As a result, an optical bounce in
transmission curve is experimentally observed when the light is normally
incident on the cell, which is induced by the backflow effect. In our
experiments, this phenomenon was only observed at the
edge of “on” state. We
speculate the reason as follows. In H-PDLCs, the nematic configurations in most
LC droplets are generally bipolar, as shown in
Figure 10(a). When an external electric field is applied on
H-PDLCs, the nematic director realigns along the electric field direction. At
the same time, an internal electric field is induced due to the impurities
(mobile ions) in H-PDLCs, which thus decreases the external electric field.
Then due to the balance between the elastic torque and the electric torque in
the LC droplets, and the delay between the external electric field and the
induced ion field, an optical bounce in transmission curve was observed at the
edge of “on” state. After the removal of the external electric field, the
nematic director configurations gradually revert to the original status due to
the elastic torque, where the optical bounce would be difficult to be observed
at the edge of “off” state.For
acrylate-based H-PDLCs, reported values ofτon vary from 25 μs
[107] to 750 μs
[35] and the reported τoff values are slightly longer,
ranging from 44
[107, 108] to 1000 μs
[109]. For the thoil-ene-based H-PDLCs, the reported
values of τon vary from 550 μs to 6.7 ms and the reported τoff values vary from 1.2 milliseconds
to 2.2 milliseconds
[48, 110, 111], which are generally much longer than those of the
acrylate-based H-PDLCs. This is expected from Wu’s model
[86] since there is no field to drive the LC back to the
zero field state. They expressed τoff and τon as (48)τoff=γ1a2k33(ℓ2−1),(49)τon=γ1ΔεE2+k33(ℓ2−1)/a2, where γ1 is the rotational viscosity coefficient of LC.As
can be seen from (48), the off time is mainly controlled by elastic forces
for most PDLC-based devices. Most experimental results show that the off time
is generally much slower than the on time. To improve the off time, Kitzerow
developed dual frequency H-PDLCs, which were electrically driven at both an on
and off state [113]. Using a dual-frequency LC where an electric field
is employed to turn the grating off, the switching times can be much improved
to a few milliseconds. Compared to conventional nematic-positive dielectric LCs
where the 100 ms was typically obtained when turning off the voltage, this off
speed is faster. Due to the large period the gratings where large LC droplets
existed, these speeds are slow compared to those of conventional Bragg gratings.
However, it showed a good method to improve the response time.


## 9. Applications

In the last several years, new applications
have been developed based on H-PDLC, mainly in three aspects: (i) H-PDLC photonic crystals (PhCs), (ii) mirrorless lasing from dye-doped H-PDLC, and (iii) sensing applications. It is believed that
H-PDLC will have additional applications in photonics or other fields.


### 9.1. Photonic Crystals

Recently, much interest was
focused on fabricating PhCs based on H-PDLC. PhCs refers to those structures
with periodic dielectric materials in the optical range, where light in special
frequency range is forbidden in the photonic bandgap. As a new class of
photonic bandgap material, combining the holography technique and electrically
controlled switchability, H-PDLC PhCs showed many advantages over conventional PhCs, including single-step
and easy fabrication, field-dependent switchability, and fast response. Tondiglia et al., firstly fabricated H-PDLC
PhCs in 2002  [39]. H-PDLC gratings (transmission or reflection mode)
can be viewed as the simplest 1D PhCs. Many 2D and 3D PhCs, have also been
demonstrated using H-PDLC materials, including orthorhombic
(Figure 52)
[112], face-centered cubic
(Figure 53) [114, 116], transverse square
(Figure 54)
[115, 117], diamond-like lattices [118], and Penrose structure
[119]. Theoretically and experimentally, using
three and four coherent beams, five 2D and all fourteen 3D Bravais lattices can be formed
using H-PDLC materials, respectively [120]. With five or more beams, even more complex quasicrystal
structures were also investigated
[41, 121]. Enhanced diffraction efficiency can be achieved by
nanoparticle doped H-PDLC PhCs
[122]. Generally, to achieve   these structures, a
relatively complicated optical setup is generally used to create multibeam
interference pattern in all these fabrications. However, it is possible to
reduce the optics complexity and fabricate the complicated structures. Only using
a single-diffraction element, a photomask, which creates a three-beam
interference pattern, we successfully demonstrated 2D H-PDLC PhCs [40]. Using a single prism with top-cutting, 2D and 3D
H-PDLC PhCs were also fabricated
[123, 124]. This single element implementation improves
the alignment and stability of the optical setup, making it more robust than
the multiple beam setups reported previously.SEM images of sample fabricated in thesp configuration with θi=45°, θ=17.28°. (a) 3D perspective. (b)
Top view [112].
(a)(b)SEM images of the fcc lattice in H-PDLCs: (a) macroscopic fracture
planes follow the mesoscopic crystal lattice directions; (b) the (1 0 0) plane;
(c) two magnified views of (a), showing the (0 0 1) plane parallel to the
substrate; (d) two views of the (1 1 1) face. For both (c) and (d) the scale
bars of the insets correspond to 200 nm
[114].
(a)(b)(c)(d)SEM images. (a) Low magnification; (b) closeup ofXZ-face viewed from a slightly different perspective than in (a); (c)
side view of cylindrical LC cavities; (d) closeup
of LC cavities [115].
(a)(b)(c)(d)Figures55(a)
and 55(b) show the schematic of the mask and three
diffracted beams to fabricate 2D H-PDLC PhCs only using a photomask. When a
collimated Ar+ laser beam impinges on the mask, which produces three
diffracted beams, a diffraction pattern will be produced at their intersection
region. In our experiment, each grating on the mask has an area of 8 × 8 mm2 and the grating period is 4 μm.
A cell filled with the LC/prepolymer mixture is exposed to the diffraction
pattern. The LC and polymer will redistribute because of the polymerization of
the prepolymer induced by the light intensity, thus forming a 2D structure
inside the cell.(a) Schematic of the
mask and (b) three first-order
diffracted beams.
(a)(b)The electrical field   distribution of
multibeam interference can be generally described by(50)I(r)=[∑j=1nEj(r)exp(ik⋅r+iϕj)]×[∑j=1nEj*(r)exp(−ik⋅r+iϕj)]=∑j=1n|Ej|2+∑i≠jnEi⋅Ej*exp[i(ki−kj)⋅r+iϕij], where E is the amplitude, k is the wave vector, i and j are integers, ϕij
is the initial phase
difference between two incident waves, and r is the position
vector. The orientation of the wave vector of the three beams can be defined as (51)k^1=sinθcosφ1e^x+sinθsinφ1e^y+cosθe^z,(52)k^2=sinθcosφ2e^x+sinθsinφ2e^y+cosθe^z,(53)k^3=sinθcosφ3e^x+sinθsinφ3e^y+cosθe^z, where k^ is unit wave vector, e^
is unit coordinate vector, θ is the angle between the laser beam and z-axis, which equals the first-order
diffraction angle, and φ
is the angle between the projection of the laser
beam on the x-y plane and the x-axis
(see Figure 55). Substituting
(51)–(53) into
(50)
with θ  =
7.4°, φ1 = 180°, φ2=−60°, and φ3 =  60°, we   have (54)I=(E1+E2+E3)⋅(E1+E2+E3)*=|E1|2+|E2|2+|E3|2+2E1⋅E2cos(−32kxsinθ+32kysinθ)+2E1⋅E3cos(−32kxsinθ−32kysinθ)+2E2⋅E3cos(3kysinθ).The simulated 3D interference pattern is
shown in Figure56. It is worth mentioning that the period of this
triangular lattice is equal to two thirds of the diffraction grating period, that
is, 2.67 μm,
which does not depend on the beam wavelength
[125]. Therefore, the PBGs can be easily engineered by
changing the grating period.Figure 56
Simulated 3D interference pattern. The
color bar shows the intensity distribution.Figure57(a)
shows an AFM image of the surface, which was
obtained after the liquid crystals were removed in ethanol. It reveals a clear
hexagonal morphology with a lattice constant of about 2.5 μm, which is in good agreement with the
simulation pattern
(Figure 56), considering the general 5–10% volume
shrinkage for the acrylate monomer during the photo-induced polymerization. It
is interesting to note in
Figure 57(a), in a hexagonal cell, the height of the central
point is slightly different from its surrounding six points, which are almost
the same in height. Figure
57(b) shows the surface morphologies of the 2D H-PDLC
PhCs observed under a high-resolution optical microscope (HiROX). The inset SEM
image in Figure 57(b) shows the cross-section morphology of the sample,
where columnar structure is clearly seen, which
matches the simulation result
in  Figure 56.(a) AFM and (b) optical microscopy images
showing the surface morphology of the 2D H-PDLC
PhC and SEM image (the inset of
(b)  showing the cross-section morphology.
(a)(b)The diffraction
patterns of the H-PDLC PhCs were checked to confirm the quasicrystal
structure. Figures58(a)
and 58(b) show the visible diffraction pattern
produced by a normally incident He-Ne laser beam operating at 543 nm and a collimated
broadband white beam for our sample. From
Figure 58(a), we can see clear hexagonal diffraction spots which
match well with our AFM, optical, and SEM images of a 2D hexagonal lattice
(Figure 57). The diffracted spots originating from (0 1 1¯) and (1 1 2¯) surfaces
are labeled in Figure
58(a). The images clearly reveal the presence of
quasiperiodicity within the sample. The observed points are sharp and
symmetrically distributed. As reported by Gorkhali et al.
[41], all diffraction points in the first and higher
orders should show an N-fold symmetry and have  2N diffracted points, where N  is the number of interference beams
used to produce the PhC. For our case, N =
3, in good agreement with the prediction, we can clearly see a 3-fold symmetry
and 6 diffracted points for the same order of diffracted beams.Visible diffraction patterns of the H-PDLC PhCs produced by (a) a normally
incident He-Ne laser beam and (b) a
collimated broadband white beam.
(a)(b)3D
H-PDLC PhCs can be fabricated using a top-cup prism, as shown in
Figure59(a). A laser beam is collimated first and then impinges
normally onto the specially designed prism, which is made of BK7 glass. The
side lengths of the top- and bottom-surfaces (isosceles triangle) are 1 and 6 cm, respectively, and the height is 2.5 cm. Emerging from the prism are one
directly transmitted beam k0 in the center and three side beams, k1, k2, and k3, by the refraction
from three tilted side surfaces of the prism, as shown in
Figure 59(b). These four beams overlap at the bottom surface of
the prism and interfere with each other, forming a 3D intensity pattern. The
light intensity pattern can be described by (55)I=(E0+E1+E2+E3)⋅(E0+E1+E2+E3)*=|E0|2+|E1|2+|E2|2+|E3|2+2E0⋅E1cos(kxsinθ+kz−kzcosθ)+2E0⋅E2cos(−12kxsinθ+32kysinθ+kz−kzcosθ)+2E0⋅E3cos(−12kxsinθ−32kysinθ+kz−kzcosθ)+2E1⋅E2cos(−32kxsinθ+32kysinθ)+2E1⋅E3cos(−32kxsinθ−32kysinθ)+2E2⋅E3cos(3kysinθ).(a)
Schematic of the specially designed prism and (b) four-beam interference
configuration.
(a)(b)From (55), the periods a, b, and c along the x, y, and z directions depend on the angle θ(56)a=λw3neffsinθ,b=λwneffsinθ,c=λw2neff(1−cosθ), where λw is the writing wavelength, and neff  is the effective refractive index of the recording materials. In our
experiment, λw  =  514.5 nm, assuming neff = 1.59 according to the
LC concentration in the homogeneous PDLCs,
θ=24.1°, we can theoretically
obtain a = 458 nm,
b = 792 nm, and
c = 1856 nm.With
the 4-beam intensity ratio of 3:1:1:1 estimated,
Figure60
shows the theoretically calculated 3D pattern of the
spatial intensity distribution of the four-beam interference. Therefore, the
PBGs can be easily engineered by changing the cutting angle of the prism.Figure 60
Simulated 3D interference
pattern. The color bar shows the light intensity
distribution.In our experiment, the intensities of the
four beamsk0,
k1, k2, and k3 are 58, 21, 22, and 21 mW/cm2, respectively, which is very close to the estimated ratio.
Figures 61(a)
and 61(b) show the AFM images of the surface
morphologies with different scanning areas of 10 ×10 μm2 and 4 ×4 μm2,
respectively. Figures
62(a) and
62(b) show the SEM images of the surface and the
cross-section for the sample, respectively, which are in good agreement with
the simulation pattern. It can be seen from
Figure 62
that the surface structure is a triangular lattice
with a lattice constant of about 420 ± 20 nm, which is in good
agreement with the theoretical calculation according to the geometrical
structure (Figure 60).Surface AFM images of the 3D H-PDLC PhC
sample in area of (a) 10 ×10μm2
and (b) 4 ×4 μm2.
The hexagonal structures are indicated in the
dashed circles.
(a)(b)(a) SEM images of the surface and (b) cross-section
of 3D H-PDLC PhC sample.
(a)(b)Figures63(a) and
63(b) show the visible diffraction pattern
produced by a normally incident He-Ne laser beam operating at 543 nm and a broadband
white beam for our H-PDLC PhC sample fabricated. From
Figure 63(a), we can see that three diffracted points are
reconstructed when a laser beam is normally incident on the sample. It is worth
mentioning that the three ellipse light spots in
Figure 63(a) are induced by the edges of the top surface of the
prism. A Kossel ring is also observed in the center of the diffraction pattern,
which may be caused by the interference between the impinging four beams and the
scattered light. Due to a decreased lattice constant, the white light
diffraction exhibits a much larger dispersion
(Figure 63(b)) compared to that of the 2D H-PDLC PhCs
(Figure 58(b)).Diffraction patterns of the H-PDLC PhCs
produced by (a) a normally incident He-Ne laser beam and (b) a broadband white
beam.
(a)(b)Figure64
shows the changes of the diffraction and the
transmission intensity as functions of applied voltage. From
Figure 64, we can see that, with the increase of applied
voltage, the diffraction intensity decreases, while the transmission intensity
increases, due to the refractive indices matching between the liquid crystal
and polymer matrix. The switching electric field is about 7.2 V/μm. Due to the large LC concentration used in
our experiment, the driving voltage decreases a great deal compared to the low
LC concentration case.Figure 64
Diffraction and transmission intensities change as functions
of applied voltage.Figure65
shows the measured electro-optical response time when
the sample was driven by a square voltage of 185 Vrms (6.2 V/μm)
with a frequency of 20 Hz. From
Figure 65, the rise time (10%–90% intensity
changed) and the fall time (90%–10% intensity
changed), are about 1.75 and 1.09 milliseconds, respectively. The response time
is relatively slow due to the large LC concentration. With a decrease in the LC
concentration, the response time can be expected to be smaller.Figure 65
Electro-optical response time measurement
of 3D H-PDLC PhC sample.For
H-PDLC PhCs, the small refractive index contrast between liquid crystal and
polymer matrix hinders their applications. The general refractive index
difference can be about 0–0.4, mainly
depending on the LC materials. However, it is still possible to find
applications where large index contrast is not needed, such as superprism
effect. Li et al. has observed
the superprism phenomenon based on 2D H-PDLC structures
[126]. When a TE-polarized white light is incident onto an
H-PDLC film, it is dispersed to yield a continuous spectrum distributed from
red to blue, with an angle ~50°. Jakubiak et al. demonstrated dynamic lasing from dye-doped 2D H-PDLC PhCs
[42]. On the other hand, due to the anomalous dispersion
characteristics at the band edge of PhCs, larger optical nonliearities can be
produced in PhCs. A dramatic enhancement in the efficiency of third-harmonic
generation (THG) has been observed in 1D H-PDLC PhCs when the fundamental
wavelength approaches the low-energy edge of the first photonic band gap [127].


### 9.2. Mirrorless Lasing

The
dye-doped H-PDLC grating (either reflection or transmission mode) itself serves
as both a resonant cavity and a gain medium, making it promising in
electrically tunable lasers with low threshold. Since 2003, Jakubiak et al. demonstrated distributed
feedback (DFB) lasing from dye-doped H-PDLC reflection grating [128].
Lucchetta et al. reported lasing emission from
a simple wafer structure using an H-PDLC reflection grating as a reflection
mirror [129] and later achieved light amplification in dye-doped
H-PDLC reflection grating [130]. Much work has been done in the past two years about
dye-doped H-PDLC lasing effect
[49, 131–133]. The lasing emission can also be obtained using
H-PDLC grating only as a distributed feedback element by He and his coworkers [134]. Most of above work regarding the lasing emission
are based on H-PDLC reflection gratings. However, in such cases, the overall
gain length is limited to the thickness of the film. To increase the lasing
efficiency, it is desirable to increase the film thickness. However, in
reflection geometry, an increase of film thickness results in an increase of the
required switching electric field. Thus, a tradeoff between cavity length and
switching field is necessary. This problem can be overcome if the H-PDLC
transmission mode grating is used. Hsiao et
al. reported the lasing emission from dye-doped H-PDLC transmission
grating [135].
Compared to the
reflection mode, the transmission mode grating offers a longer gain length
without increasing the film thickness.We
systematically investigated the single-mode lasing properties from the
dye-doped H-PDLC transmission gratings and showed much improved lasing
properties including lower threshold, narrower linewidth, and higher Q factor,
as shown in Figure66. We also found that LC concentration played an
important role in the lasing generation and wavelength selection. In our
experiments, an LC concentration of 35 wt% was an approximately critical value
to obtain a single-mode lasing from dye-doped H-PDLC. With the decrease of the LC
concentration, the lasing wavelength was blue shifted. Above this
concentration, only amplified spontaneous emission (ASE) was observed.
Typically, a 30 wt% LC concentration was used for H-PDLC transmission gratings
to achieve high diffraction efficiency. However, for lasing generation, the LC
concentration of around 20 wt% was found to be the best tradeoff between
sufficient index modulation and optical scattering in the samples. We changed
the LC and TMPTA concentrations and kept the other material concentrations
fixed. The detailed weight percentage of each component used in the material
syrup is shown in
Table 3.Table 3
wt% of each component used in the
prepolymer syrup for samples
1–6.
No.TMPTANVPNPGRBOADCME7167.17.80.90.68.01.014.6263.15.60.70.59.21.219.7357.86.00.70.59.51.224.3453.66.50.80.57.41.429.8547.67.40.90.68.11.234.2634.16.30.70.68.41.148.8Figure 66
Output lasing intensity from DCM-doped H-PDLC transmission grating as a
function of the laser pumping energy. The inset shows the lasing and the pump
laser spectra.Figure67 shows the normalized lasing spectra for H-PDLC
samples with various LC concentrations excited by about two times of the
corresponding threshold. It can be seen from
Figure 67
that, the linewidth of the lasing peak becomes
narrower with the decrease of the LC concentration. The full width at half
maximum (FWHM) of the lasing peak centering at 584 nm was less than 0.8 nm. The
transmission curves along the grating vector direction are also theoretically
calculated, as shown in
Figure 67. The refractive index of polymer matrices was assumed
to be 1.54. The other data used in our calculations were tabulated in Table 4. It is worth mentioning that in our calculations, the
wavelength dispersion of the refractive indices of LC and polymer used are not considered because the refractive index changes of LC
[136] and polymer
[137] are small enough to be ignored. It is clear that the
lasing action happens at one edge of the reflection band. The inset in
Figure 67
shows a typical emission photograph of the dye-doped
H-PDLC, where a sharp lasing point can be clearly observed. The estimated
divergence angle from the far-field pattern was ~15 mrad and ~65 mrad in the
directions perpendicular and parallel to the substrates, respectively.Table 4
Data used for the transmission curve
calculation.ΛG is the grating pitch, VLC:Vp is the volume ratio of LC-rich lamellae to
polymer-rich lamellae, respectively,
Δn1 is the index
modulation.
No.ΛG (μm)VLC:VpΔn110.56416:840.0520.57225:750.0730.58345:550.0940.58450:500.1050.58455:450.11Figure 67
Normalized lasing spectra for H-PDLC samples with various LC concentrations excited
by about two times of corresponding threshold.
The inset shows a typical
emission photograph of the dye-doped H-PDLC.As
reported previously, lasing properties of H-PDLC transmission gratings are
strongly dependent on the morphology of the grating. In our previous report,
the morphology significantly changed in H-PDLC transmission gratings as the LC
concentration changed. At a higher concentration, the volume fraction of
LC-rich lamella increases and the LC droplets become larger. As a result, a
larger scattering loss will be induced and the lasing has a larger threshold
and wider FWHM. At a lower concentration, the volume fraction of LC-rich
lamellae decreases and the LC droplets become smaller. Within the LC-rich
lamellae, a large amount of polymer exists and the index modulation is lowered
accordingly. As a result, only a higher threshold can sustain enough
distributed feedback, and a narrower FWHM is obtained due to the smaller
scattering loss. Moreover, lower LC concentration reduces the index modulation,
resulting in a blue-shifted bandgap. Therefore, the lasing wavelength is blue shifted
accordingly.For the devices based on H-PDLC, a distinct
advantage is that they can be tuned or switched by an external stimulus. Hsiao et al. reported the electrically
switchable lasing emission from the dye-doped H-PDLC transmission gratings [135]. Besides the electric method, the lasing can be also
thermally switched. In our experiments, during the lasing measurement, a heater
is used to control the temperature of the samples. The controllable temperature
ranges from 20 to 80°C, with an accuracy of about 3°C.Figure68
shows the emission spectra from dye-doped H-PDLC
gratings used no. 1 material
syrup at various temperatures with a fixed pumping energy of
40 μJ/pulse. From
Figure 68, we can see that the lasing can be thermally
switched. It is interesting to note that at a temperature of 30°C,
another lasing peak centered at 595 nm appears in the emission envelope, as
shown in
Figure 68, which means at this temperature a sufficient gain
can also be obtained for 595 nm. The switching mechanism of the H-PDLC grating
is due to the index modulation of the phase separated LC droplets. Generally,
H-PDLC    gratings show anisotropic more or less because there is a known volume
shrinkage during the grating formation
[14, 138], which makes the LC droplets anisotropic. With the
increase of the temperature, the optical anisotropy reduces and accordingly the
effective refractive index of the LC changes and at some temperature, the
effective refractive index of the LC matches closely with the refractive index
of the polymer matrix. As a result, the lasing emission disappears. Unlike
described in [42], where the lasing wavelength shifted around 5 nm, in
our experiments, the effective refractive index does not change so much that
there is no shift in the lasing wavelength. From
Figure 68, we can see that, at the temperature of  45°C,
both original and new appeared lasing peaks nearly disappear. After cooling
down, the lasing emission appears again.Figure 68
The emission spectra from dye-doped H-PDLC
gratings at different temperatures.


### 9.3. Sensors Based on Reflective H-PDLCs

H-PDLC reflection gratings are Bragg gratings formed of alternating
layers of liquid crystals and polymer matrix as shown in
Figure69. They reflect a certain wavelength of light
determined by the Bragg’s grating equation given by (57)Λ=λ2neffsinθ, where Λ is the fringe spacing of the grating vector, n is the effective refractive index of
the polymer and liquid crystal composition, θ is the angle at which the light source is
incident, and λ is
the wavelength of the reflected light. The reflected wavelength of light is
proportional to the fringe spacing of the gratings as can be seen from
(57). Hence, theoretically decreasing the fringe spacing
reduces the wavelength of the reflected light. On the other hand, if the fringe spacing is
fixed, the reflected light can be shifted by changing the effective refractive
index.Figure 69
Illustration of reflective H-PDLCs. The LC
droplets and polymer matrix are seen
in alternating layers [139].


#### 9.3.1. Pressure Sensor

Based
on the above concept, it can be applied to create an HPDLC pressure sensor. The
fringe spacing is reduced by applying pressure perpendicular to the surface of
the HPDLC and parallel to the grating vector. The wavelength reflected is
measured for different applied pressure and the results are analyzed.In
one paper [140], the authors strained an H-PDLC reflection film
perpendicular to the grating vector and observed a blue shift in the peak
reflection wavelength of the film. This shift was caused by the Poisson
contraction of the polymer segments of the grating parallel to the grating
vector as the film was stretched perpendicular to the grating vector. Fontecchio
et al. developed hydrostatic pressure sensors based on H-PDLC reflection gratings
[139, 141].
Figure 70
shows the testing schematic. The light emitted from
the fiber was collimated by a lens and spatially filtered. This light was then incident
on the sensor under test at an angle of ~30° relative to the sensor normal. The
light reflected from the sensor was focused onto a fiber, which was connected
to spectrometer with a high resolution. Changing the material formation can
greatly improve the sensitivity of H-PDLC pressure sensors. The experimental
results show that increasing the initiator concentration makes the H-PDLC more
elastic. Figure 71
shows the response for the difunctional polymer with
various initiator concentrations. A clear difference can be observed from
Figure 71
that the largest wavelength shift was obtained at the
initiator concentration of 21 wt%.Figure 70
The configuration used to measure the reflected spectrum of the H-PDLC pressure
sensors. Light is incident on the film at ~30° to
the sensor normal [141].Figure 71
Wavelength versus pressure response of
difunctional HPDLC with pressure applied
from 0–20 psi [139].


#### 9.3.2. Chemical Sensor

With
special treatment, the reflective H-PDLCs can contain many air voids without
any damage to the grating structures. Therefore, the Bragg reflection notch of
these gratings can then be shifted by filling the voids inside the grating
structure with solvent vapor. The high porosity of the grating film allows
chemical vapors to easily permeate into the void regions, consequently the
average refractive index is changed and the corresponding reflective wavelength
shifts according to (57). The shifted reflective wavelength can be observed
easily by eye due to the high refractive index contrast of the grating films.
Thus, these holographic porous polymer gratings can act as colorimetric vapor sensors.An easy way to create the voids in H-PDLCs
is to simply add a nonreactive solvent, such as acetone or toluene, into the
prepolymer syrup prior to holographic exposure. After exposure, the porous
acrylate polymer grating structures can be created when the nonreactive solvent
evaporates upon exposing the polymerized film to air. Porous H-PDLC
reflection grating used to detect chemical vapor has
been successfully demonstrated
[142], where 20 wt% toluene was used as nonactive
solvent. When this porous grating was exposed to the air containing various
concentration of acetone vapor, different reflection bands were clearly
observed, which was induced by the refractive index change, as shown in
Figure 72. A typical cycling behavior of the porous grating
subjected to alternating acetone vapor is shown in
Figure 73.Figure 72
The transmission spectra of a typical grating film in air containing various
concentrations of acetone vapor (volume-%) relative to 1 atm (101.325 kPa) air
pressure [142].Figure 73
Cycling behavior of the porous grating subjected to alternating acetone vapor
from 0.2 to 1 mbar (0.02 to 0.1 Pa)
[142].The
big advantages of optical sensors are faster, safer, and easier to implement compared to those electrical
sensors [143]. The reflective H-PDLC gratings show themselves
potentially useful in chemical or pressure sensing, although the long term
stability is still problematic for the H-PDLC materials.


### 9.4. Neutron-Optical Devices Based on H-PDLC

Besides the applications listed above, it is
worth mentioning a latest emerging application based on H-PDLCs. It is H-PDLC-based
neutron-optical devices
[144, 145]. H-PDLCs can act as extremely efficient gratings not
only for light but also for neutrons. H-PDLCs show similar diffraction behavior
for the neutrons like light diffraction, as shown in
Figure 74. The results showed that the light-induced
refractive-index modulation for neutrons is about 10−6, that is,
nearly 2 orders of magnitude larger than in the best photo-neutron-refractive
materials probed up to now, which makes H-PDLC promising as new materials to
fabricate neutron-optical devices for cold and ultracold neutrons, such as beam
splitters, lenses, and mirrors.Figure 74
Diffraction pattern of an H-PDLC at a
wavelength ofλ = 1.96 nm. Diffraction up to the ± second order is visible (bottom). The data
points result from summing up the box counts of 30 pixels along the y-direction around the centers of diffraction
spots, so that the second-order peaks are clearly
visible (top) [144].


## 9.1. Photonic Crystals

Recently, much interest was
focused on fabricating PhCs based on H-PDLC. PhCs refers to those structures
with periodic dielectric materials in the optical range, where light in special
frequency range is forbidden in the photonic bandgap. As a new class of
photonic bandgap material, combining the holography technique and electrically
controlled switchability, H-PDLC PhCs showed many advantages over conventional PhCs, including single-step
and easy fabrication, field-dependent switchability, and fast response. Tondiglia et al., firstly fabricated H-PDLC
PhCs in 2002  [39]. H-PDLC gratings (transmission or reflection mode)
can be viewed as the simplest 1D PhCs. Many 2D and 3D PhCs, have also been
demonstrated using H-PDLC materials, including orthorhombic
(Figure 52)
[112], face-centered cubic
(Figure 53) [114, 116], transverse square
(Figure 54)
[115, 117], diamond-like lattices [118], and Penrose structure
[119]. Theoretically and experimentally, using
three and four coherent beams, five 2D and all fourteen 3D Bravais lattices can be formed
using H-PDLC materials, respectively [120]. With five or more beams, even more complex quasicrystal
structures were also investigated
[41, 121]. Enhanced diffraction efficiency can be achieved by
nanoparticle doped H-PDLC PhCs
[122]. Generally, to achieve   these structures, a
relatively complicated optical setup is generally used to create multibeam
interference pattern in all these fabrications. However, it is possible to
reduce the optics complexity and fabricate the complicated structures. Only using
a single-diffraction element, a photomask, which creates a three-beam
interference pattern, we successfully demonstrated 2D H-PDLC PhCs [40]. Using a single prism with top-cutting, 2D and 3D
H-PDLC PhCs were also fabricated
[123, 124]. This single element implementation improves
the alignment and stability of the optical setup, making it more robust than
the multiple beam setups reported previously.SEM images of sample fabricated in thesp configuration with θi=45°, θ=17.28°. (a) 3D perspective. (b)
Top view [112].
(a)(b)SEM images of the fcc lattice in H-PDLCs: (a) macroscopic fracture
planes follow the mesoscopic crystal lattice directions; (b) the (1 0 0) plane;
(c) two magnified views of (a), showing the (0 0 1) plane parallel to the
substrate; (d) two views of the (1 1 1) face. For both (c) and (d) the scale
bars of the insets correspond to 200 nm
[114].
(a)(b)(c)(d)SEM images. (a) Low magnification; (b) closeup ofXZ-face viewed from a slightly different perspective than in (a); (c)
side view of cylindrical LC cavities; (d) closeup
of LC cavities [115].
(a)(b)(c)(d)Figures55(a)
and 55(b) show the schematic of the mask and three
diffracted beams to fabricate 2D H-PDLC PhCs only using a photomask. When a
collimated Ar+ laser beam impinges on the mask, which produces three
diffracted beams, a diffraction pattern will be produced at their intersection
region. In our experiment, each grating on the mask has an area of 8 × 8 mm2 and the grating period is 4 μm.
A cell filled with the LC/prepolymer mixture is exposed to the diffraction
pattern. The LC and polymer will redistribute because of the polymerization of
the prepolymer induced by the light intensity, thus forming a 2D structure
inside the cell.(a) Schematic of the
mask and (b) three first-order
diffracted beams.
(a)(b)The electrical field   distribution of
multibeam interference can be generally described by(50)I(r)=[∑j=1nEj(r)exp(ik⋅r+iϕj)]×[∑j=1nEj*(r)exp(−ik⋅r+iϕj)]=∑j=1n|Ej|2+∑i≠jnEi⋅Ej*exp[i(ki−kj)⋅r+iϕij], where E is the amplitude, k is the wave vector, i and j are integers, ϕij
is the initial phase
difference between two incident waves, and r is the position
vector. The orientation of the wave vector of the three beams can be defined as (51)k^1=sinθcosφ1e^x+sinθsinφ1e^y+cosθe^z,(52)k^2=sinθcosφ2e^x+sinθsinφ2e^y+cosθe^z,(53)k^3=sinθcosφ3e^x+sinθsinφ3e^y+cosθe^z, where k^ is unit wave vector, e^
is unit coordinate vector, θ is the angle between the laser beam and z-axis, which equals the first-order
diffraction angle, and φ
is the angle between the projection of the laser
beam on the x-y plane and the x-axis
(see Figure 55). Substituting
(51)–(53) into
(50)
with θ  =
7.4°, φ1 = 180°, φ2=−60°, and φ3 =  60°, we   have (54)I=(E1+E2+E3)⋅(E1+E2+E3)*=|E1|2+|E2|2+|E3|2+2E1⋅E2cos(−32kxsinθ+32kysinθ)+2E1⋅E3cos(−32kxsinθ−32kysinθ)+2E2⋅E3cos(3kysinθ).The simulated 3D interference pattern is
shown in Figure56. It is worth mentioning that the period of this
triangular lattice is equal to two thirds of the diffraction grating period, that
is, 2.67 μm,
which does not depend on the beam wavelength
[125]. Therefore, the PBGs can be easily engineered by
changing the grating period.Figure 56
Simulated 3D interference pattern. The
color bar shows the intensity distribution.Figure57(a)
shows an AFM image of the surface, which was
obtained after the liquid crystals were removed in ethanol. It reveals a clear
hexagonal morphology with a lattice constant of about 2.5 μm, which is in good agreement with the
simulation pattern
(Figure 56), considering the general 5–10% volume
shrinkage for the acrylate monomer during the photo-induced polymerization. It
is interesting to note in
Figure 57(a), in a hexagonal cell, the height of the central
point is slightly different from its surrounding six points, which are almost
the same in height. Figure
57(b) shows the surface morphologies of the 2D H-PDLC
PhCs observed under a high-resolution optical microscope (HiROX). The inset SEM
image in Figure 57(b) shows the cross-section morphology of the sample,
where columnar structure is clearly seen, which
matches the simulation result
in  Figure 56.(a) AFM and (b) optical microscopy images
showing the surface morphology of the 2D H-PDLC
PhC and SEM image (the inset of
(b)  showing the cross-section morphology.
(a)(b)The diffraction
patterns of the H-PDLC PhCs were checked to confirm the quasicrystal
structure. Figures58(a)
and 58(b) show the visible diffraction pattern
produced by a normally incident He-Ne laser beam operating at 543 nm and a collimated
broadband white beam for our sample. From
Figure 58(a), we can see clear hexagonal diffraction spots which
match well with our AFM, optical, and SEM images of a 2D hexagonal lattice
(Figure 57). The diffracted spots originating from (0 1 1¯) and (1 1 2¯) surfaces
are labeled in Figure
58(a). The images clearly reveal the presence of
quasiperiodicity within the sample. The observed points are sharp and
symmetrically distributed. As reported by Gorkhali et al.
[41], all diffraction points in the first and higher
orders should show an N-fold symmetry and have  2N diffracted points, where N  is the number of interference beams
used to produce the PhC. For our case, N =
3, in good agreement with the prediction, we can clearly see a 3-fold symmetry
and 6 diffracted points for the same order of diffracted beams.Visible diffraction patterns of the H-PDLC PhCs produced by (a) a normally
incident He-Ne laser beam and (b) a
collimated broadband white beam.
(a)(b)3D
H-PDLC PhCs can be fabricated using a top-cup prism, as shown in
Figure59(a). A laser beam is collimated first and then impinges
normally onto the specially designed prism, which is made of BK7 glass. The
side lengths of the top- and bottom-surfaces (isosceles triangle) are 1 and 6 cm, respectively, and the height is 2.5 cm. Emerging from the prism are one
directly transmitted beam k0 in the center and three side beams, k1, k2, and k3, by the refraction
from three tilted side surfaces of the prism, as shown in
Figure 59(b). These four beams overlap at the bottom surface of
the prism and interfere with each other, forming a 3D intensity pattern. The
light intensity pattern can be described by (55)I=(E0+E1+E2+E3)⋅(E0+E1+E2+E3)*=|E0|2+|E1|2+|E2|2+|E3|2+2E0⋅E1cos(kxsinθ+kz−kzcosθ)+2E0⋅E2cos(−12kxsinθ+32kysinθ+kz−kzcosθ)+2E0⋅E3cos(−12kxsinθ−32kysinθ+kz−kzcosθ)+2E1⋅E2cos(−32kxsinθ+32kysinθ)+2E1⋅E3cos(−32kxsinθ−32kysinθ)+2E2⋅E3cos(3kysinθ).(a)
Schematic of the specially designed prism and (b) four-beam interference
configuration.
(a)(b)From (55), the periods a, b, and c along the x, y, and z directions depend on the angle θ(56)a=λw3neffsinθ,b=λwneffsinθ,c=λw2neff(1−cosθ), where λw is the writing wavelength, and neff  is the effective refractive index of the recording materials. In our
experiment, λw  =  514.5 nm, assuming neff = 1.59 according to the
LC concentration in the homogeneous PDLCs,
θ=24.1°, we can theoretically
obtain a = 458 nm,
b = 792 nm, and
c = 1856 nm.With
the 4-beam intensity ratio of 3:1:1:1 estimated,
Figure60
shows the theoretically calculated 3D pattern of the
spatial intensity distribution of the four-beam interference. Therefore, the
PBGs can be easily engineered by changing the cutting angle of the prism.Figure 60
Simulated 3D interference
pattern. The color bar shows the light intensity
distribution.In our experiment, the intensities of the
four beamsk0,
k1, k2, and k3 are 58, 21, 22, and 21 mW/cm2, respectively, which is very close to the estimated ratio.
Figures 61(a)
and 61(b) show the AFM images of the surface
morphologies with different scanning areas of 10 ×10 μm2 and 4 ×4 μm2,
respectively. Figures
62(a) and
62(b) show the SEM images of the surface and the
cross-section for the sample, respectively, which are in good agreement with
the simulation pattern. It can be seen from
Figure 62
that the surface structure is a triangular lattice
with a lattice constant of about 420 ± 20 nm, which is in good
agreement with the theoretical calculation according to the geometrical
structure (Figure 60).Surface AFM images of the 3D H-PDLC PhC
sample in area of (a) 10 ×10μm2
and (b) 4 ×4 μm2.
The hexagonal structures are indicated in the
dashed circles.
(a)(b)(a) SEM images of the surface and (b) cross-section
of 3D H-PDLC PhC sample.
(a)(b)Figures63(a) and
63(b) show the visible diffraction pattern
produced by a normally incident He-Ne laser beam operating at 543 nm and a broadband
white beam for our H-PDLC PhC sample fabricated. From
Figure 63(a), we can see that three diffracted points are
reconstructed when a laser beam is normally incident on the sample. It is worth
mentioning that the three ellipse light spots in
Figure 63(a) are induced by the edges of the top surface of the
prism. A Kossel ring is also observed in the center of the diffraction pattern,
which may be caused by the interference between the impinging four beams and the
scattered light. Due to a decreased lattice constant, the white light
diffraction exhibits a much larger dispersion
(Figure 63(b)) compared to that of the 2D H-PDLC PhCs
(Figure 58(b)).Diffraction patterns of the H-PDLC PhCs
produced by (a) a normally incident He-Ne laser beam and (b) a broadband white
beam.
(a)(b)Figure64
shows the changes of the diffraction and the
transmission intensity as functions of applied voltage. From
Figure 64, we can see that, with the increase of applied
voltage, the diffraction intensity decreases, while the transmission intensity
increases, due to the refractive indices matching between the liquid crystal
and polymer matrix. The switching electric field is about 7.2 V/μm. Due to the large LC concentration used in
our experiment, the driving voltage decreases a great deal compared to the low
LC concentration case.Figure 64
Diffraction and transmission intensities change as functions
of applied voltage.Figure65
shows the measured electro-optical response time when
the sample was driven by a square voltage of 185 Vrms (6.2 V/μm)
with a frequency of 20 Hz. From
Figure 65, the rise time (10%–90% intensity
changed) and the fall time (90%–10% intensity
changed), are about 1.75 and 1.09 milliseconds, respectively. The response time
is relatively slow due to the large LC concentration. With a decrease in the LC
concentration, the response time can be expected to be smaller.Figure 65
Electro-optical response time measurement
of 3D H-PDLC PhC sample.For
H-PDLC PhCs, the small refractive index contrast between liquid crystal and
polymer matrix hinders their applications. The general refractive index
difference can be about 0–0.4, mainly
depending on the LC materials. However, it is still possible to find
applications where large index contrast is not needed, such as superprism
effect. Li et al. has observed
the superprism phenomenon based on 2D H-PDLC structures
[126]. When a TE-polarized white light is incident onto an
H-PDLC film, it is dispersed to yield a continuous spectrum distributed from
red to blue, with an angle ~50°. Jakubiak et al. demonstrated dynamic lasing from dye-doped 2D H-PDLC PhCs
[42]. On the other hand, due to the anomalous dispersion
characteristics at the band edge of PhCs, larger optical nonliearities can be
produced in PhCs. A dramatic enhancement in the efficiency of third-harmonic
generation (THG) has been observed in 1D H-PDLC PhCs when the fundamental
wavelength approaches the low-energy edge of the first photonic band gap [127].


## 9.2. Mirrorless Lasing

The
dye-doped H-PDLC grating (either reflection or transmission mode) itself serves
as both a resonant cavity and a gain medium, making it promising in
electrically tunable lasers with low threshold. Since 2003, Jakubiak et al. demonstrated distributed
feedback (DFB) lasing from dye-doped H-PDLC reflection grating [128].
Lucchetta et al. reported lasing emission from
a simple wafer structure using an H-PDLC reflection grating as a reflection
mirror [129] and later achieved light amplification in dye-doped
H-PDLC reflection grating [130]. Much work has been done in the past two years about
dye-doped H-PDLC lasing effect
[49, 131–133]. The lasing emission can also be obtained using
H-PDLC grating only as a distributed feedback element by He and his coworkers [134]. Most of above work regarding the lasing emission
are based on H-PDLC reflection gratings. However, in such cases, the overall
gain length is limited to the thickness of the film. To increase the lasing
efficiency, it is desirable to increase the film thickness. However, in
reflection geometry, an increase of film thickness results in an increase of the
required switching electric field. Thus, a tradeoff between cavity length and
switching field is necessary. This problem can be overcome if the H-PDLC
transmission mode grating is used. Hsiao et
al. reported the lasing emission from dye-doped H-PDLC transmission
grating [135].
Compared to the
reflection mode, the transmission mode grating offers a longer gain length
without increasing the film thickness.We
systematically investigated the single-mode lasing properties from the
dye-doped H-PDLC transmission gratings and showed much improved lasing
properties including lower threshold, narrower linewidth, and higher Q factor,
as shown in Figure66. We also found that LC concentration played an
important role in the lasing generation and wavelength selection. In our
experiments, an LC concentration of 35 wt% was an approximately critical value
to obtain a single-mode lasing from dye-doped H-PDLC. With the decrease of the LC
concentration, the lasing wavelength was blue shifted. Above this
concentration, only amplified spontaneous emission (ASE) was observed.
Typically, a 30 wt% LC concentration was used for H-PDLC transmission gratings
to achieve high diffraction efficiency. However, for lasing generation, the LC
concentration of around 20 wt% was found to be the best tradeoff between
sufficient index modulation and optical scattering in the samples. We changed
the LC and TMPTA concentrations and kept the other material concentrations
fixed. The detailed weight percentage of each component used in the material
syrup is shown in
Table 3.Table 3
wt% of each component used in the
prepolymer syrup for samples
1–6.
No.TMPTANVPNPGRBOADCME7167.17.80.90.68.01.014.6263.15.60.70.59.21.219.7357.86.00.70.59.51.224.3453.66.50.80.57.41.429.8547.67.40.90.68.11.234.2634.16.30.70.68.41.148.8Figure 66
Output lasing intensity from DCM-doped H-PDLC transmission grating as a
function of the laser pumping energy. The inset shows the lasing and the pump
laser spectra.Figure67 shows the normalized lasing spectra for H-PDLC
samples with various LC concentrations excited by about two times of the
corresponding threshold. It can be seen from
Figure 67
that, the linewidth of the lasing peak becomes
narrower with the decrease of the LC concentration. The full width at half
maximum (FWHM) of the lasing peak centering at 584 nm was less than 0.8 nm. The
transmission curves along the grating vector direction are also theoretically
calculated, as shown in
Figure 67. The refractive index of polymer matrices was assumed
to be 1.54. The other data used in our calculations were tabulated in Table 4. It is worth mentioning that in our calculations, the
wavelength dispersion of the refractive indices of LC and polymer used are not considered because the refractive index changes of LC
[136] and polymer
[137] are small enough to be ignored. It is clear that the
lasing action happens at one edge of the reflection band. The inset in
Figure 67
shows a typical emission photograph of the dye-doped
H-PDLC, where a sharp lasing point can be clearly observed. The estimated
divergence angle from the far-field pattern was ~15 mrad and ~65 mrad in the
directions perpendicular and parallel to the substrates, respectively.Table 4
Data used for the transmission curve
calculation.ΛG is the grating pitch, VLC:Vp is the volume ratio of LC-rich lamellae to
polymer-rich lamellae, respectively,
Δn1 is the index
modulation.
No.ΛG (μm)VLC:VpΔn110.56416:840.0520.57225:750.0730.58345:550.0940.58450:500.1050.58455:450.11Figure 67
Normalized lasing spectra for H-PDLC samples with various LC concentrations excited
by about two times of corresponding threshold.
The inset shows a typical
emission photograph of the dye-doped H-PDLC.As
reported previously, lasing properties of H-PDLC transmission gratings are
strongly dependent on the morphology of the grating. In our previous report,
the morphology significantly changed in H-PDLC transmission gratings as the LC
concentration changed. At a higher concentration, the volume fraction of
LC-rich lamella increases and the LC droplets become larger. As a result, a
larger scattering loss will be induced and the lasing has a larger threshold
and wider FWHM. At a lower concentration, the volume fraction of LC-rich
lamellae decreases and the LC droplets become smaller. Within the LC-rich
lamellae, a large amount of polymer exists and the index modulation is lowered
accordingly. As a result, only a higher threshold can sustain enough
distributed feedback, and a narrower FWHM is obtained due to the smaller
scattering loss. Moreover, lower LC concentration reduces the index modulation,
resulting in a blue-shifted bandgap. Therefore, the lasing wavelength is blue shifted
accordingly.For the devices based on H-PDLC, a distinct
advantage is that they can be tuned or switched by an external stimulus. Hsiao et al. reported the electrically
switchable lasing emission from the dye-doped H-PDLC transmission gratings [135]. Besides the electric method, the lasing can be also
thermally switched. In our experiments, during the lasing measurement, a heater
is used to control the temperature of the samples. The controllable temperature
ranges from 20 to 80°C, with an accuracy of about 3°C.Figure68
shows the emission spectra from dye-doped H-PDLC
gratings used no. 1 material
syrup at various temperatures with a fixed pumping energy of
40 μJ/pulse. From
Figure 68, we can see that the lasing can be thermally
switched. It is interesting to note that at a temperature of 30°C,
another lasing peak centered at 595 nm appears in the emission envelope, as
shown in
Figure 68, which means at this temperature a sufficient gain
can also be obtained for 595 nm. The switching mechanism of the H-PDLC grating
is due to the index modulation of the phase separated LC droplets. Generally,
H-PDLC    gratings show anisotropic more or less because there is a known volume
shrinkage during the grating formation
[14, 138], which makes the LC droplets anisotropic. With the
increase of the temperature, the optical anisotropy reduces and accordingly the
effective refractive index of the LC changes and at some temperature, the
effective refractive index of the LC matches closely with the refractive index
of the polymer matrix. As a result, the lasing emission disappears. Unlike
described in [42], where the lasing wavelength shifted around 5 nm, in
our experiments, the effective refractive index does not change so much that
there is no shift in the lasing wavelength. From
Figure 68, we can see that, at the temperature of  45°C,
both original and new appeared lasing peaks nearly disappear. After cooling
down, the lasing emission appears again.Figure 68
The emission spectra from dye-doped H-PDLC
gratings at different temperatures.


## 9.3. Sensors Based on Reflective H-PDLCs

H-PDLC reflection gratings are Bragg gratings formed of alternating
layers of liquid crystals and polymer matrix as shown in
Figure69. They reflect a certain wavelength of light
determined by the Bragg’s grating equation given by (57)Λ=λ2neffsinθ, where Λ is the fringe spacing of the grating vector, n is the effective refractive index of
the polymer and liquid crystal composition, θ is the angle at which the light source is
incident, and λ is
the wavelength of the reflected light. The reflected wavelength of light is
proportional to the fringe spacing of the gratings as can be seen from
(57). Hence, theoretically decreasing the fringe spacing
reduces the wavelength of the reflected light. On the other hand, if the fringe spacing is
fixed, the reflected light can be shifted by changing the effective refractive
index.Figure 69
Illustration of reflective H-PDLCs. The LC
droplets and polymer matrix are seen
in alternating layers [139].


### 9.3.1. Pressure Sensor

Based
on the above concept, it can be applied to create an HPDLC pressure sensor. The
fringe spacing is reduced by applying pressure perpendicular to the surface of
the HPDLC and parallel to the grating vector. The wavelength reflected is
measured for different applied pressure and the results are analyzed.In
one paper [140], the authors strained an H-PDLC reflection film
perpendicular to the grating vector and observed a blue shift in the peak
reflection wavelength of the film. This shift was caused by the Poisson
contraction of the polymer segments of the grating parallel to the grating
vector as the film was stretched perpendicular to the grating vector. Fontecchio
et al. developed hydrostatic pressure sensors based on H-PDLC reflection gratings
[139, 141].
Figure 70
shows the testing schematic. The light emitted from
the fiber was collimated by a lens and spatially filtered. This light was then incident
on the sensor under test at an angle of ~30° relative to the sensor normal. The
light reflected from the sensor was focused onto a fiber, which was connected
to spectrometer with a high resolution. Changing the material formation can
greatly improve the sensitivity of H-PDLC pressure sensors. The experimental
results show that increasing the initiator concentration makes the H-PDLC more
elastic. Figure 71
shows the response for the difunctional polymer with
various initiator concentrations. A clear difference can be observed from
Figure 71
that the largest wavelength shift was obtained at the
initiator concentration of 21 wt%.Figure 70
The configuration used to measure the reflected spectrum of the H-PDLC pressure
sensors. Light is incident on the film at ~30° to
the sensor normal [141].Figure 71
Wavelength versus pressure response of
difunctional HPDLC with pressure applied
from 0–20 psi [139].


### 9.3.2. Chemical Sensor

With
special treatment, the reflective H-PDLCs can contain many air voids without
any damage to the grating structures. Therefore, the Bragg reflection notch of
these gratings can then be shifted by filling the voids inside the grating
structure with solvent vapor. The high porosity of the grating film allows
chemical vapors to easily permeate into the void regions, consequently the
average refractive index is changed and the corresponding reflective wavelength
shifts according to (57). The shifted reflective wavelength can be observed
easily by eye due to the high refractive index contrast of the grating films.
Thus, these holographic porous polymer gratings can act as colorimetric vapor sensors.An easy way to create the voids in H-PDLCs
is to simply add a nonreactive solvent, such as acetone or toluene, into the
prepolymer syrup prior to holographic exposure. After exposure, the porous
acrylate polymer grating structures can be created when the nonreactive solvent
evaporates upon exposing the polymerized film to air. Porous H-PDLC
reflection grating used to detect chemical vapor has
been successfully demonstrated
[142], where 20 wt% toluene was used as nonactive
solvent. When this porous grating was exposed to the air containing various
concentration of acetone vapor, different reflection bands were clearly
observed, which was induced by the refractive index change, as shown in
Figure 72. A typical cycling behavior of the porous grating
subjected to alternating acetone vapor is shown in
Figure 73.Figure 72
The transmission spectra of a typical grating film in air containing various
concentrations of acetone vapor (volume-%) relative to 1 atm (101.325 kPa) air
pressure [142].Figure 73
Cycling behavior of the porous grating subjected to alternating acetone vapor
from 0.2 to 1 mbar (0.02 to 0.1 Pa)
[142].The
big advantages of optical sensors are faster, safer, and easier to implement compared to those electrical
sensors [143]. The reflective H-PDLC gratings show themselves
potentially useful in chemical or pressure sensing, although the long term
stability is still problematic for the H-PDLC materials.


## 9.3.1. Pressure Sensor

Based
on the above concept, it can be applied to create an HPDLC pressure sensor. The
fringe spacing is reduced by applying pressure perpendicular to the surface of
the HPDLC and parallel to the grating vector. The wavelength reflected is
measured for different applied pressure and the results are analyzed.In
one paper [140], the authors strained an H-PDLC reflection film
perpendicular to the grating vector and observed a blue shift in the peak
reflection wavelength of the film. This shift was caused by the Poisson
contraction of the polymer segments of the grating parallel to the grating
vector as the film was stretched perpendicular to the grating vector. Fontecchio
et al. developed hydrostatic pressure sensors based on H-PDLC reflection gratings
[139, 141].
Figure 70
shows the testing schematic. The light emitted from
the fiber was collimated by a lens and spatially filtered. This light was then incident
on the sensor under test at an angle of ~30° relative to the sensor normal. The
light reflected from the sensor was focused onto a fiber, which was connected
to spectrometer with a high resolution. Changing the material formation can
greatly improve the sensitivity of H-PDLC pressure sensors. The experimental
results show that increasing the initiator concentration makes the H-PDLC more
elastic. Figure 71
shows the response for the difunctional polymer with
various initiator concentrations. A clear difference can be observed from
Figure 71
that the largest wavelength shift was obtained at the
initiator concentration of 21 wt%.Figure 70
The configuration used to measure the reflected spectrum of the H-PDLC pressure
sensors. Light is incident on the film at ~30° to
the sensor normal [141].Figure 71
Wavelength versus pressure response of
difunctional HPDLC with pressure applied
from 0–20 psi [139].


## 9.3.2. Chemical Sensor

With
special treatment, the reflective H-PDLCs can contain many air voids without
any damage to the grating structures. Therefore, the Bragg reflection notch of
these gratings can then be shifted by filling the voids inside the grating
structure with solvent vapor. The high porosity of the grating film allows
chemical vapors to easily permeate into the void regions, consequently the
average refractive index is changed and the corresponding reflective wavelength
shifts according to (57). The shifted reflective wavelength can be observed
easily by eye due to the high refractive index contrast of the grating films.
Thus, these holographic porous polymer gratings can act as colorimetric vapor sensors.An easy way to create the voids in H-PDLCs
is to simply add a nonreactive solvent, such as acetone or toluene, into the
prepolymer syrup prior to holographic exposure. After exposure, the porous
acrylate polymer grating structures can be created when the nonreactive solvent
evaporates upon exposing the polymerized film to air. Porous H-PDLC
reflection grating used to detect chemical vapor has
been successfully demonstrated
[142], where 20 wt% toluene was used as nonactive
solvent. When this porous grating was exposed to the air containing various
concentration of acetone vapor, different reflection bands were clearly
observed, which was induced by the refractive index change, as shown in
Figure 72. A typical cycling behavior of the porous grating
subjected to alternating acetone vapor is shown in
Figure 73.Figure 72
The transmission spectra of a typical grating film in air containing various
concentrations of acetone vapor (volume-%) relative to 1 atm (101.325 kPa) air
pressure [142].Figure 73
Cycling behavior of the porous grating subjected to alternating acetone vapor
from 0.2 to 1 mbar (0.02 to 0.1 Pa)
[142].The
big advantages of optical sensors are faster, safer, and easier to implement compared to those electrical
sensors [143]. The reflective H-PDLC gratings show themselves
potentially useful in chemical or pressure sensing, although the long term
stability is still problematic for the H-PDLC materials.


## 9.4. Neutron-Optical Devices Based on H-PDLC

Besides the applications listed above, it is
worth mentioning a latest emerging application based on H-PDLCs. It is H-PDLC-based
neutron-optical devices
[144, 145]. H-PDLCs can act as extremely efficient gratings not
only for light but also for neutrons. H-PDLCs show similar diffraction behavior
for the neutrons like light diffraction, as shown in
Figure 74. The results showed that the light-induced
refractive-index modulation for neutrons is about 10−6, that is,
nearly 2 orders of magnitude larger than in the best photo-neutron-refractive
materials probed up to now, which makes H-PDLC promising as new materials to
fabricate neutron-optical devices for cold and ultracold neutrons, such as beam
splitters, lenses, and mirrors.Figure 74
Diffraction pattern of an H-PDLC at a
wavelength ofλ = 1.96 nm. Diffraction up to the ± second order is visible (bottom). The data
points result from summing up the box counts of 30 pixels along the y-direction around the centers of diffraction
spots, so that the second-order peaks are clearly
visible (top) [144].


## 10. Several Issues of H-PDLCs

### 10.1. Driving Voltage

In
H-PDLC, the LC droplets are so small (usually in the order of nanometers) that the surface area of interaction between polymer matrix
and LC droplets is strongly enlarged, and hence the anchoring energy of LC
droplets is greatly increased. Thus, a high driving voltage will be needed to reorientate
the directors of LC molecules. This is the main reason why the driving voltage
in H-PDLC gratings is higher than that in conventional PDLC devices. How to
reduce the driving voltage is the key for H-PDLC applications. As a
matter of fact, many factors affect the driving voltage of H-PDLCs, such as the
ratios of components in the material formulation, morphologies of gratings,
adding a small amount of surfactant
[88, 90, 91] or high dielectric anisotropy material [87], and fluorination of polymer matrix
[92, 93]. Many researchers studied the morphology effect on
the driving voltages
[71, 81, 146]. For example, with suitable LC weight ratio, two
different grating morphologies in the LC-rich region, droplet-like (most
H-PDLCs) and channel-like (POLYCRYPS gratings), can be formed, which greatly
affect the driving voltage. Generally, the channel-like H-PDLC gratings have a
much lower driving voltage compared to the droplet-like ones. However, the
droplet-like H-PDLCs usually show much faster response time compared to the
channel-like ones. As a result, from the application view point, a good
tradeoff between the driving voltage and response time is taken into account.
On the  other hand, adding a small
portion of surfactant or partial
fluorination of polymer may effectively reduce the
driving voltage, as discussed in
Section 7.5. However, adding another component
into the prepolymer mixture will increase the complexity of material
formulation as a kind of pollutant.


### 10.2. Holographic Scattering

The history of holographic scattering (HS) is
as long as the history of the photorefractive effect. The first photograph of
the HS phenomenon was found in 1966 when Ashkin et al. recognized the phenomenon of optical damage resulted from
a light-induced refractive-index change [147]. Rather soon the photorefractive effect was utilized
for the storage of volume phase holograms
[148, 149], thus opening a new
field for nonlinear optics.The generic observation of HS is the
following: if a laser beam propagates through a photorefractive crystal there
is a gradual increase of light scattering with time, and thus a considerable
decrease of the transmission. This kind of scattering shares two characteristic
properties with volume holograms: it builds up with a time constant of the same
order of magnitude characteristic for holographic recording and disappears
immediately upon a slight rotation of the crystal or a change of the
wavelength, just in the same way as the reconstructed wave fields of volume
holograms do upon violation of Bragg’s condition.For H-PDLCs, most researchers focused on
developing their applications. However, very little is known about optical
imperfections in the H-PDLC structures, which is very important as they
determine the limits of the H-PDLC applicability in any realistic device. One
of them is the evolution of unintentional photo-induced light scattering, known
as holographic scattering (HS) in photorefractive media. This effect emerges
from an initial scattering of the incident beam (pump beam) from
inhomogeneities within the sample. The interference of the incident and
scattered light produces a spatial modulation of intensity that is transferred
to weak refractive-index gratings. Subsequently, the pump beam is diffracted
from these gratings. If the diffracted beam and the scattered beam are in
phase, the latter will be amplified at the expense of the pump beam. This
amplification process continues until certain limitations, that is, pump beam
depletion, lead to a steady state. Finally, a multitude of parasitic holograms
with different amplitudes and directions of grating vectors are recorded in the
medium. As the parasitic holograms build up simultaneously with the desired
primary hologram, they are also reconstructed at the same time. HS is a general
phenomenon occurring in photosensitive materials.Ellabban et al. studied the holographic scattering in H-PDLCs
[150, 151].
Figure 75
shows the intensity distribution of the far-field
scattered light monitored at different times of the UV exposure. A corona of
scattered light develops spatially symmetric around the transmitted beam. Both
the diameter and the intensity of the corona increase with time. Harbour et al. investigated the anisotropic scattering induced by the LC
droplets during the formation of H-PDLC gratings
[152], which showed that p-polarized light had a
larger scattering than the s-polarized one.Figure 75
(Color online) Far-field scattering patterns observed at different recording
times of the UV beam,λp = 351 nm and Ip
= 9 mW/cm2. The central
white spot corresponds to the transmitted beam
[150].Using
an He-Ne laser, the diffraction patterns at different angles of the probe beam
were probed with respect to the sample normal. By rotating the sample, the
symmetric corona of the scattered light transforms into two characteristic
bright rings, as shown in
Figure76. The diameter of these rings changes with the readout
angle and the wavelength. Forshaw explained these ring patterns are
characteristic for holographic scattering in terms of the Ewald sphere construction
[153]. The
intersection of the Ewald sphere (allowed wave vectors of propagation in the
medium), with the structure factor (primary and conjugate sphere [153, 154]), that
is, the region in reciprocal space spanned by the recorded grating vectors,
results in two cones. The projection of these cones on a screen then produces
two bright rings. The apex angle of the cones derived from the Ewald-sphere
construction is given by the following equation: (58)ξ=2arctan[sinθrcosθr±λp/λr], where θr is the readout angle measured with respect
to the normal incidence of the readout beam within the medium. The positive
sign is assigned to the conjugate sphere, the negative sign to the primary
sphere.Figure 76
(Color online) Measured and calculated apex angle of the conjugate image versus
readout angle forλr1 =  633 and λr2 = 543 nm. Inset: far-field scattering pattern observed at θr=−14° using λr1 = 633 nm. The
white spot corresponds to the transmitted beam
[150].In general, a big
limitation of thick holographic recording media is connected with the origin of
strong light-induced scattering during the process of optical recording. The
presence of parasitic gratings (noise gratings) transfers almost all the light
from the initial beam to the scattering directions and greatly corrupts the
quality of any optical system. At the present, limited work has been done
regarding the suppression of the HS for H-PDLCs.


### 10.3. Polarization Dependence

The polarization
of the diffracted light depends on many factors, for example, monomers, liquid
crystals, exposure conditions, and substrates. Karasawa and Taketomi once
investigated the effect of materials systems on the polarization behavior of H-PDLCs
[155]. They showed the diffraction efficiency of the
gratings strongly depended on the polarization of incoming light. Depending on
the materials used, the diffraction properties are such that either p- or s-polarized light is strongly diffracted while the light with the
other polarization is weakly diffracted. Sutherland et al. studied the polarization properties both theoretically
and experimentally in detail
[73, 74].For LC-polymer composite
optical switch, polarization-dependent loss (PDL) is a big concern. Generally,
the conversion of the monomer molecules into a polymer network is accompanied
with closer packing of molecules, which leads to contraction of the composite
known as polymerization shrinkage. When the polymer shrinks, the LC droplets
are compressed, which makes the symmetry axis of the rod-shape LC molecules in
the droplet preferentially align along a common direction. This effect has been
verified experimentally with in situ
spectroscopy
[138, 156]. The shrinkage results in a polarization sensitive
diffraction since the optical axis is on average along the same direction for
all droplets, therefore making diffraction efficiency sensitive to the input
polarization. However, in our experiment, the shrinkage was only about 2% which
is significantly smaller than the reported data, which are usually 5% ~ 10%
[48, 157]. The smaller polymerization shrinkage reduces the
PDL remarkably. The main reason for the lower shrinkage in our experiment is that,
weaker exposure intensity and longer exposure time were used to decrease the
shearing strength in the polymerization process.
Figures 77(a) and
77(b) show the diffraction efficiencies measured
for p- and s-polarized light for a wavelength of 632.8 nm, respectively. Using
the diffraction efficiency obtained in
Figures 77(a)
and 77(b), the PDL was calculated to be 0.03 dB, by
comparing the insertion loss difference between p- and s-polarized light.
It is   worth mentioning that,
Karasawa and Taketomi have reported that diffraction
efficiency for p-polarization is much
higher than that for s-polarization
in acrylate systems
[155], similar to that in
Figure 78, which is also found in our experiments.
Figure 78
shows the diffraction efficiency for the sample
fabricated in larger exposure intensity of 30 mW/cm2. From
Figure 78(a), it can be seen that, for p-polarization case, the left side lobe (more than 20%) is much larger
than the right one. This case is called overmodulation. The main reason is
large shrinkage caused by intense exposure which makes the liquid crystals
preferably aligned along one direction. From
Figures 77
and 78, the angular bandwidth (full width at half maximum) is
approximately 2°.
According to the Kogelnik’s coupled-wave theory
[64], with increased thickness of LC-polymer composite
films, the bandwidth will become narrower.Diffraction efficiency as a function of incident angle for (a)p- and (b) s-polarized light.
The data is for an H-PDLC transmission grating
with Λ≈ 0.5 μm
probed at 632.8 nm. The grating thickness is about 10 μm. A fit to coupled-wave theory yields (a) n1 = 0.054 (p-polarization) and (b) n1 = 0.019 (s-polarization).
(a)(b)Diffraction efficiency as a function of incident angle for (a)p-
and (b) s-polarized light. The data is for a HPDLC
transmission grating with Λ≈ 0.5 μm
probed at 632.8 nm. The grating thickness is about 10 μm. A fit to coupled-wave theory yields (a) n1 = 0.125 (p-polarization) and (b) n1 = 0.048 (s-polarization). High side lobe
indicates overmodulation.
(a)(b)Smaller shrinkage is expected to reduce the shear force, thus decreasing the polarization dependence of H-PDLCs. Researchers have shown that small shrinkage could be obtained when a weak electric field was applied on the material film during the fabrication [158]. This is a good way to reduce the polarization
dependence although the researchers didn’t discuss it in their paper.


### 10.4. Aging (Lifetime)

The lifetime of
H-PDLC is also a problem to be solved. Without any sealing, the performance of
H-PDLC decays quickly after two or three months. Colegrove et al. studied the effect of the
monomer functionality on the aging of acrylate-based H-PDLCs and found that the
H-PDLCs formed with lower functionality monomers have better stability than
those formed with higher functionality monomers
[159]. For hexafunctional material, the LC droplets are
connected and there is almost no polymer wall in the LC rich lamellae to
support the polymer rich lamellae and substrates. LC may slowly leak out and
the performance of H-PDLCs then decayed much. For trifunctional material, the
LC droplets are discrete and there are thicker polymer walls in the LC rich
lamellae to support the polymer rich lamellae and substrates. There is no way
for LC to leak out and the H-PDLCs show relatively long-term stability. Natarajan
et al. compared the aging of reflection
gratings based on acrylate and thiol-ene materials
[48], respectively, as shown in
Figure 79. For the much degraded acrylate-based H-PDLC, one
possible reason is that the exposure is not enough. So after exposure, the
materials can still continue to react with each other under the ambient light.
Given only a 50% conversion because of rapid vitrification, a substantial
number of double bonds are present that can react slowly over time. The rapid
gelation also traps a considerable amount of stress in the system. The fast
gelation freezes a nonequilibrium network, which, over time, tries to
equilibrate by stress relaxation via molecular motion. Such postillumination
effects seem to be absent in thiol-ene gratings. The reason may be due to the
much higher conversion obtained in the thiol-ene systems. Because all of the
reactive double bonds are consumed, nothing exists to continue slow dark
reactions, and the late gelation (at conversion approaching 100%) eliminates large
stresses. Another reason is that the acrylate materials themselves are not
stable. They react with, for example, oxygen in air. The third reason is that,
the materials operated under high electric field are vulnerable to be broken
down. H-PDLC is a switchable device controlled by electric field. However,
after repeating many times, the material properties may be altered.Electrical switching behavior (diffraction efficiency versus voltage) of (a) acrylate
reflection gratings, and (b) thiol-ene reflection gratings with aging,
respectively [48].
(a)(b)


## 10.1. Driving Voltage

In
H-PDLC, the LC droplets are so small (usually in the order of nanometers) that the surface area of interaction between polymer matrix
and LC droplets is strongly enlarged, and hence the anchoring energy of LC
droplets is greatly increased. Thus, a high driving voltage will be needed to reorientate
the directors of LC molecules. This is the main reason why the driving voltage
in H-PDLC gratings is higher than that in conventional PDLC devices. How to
reduce the driving voltage is the key for H-PDLC applications. As a
matter of fact, many factors affect the driving voltage of H-PDLCs, such as the
ratios of components in the material formulation, morphologies of gratings,
adding a small amount of surfactant
[88, 90, 91] or high dielectric anisotropy material [87], and fluorination of polymer matrix
[92, 93]. Many researchers studied the morphology effect on
the driving voltages
[71, 81, 146]. For example, with suitable LC weight ratio, two
different grating morphologies in the LC-rich region, droplet-like (most
H-PDLCs) and channel-like (POLYCRYPS gratings), can be formed, which greatly
affect the driving voltage. Generally, the channel-like H-PDLC gratings have a
much lower driving voltage compared to the droplet-like ones. However, the
droplet-like H-PDLCs usually show much faster response time compared to the
channel-like ones. As a result, from the application view point, a good
tradeoff between the driving voltage and response time is taken into account.
On the  other hand, adding a small
portion of surfactant or partial
fluorination of polymer may effectively reduce the
driving voltage, as discussed in
Section 7.5. However, adding another component
into the prepolymer mixture will increase the complexity of material
formulation as a kind of pollutant.


## 10.2. Holographic Scattering

The history of holographic scattering (HS) is
as long as the history of the photorefractive effect. The first photograph of
the HS phenomenon was found in 1966 when Ashkin et al. recognized the phenomenon of optical damage resulted from
a light-induced refractive-index change [147]. Rather soon the photorefractive effect was utilized
for the storage of volume phase holograms
[148, 149], thus opening a new
field for nonlinear optics.The generic observation of HS is the
following: if a laser beam propagates through a photorefractive crystal there
is a gradual increase of light scattering with time, and thus a considerable
decrease of the transmission. This kind of scattering shares two characteristic
properties with volume holograms: it builds up with a time constant of the same
order of magnitude characteristic for holographic recording and disappears
immediately upon a slight rotation of the crystal or a change of the
wavelength, just in the same way as the reconstructed wave fields of volume
holograms do upon violation of Bragg’s condition.For H-PDLCs, most researchers focused on
developing their applications. However, very little is known about optical
imperfections in the H-PDLC structures, which is very important as they
determine the limits of the H-PDLC applicability in any realistic device. One
of them is the evolution of unintentional photo-induced light scattering, known
as holographic scattering (HS) in photorefractive media. This effect emerges
from an initial scattering of the incident beam (pump beam) from
inhomogeneities within the sample. The interference of the incident and
scattered light produces a spatial modulation of intensity that is transferred
to weak refractive-index gratings. Subsequently, the pump beam is diffracted
from these gratings. If the diffracted beam and the scattered beam are in
phase, the latter will be amplified at the expense of the pump beam. This
amplification process continues until certain limitations, that is, pump beam
depletion, lead to a steady state. Finally, a multitude of parasitic holograms
with different amplitudes and directions of grating vectors are recorded in the
medium. As the parasitic holograms build up simultaneously with the desired
primary hologram, they are also reconstructed at the same time. HS is a general
phenomenon occurring in photosensitive materials.Ellabban et al. studied the holographic scattering in H-PDLCs
[150, 151].
Figure 75
shows the intensity distribution of the far-field
scattered light monitored at different times of the UV exposure. A corona of
scattered light develops spatially symmetric around the transmitted beam. Both
the diameter and the intensity of the corona increase with time. Harbour et al. investigated the anisotropic scattering induced by the LC
droplets during the formation of H-PDLC gratings
[152], which showed that p-polarized light had a
larger scattering than the s-polarized one.Figure 75
(Color online) Far-field scattering patterns observed at different recording
times of the UV beam,λp = 351 nm and Ip
= 9 mW/cm2. The central
white spot corresponds to the transmitted beam
[150].Using
an He-Ne laser, the diffraction patterns at different angles of the probe beam
were probed with respect to the sample normal. By rotating the sample, the
symmetric corona of the scattered light transforms into two characteristic
bright rings, as shown in
Figure76. The diameter of these rings changes with the readout
angle and the wavelength. Forshaw explained these ring patterns are
characteristic for holographic scattering in terms of the Ewald sphere construction
[153]. The
intersection of the Ewald sphere (allowed wave vectors of propagation in the
medium), with the structure factor (primary and conjugate sphere [153, 154]), that
is, the region in reciprocal space spanned by the recorded grating vectors,
results in two cones. The projection of these cones on a screen then produces
two bright rings. The apex angle of the cones derived from the Ewald-sphere
construction is given by the following equation: (58)ξ=2arctan[sinθrcosθr±λp/λr], where θr is the readout angle measured with respect
to the normal incidence of the readout beam within the medium. The positive
sign is assigned to the conjugate sphere, the negative sign to the primary
sphere.Figure 76
(Color online) Measured and calculated apex angle of the conjugate image versus
readout angle forλr1 =  633 and λr2 = 543 nm. Inset: far-field scattering pattern observed at θr=−14° using λr1 = 633 nm. The
white spot corresponds to the transmitted beam
[150].In general, a big
limitation of thick holographic recording media is connected with the origin of
strong light-induced scattering during the process of optical recording. The
presence of parasitic gratings (noise gratings) transfers almost all the light
from the initial beam to the scattering directions and greatly corrupts the
quality of any optical system. At the present, limited work has been done
regarding the suppression of the HS for H-PDLCs.


## 10.3. Polarization Dependence

The polarization
of the diffracted light depends on many factors, for example, monomers, liquid
crystals, exposure conditions, and substrates. Karasawa and Taketomi once
investigated the effect of materials systems on the polarization behavior of H-PDLCs
[155]. They showed the diffraction efficiency of the
gratings strongly depended on the polarization of incoming light. Depending on
the materials used, the diffraction properties are such that either p- or s-polarized light is strongly diffracted while the light with the
other polarization is weakly diffracted. Sutherland et al. studied the polarization properties both theoretically
and experimentally in detail
[73, 74].For LC-polymer composite
optical switch, polarization-dependent loss (PDL) is a big concern. Generally,
the conversion of the monomer molecules into a polymer network is accompanied
with closer packing of molecules, which leads to contraction of the composite
known as polymerization shrinkage. When the polymer shrinks, the LC droplets
are compressed, which makes the symmetry axis of the rod-shape LC molecules in
the droplet preferentially align along a common direction. This effect has been
verified experimentally with in situ
spectroscopy
[138, 156]. The shrinkage results in a polarization sensitive
diffraction since the optical axis is on average along the same direction for
all droplets, therefore making diffraction efficiency sensitive to the input
polarization. However, in our experiment, the shrinkage was only about 2% which
is significantly smaller than the reported data, which are usually 5% ~ 10%
[48, 157]. The smaller polymerization shrinkage reduces the
PDL remarkably. The main reason for the lower shrinkage in our experiment is that,
weaker exposure intensity and longer exposure time were used to decrease the
shearing strength in the polymerization process.
Figures 77(a) and
77(b) show the diffraction efficiencies measured
for p- and s-polarized light for a wavelength of 632.8 nm, respectively. Using
the diffraction efficiency obtained in
Figures 77(a)
and 77(b), the PDL was calculated to be 0.03 dB, by
comparing the insertion loss difference between p- and s-polarized light.
It is   worth mentioning that,
Karasawa and Taketomi have reported that diffraction
efficiency for p-polarization is much
higher than that for s-polarization
in acrylate systems
[155], similar to that in
Figure 78, which is also found in our experiments.
Figure 78
shows the diffraction efficiency for the sample
fabricated in larger exposure intensity of 30 mW/cm2. From
Figure 78(a), it can be seen that, for p-polarization case, the left side lobe (more than 20%) is much larger
than the right one. This case is called overmodulation. The main reason is
large shrinkage caused by intense exposure which makes the liquid crystals
preferably aligned along one direction. From
Figures 77
and 78, the angular bandwidth (full width at half maximum) is
approximately 2°.
According to the Kogelnik’s coupled-wave theory
[64], with increased thickness of LC-polymer composite
films, the bandwidth will become narrower.Diffraction efficiency as a function of incident angle for (a)p- and (b) s-polarized light.
The data is for an H-PDLC transmission grating
with Λ≈ 0.5 μm
probed at 632.8 nm. The grating thickness is about 10 μm. A fit to coupled-wave theory yields (a) n1 = 0.054 (p-polarization) and (b) n1 = 0.019 (s-polarization).
(a)(b)Diffraction efficiency as a function of incident angle for (a)p-
and (b) s-polarized light. The data is for a HPDLC
transmission grating with Λ≈ 0.5 μm
probed at 632.8 nm. The grating thickness is about 10 μm. A fit to coupled-wave theory yields (a) n1 = 0.125 (p-polarization) and (b) n1 = 0.048 (s-polarization). High side lobe
indicates overmodulation.
(a)(b)Smaller shrinkage is expected to reduce the shear force, thus decreasing the polarization dependence of H-PDLCs. Researchers have shown that small shrinkage could be obtained when a weak electric field was applied on the material film during the fabrication [158]. This is a good way to reduce the polarization
dependence although the researchers didn’t discuss it in their paper.


## 10.4. Aging (Lifetime)

The lifetime of
H-PDLC is also a problem to be solved. Without any sealing, the performance of
H-PDLC decays quickly after two or three months. Colegrove et al. studied the effect of the
monomer functionality on the aging of acrylate-based H-PDLCs and found that the
H-PDLCs formed with lower functionality monomers have better stability than
those formed with higher functionality monomers
[159]. For hexafunctional material, the LC droplets are
connected and there is almost no polymer wall in the LC rich lamellae to
support the polymer rich lamellae and substrates. LC may slowly leak out and
the performance of H-PDLCs then decayed much. For trifunctional material, the
LC droplets are discrete and there are thicker polymer walls in the LC rich
lamellae to support the polymer rich lamellae and substrates. There is no way
for LC to leak out and the H-PDLCs show relatively long-term stability. Natarajan
et al. compared the aging of reflection
gratings based on acrylate and thiol-ene materials
[48], respectively, as shown in
Figure 79. For the much degraded acrylate-based H-PDLC, one
possible reason is that the exposure is not enough. So after exposure, the
materials can still continue to react with each other under the ambient light.
Given only a 50% conversion because of rapid vitrification, a substantial
number of double bonds are present that can react slowly over time. The rapid
gelation also traps a considerable amount of stress in the system. The fast
gelation freezes a nonequilibrium network, which, over time, tries to
equilibrate by stress relaxation via molecular motion. Such postillumination
effects seem to be absent in thiol-ene gratings. The reason may be due to the
much higher conversion obtained in the thiol-ene systems. Because all of the
reactive double bonds are consumed, nothing exists to continue slow dark
reactions, and the late gelation (at conversion approaching 100%) eliminates large
stresses. Another reason is that the acrylate materials themselves are not
stable. They react with, for example, oxygen in air. The third reason is that,
the materials operated under high electric field are vulnerable to be broken
down. H-PDLC is a switchable device controlled by electric field. However,
after repeating many times, the material properties may be altered.Electrical switching behavior (diffraction efficiency versus voltage) of (a) acrylate
reflection gratings, and (b) thiol-ene reflection gratings with aging,
respectively [48].
(a)(b)


## 11. Summary and Remarks

In summary,
current status of H-PDLCs including materials, fabrication, performance
optimization, applications, and existing issues has been reviewed. The H-PDLC technique
has and will continue to create new applications. The ability to selectively
control the diffraction properties of an optical element provides enormous
freedom in the design and implementation of optical systems. Although
impressive performance of H-PDLCs have been demonstrated to date, some fundamental
issues are still not completely understood, especially in the process of the structure
formation, in which polymerization, phase separation, and diffusion occur and
interact with each other. Researchers have made much effort to overcome the
issues existed in H-PDLCs, which pushes the H-PDLCs to a practical application
stage.



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*Source: 684349-2009-04-27.xml*