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.

Figure 1: Different polymer structures. (a) A linear polymer chain. (b) A branched chain. (c) A cross-linked network.

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 Figure 2(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.

Figure 2: Schematic holographic recording for (a) transmission and (b) reflection gratings, respectively.

1.3.2. Raman-Nath and Bragg Gratings

Generally, two types of diffraction are distinguished by defining a dimensionless Cook-Klein parameter : where is the thickness of the grating, is the grating period, is the spatially averaged refractive index of the recording medium, and is the incident wavelength.

A “thick” or volume grating () 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 where is the amplitude of refractive index modulation of the material, is the Bragg angle of the incident light within the material.

On the other hand, “thin” gratings () 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 where is the first-order Bessel function of the first kind, is the depth of the gratings grooves, and 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  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].

Figure 3: 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].

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.

Figure 4: 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].

Figure 5: Optical polarizing microscopy of a polarization insensitive FLC H-PDLC grating (a) between crossed polarizers, (b) between crossed polarizers [25].

Figure 6: Optical polarizing microscopy of a polarization insensitive FLC H-PDLC grating (a) between crossed polarizers, (b) between crossed polarizers [25].

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.

Figure 7: 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].

Figure 8: SEM micrographs for a transmission HPDLC prepared (a) without and with (b) 0.5%, (c) 1% azo dye [30].

1.7. Nematic Director Configurations in PDLCs

A typical example of PDLCs is the light valve configuration presented in Figure 9. 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, , (perpendicular to the nematic director) approximately matches the refractive index, , 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.

Figure 9: 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.

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 elastic , interfacial , and field parts.

The nematic free-energy density f_e can be expressed as where , , and are the splay, twist, and bend elastic constants, respectively, and is the director axis.

The interaction of the liquid crystal with the surrounding medium is described by a simple contact interaction characterized by , the preferred anchoring direction on the droplet surface and the anchoring strength . The vector in (5) defines points on the droplet surface.

The interaction with an external magnetic field is described by where is the permeability of free space, is the external magnetic field, and is the difference between the principal values of the susceptibility tensor corresponding to the directions parallel and perpendicular to .

The minimization of the total free energy 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 Figure 10 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.

Figure 10: 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.

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, can be achieved, and the Bragg grating disappears. If and when the condition is met, the beam is no more diffracted.

Figure 11: Schematic of an H-PDLC transmission grating.

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 A 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 A 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 Figure 12. 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. Figure 15 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.

Figure 15: Experimental setups of holographic (a) transmission and (b) reflection grating recording, respectively.

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 () at room temperature. The diffraction efficiency for - and -polarized light was measured and compared, respectively.

(ii) Response Time
Figure 16 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 Figure 17. 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 along -axis direction.

Ignoring interactions between various components, the chemical potential for the ith component of the mixture may be approximated by where is the chemical potential of the pure th component, is the number of molecules of the th component, is Boltzmann's constant, and is the absolute temperature. Under thermodynamic equilibrium, the sum 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 Section 1.7, the total droplet energy is minimized at a critical droplet radius, , which is proportional to the surface tension of the droplet, . 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:

Propagation:

Termination:

Inhibition by Oxygen:

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]: where is the monomer concentration, is the polymerization rate, and 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 is , which denotes that the monomers convert into polymer in unit volume. Therefore, the concentration of the polymer can be written as the concentration of liquid crystal can be written as In the whole system, , , and are satisfying the equation . 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 where is the average intensities, is the fringe visibility, , and is the grating pitch. We assume the polymerization rate to be proportional to the exposure intensities, so we may write where , and is a constant.

For our case, the monomer concentration will also be periodic and an even function of . Thus, we can write , , and as Fourier series:

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: where , . We can also treat , with the same method. Finally, the equations are dependent on four parameters: the ratio of diffusion rate to polymerization rate, , the constant that characterizes the rate of decrease of the diffusion coefficients, , the shrinkage rate when the monomers polymerize, , and the fringe visibility, . 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 , with , , , and . 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.

Figure 18: The harmonics of (a) monomer, (b) polymer, and (c) liquid crystal concentration as a function of time, respectively.

The ratio of diffusion rate to polymerization rate 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 for different , with , , and . In general, the polymer concentration increases with the exposure and will reach a saturation value. We can see that the saturation depends strongly on . Great results in large saturation values. However, for , 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 and . From Figure 19(c), we can see the smaller the , the stronger the second harmonic. When , the harmonics whose order more than one can be ignored because the zero and first-order harmonics dominate absolutely.

Figure 19: The amplitude of each harmonic of polymer concentration as a function of exposure for different with , , and .

Figure 20 shows the relationship between the saturation of the first and second harmonics and the fringe visibility for different . We can see that the larger the , the more linear the saturation of the harmonics. For , the saturation of the harmonics are completely linear. We also can see that the second harmonic is almost zero when , which means no influence for the polymerization for the second harmonic.

Figure 20: The relationship between the saturation of the first and second harmonics and the fringe visibility for different .

Figure 21 shows the relationship between the saturation of the first and second harmonics and . We can see that αdoes not affect the grating formation strongly.

Figure 21: The relationship between the saturation of the first and second harmonics and .

Figure 22 shows the polymer distribution profile for different . The profile is purely sinusoidal for large . When the decreases, the higher harmonics will be obtained. So a large can produce a good grating structure.

Figure 22: The polymer distribution profile for different .

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 , which is perpendicular to the grating planes. Generally, the grating vector makes an angle with respect to the film normal. Light is incident on the film at an angle , 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 -polarized. Light polarized in the plane of incidence is said to be -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 as the droplet director. In the absence of an electric field, 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 where is the average irradiance, is the fringe visibility, , and 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 where is the matrix index, 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 where is the optical wavelength and is the physical thickness of the grating. To be in the thick grating regime, we must have . Typical gratings used in the visible spectrum have  ~ 1.5 and  ~ 0.2–1.0 μm. Thus, the applicable thickness for the visible spectrum is in the range  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 for -polarization and for -polarization. The quantities are called the obliquity factors. The angle of incidence may vary slightly about the principal angle, which we designate as the Bragg angle . At this angle of incidence, the wavelength of maximum coupling is called the Bragg wavelength and is defined by 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 where is an adjustable parameter, is the polarization ( or ) and the subscript signifies that the value of depends on the propagation direction of the reference (signal) wave.

We defined a complex detuning parameter where is due to a loss mechanism and is due to a dephasing caused by angular and spectral departures from the Bragg condition. We have

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 where is the Rayleigh-Gans scattering coefficient for a spherical particle of radius a, with for -polarization, for -polarization, and

We further define a scattering transmission factor given by for transmission gratings.

We now recognize that because the terms that involve scattering depend on polarization, and should carry the subscript to signify the appropriate polarization, and all of the preceding equations apply, with (37) used for -polarization and (38) used for -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 for the diffraction efficiency of a transmission grating, where the asterisk () signifies complex conjugate and

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

6.2. Numerical Results

For the case of an unslanted grating, the diffraction efficiency is solved numerically using Mathcad. Figure 24 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.

Figure 24: Angular dependence of diffraction efficiency for a transmission H-PDLC grating. Key parameters: (external), , = 10 μm, = 633 nm, = 0.020, (a) = 0.015, (b) = 0.025, (c) = 0.040, and (d) = 0.050.

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. Figure 25 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.

Figure 25: Angular dependence of diffraction efficiency for a transmission H-PDLC grating, illustrating (a) normal and (b) overmodulated cases. Key parameters: (external), , = 10 μm, = 633 nm, and = 0.020, (a) = 0.040, (b) = 0.070.

The film thickness, , and the index modulation amplitude, , 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.

Figure 26: Angular dependence of diffraction efficiency for a transmission H-PDLC grating, illustrating angular bandwidth for various and . Key parameters: (external), , = 633 nm, = 0.020, (a) = 20 μm, = 0.026, (b) =16 μm, = 0.034, (c) = 10 μm, = 0.052, and (d) = 6 μm, = 0.088.

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 Figure 27. 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 radius , illustrating the effects of scattering. Key parameters: (external), , = 10 μm, and = 633 nm.

Generally, the diffraction efficiency of H-PDLC gratings has polarization dependence more or less because of the anisotropy of LC. Figure 28 illustrates this effect. In general, -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: (external), , = 10 μm, = 633 nm, = 0.020, = 0.050 (-polarization), and = 0.016 (-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 Figure 29 [76]. In case (a) shown in Figure 29, if the time to diffuse across 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 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 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 , 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 . 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. , , and are nucleation time, gelation time, and diffusion time to , respectively. 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 Figure 30 [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/, 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 = 10 mW/ and = 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. Figure 31 shows the effect of the exposure temperature on the diffraction efficiency of a transmission H-PDLC grating. At the temperature range of , 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].

Figure 33 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 () 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].

Figure 33: 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].

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. Figure 34 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.

Figure 35: 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%.

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.

Figure 36: 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.

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 molecule -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.

Figure 37: SEM images of H-PDLC transmission gratings with (a) 4 wt% and (b) 15 wt% NVP. Scale bars represent 600 nm [83].

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] where is the HPDLC film thickness, is the droplet radius, is the effective elastic constant, is the vacuum dielectric constant, is the LC dielectric anisotropy, is the droplet aspect ratio, with and 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, , where is the elastic torque per unit volume and 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 ~ 5 μm 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, , is 20 μm, the elastic constant, , is 1.71 ×  N, the dielectric anisotropy, , is 6.49, and assuming an aspect ratio of 1.1, for LC droplets with = 2 μm and 0.02 μm, the corresponding threshold voltage 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 ( = 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.

Figure 38 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. Figures 39(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.

Figure 39: 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 Figure 12 and E7, respectively.

Figure 40 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 Figure 12 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.

Figure 41: LVHRSEM photomicrographs of (a) standard formulation, (b) 13.2 mol% MA, and (c) 11.7 mol% HFIPA holographic PDLC films [92].

Figure 42: 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].

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, , is chosen to be as close as possible to the ordinary refractive index, , of LC. This helps to reduce the diffraction loss in the transparent state. Moreover, the birefringence of LC, , 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.

The 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 Si substrate to form a polymer thin film, the refractive index, , 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.

Figure 43: Measurement setup of the refractive index .

From the table, we can see that the refractive index 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 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, 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.

Figure 44: 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 1 μm for both panels [100].

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.

Figure 45: Grating morphology (oligomer/EHA = 3:1, 35 wt.-% LC): (a) without silica, = 1.35 μm, and = 0.58 μm, (b) with Aerosil 200, = 1.47 μm and = 0.76 μm [101].

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].

Figure 47 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 Figure 48 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. Figure 50 shows the case when the LC droplets under an electric field, where is the Bragg angle and 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 where is the angle between the symmetry axis of LC droplets and the Bragg plane without voltage applied and is a critical field for switching which depends on properties of the LC droplet and surrounding polymer, where and are the electrical conductivities of the LC and polymer, respectively, is the elastic bend force constant, and 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 -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 , 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 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 where is the highest diffraction efficiency, is the lowest diffraction efficiency, is the highest transmission efficiency, and 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, , 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, , 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 , measured from the rising edge of the voltage pulse, is about 36 μs. The , measured from the fall edge of the voltage pulse, is about 160 μs.

Figure 51: Variation of diffracted light intensity corresponding to (a) a square driving voltage, (b) the magnified rising edge, and (c) the falling edge of (a).

Another interesting thing to note is that, in Figure 51(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 of vary from 25 μs [107] to 750 μs [35] and the reported values are slightly longer, ranging from 44 [107, 108] to 1000 μs [109]. For the thoil-ene-based H-PDLCs, the reported values of vary from 550 μs to 6.7 ms and the reported 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 and as where 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.

Figure 52: SEM images of sample fabricated in the sp configuration with , . (a) 3D perspective. (b) Top view [112].

Figure 53: 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].

Figure 54: SEM images. (a) Low magnification; (b) closeup of -face viewed from a slightly different perspective than in (a); (c) side view of cylindrical LC cavities; (d) closeup of LC cavities [115].

Figures 55(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 A 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 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.

Figure 55: (a) Schematic of the mask and (b) three first-order diffracted beams.

The electrical field distribution of multibeam interference can be generally described by where is the amplitude, is the wave vector, and are integers, is the initial phase difference between two incident waves, and is the position vector. The orientation of the wave vector of the three beams can be defined as