Polymer-Stabilized Blue Phase Liquid Crystals for Photonic Applications

Transcription

1 Polymer-Stabilized Blue Phase Liquid Crystals for Photonic Applications Yan Li,* Shuaijia Huang, Pengcheng Zhou, Shuxin Liu, Jiangang Lu, Xiao Li, and Yikai Su Polymer-stabilized blue phase liquid crystal (PS-BPLC) is emerging as a promising candidate for next-generation photonic applications due to its attractive features: nano-scale structure that enables sub-millisecond response time, self-assembly that eliminates the need for surface alignment, and threedimensional cubic structure so that it is quasi-isotropic without applied field. Here, we will look into the photonic properties of PS-BPLC microscopically and macroscopically, and will focus on the non-display photonic applications based on these properties. First we will give a general introduction to the polymer stabilization process, general photonic properties, electric field effects and desirable electro-optical properties of PS-BPLC. Next we will present applications based on the microscopic photonic properties in the cubic structures with double twist cylinders: photonic band gap, scattering and unwinding of the double twist structure under electric field. Then, we will cover applications based on the macroscopic refractive index change of PS-BPLC under electric fields, whose mechanisms are further classified into phase retardation, phase modulation, and resonance condition change. Finally we will look into the remaining challenges and future perspectives of PS-BPLC for photonic applications. 1. Introduction Liquid crystal (LC) [1 3] is a soft material with large birefringence, whose refractive index can be conveniently controlled by external stimuli such as electric field, magnetic field and temperature. LC has found widespread applications [4 17] in displays, optical communications, spatial light modulators, tunable lenses, non-mechanical beam steering devices, wave front control devices and so on. Conventional nematic LC devices offers light-weightness, large tuning range and low power consumption. However, the response time is usually slow, especially when a thick LC cell is employed. Moreover, nematic LC devices require polyimide layers or photo-alignment [18,19] treatment to realize LC director alignment. Blue phase liquid crystal (BPLC) [20,21] is among the most fascinating soft materials. The three-dimensional nanostructures [22] Prof. Y. Li, S. Huang, P. Zhou, S. Liu, J. Lu, Dr. X. Li, Prof. Y. Su National Engineering Lab for TFT-LCD Materials and Technologies Department of Electronic Engineering Shanghai Jiao Tong University Shanghai , China yan.li@sjtu.edu.cn DOI: /admt are self-assembled and no alignment layer is needed. Due to the short coherent length, BPLC achieves fast response time in the submillisecond range, [23] making it attractive for many electro-optical applications that require rapid switching. Moreover, BPLC offers quasi-optically isotropic off-state for off-resonant wavelength, [24] and exhibits Kerr constant thousands of times higher than conventional Kerr media. However, blue phases (including BPI, BPII and BPIII) are only stable within a very narrow temperature range between chiral nematic and isotropic phases. [20] Great efforts were devoted to understanding the structures of blue phases, both experimentally and theoretically. [25 32] BPIII is an amorphous structure,while BPI and BPII are both cubic structures made of double twist cylinders (DTCs) but arranged differently as shown in Figure 1a. Inside each DTC, liquid crystal directors are twisted from 45 o to +45 o about any radius of the cylinder. However, as the cylinders are symmetrically arranged in three dimensions, it is impossible to make the directors match everywhere. Thus, defects occur at the points where the DTCs are in contact to relieve the elastic strain energy. As a result, blue phases only exist within a narrow temperature range (0.5 2 C), [33] which had hindered them from practical applications for decades. Much research work has been carried out in order to broaden the temperature range of blue phases. [34 46] Among them, polymer stabilization [39] is the most commonly used method, which was first proposed by Kikuchi et al. in By selectively concentrating the cross-linked polymer network in the disclination lines, the DTC structure was stabilized with a wide temperature range over 60 K. In the early years, polymer-stabilized blue phase liquid crystal was mainly employed for display applications. With fast response time, it could enable color sequential display and triple the optical efficiency; [47] with natural self-assembly, it does not require any alignment layer; and with quasi-isotropic dark state, it could achieve high contrast ratio and wide viewing angle. In 2008, Samsung demonstrated the first PS-BPLC display prototype at Society for Information Display exhibition. [48] In 2015, AU Optronics also demonstrated a PS-BPLC display using new wall electrodes, which could be driven by conventional integrated circuit. [49] Extensive work has been done on improving PS-BPLC display performances from both material 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (1 of 28) wileyonlinelibrary.com

2 side [50 61] and device side. [62 72] In 2006, Yokoyama et al. demonstrated laser emission in PS-BPLC and introduced PS-BPLC into non-display applications. [73] More photonic applications based PS-BPLC were explored afterwards such as lasers, [74,75] gratings, [76 82] lenses, [83 89] spatial phase modulators, [90 92] and so on. [93 95] PS-BPLC is becoming a strong contender for various photonic applications. 2. Polymer Stabilization of Blue Phase The material preparation process [39,96] of PS-BPLC is shown in Figure 1b. First, a blue phase precursor is made by uniformly mixing a nematic LC host, a chiral dopant, monomers and a small fraction of photo initiator. Then the sample is exposed to curing light illumination for a certain dosage at blue phase temperature. The polymer network starts to aggregate on the disclination cores in a random coil conformation, stabilizing the blue phase structure. [39] Traditionally, UV curing light sources are used in the polymer stabilization of BPLC. In 2015, Yuan et al. realized the polymerization of blue phase by a visible light for the first time employing a visible curable photo initiator Rose Bengal. [97] 3. General Photonic Properties In PS-BPLC, the three dimensional DTC structures are stabilized by polymer networks, exhibiting the following general photonic properties over a broad temperature range: photonic band gap, [33,98] scattering, [74] optical rotatory power [24] and isotropic refractive index at voltage-off state Bragg Reflection and Photonic Band Gap Due to the self-assembled cubic lattice structures, like photonic crystals, Bragg reflection occurs in BPLC if the wavelengths are comparable to the lattice constant. [22,93,99] For a broadband incident light, a range of wavelengths achieves high reflection near the Bragg wavelengths, resulting in photonic band gaps. The maximum Bragg reflection wavelength λ B in a BPLC composite can be expressed as: [20] λ B = 2na h + k + l (1) hundred microns by changing experimental conditions such as the temperature-changing rate, [74,75] applied electric field [100,101] or alignment layers. [70] The Bragg reflection wavelength λ B is sensitive to incident angle variation, and the bandwidth of the photonic band in PS-BPLC is much narrower than that in cholesteric liquid crystal. [102] 3.2. Scattering Yan Li received her B.S. (2005) and M. S. (2007) degree from Zhejiang University, and her Ph.D. degree (2012) from College of Optics and Photonics, University of Central Florida. Her research area includes blue phase liquid crystal devices, 3D displays and fast liquid crystal displays. Yikai Su received the Ph.D. degree in EE from Northwestern University, Evanston, IL, USA in Prior to joining Shanghai Jiao Tong University (SJTU) in 2004, he worked at Bell Laboratories, New Jersey, US. He is currently a full professor of the department of Electronic Engineering, the chapter chair of IEEE Photonics Society in Shanghai, and a faculty advisor of the SJTU OSA student chapter. Aside from Bragg reflection resulted from the cubic structures, scattering also occurs due to the disordered platelet domain boundaries and the index mismatch between polymer and liquid crystal. [74,75] The scattering is not obvious in a thin PS- BPLC cell but is more pronounced in a thick sample or a bulky capillary tube. where n is the average refractive index and a is the lattice constant of blue phase; h, k and l are Miller indices of various crystal orientation planes. The lattice constant a of BPI is the same as the helical pitch length P, and that of BPII is P/2. [20] Thus, the Bragg reflection color could be tuned by varying the helical pitch P, which is mainly determined by chiral dopant concentration and its helical twisting power. Shown in Figure 1c is the picture of a PS-BPLC taken under a polarizing microscope in reflective mode. One can see multiple platelet domains with different colors, which are the Bragg reflections corresponding to different crystal orientation planes. The domain size of the platelets varies from several microns to several 3.3. Optical Rotatory Power There is twisting power in each of the nano-scale DTCs that are symmetrically arranged in three dimensions. The average twisting power in multiple disordered domains leads to a weak optical rotatory effect for the light passing through a PS-BPLC cell. That is, the linear polarized incident light would be converted to quasi-linearly (elliptically) polarization with its long axis rotated by a small angle. [24] To quantitatively evaluate this rotatory effect, optical rotatory power (ORP) is defined as ϕ = α, where α is d the rotation angle, and d is the gap of the PS-BPLC cell. Liu et al (2 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

3 Figure 1. a) Cubic structures of BPI and BPII. b) Material preparation process of a PS-BPLC. c) Platelet texture of a PS-BPLC under a polarizing microscope. found that ORP is proportional to the square of the LC birefringence Δn, and inversely proportional to (λ 2 /λ B 2-1), where λ is the operation wavelength. ORP can be positive or negative. A positive ORP means polarization rotation in the right-handed direction, and a negative value means rotation in the left-handed direction. As the operation wavelength gets closer to the Bragg reflection wavelength λ B, the rotation angle and ORP increase dramatically. On the other hand, when the wavelength is much larger than λ B, ORP is approximately inversely proportional to λ 2 /λ B Isotropic Refractive Index For wavelengths far away from Bragg reflection, macroscopically, PS-BPLC appears quasi-optically isotropic due to the three dimensional symmetric structure. The quasi-optically isotropic means that, a PS-BPLC layer acts just like an isotropic medium with a refractive index n iso, [103] except that there is a small polarization rotation effect as discussed in the above section. [24] Therefore, for applications utilizing the isotropic 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (3 of 28) wileyonlinelibrary.com

4 refractive index property, the Bragg reflection wavelength λ B of the lattice structure should be chosen outside of the operation wavelength range. For instance, for transmissive displays and photonic devices operated in the visible region, λ B is usually tuned to UV region (<380 nm). 2 K = n /( λe ). (4) s s Assuming the average refractive index keeps the same with and without an electric field, n o (E) and n e (E) could be approximately expressed using the following two equations respectively: [103] 4. Electric Field Effect When an electric field is applied in a PS-BPLC sample, there are three types of response processes: local reorientation, lattice distortion and phase transition. [ ] If the field strength is below the critical field E c, local reorientation dominates, and a fast response time can be obtained. [23] During the local reorientation process, liquid crystal molecules inside the DTCs of BPLC tend to align parallel to the electric field if the dielectric anisotropy Δε > 0 (or perpendicular to the electric field if Δε < 0). [108] Since the electric field is relatively low, LC molecules are mostly confined within the DTCs whose diameter is about several hundred nanometers. Thanks to short coherent length, [20] response time is usually in the submillisecond range, which is much faster than the Freedericksz transition [5] in nematic LC devices. When the electric field is larger than E c, electrostriction effect [109,110] starts to manifest, resulting in slower response. As the polymer network is deformed, the three-dimensional lattice structure of BPLC is distorted as well. Lattice distortion usually involves as many as 10 7 LC molecules, and its response time is in the range of several milliseconds or longer. [61] According to Equation (1), the electric field induced change of lattice constant a would also lead to a shift in the Bragg reflection wavelength. [102] With an even higher electric field is applied, an irreversible phase transition might occur. A blue phase may transfer to another blue phase [102] or to chiral nematic phase, and ultimately to nematic phase. [107,111] This transition is usually in the order of seconds. Hence, the overall response time becomes faster, but the tradeoff is a higher operation voltage owing to more rigid polymer network. A higher polymer concentration is helpful in increasing E c, and suppressing electrostriction and phase transition. [61] Macroscopically, under an external electric field, PS-BPLC turns from quasi-optically isotropic into optically anisotropic, resulting in an increased refractive index n e (E) along the E field direction and a decreased index n o (E) in the orthogonal directions. The induced birefringence is almost proportional to E 2 and can be approximated by Kerr effect in the low field region as: [112] 2 n ( E) = n ( E) n ( E) = λke, (2) ind e o where K is Kerr constant. In the higher field region, the induced birefringence gradually saturates following the extended Kerr model: [113] 2 nind( E) = ns[1 exp( ( E/ Es))], (3) where n s is the saturation birefringence and E s the saturation electric field. And Kerr constant is thus expressed as: no( E) niso nind( E)/3, (5) ne( E) niso + 2 nind( E)/3. (6) In general, when wave propagation direction has an angle θ with respect to the electric field, the ordinary polarization sees no while the extraordinary polarization sees neff = none/ (ne2cos2θ + no2sin2θ 1/2. [5] In the special case when the incident light propagates along the direction of electric field, it perceives the same refractive index no regardless of polarization. Hence the electro-optical performances of the PS-BPLC devices would be polarization independent. The polarization independent property is important for enhancing optical efficiency of photonic devices. By eliminating the need for a polarizer, which either absorbs or reflects about half of the unpolarized incident light, the optical efficiency could be improved by more than 2 times. 5. Electro-Optical Parameters of PS-BPLCs 5.1. Kerr Constant Kerr constant is one of the most important parameters of PS-BPLC. According to Equation (2), a larger Kerr constant would result in lower electric field (voltage) to induce the same amount of birefringence. According to Gerber s model, Kerr constant is determined by the birefringence ( n), dielectric anisotropy ( ε) of LC host, the average elastic constant (k) and pitch length (P) of BPLC composite as: [106] 2 n P K ε 2 k λ(2 π) (7) Depending on the polarity of ε, Kerr constant K can be positive or negative. [108,114] To increase Kerr constant and lower operation voltage, various approaches have been proposed such as having large Δn, Δε, [50,51, ] increasing pitch length P, [70,118] and decreasing elastic constant k. [57,59,60] During the past decade, remarkable progress has been made in improving Kerr constant in PS-BPLC. In 2005 the largest Kerr constant of PS-BPLC reported was 0.37 nmv 2,(for 632 nm at 293 K) [119] but by 2009, the number hit 10 nmv 2. [63,120] And by 2015, an even higher Kerr constant K = nmv 2 was achieved for λ = 633 nm. [52] 5.2. Response Time When electric E is low, say E < E c, where E c is determined by the stiffness of the polymer network, the relaxation of BPLC (4 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

5 is mainly governed by local reorientation inside the DTCs. Thanks to the short coherent length, response time is usually in the submillisecond range. The relaxation time (with the same applied voltage) of local reorientation τ 1 is insensitive to polymer concentration or cell gap variation, but mainly determined by its rotational viscosity (γ 1 ), elastic constant k and pitch length P as: [121] 2 2 τ1 = γ 1P /[ k(2 π )] (8) When E >E c, the relaxation exhibits a double relaxation property, as the contribution of lattice distortion starts to increase. [61] The lattice distortion recovering is a relatively slow process, in the order of a few milliseconds or longer, and the process is affected by polymer concentration. A higher polymer concentration leads to more rigid polymer network, thus the lattice is more likely to resist the distortion with the same applied voltage. With a smaller distortion, the time it takes to recover the lattice distortion τ 2 is shorter. The total relaxation time τ, which is determined by the two relaxation processes, is also affected by applied voltage. With a higher voltage, the local reorientation angle is larger, so it takes a longer time for the LC molecules to go back to the original twisted state; a higher voltage also induces a larger lattice distortion, and consequently, the recovering is slower as well. To achieve a fast response time, it is important to drive PS-BPLC with electric fields below E c. In that case, τ can be reduced to approximately τ 1. In addition methods to reduce the reorientation response time have been proposed such as decreasing the helical pitch P (increasing chiral dopant concentration), [70,122] reducing viscosity γ 1 with dilutors, [57,122] and increasing elastic constant k according to Equation (8). [59,122] 5.3. Figure of Merit From Equations (7) and (8), one can see that there are tradeoffs between Kerr constant and response time. Improving the Kerr constant may hurt the response time, and vice versa. Thus to comprehensively evaluate the electro-optical performance of PS-BPLC, a figure of merit is defined as: [123] FoM = K (9) τ A high figure of merit requires a larger Kerr constant K and a fast response time τ Hysteresis Hysteresis in PS-BPLC is the discrepancy of electro-optical properties when driven by ascending and descending voltages. [124,125] It affects the accuracy of grayscale control and thus should be minimized. Hysteresis is defined as the ratio of half-maximum transmittance voltage between forward and backward voltage scans ΔV to the maximum transmittance voltage V p. The hysteresis in blue phase is mainly caused by the electrostriction effect and it is a complicated phenomenon which involves the relaxation ability of BPLC, the steric hindrance of polymer network and the anchoring between BPLC and polymer network. [126] As the electric field exceeds E c, the DTC structure starts to unwind and the LC relaxation process does not follow the same route as the rising path, leading to a noticeable hysteresis. [127] Since electrostriction is the root cause of hysteresis at high electric fields, methods have been proposed to reduce hysteresis by suppressing lattice distortion such as increasing polymer concentration, [59,61] improving experimental conditions to achieve more uniform polymer network [128,129] and so on. PS-BPLC materials with a large Kerr constant, fast response time, high figure of merit value and low hysteresis are highly desirable, and would play a critical role in improving the electro-optical performances of PS-BPLC devices. 6. Photonic Applications PS-BPLC has been employed in widespread photonic applications based on the aforementioned properties. Microscopically, the self-assembled lattice structures composed of double twist cylinders result in a natural photonic band gap; the disordered platelet boundaries and index mismatch between polymer and LC lead to scattering; and the LC reorientation under electric field results in the unwinding of DTCs. On the other hand, macroscopically, the refractive index of PS-BPLC can be controlled by electric fields according to extended Kerr effect. As birefringence is induced along the direction of electric field, the quasi-isotropic PS-BPLC is turned to anisotropic. Under certain circumstances, o- wave and e- wave experience ordinary refractive index n o and effective refractive n eff, respectively, thus resulting in phase retardation and polarization change of the light passing through it. Under other conditions, when the light propagation direction is parallel to the optic axis of the PS-BPLC refractive index ellipsoid, the same index n o and phase is seen by different polarizations, thus polarization independence is achieved. By modulating the phase spatially either by non-uniform electric field, or non-uniform Kerr constant, a phase profile modulation with a specific light directing property can be realized. Moreover, the refractive index variation would change the resonance conditions of interference optical filters, shifting the resonant wavelength or modulating the interference intensity. In the following part, we will present the various applications of PS-BPLC classified by their physics underneath, as well as the analysis on the pros and cons of the devices. The selected devices are good representatives of PS-BPLC photonic applications associated with certain physical properties. Some are pioneer work in certain photonic applications, while others are important work on improving the performances of the devices towards practical applications. We hope the paper would provide an up-to-date and comprehensive review on recent development and progress of PS-BPLC in photonic applications, and guide researchers to focus on and address the most important issues remaining in this area in the future Photonic Band Gap: Lasing Due to cubic structures with lattice periods, selective Bragg reflection occurs in BPLCs over a range of wavelength, that is, 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (5 of 28) wileyonlinelibrary.com

6 Figure 2. a) Platelet textures of the PS-BPLC under a polarizing microscope. b) Experimental setup for measuring reflection and emission spectra. c) Reflectance and transmittance spectra of the PS-BPLC. The upper subfigure is for the orange platelet and the lower one is for the blue platelet. d) Laser emission spectra measured in r-cp and l-cp states in the orange platelet (110 crystal). R-cp is right-handed circular polarization and l-cp is left-handed circular polarization. Reproduced with permission. [73] Copyright 2006, Wiley. the photonic band gap or stop band. [73] Owing to the band-edge effect, [ ] lasing could be excited with its peak wavelength located at the high-energy edge of the stop band as long as the gain overcomes the loss. In 2002, Cao et al. demonstrated laser emission in pure BPLC based on the band edge effect, but the temperature range was very narrow. [133] In 2006, laser emission was realized in PS-BPLC by Yokoyama et al. over a wide temperature range 35 C. [73] The BPLC precursor was prepared by mixing a nematic liquid crystal (JC-1041XX/5CB/ISO-(6OBA) 2 ), monomers (12A/ RM257) and a photo initiator (DMPAP) uniformly in the dark. With additional 0.5 wt% laser dye Py597, the sample was filled into a cell with a 13 μm cell gap. By cooling the LC cell at a slow cooling rate 0.1 C min 1, BPI appeared at 39.3 C with domain size up to 50 μm, and then it was stabilized by UV light. In Figure 2a, a microscopic picture of the cured PS-BPLC at room temperature is shown. One can see the characteristic blue phase texture with more color than blue. Without an alignment layer, the BP cubic lattices tend to orient differently from domain to domain, and thus have a set of lattice vectors, (110), (200) and (211) with reflected wavelengths proportional to λ 0, λ 0 /2 1/2 and λ 0 /2 1/3, respectively, as indicated in Equation (1) for BPI. As a result, different colors of reflection are observed. Since the lattice vectors are responsible for the selective Bragg reflections, one can quantitatively investigate the orientation of the blue phase lattice by measuring the reflective optical spectra of the sample. The measurement setup is shown in Figure 2b where white light is reflected by the PS-BPLC sample surface and directed to a spectrometer (USB2000, Ocean Optics). From the reflection spectrum of the orange platelet in Figure 2c, a reflection band is found centered at 647 nm, indicating that in the orange platelet, blue phase lattice structure was preferentially oriented with the (110) plane. And in the blue platelet, the reflection band was centered at 462 nm, which is believed to be associated with the (200) reflection. With the laser dye absorption peak around 536 nm, a pulsed Q-switched Nd:YAG laser (532 nm, 8 ns pulse) was employed to excite laser emission in an orange platelet of the PS-BPLC sample. The excitation laser beam was conducted to the optical microscope and focused to a 50 μm spot at the sample surface through an X20 objective as depicted in Figure 2b. The laser emission was recorded and analyzed using a spectrometer (6 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

7 With the pulsed excitation, right-handed circular polarized single-mode lasing was observed whose spectrum is shown in Figure 2d. The lasing peak wavelength is around 623 nm, which is indeed at the high-energy edge of the stop band due to the (110) reflection. The emission line width is 0.09 nm. Such a narrow bandwidth indicates a high cavity quality (Q) in the blue phase lattice structure. The authors also investigated the effect of excitation energy variation on laser emission intensity. They found that there is a threshold excitation energy 8.3 nj per pulse (or energy per excited area of 0.42 mj cm 2 ) at room temperature. The laser emission intensity grows with excitation energy as long as it exceeds the threshold energy. Owing to the polymer network, blue phase structure could be stabilized over a large range of temperature. Thus, the lasing emission was measured in the PS-BPLC sample between 2 and 38 C to understand the influence of temperature variation. They found that as temperature increases, lasing wavelength is gradually shifted towards the short wavelength, while the threshold energy remains a constant between 2 and 26 C, but is slightly increased at higher temperatures. The wavelength shift is reversible during several repeated temperature change measurements. By the temperature of 40 C no laser emission was detected since the sample had been transferred into isotropic phase. Thanks to the polymer network, the laser emission could be observed over a 35 C temperature range, including room temperature. It exhibits a low threshold excitation energy of about 8.3 nj per pulse and a narrow spectral line width less than 0.1 nm at room temperature. However, lasing emission only occurs in the small single-domain platelet (tens of microns). For practical use, it is necessary to obtain a large-area single domain of blue phase, which could be achieved by means of applying an electric field [100,101] or using an alignment layer. [70] 6.2. Scattering: Random Lasing A uniform single domain of blue phase is preferable for laser emission based on band edge effect. On the other hand, scattering in multiple disordered platelets of BPLC would lead to another type of lasing: random lasing. Random lasing, [134,135] which arises from multiple scattering and interference effect in a chaotic amplifying medium, has found wide applications in speckle-free imaging, [136] medical diagnostics [137] and document coding. [135] In BPLC, the discon - tinuous grain boundaries among platelets give rise to multiple scattering, and in PS-BPLC, the refractive index mismatch between polymer and liquid crystal results in additional light scattering. The scattering, when coupled with gain provided by a laser dye, leads to random lasing as reported by Chen et al. [74,75] In their experiments, the authors prepared a BPLC sample and a PS-BPLC precursor sample, which had slightly different composites, but the same 1 wt% laser dye. The samples were injected into quartz capillary tubes with a length of 2 cm and a diameter of 100 μm. The volume of the tubes is relatively large so that light could follow closed-loop paths and experience resonant feedback in any direction. The tubes filled with the precursor were polymerized at the temperature of 39 C, resulting in a PS-BPLC with the BPI-ISO transition temperature at 56.2 C. As illustrated in Figure 3a, when light undergoes multiple scattering, some manages to return to their starting point with constructive interference. Thus the closed-loop paths lead to coherent (resonant) feedback in the gain medium. If the gain exceeds the scattering loss along the path, random lasing occurs. In the experiment for investigating random lasing action, an optically excited second harmonic Q-switched Nd: YAG laser (λ = 532 nm) was used as the pump, which was operated with a pulse duration of 8 ns and a repetition rate of 1 Hz. The laser beam was focused onto the sample with a spot size (elliptical in shape) mm 2 ( 90 μm along x-direction and 2.5 mm along y-direction). A spectrometer was placed at the end of the capillary tube to detect the emitted signal. The emission spectra of a pure BPLC tube and a PS-BPLC tube are plotted in Figure 3c and d respectively. The emission profile of the pure BPLC (at room temperature) consists of several discrete lasing modes (Δλ = 1.2 nm) due to the randomly distributed BP platelets. When the BPLC was cooled to cholesteric phase, the platelets disappeared and the highly diffusive focal conic texture lead to random diffusive walk instead of resonant closed loops. Thus a relatively even profile (Δλ = 8 nm) was generated. When the BPLC was heated above clearing point, BP platelets also disappeared and the emission became mainly spontaneous due to lack of scattering. Moreover, even with the same experiment conditions, the emission profile of a pure BPLC tube changed stochastically from pulse to pulse. With a slower cooling rate, larger platelets were formed, resulting in more stable and repeatable emission spectra. On the other hand, the PS-BPLC tube exhibited several different behaviors attributed to the more stable structure anchored by the polymer network. When the cooling and heating processes had been repeated several times, the platelet texture tended to be stabilized over time and the emission modes were similar in almost every pulse. Another distinction from pure BPLC is that even when the PS-BPLC was heated above clearing point, laser emission could still be observed. Although the blue phase double twist cylinder structure vanished in the isotropic phase, the index mismatch between polymer and LC still existed, giving rise to scattering and enabling laser emission. Figure 3b shows the dependences of the peak emission intensity and linewidth in a PS-BPLC tube on excitation energy density per pulse at room temperature. One can see that there is threshold energy density 401 μj mm 2 per pulse. The random lasing in BPLC exhibits emission spectra with broad bandwidth, which could be tuned by temperature variation; but in this un-optimized set up, the threshold energy is fairly high. It is interesting to observe the occurrence of random laser emission in pure BPLC and PS-BPLC, as well as their unique laser emission properties. With broad temperature range, alignment free, optically isotropy and polarization independence, PS-BPLC should be attractive in the field of random lasing. And the investigation in this pioneer work should inspire more new explorations in related areas WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (7 of 28) wileyonlinelibrary.com

8 Figure 3. a) Diagrammatic sketch of random laser action in the dye-doped BPLC sample. b) The peak intensity and line width of the emission in a PS-BPLC sample as functions of the excitation energy density. c) Emission spectra of the pure BPLC sample in different phases. d) Emission spectra of the PS-BPLC sample in different phases. Reproduced with permission. [74] Copyright 2012, The Optical Society Unwinding of DTCs: Dye Doped Electro-Optical Switch Lin et al. demonstrated a reflective electro-optical switch using a dye-doped PS-BPLC composite based on the unwinding of DTCs in response to electric fields. [138] The switch does not require a polarizer, and can be switched from a normally dark state to a voltage-assisted bright state. The switch could be used for shutter glasses of three dimensional displays, electronic papers etc. The operation principle of the switch is shown in Figure 4. At voltage-off state, the dye molecules align with LC directors in the double twist configuration. Thus light polarized in any direction experiences the same absorption coefficient, α ave (α // +2 α )/3, where α // is the absorption coefficient Figure 4. Structure and operation principle of the dye doped polymer-stabilized blue phase liquid crystal switch at a) voltage-off state and b) voltageon state (8 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

9 along the long axis of dye molecules, α is the absorption coefficient perpendicular to the long axis. As a result, a dark state is achieved due to dye absorption. When a relatively large voltage is applied between the two indium-tin-oxide (ITO) electrodes, LC molecules tend to unwind and reorient vertically. Hence, the absorption coefficient is reduced to a value approximately equal to α. Consequently, the absorption drops dramatically and a polarization independent bright state is obtained in reflective mode. By varying the voltage, different gray levels of reflectance can be realized. The reflectance of the switch increases from 21% to 68% as voltage increases from 0 to 100 V rms, giving a contrast ratio 3.23:1. Here the absorption coefficients of the dye at λ = 543 nm are α = 1.35 μm 1 and α // = μm 1, respectively. When V>100 V rms, the reflectance starts to saturate since both LC and dye molecules have been reoriented almost perpendicular to the substrates. The voltage-dependent-reflectance curves do not change much as the polarization of incident light is varied. Hence, the device exhibits polarization independent property. However, there is a noticeable hysteresis between the forward and backward scans, due to the relatively large electric field (for the 7 μm LC cell), and the intrinsic properties of this particular BPLC material. The rise time of the switch is 1.16 ms and decay time is 4 ms as it is switched between 0 and 100 V rms. The decay time is relatively slow compared to other PS-BPLC devices. That is because under high electric field, LC molecules are reorientated with a large angle, and thus it takes a longer time to go back the double twist state. Moreover, lattice distortion starts to occur, further slowing down the response. The three-dimensional DTC structure of BPLC allows for polarization free operation of the switch at both off and on states, and thus no polarizer is needed. Without light loss due to polarizer, the switch could achieve high optical efficiency for unpolarized light. However, the contrast ratio is fairly low, which could be improved by choosing dyes with higher dichroism ratios. [139] 6.4. Phase Retardation: Variable Optical Attenuator (VOA) Variable optical attenuator is a useful fiber-optic device, which could reduce the power of an optical signal to different degrees. [140] VOA is an important device in various areas such as telecommunication, sensing and integrated optics. Hu et al. proposed a polarization-independent reflective type variable optical attenuator using an in-plane-switching (IPS) PS-BPLC cell. [141] Featuring a normally-off state, the VOA can be tuned over a range of -29 db from 1480 nm to 1550 nm with attenuation fluctuation less than 0.4 db. Covering the whole telecomm S-band and part of the C-band, [141] the VOA may open the gateway to wider applications of PS-BPLC in fiber-optics. The operation principle of the proposed VOA is illustrated in Figure 5. As light passes through the polarization beam displacer (PBD), o-beam and e-beam are vertically displaced by a small distance without changing the propagation direction. An IPS PS-BPLC cell, which has electrode width and electrode gap both 10 μm, and cell gap 9.5 μm, is placed behind the PBD. The electrode strip direction is set 45 o with the polarization directions of o-beam and e-beam. At voltage-off state, the Figure 5. Working principle of the PS-BPLC based VOA a) voltage-off state and b) voltage-on state WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (9 of 28) wileyonlinelibrary.com

10 Figure 6. a) Working principle of the PS-BPLC microlens with a hole electrode. b) Measured CCD images of 2D microlens array at 0 and 100 V rms. Panel (b) reproduced with permission. [87] Copyright 2010, American Institute of Physics. PS-BPLC is quasi optically isotropic, and no phase retardation is experienced by either o- or e-beam. Thus the polarization of either beam is unchanged, and the reflected beams cannot be coupled back into the incident location as shown in Figure 5a. And that is the dark state. When there is an applied voltage, birefringence is induced in the PS-BPLC. O-beam and e-beam will experience the same amount of phase retardation after a roundtrip and position swap. If the total accumulated phase retardation is π, the polarization directions of both beams will be rotated by 90 o. Thus, after passing through the PBD again, both beams are coupled back as shown in Figure 5b and a bright state is achieved. By varying the applied voltage, the phase retardation other than 0 or π can be achieved, and the output intensity can be adjusted to different gray levels. The attenuations (db) at different voltages were measured. As soon as voltage increases, the attenuation decreases continuously, showing no threshold voltage, similar to an IPS BPLC display. With the Kerr constant of the PS-BPLC 1.87 nmv 2, a maximum (0 db) transmitted intensity is achieved at 37.5 V for λ = 1550 nm, while the maximum attenuation (-29.2 db) is at 0 V. So the VOA can provide an attenuation range of db for λ = 1550 nm. The attenuation over the spectrum range from 1480 nm to 1550 nm could be conveniently tuned by voltage, and the attenuation fluctuation is relatively small. Thanks to the low operation voltage, the main electric field effect involved is local reorientation. Hence, the hysteresis is rather small and response times at different voltages are all in the submillisecond range. However, there are still some scattering causing optical loss, and the transmittance of the PS-BPLC cell is relatively low due to the dead zones in the IPS mode. [62] Employing uniform electric fields such as in the case of vertical field driving mode [69] can help boost the optical efficiency Phase Modulation As the macroscopic refractive index of a PS-BPLC is controlled by electric field according to extended Kerr effect, the phase accumulated along the optical path of light, is modulated as well. The phase profile can be controlled by non-uniform electric fields or non-uniform Kerr constant distribution. If the electric field in a PS-BPLC device is parallel to the light propagation direction, it tends to exhibit polarization independent property; [85] if there are electric field component perpendicular to light propagation direction, it will behave differently for o- and e-waves. Under the latter circumstance, usually either pure o- or e-wave is used to get pure phase modulation Lenses Hole-Patterned Electrode Lens: In 2010, Prof. Lin from Taiwan National Chiao Tung University demonstrated a microlens array using a PS-BPLC. [87] It employs a patterned electrode to generate inhomogeneous electric field and realize a lens phase profile. The lens array exhibits relatively fast response and polarization insensitivity. The device structure and operation principle of a microlens in the array are shown in Figure 6a. The PS-BPLC is sandwiched between two ITO glass substrates. The cell gap is maintained as 20 μm. An Aluminum electrode, which has a hole with a (10 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

11 diameter of 250 μm in the center, is coated on the top glass substrate. And a planar ITO electrode is coated on the bottom substrate. With the absence of electric voltage, the PS- PBLC is quasi-optically isotropic, and the effective optical index-ellipsoid is sphere-like. The off-state refractive index of the PS-BPLC is n iso. When a voltage is applied across the cell, inhomogeneous vertical electric fields are generated due to the hole pattern of the top electrode. Since the electric field is much stronger at the edge than that in the center of the hole, the induced refractive index ellipsoid of the PS-PBLC is elongated to different degrees along the radius as shown in Figure 6a. If the incident light is in the vertical direction as well, which is parallel to the optic axis of the anisotropic BPLC, it will experience ordinary refractive index n o (E) n iso -Δn(E)/3 regardless of polarization, making the device polarization insensitive. At the edge of the aperture, n o is lower than that in the center, due to larger induced birefringence Δn(E). Hence, with the uniform cell gap and non-uniform refractive index, a positive-lens-like phase profile is achieved. By varying the applied voltage, the phase profile can be continuously adjusted, resulting in the change of focal length. With a 100 V rms voltage, a 13.1 cm focal length is obtained. Figure 6b shows the images captured by a charge-coupled device (CCD) of a collimated unpolarized laser beam after passing through the lens array. The CCD was placed at a distance 13 cm from the lens array. The left image is at voltageoff state, and the right image was taken at 100 V rms. One can clearly see focal spots with an applied voltage of 100 V rm. And this focusing effect is independent of light polarization state thanks to the vertical electric field applied. The hole-patterned electrode PS-BPLC lens is simple, fast response and with polarization insensitivity, but the lens profile shape cannot be well controlled. The operation voltage is still high. Curved Electrode Lens: Li et al. proposed a PS-BPLC microlens design employing a curved ITO electrode. [85] With a buffering polymer layer beneath the curved electrode, a non-uniform electric field with little horizontal component is generated, giving rise to good polarization independence. By shaping the curved electrode, the phase profile of the lens can be optimized to achieve a parabolic shape, which is desirable for suppressing aberrations. The cross section of the microlens array is shown in Figure 7. A curved ITO electrode is coated on the inner surface of the top glass substrate. Beneath the ITO electrode, there is a polymer buffering layer. The edge thickness of the polymer layer d 2 is much smaller than the center thickness d 1 due to the curved shape of the top electrode. Between the polymer layer and a bottom flat ITO electrode, there is a uniform PS-BPLC layer with a thickness of d LC. As shown in Figure 7, at voltage-off state, the PS-BPLC exhibits uniform and isotropic refractive index n iso. Thus, phase profile is flat, and normal incident light will pass through the cell without changing direction. With a voltage drop between Figure 7. Working principle of the PS-BPLC microlens with a curved electrode. the two ITO electrodes, a non-uniform vertical field is generated in the PS-BPLC layer. In the center of the lens where the gap is the largest, the electric field is the weakest, and induced birefringence is the smallest; and at the edge where the gap is the thinnest, the induced birefringence is the largest. For normally incident light, it sees a reduced refractive index n o (E), which decreases with radius from the center to the edge. Hence, a positive lens phase profile is formed. To validate the design concept, simulation was carried out. First, the distribution of electric potential in the PS-BPLC layer was obtained using a commercial software Dimos (AUTRONIC- MELCHERS, Germany). Then electric field was extracted using Possion s equation. [142] Next, according to extended Kerr model, the refractive index ellipsoids of the anisotropic PS-BPLC were calculated. The magnitudes of refractive index along long and short axes are n e (E) n iso +2Δn(E)/3 and n o (E) n iso -1Δn(E)/3, respectively. The direction of the long axes was assigned along the direction of electric field. The phase profiles for polarizations parallel and perpendicular to the paper plane were accumulated along the optical path, respectively. In such a design, the shape of the curved ITO electrode plays a key role in determining the phase profile. With an optimized electrode shape like the Eiffel-Tower, a phase profile resembling a parabolic shape is realized. Thus the spherical aberration could be minimized. The focal length of a microlens in the array can be calculated according to: [85] f LC 2 = R (10) 2 δned ( ) where δn(e) is refractive index difference between the center and edge of the lens, d the cell gap, and R the semi-diameter of the lens aperture. Assuming that the structural parameters are R = 225 μm, d 1 = 76 μm, d 2 = 2 μm, and d LC = 17 μm, and the blue phase material has a saturation birefringence Δn = 0.2 and saturation field E s = 5.6 V/μm, the focal length of the microlens could be tuned continuously from infinity to 4 cm for 633 nm as voltage increases from 0 to 100 V rms. Moreover, the focal lengths for the orthogonal polarizations (parallel and perpendicular) overlap very well, proving the lens is indeed 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (11 of 28) wileyonlinelibrary.com

12 polarization independent. This is attributed a lot to the buffering polymer layer beneath the curved electrode. Since electric field tends to be perpendicular to the surface of conductive electrodes, it has relatively large horizontal component near the curved electrode. If a horizontal electric field component is present in the PS-BPLC layer, birefringence will be induced in directions other than vertical, leading to different refractive indices for different polarizations. Thanks to the buffering layer, a great portion of horizontal electric field component is confined in the polymer layer instead of the BPLC layer, resulting in polarization independence. Of course, the introduction of such a polymer layer will inevitably shield some voltage drop, and increase the operation voltage. Moreover, it is relatively difficult to fabricate such a curved electrode with desired shape. Multi-Ring Electrode Lens: Lee et al. proposed a polarization insensitive PS-BPLC lens whose phase profile was realized by controlling the voltages on multiple electrodes. [83] With all electrodes being flat planar structures, the fabrication of the lens would be much simpler. Moreover, the voltages can be dynamically tuned so that a favorable parabolic phase profile could be achieved at any focal length. The cross section of the lens is shown in Figure 8a. There are multiple ring electrodes with different widths on the top glass substrate and a planar electrode on the bottom substrate. To smoothen the phase profile, there is a thin dielectric layer beneath the top ring electrodes. Its dielectric constant is chosen to be relatively high, so that voltage shielding effect could be suppressed. Otherwise a great portion of voltage will be dropped on the dielectric layer instead of being utilized by the PS-BPLC layer. The voltages on the ring electrodes are adjusted to realize a desired phase profile. The high dielectric constant layer also shields the fringing field between adjacent ring electrodes. So in the PS-BPLC layer, the electric field is almost vertical, reducing the polarization dependency. The simulation results verify that indeed the phase profile is insensitive to polarization variation. The multi-electrode PS-BPLC lens possesses several attractive features: fast response, polarization insensitivity, simple structure and parabolic phase profile, but multiple data addressing is needed for multiple electrodes. Resistive Film Electrode Lens: Li et al. proposed a PS-BPLC cylindrical lens using a resistive film whose phase profile could approximate parabolic shape in a large tuning range only using one data addressing. [84] As depicted in Figure 8b, a PS-BPLC layer is sandwiched between a bottom ITO electrode and a top resistive film. On top of the film, there is one center ITO electrode strip in the middle, and one edge ITO electrode strip on each edge. The resistive film is transparent and has a large resistance. [143,144] Thus when there is a voltage between the edge Figure 8. Working principle of a) the PS-BPLC GRIN lens with multi-ring electrode and b) the PS-BPLC cylindrical lens with a resistive film. electrodes and the center electrode, the electric potential on the film is almost linearly changing. If the electric field is relatively low, induced birefringence basically follows Kerr effect. So the linear varying potential on the resistive film leads to a parabolic distribution of refractive index and phase automatically. The lens could realize parabolic phase profile within a large tuning range using one data addressing, making full use of the Kerr effect. But the fabrication process is complicated, and there might be some unwanted heat due to current flowing in the resistive film. Two Kerr-Constant Layer Lens: Li et al. also proposed an adaptive microlens consisting two PS-BPLC layers, which are separated by an curved interface. [88] The top PS-BPLC layer resembles a convex lens and bottom layer is like a concave lens. The Kerr constant of top layer PS-BPLC is much smaller than that in the bottom layer. At zero-voltage state, the PS-BPLCs in both layers are in quasi-optically isotropic state with a refractive index n iso, resulting in a flat phase profile. When a voltage is applied between top and bottom ITO electrodes, a vertical electric field is generated with good uniformity because of dielectric constant match in the two BPLC layers. In the top layer, owing to the small Kerr constant, induced birefringence is negligible and refractive index remains almost unchanged n iso. In the bottom layer, however, much larger refractive index is induced in the vertical direction. For normal incident light, it sees n o (E) in the bottom PS-BPLC layer and n iso in the top layer. Since (12 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

13 n o (E) < n iso, a positive lens structure is revealed. The phase profile can be calculated using: [ ] Φ ( re) = n n ( E) d() r (11), iso o where r is the distance from the center of the lens, and d(r) the thickness of the top PS-BPLC layer. If the interface has a parabolic shape, then the profile shape will always maintain the parabolic shape. As voltage is varied, different focal lengths can be obtained. Besides fast response and polarization independence, the lens is capable of generating the desired parabolic phase profile within a large dynamic range. However, the fabrication of such two-layer structure is rather challenging. Spatially Distributed Kerr Constant Lens: Lin et al. also presented a PS-BPLC microlens array utilizing spatially-distributed Kerr constant. The Kerr constant of the PS-BPLC varies parabolically as a function of radius. Therefore, with a uniform vertical electric field, a parabolic phase profile can be achieved for normal incidence at any applied voltage for any polarization. But the difficulty lies in the formation of BPLC materials with the desired distribution of Kerr constant. Fresnel Lens: Aside from PS-BPLC lenses with a continuously tunable focal length, a Fresnel type PS-BPLC lens was demonstrated with continuously tunable efficiency and fixed focal length by Lin et al. [86] In the proposed structure, the top electrode has the Fresnel even-zone pattern. When a voltage is applied, electric field is concentrated in the even zones. Thus the induced refractive index is smaller in the even zones than that in the odd zones according to extended Kerr effect. For normally incident light, it sees n o, and accumulates the phase in even and odd zones. Therefore, the Fresnel phase profile can be achieved. By varying the applied voltage, the phase contrast can be modulated, and efficiency be tuned. The grating achieves a maximum diffraction efficiency 34% at 130 V (E = 4.81 V μm 1 ), and exhibits polarization independence at different voltages. Compared to conventional nematic LC lenses, PS-BPLC lenses could easily achieve polarization insensitivity, which could remove the need for a polarizer in front of the devices, and thus double optical efficiency if incident light is unpolarized. And the submillisecond fast response, which is independent of cell gap, would enable PS-BPLC lenses to be used for wider applications that require rapid change of focal length. However, the main problem with most PS-BPLC lens is that only a small phase difference can be achieved with a high operation voltage ( 100V), since the refractive index change is from n iso to n o, which is less than 1/3 of the intrinsic birefringence of LC host. And that leads to relatively long focal length and small numerical aperture. Hence, PS-BPLC lenses are usually in the forms of microlens arrays or GRIN lenses. The extension of aperture and reduction of focal length rely heavily on the material and device advancements on reducing the operation voltage. could be formed. To realize a PS-BPLC grating, one can either use non-uniform electric field in a uniform PS-BPLC material, or use uniform electric field in a non-uniform material. For the former, the device structure is more complicated in order to realize the desired electric field distribution; whereas for the latter, more efforts are needed in preparing materials with periodic electro-optical properties. In-Plane-Switching Grating: Yan et al. demonstrated a polymer-stabilized blue phase liquid crystal grating using an IPS electrode cell in [76] The grating exhibits a high diffraction efficiency for e-wave due to a sharp phase profile formed in the PS-BPLC. The device structure of the grating is shown in Figure 9a. On the inner surface of one glass substrate, there are interdigital in-plane-switching ITO electrodes. Here both the electrode width and electrode gap are 10 μm; in the 7.5 μm gap between the top and bottom substrates, there is a PS-BPLC layer. With the absence of electric voltage, due to the index mismatch between the thin ( 40 nm) ITO electrodes and the quasi-isotropic BPLC, light is slightly diffracted. This diffraction effect is negligible and most beam energy is still concentrated in the zeroth order as shown in Figure 9b. With a voltage is dropped between adjacent electrodes, an electric field with periodic distribution is formed. In the region right above the electrodes, electric field is mostly vertical, resulting in a reduced refractive index n o for both parallel and perpendicular polarizations. On the other hand, in the region between the interdigital electrodes, electric field is mostly horizontal. Then perpendicular wave (o-wave) will experience a reduced index n o (E), while parallel wave (e-wave) will experience an increased index n e (E). Because of the periodic refractive index distribution, periodic accumulated phase distribution is formed and as a result diffraction occurs. The polarization parallel to and the polarization perpendicular to the paper plane, experience dramatically different phase change in most regions for a probe beam. The total phase contrast of parallel polarization is much larger than that of the orthogonal polarization, and thus, a larger diffraction efficiency can be achieved at the same applied voltage. Diffraction pattern is shown in the lower part of Figure 9b when the incident light is polarized parallel to the paper plane and behaves as e-wave at 160 V. One can see that a great amount of energy is transferred to the first orders. The diffraction efficiencies for different orders versus applied voltage for parallel polarization were measured. Here, the driving voltage is an 1 khz square wave. As voltage increases, the first order diffraction efficiency increases first Gratings When the phase of a PS-BPLC device is spatially modulated with a period, a grating Figure 9. a) Working principle of the PS-BPLC grating using an IPS electrode cell. b) Recorded diffraction patterns at 0 V and 160 V. Panel (b) reproduced with permission. [76] Copyright 2011, The Optical Society WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (13 of 28) wileyonlinelibrary.com

14 and then decreases, achieving high peak transmittance 40% at about 160 V. Unlike in conventional LC gratings where LC director distribution is smoothed out, in PS- BPLC gratings, induced birefringence well follows the electric field due to the short coherent length of BPLC material. At the edges of the electrodes, the abrupt change of electric field results in a sharp rectangle-like phase profile, and consequently, the diffraction efficiency is greatly enhanced. The high driving voltage is one of its main disadvantages. The response time of the PS-BPLC grating was measured as it was switched between zero voltage and 160 V. The switch-on and switch-off times are both less than one millisecond. 1D/2D Switchable Grating Using Orthogonal IPS Electrode Groups: In 2012, Zhu et al. from Shanghai Jiao Tong University demonstrated a 1D/2D switchable PS-BPLC grating using two orthogonal in-plane-switching electrode groups. [77] As shown in Figure 10a, the interdigital electrodes on the top and bottom glass substrates are orientated 90 with each other. At voltageoff state, there is only negligible diffraction effect caused by the index mismatch between the ITO electrodes and PS-BPLC as shown in Figure 10b. By applying a voltage between the top interdigital electrodes, while keeping the bottom electrodes are floating, a 1D grating is formed as periodic refractive index distribution is formed near the top substrate along y axis. Its electro-optical properties are similar to those of the single-side IPS PS-BPLC grating. [76] On the other hand, if the bottom interdigital electrodes have voltage on, while the top ones floating, another 1D grating is formed but oriented along x direction. The 1D grating diffraction patterns are shown in Figure 10b. When a voltage is applied between both top interdigital electrodes and between bottom interdigital electrodes, the top and bottom layers of BPLC would exhibit orthogonal refractive index distributions. As a result, a 2D grating is switched on and the diffraction pattern is shown in Figure 10b. In 1D mode, as voltage increases, the zeroth order intensity decreases and higher order intensities start to rise. At 42.5 V, the first order achieves a peak diffraction efficiency of 37.2%. When the grating is operated in 2D mode, the voltage drop between bottom adjacent electrodes and that between top adjacent electrodes are kept the same. With increased voltage, diffraction efficiencies of the surrounding orders increase as well. At about 55 V, the diffraction efficiencies of 01, 10 and 11 orders reach 11.3%. In order to understand the diffraction phenomenon, simulation was carried out to calculate the phase profile in the grating. In the 1D mode (voltage applied between bottom interdigital electrodes), the phase profile is slightly asymmetric due to the existence of the top electrodes, and thus deviates from a rectangular shape. So the diffraction efficiency for 1D operation is slightly lower than that in the single-side IPS grating. [76] The measured rise time is 561 μs and decay time is 910 μs. The grating still employs in-plane-switching electric field, and it exhibits similar electro-optical properties as the previous one: fast response and high diffraction efficiency. The lower Figure 10. a) Schematic diagram of the 1D/2D switchable PS-BPLC grating using orthogonal IPS electrodes. b) Diffraction patterns of the PS-BPLC grating using orthogonal IPS electrodes at different voltages. c) Structures and working principles of the 1D grating and 2D grating using vertical fields. Panel (b) reproduced with permission. [77] Copyright 2012, American Institute of Physics (14 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

15 operation voltage 42 V is achieved by using a larger-kerr-constant BPLC material, with saturation birefringence 0.12 and saturation electric field 4 V μm 1. With orthogonally arranged IPS electrode strips, the grating can be conveniently switched between 1D mode and 2D mode. 1D/2D Gratings Driven by Vertical Fields: The lateral field (in-plane-switching) tends to yield relatively large refractive index difference δn(e) (for completely horizontal electric field, δn(e) n e (E)-n o (E) = Δn(E)) in a PS-BPLC cell, however, the horizontal component of electric field leads to different refractive indices for different polarizations. Later in 2012, Zhu et al. from Nanjing University proposed a vertical field driving method to realize 1D/2D polarization independent PS-BPLC gratings. [79] Aside from high efficiency and fast response, the diffraction effect of the gratings is independent of light polarization thanks to the vertical field employed. The device structure and working principle of a 1D PS-BPLC grating using a vertical field are depicted in Figure 10c. On the bottom substrates, there are strip electrodes (electrically connected) with electrode width 10 μm and electrode gap 10 μm. On the top substrate, there is a planar ITO electrode. The cell gap is also 10 μm. At voltage-on state, the vertical field is the strongest in the PS-BPLC regions on top of the bottom strip electrodes. Thus in these regions, birefringence is induced in the vertical direction, and a reduced refractive index is experienced by normally incident light regardless of polarization; whereas in the regions between the strip electrodes, the refractive index of PS-BPLC remains approximately unchanged as n iso, which is also independent of polarization. Therefore, with the assistance of the patterned vertical field, periodic refractive index distribution and phase profile are formed, and a polarization independent 1D grating is realized. The device structure of a 2D BPLC grating driven by a vertical field is also shown in Figure 10c. There are orthogonal strip electrodes on top and bottom substrates, and no voltage difference between adjacent electrodes on the same substrate. The electrode width and gap are the same as in the 1D grating, but the cell gap is slightly larger 12 μm. When a voltage drop exists between top and bottom electrodes, a vertical field with orthogonal lateral periodic distributions is generated. In the regions where the top and bottom electrodes are overlapped, vertical field is the strongest, and BPLC exhibits a significantly reduced refractive index n o (E); while in the other regions, electric field is much weaker, and the refractive index of BPLC remains almost unaltered as n iso. Consequently, a 2 dimensional refractive index distribution is obtained, and the 2D grating is switched on. Similar to the 1D grating, due to vertical field driving, the electro-optical performances of the 2D grating are also polarization independent. As the 1 khz square-wave voltage applied on the 1D grating increases, from 0 to 55 V, the transmittance of first order keeps on increasing as well, without reaching a maximum for a 633 nm probe beam. But, at 55 V, the first order diffraction still reaches 38.7%. For the 2D grating, a maximum diffraction efficiency 17.8% is achieved at 60 V. Moreover, as the polarization angle of the incident linear polarized light changes, the variation of diffraction intensities is negligible, proving that the gratings are indeed polarization independent. In the vertical field driven BPLC gratings, the refractive index difference between the field-strong regions and fieldweak regions δn (n e -n o )/3 is much smaller than that in the in-plane-switching structure [76] δn (n e -n o ). However, since the vertical field penetrates deeper into the whole LC layer (12 um), all these LC molecules would contribute to the phase accumulation along the optical path, while in in-plane-switching structures, the penetration depth of electric field is rather small 3 5 μm. Therefore the total accumulated phase differences are comparable in the two cases, and diffraction efficiencies are similar. The response times of the grating are also in the submillisecond range. Dual Period Grating: In 2015, Yan et al. from Southeast University proposed a dual-period tunable PS-BPLC grating combining in-plane-switching field and vertical field. [81] The smallperiod grating achieves a peak diffraction efficiency of 35.3% and the large-period grating has a maximum efficiency of 28.7%. The device structure and working principle are illustrated in Figure 11a. The cell consists of a planar ITO electrode and a pair of interdigital electrodes (Comb A and Comb B) on two substrates, respectively. There are two operation modes with different voltage driven schemes: large-period mode and smallperiod mode. If it is operated in the large-period mode, one of the interdigital electrodes (Comb A or Comb B) is floating, and between the second interdigital electrode (Comb B or Comb A) and the planar electrode, there is a voltage drop. Thus vertical electric field is the strongest in the PS-BPLC layer on top of the second interdigital electrode, inducing birefringence; while in other regions, PS-BPLC is quasi-optically isotropic. Resultantly, a grating profile whose period Λ L = 2(w+l) is formed. When the grating is operated in the small-period mode, a voltage is applied between the top planar electrode and the two interdigital electrodes (Comb A and Comb B are electrically connected). Then periodic electric field and induced birefringence distribution are achieved with a period Λ S = w+l. The diffraction patterns of the dual period grating with different applied voltages (100 Hz) are displayed in Figure 11b. The left-side patterns are for the large-period mode, and the right-side ones are for the small-period mode. One can see that as voltage increases, energy is transferred from the zeroth order to higher orders. In both modes, the +mth order and -mth have similar intensities for the symmetric structures. The diffraction angle of the first order in the large-period mode is measured as 0.565, and that in the small-period mode is The angles agree well with the theoretical values predicted by sinθ m = mλ/λ, where m is the diffraction order, θ m is the diffraction angle of the mth order, and Λ is the grating period. By changing the driving scheme, large period mode and small period mode can be switched conveniently. The grating could realize 5 optical switching ports while the conventional grating could only realize 3. The small-period mode has high diffraction efficiency while the large-period mode has lower efficiency. The response time is fast but voltage is high. Fork Gratings: Optical vortices with helical wave fronts [145,146] have found wide applications in astronomy, informatics and micro-manipulation. Fork grating, which has dislocations in the center, is a diffraction grating that can conveniently generate optical vortices. [147,148] In 2014, Hu et al. demonstrated a 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (15 of 28) wileyonlinelibrary.com

16 Figure 11. a) Schematic drawing of the device structure and working principle of the dual period PS-BPLC grating. b) Diffraction patterns of the grating in large period mode (left) and small period mode (right). Panel (b) reproduced with permission. [81] Copyright 2015, The Optical Society. fast-responsive fork grating using a PS-BPLC cell, and realized optical vortex generation. [149] The helical wave front of an optical vortex could be expressed by: Ψ 1 = exp( imθ) (12) where Ψ 1 is the complex amplitude of the electric field, θ is the azimuthal angle of a cylindrical coordinate system (r,θ, z) around the z axis, which is the propagation direction, and m is the topological charge, which can be a positive or negative integer. If such a wave front interferes with collimated reference beam Ψ 2 = exp(ikx), where k is the spatial frequency indicating the tilting angle of the reference beam, then the interference pattern or the hologram could be: H = Ψ 1 +Ψ 2 = exp( imθ) + exp( ikx) = 2[1+ cos( kx mθ)] 2 2 (13) where θ = tan 1 (y/x). The interference pattern with m = 1 resembles the shape of a folk as shown in Figure 12a. Therefore, by generating such a fork-grating phase profile, the helical wave front can be reconstructed if shone with a collimated reading beam. In order to transfer such holograms into a PS-BPLC cell, the authors adopted a multi-step microlithography method to fabricate fork patterned electrodes. [150] The pattern was generated by a computer and loaded on a Digital Micromirror Device (DMD), which served as a dynamic mask for the photoresist. After exposure and development, the patterns were transferred to the ITO layer. The patterned ITO substrate was paired with another planar ITO glass substrate. In between a 12 μm PS- BPLC layer is sandwiched. Thus, by controlling the voltage between the fork ITO electrode and planar ITO electrode, one can control the refractive index contrast and phase difference between adjacent regions conveniently. The physics of the grating are similar to those (16 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

17 Figure 12. a) Schematic drawing of a fork grating electrode with m = 1. Recorded images of the optical vortex captured by a CCD at b) off state and c) on state. Reproduced with permission. [149] Copyright 2014, The Optical Society. PS-BPLC devices using patterned electrodes. [79,86] At zerovoltage state, since the refractive index is uniform across the PS-BPLC cell, only a Gaussian beam is seen in the zeroth order as shown in Figure 12b. When an 80 V rms voltage is applied, optical vortices are observed in the ±1 orders with a characteristic zero energy spot in the center shown in Figure 12c. The brightness (efficiency) of the diffraction orders can be continuously tuned by voltage. At 95 V rms, the efficiency achieves the maximum value 33%. The efficiency is relatively high compared with traditional fork gratings, whose efficiency is usually 13 27%. [ ] But still it is lower than the theoretical limit 40%, which should be attributed to the phase retardation induced by fringing field. Moreover, the voltage-dependent-efficiency curve is insensitive of the polarization of the probe beam under the vertical electric field. The response times of the first order diffraction intensity were also measured as the device was switched between 0 and 50 V rms. The rise time is 364 μs and decay time is 571 μs. The authors also fabricated a PS-BPLC fork grating array. Each fork was assigned with a different m value from 1 to 4. By applying an 80 V rms voltage, the fork structures were clearly revealed in the PS-BPLC. The array could enable rapid changing of orbital angular momentum (OAM), and thus holds great potential in OAM based informatics and micro-manipulations. The fork grating belongs to the gratings driven by vertical field generated by patterned electrodes, but is specially designed for the purpose of optical vortex generation. So it has the general features of those gratings: fast response, polarization independence, high diffraction efficiency and high operation voltage. The optical vortex generator based PS-BPLC holds potential in areas of astronomy, informatics and micro-manipulation. Airy Beam Generator: Airy beam is a diffraction-free beam that accelerates as it propagates. [154,155] It is widely used in optical manipulation, plasma channel generation, optical vortex generation and so on. [ ] Luo et al. demonstrated an electrically tunable/switchable Airy beam using a PS- BPLC cell. The authors first obtained a phase profile by doing the Fourier transform for a two-dimensional Airy Beam with finite energy. [154] Then the continuous phase profile, which ranged from -11.5π to 11.5π, was converted to a binary phase pattern (0 or π values only). With photolithographic method, the binary pattern was transferred to an ITO glass. As the patterned ITO glass was assembled with anther planar ITO glass substrate on the top, a LC cell was formed with a gap d = 8 μm. The cell was filled with a BPLC precursor and then stabilized by UV illumination. Without a voltage, PS-BPLC exhibits an isotropic refractive index n iso, and the phase pattern is not revealed. With a voltage applied, the phase difference between the regions with and without bottom electrodes is induced. As the applied voltage increases, the phase difference increase from 0 to π. To generate an Airy beam, a He-Ne laser beam was expanded and collimated to illuminate the PS-BPLC cell, which was located at the front focal plane of a spherical lens. Thus, the lens performed Fourier transform for the phase profile on the PS-BPLC, and near the back focal length, an Airy beam was reconstructed. With an 120 V voltage, the Airy beam was the brightest and clearest, indicating the phase difference was approximately π. With even higher applied voltage, the Airy beam will become weaker. For the aforementioned PS-BPLC gratings (in-planeswitching or vertical field driven), the grating is formed by using uniform BPLC materials and non-uniform electric field. For those gratings, conventional the material treatment is performed for PS-BPLC, but more efforts are made in electrode design. An alternative way to realize diffraction effect is to use non-uniform material but uniform electric field. Hybrid Grating with Different Curing Temperatures: Lin et al. proposed a hybrid PS-BPLC grating utilizing the dependence of Kerr constant on temperature. [78] With the assistance of a photomask, alternating PS-BPI and PS-BPII regions are obtained by curing at different temperatures. When a uniform electric field is applied, due to the different Kerr constants [159,160] in the PS-BPI and PS-BPII regions, alternating high and low refractive indices are induced, and the diffraction effect can be observed. As it is driven by vertical electric field, the electro-optical 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (17 of 28) wileyonlinelibrary.com

18 Figure 13. a) Fabrication process of the hybrid PS-BPLC grating. b) Fabrication process and voltage-on state of the polymer slices based PS-BPLC grating. properties of the hybrid grating do not depend on the polarization direction of normally incident light. The fabrication process of the grating is shown in Figure 13a. A cell with two planar ITO electrodes but no alignment layer was filled with a BPLC precursor. The cell gap was maintained at 7.5 μm. First, the cell was cured by UV illumination for 30 s in BP I phase at 34 C as it was covered by a photomask whose grating period is 100 μm. Thus, in the irradiated regions, BPLC was stabilized in BPI phase, while in the unirradiated regions, the precursor remained unchanged. Then the sample was reheated to isotropic state and then cooled down to 38 C in BPII phase. During the second exposure, the photomask was removed, so that the rest of the precursor was stabilized in BPII phase. Since the diffusion rate of monomers at different temperatures is different, the polymer network strengths in PS-BPI and PS-BPII regions are also different. A stronger and denser polymer network implies a smaller Kerr constant, and smaller induced birefringence with the same applied voltage; whereas a weaker polymer network indicates a larger Kerr constant. When no voltage is applied between the two ITO electrodes, there is no induced birefringence in either PS-BPI and PS-BPII regions. Due to the quasi- isotropic state of the PS-BPLCs, the two regions have the same refractive index n iso. Therefore, there is no grating structure due to the uniform index distribution. When a voltage is applied, a nearly uniform vertical electric field is generated, but different induced birefringence Δn ind in PS-BPI regions and PS-BPII regions owing to different Kerr (18 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

19 constants. Therefore, the normally incident light experiences different ordinary refractive indices of the anisotropic media n o (E) n iso -1/3Δn ind (E) in different regions. Thus a non-uniform optical phase profile is achieved, and the grating is turned on. As the applied voltage increases, the index difference between PS-BPI and PS-BPII also increases, resulting in a higher diffraction efficiency. By 150 V, the first order diffraction efficiency researches 0.8%. In order to better understand the diffraction phenomenon, the authors also investigated the induced refractive index change in PS-BPI and PS-BPII regions indirectly using two VFS cells. Both cells were filled with the same BPLC precursor as the grating sample, and cured at 34 C and 38 C, respectively. Their index change versus voltage was measured experimentally using the similar optical setup as reported by Cheng et al. [69] The refractive index difference between the two VFS cells increases with applied voltage, and achieves at 150 V. Accordingly the theoretical diffraction efficiency can be calculated as 1.17%, which is very close to the measured value. The relatively low diffraction efficiency is obviously a result of small index difference between PS-BPI regions and PS-BPII regions even at a high voltage. Before polymerization, BPI phase of the precursor appears from 33.2 C to 36.2 C, and BPII appears from 36.2 C to 41 C. Thus the curing temperatures for BPI and BPII could not be chosen too far apart, consequently the polymer network strengths are not significantly different, and the Kerr constants are similar in the two regions. By using a LC host with a higher intrinsic birefringence or choosing a LC cell with a larger cell gap could help improve the diffraction efficiency. The polarization dependence of the hybrid PS-BPLC grating was studied for linearly polarized light with various polarization directions at 0 V, 75 V and 150 V at 25 C with a 633 nm probe beam. The diffraction efficiency is always insensitive to the polarization change. Moreover, the polarization properties of the diffracted beams were analyzed for 0 o and 45 o linearly polarized incident beams respectively, and they found that that the output polarization was consistent with the input polarization, further proving the grating is polarization independent. The measured rising time of the grating is 520 μs, and decay time is 430 μs when switched on and off using a 1 khz 150 V voltage at 25 C. Although the grating shows polarization independence and fast response time, the fabrication process is rather complicated. The diffraction efficiency is low as a result of small refractive index contrast achieved in the two BP phases. Polymer Slice Grating: To achieve larger index contrast and higher diffraction efficiency with a uniform filed, Yan et al. proposed a PS-BPLC grating based on periodic polymer slice structure. [80] It has a relatively high ( 38%) first-order diffraction efficiency thanks to the sharp rectangular phase profile. The fabrication process and operation principle are shown in Figure 13b. First, a photoresist layer (SU-8) was uniformly spincoated on to a glass substrate with a planar ITO electrode. Here SU-8 was on the ITO side of the substrate. Next the photoresist layer was covered with a photomask which had a grating pattern, and then was exposed to collimated UV light. After the photoresist was developed, a grating was formed on the substrate with rectangle shape, and the grating depth was equal to the photoresist thickness. Then the top ITO glass substrate was assembled using an AB glue, and a BPLC precursor was filled into the cell via capillary effect. After being exposed to UV illumination again, blue phase was stabilized in the regions between polymer slices. In the absence of applied voltage, the PS-BPLC exhibits an isotropic refractive index n iso, which is slightly smaller than the refractive index of the polymer slice n p. Hence a small diffraction effect is observed. With a voltage applied between top and bottom electrodes, birefringence is induced in the PS-BPLC along vertical direction, resulting in a decreased refractive index n o for normally light. Meanwhile, the refractive index in the polymer slice regions is fixed. Therefore, the refractive index difference and accumulated phase difference between the PS- BPLC and polymer slices increases as voltage increases. At 42 V, the phase difference achieves approximately π, resulting in the maximum diffraction efficiency 38% for the first order, and zero intensity for the 0th order. The high diffraction efficiency is due to the sharp rectangular phase profile using the photoresist layer; and the low operation voltage is mainly due to the small cell gap 5 μm. As voltage further increases, the phase difference becomes larger than π, and the diffraction efficiency for the first order starts to decrease. Driven by a vertical field, the grating is also polarization independent. With several attractive features such as high diffraction efficiency, polarization independence and fast response, the grating has shown great potential for wide applications. However, the multi-step fabrication process is rather complicated, and with the use of a photomask, the spatial frequency of the grating is limited. One-Step Holographic Grating: Recently, Yuan et al. proposed a PS-BPLC grating fabricated using an one-step holography method. [82] Utilizing interfered light, high spatial frequency could be realized at low cost. Moreover, the fabrication is rather simple. Just with a single holographic exposure, both polymer stabilization and periodic Kerr constant distribution are achieved simultaneously. The setup for the grating fabrication is depicted in Figure 13a. An empty cell with two ITO glass substrates was filled with a uniform BPLC precursor and placed at the intersection of two beams from a Nd:YAG laser (532 nm, 100 mw, Coherent). Different from those precursors mentioned before, the BPLC precursor in this experiment contained a visiblecurable photo-initiator Rose Bengal (Aldrich) and a coinitiator N-phenylglycine (Aldrich). Rose Bengal has an absorption peak near 550 nm, therefore, instead of using UV light for polymerization, they used visible green laser light to realize the polymerization and grating formation simultaneously. Due to the high coherence of laser beams, high-spatial-frequency periodic light patterns could be generated by interference without any mask. As the sample was exposed to the alternating bright and dark light fringes, polymer concentration gradient was achieved due to monomer diffusion as shown in Figure 13b. As a result, in bright regions, polymer network was more rigid, and smaller birefringence was induced when an electric field was applied; and in dark regions, polymer network was looser and induced birefringence larger with the same applied electric field. Hence, the periodic birefringence distribution was realized under a uniform vertical electric field and the grating structure was revealed WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (19 of 28) wileyonlinelibrary.com

20 Diffraction efficiency versus applied voltages (1 khz square wave) was probed by a He-Ne 633 nm laser beam. When the applied voltage is zero, there is a small diffraction efficiency η 0.9%. Although the PS-BPLC is quasi-optically isotropic, the average refractive index of PS-BPLC in bright and dark regions are different due to the polymer concentration gradient. Here the index of the polymer network chain is slightly smaller than the average refractive index of host LC. Thus, a larger polymer concentration leads to a lower average refractive index of PS- BPLC in bright regions n iso,b, ; and a smaller polymer concentration results in a higher average index in dark regions n iso,d. Owing to the index contrast between adjacent regions (δn iso = n iso,b n iso,d <0), weak diffraction occurs. By appropriating choosing index-matching monomers, the off-state diffraction could be reduced or completely eliminated. With the increase of applied voltage, diffraction efficiency decreases to zero at 50 V and then gradually increases to 19.7% by 200 V. Under the uniform electric field, periodic distribution of the field-induced birefringence is generated, due to the sinusoidal variation of the interfered light. Passing through the grating, normally incident light experiences a periodic distribution of the ordinary refractive index n o. The index contrast between bright and dark regions with an applied electric field E is expressed as: δ no( E) = no,b( E) no,d( E) n n ( E)/3 ( n n ( E)/3) iso,b B iso,d D Diffraction efficiency is related to δn o (E) by: [161] 2 2 πdδno( E) η = J1 λ (14) (15) where J 1 is the first-order Bessel function of the first kind, d is the thickness of the grating and λ is the wavelength of the probe beam. As the voltage increases, δn o (E) increases monotonically, from a negative value to a positive one. At 50 V, δn o (E) reaches zero. Based on this theoretical model, simulation was carried out. A good agreement between experimental data and simulation results was found. The grating is polarization independent thanks to the vertical electric field. And the response times of the grating are also within the submillisecond range. The one-step fabrication method based on visible holography, achieves blue phase polymerization and polymer concentration gradient simultaneously, so it offers a novel, simple and low cost approach to fabricate various PS-BPLC devices with high spatial frequency. But the diffraction efficiency is relatively low. Since there are a number of experimental factors such as temperature, light intensity, exposure time affecting both the monomer diffusion and polymerization processes during the holographic exposure, delicate optimization is needed to maximize the extent of the monomer diffusion while blue phase is being stabilized. Then the polymer concentration difference between bright and dark regions would be larger, leading to higher phase contrast and diffraction efficiency. The aforementioned PS-BPLC gratings can be divided into two groups. For the first group whose periodic phase distribution is achieved by patterned electrodes, diffraction efficiency is usually high, approaching the theoretical limit of thin gratings. The high diffraction efficiency is mainly attributed to the abrupt change of phase profile thanks to the short coherent length of BPLC. However, the spatial resolution is limited by fringing field effect at the edge of the patterned electrodes. For the second group, basically the phase difference is achieved by forming materials with periodic distribution of Kerr constant, so the electrodes are simply planar and patternless. For those fabricated using photomasks, the fabrication processes are usually complicated and spatial frequency limited as well. For those fabricated using holographic exposure method, both simple fabrication and high spatial frequency can be achieved, however, diffraction efficiency is relatively low. For both groups, again high operation voltage is a critical challenge for PS-BPLC gratings. Especially for those driven by vertical fields, which tend to exhibit the attractive polarization independent property, thicker cell gap is required to realize sufficient phase difference, resulting in even higher operation voltage General Phase Modulator The aforementioned phase modulating PS-BPLC devices like lenses, gratings are designed for specific applications. A general pixelated phase modulator, which is capable of generating arbitrary phase profile ranging from 0 to 2π, would be more desirable and find wider applications [ ] such as polarization pattern beam generator, computer generated holography, adaptive optics, beam steering, holography and optical correction. Large phase change (at least 2π), fast response and polarization independence are the desired properties for LC phase modulators. Blue phase liquid crystal with submillisecond response time, no requirement on alignment, and quasi-optically isotropic off state is a potential candidate for general phase modulators. Two Pixel PS-BPLC Phase Modulator on Silicon: The application of PS-BPLC in reflective on-silicon projection display using IPS mode was proposed by Rao et al. in [72] For the purpose of phase modulation, in 2014, Hyman et al. reported a reflective PS-BPLC on-silicon phase modulation device driven by a vertical field. [90] The proof-of principle device consisted of a silicon backplane, two aluminum pixels on the backplane, a common ITO electrode on the inner surface of the top glass cover and a PS-BPLC material. The schematic drawing of the device is depicted in Figure 14. The aluminum pixels were made by lithography patterning onto the silicon wafer with a 300 nm layer of silicon dioxide. The cell gap of the PS-BPLC device is maintained at 6 μm. By varying the voltage between an aluminum pixel and the ITO electrode, the phase of each pixel can be continuously tuned. To test its phase modulation ability, Young s double slit diffraction method was employed. A highly coherent laser beam (λ = 653 nm) impinged onto the PS-BPLC cell, which was covered by a double-slit mask. The slit width was 0.55 mm and the separation between the two slits was 0.3 mm. The slits overlapped with the aluminum pixels to ensure good contrast of the interference pattern in the far field, as well as suppressing measurement errors due to fringing field effects and reflections (20 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

21 Figure 14. Schematic of the PS-BPLC on-silicon device. from the silicon backplane between the two pixel electrodes. As the laser beam was reflected back by the PS-BP liquid crystal on silicon (LCoS), it passed through a lens to generate the far field diffraction, which was the Fourier transform of the phase profile at the PS-BP LCoS. The light pattern was further magnified by a 5x objective lens and captured by a CCD camera connected to a computer. First, the interference pattern without any voltage was captured for reference. Then, an AC voltage was applied to one pixel electrode, inducing phase change in the two pixels. The relative phase shift between the two pixels reaches 1.8π at the electric field of 20 V μm 1. The forward and backward scan curves do not overlap with each other, indicating a considerable amount of hysteresis caused by the high electric field. The phase shift measurements were carried out for different polarizations (linear polarized light with different polarization angles, and circular polarized light), and the curves are nearly identical. But the vertical field driven method inevitably increases the difficulty of achieving sufficient phase change. The refractive index changes δn = n iso -n o <Δn/3 induced by a vertical field is less than 1/3 of that in nematic LCs. Therefore, usually a high operation voltage is required. Moreover, in reality, there is not just vertical field confined on top of the pixel electrodes, but also unwanted fringing field generated between pixels due to the small electrode dimension. The fringing field effect was eliminated by using the two slit mask in their experiment, but need to be taken into consideration in real application. Low Voltage PS-BPLC Phase Modulator I: To lower operation voltage and suppress fringe field, Yan et al. from Southeast University proposed a high-resolution reflective mode PS-BPLC phase modulator with a compact optical system. [91] Numerical simulation was carried out to analyze and evaluate the performance of the phase modulator as well as the effect of fringing field. [92] The PS-BPLC cell has a planar ITO electrode on the top substrate and multiple aluminum pixel electrodes on the bottom substrate. Due to the small pixel size of the phase modulator, a fringing field with horizontal field component is generated along with the desired vertical field. Therefore, for normally incident light, the wave polarized perpendicular to the paper plane experiences ordinary refractive index n o, while the wave polarized parallel to the plane sees effective refractive index n eff. To compensate the effect of fringing field on polarization dependence, two beam splitters (BS) and two prisms are inserted into the optical path as shown in Figure 15a. A beam which is polarized parallel to the plane passes through the first beam splitter. Half of the light is reflected by the BS and directed to the PS-BPLC cell, while the other half is transmitted and then absorbed by a light barrier. The first half is then modulated by the reflective PS-BPLC cell by controlling the voltage between the aluminum pixel electrodes and ITO electrode. After the light is reflected back from the PS-BPLC cell, it encounters the first BS again, being divided into a reflective part and a transmitted part again. And the transmitted part undergoes a half wave plate whose optic axis was 45 o angle with respect to the polarization direction. Thus its polarization angle is rotated by 90, which is perpendicular to the paper plane. After passing through two prisms, and the second BS, the transmitted light enters the PS-BPLC cell again, but light is modulated by a different portion of the PS-BPLC cell. Hence, by such an optical system design, the optical phase delay by the PS-BPLC pixel is doubled compared to a traditional reflective PS-BPLC phase modulator. To evaluate the fringing field effect, simulation was carried out for the high-resolution PS-BPLC phase modulator with a pixel electrode width 4 μm and electrode gap 0.5 μm. The cell gap was assumed to be μm and the wavelength in the simulation was 532 nm. As shown in Figure 15b, the phase profile was calculated for a zero-voltage pixel region. The left adjacent pixel (not shown in the figure) had a zero voltage as well, and the right adjacent pixel (not shown in the figure) had a V voltage applied with a target phase delay of 2π. Therefore near the right-hand side edge of the pixel, a fringing field with horizontal component was generated, inducing different refractive indices for different polarizations of normally incident light: decreased index n o for perpendicular polarization (o-wave) and increased index n eff for parallel polarization (e-wave). In the proposed structure, light transverses the PS-BPLC layer as e-wave for the first two times, and passes through it as o-wave for the last two times. As a result, it accumulates both n o and n eff phase delay, thus the fringing field effect is automatically compensated. In Figure 15(b), the phase profile over the pixel in the proposed structure is represented by the pink line. For comparison, the phase profiles in a traditional reflective PS-BPLC phase modulator experienced by o-wave (o-mode) and e-wave (e-mode) were also calculated, and are represented by the blue and red curves, respectively. Due to the transverse fringing field, a phase trough was generated for the o-mode and a phase crest for the e-mode. One can see that using the proposed optical system, the phase profile was significantly improved. To quantitatively evaluate the performance of the proposed PS-BPLC phase modulator, two parameters are defined: evaluation function M ψ and affected region ratio M Λ. As a quantitative measure of the non-uniformity of the phase profile, the evaluation function M ψ is defined as: M ψ σψ ( ( x)) = = ψ ( x) 1 N x [ ψ( xi ()) ψ( x)] i ψ ( x) 2 (16) where ψ(x(i)) is the discrete distribution of the phase delay in the x direction, ψ( x) is the average phase delay value, N x is the number of discrete points along the X axis, and σ( ψ( x)) is the standard error. The affected region ratio M Λ is defined as the ratio of the affected region length to the total length of the pixel region of 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (21 of 28) wileyonlinelibrary.com

22 Figure 15. a) Configuration and working principle of the low voltage PS-BPLC phase modulator I (with an external compact optical system). P1, P2 are prisms, BS1, BS2 are beam splitters, HWP stands for half wave plate, and LB stands for light barrier. b) Phase profiles of o-mode, e-mode in a traditional reflective phase modulator and phase profile of a parallel-polarized incident wave in the low voltage PS-BPLC phase modulator I. c) Configuration and working principle of the low voltage PS-BPLC phase modulator II. Panel (b) reproduced with permission. [91] Copyright 2015, The Optical Society. interest w. The affected region is defined as the region where the phase deviates more than 1/5λ from the ideal phase value, and the total length w is the sum of pixel electrode width and half of the gap (here w = 4+0.5/2 = 4.25 μm). Small values of evaluation function M ψ and affected region ratio M Λ are desired in the phase modulator. The authors investigated the effects of several factors on M ψ and M Λ. When the electrode width decreased from 8 μm to 1.5 μm while the electrode gap was fixed at 0.5 μm, the evaluation function M ψ increased for o-and e-modes, indicating a less uniform phase profile is generated. At the same time, the affected region ratio M Λ also increases dramatically for o- and e- modes as well. However, for the proposed structure, with the decrease of electrode dimension, neither of M ψ or M Λ changes noticeably, and both of them are always much smaller than their counterparts in o- and e- modes. Therefore, it is easier to achieve smaller electrode dimension and higher resolution while maintaining good performances using the proposed phase modulator. With the proposed structure, light transverses the BPLC layer four times, reducing the cell gap required for a 2π phase delay in reflective mode by a factor of 2. The thinner cell gap results in lower operation voltage and smaller fringing field effect. [92,166] Moreover, by automatically compensating the phase delay deviation caused by fringing field, the proposed system has demonstrated superior performance than the (22 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

23 o-mode or e-mode in a traditional reflective PS-BPLC phase modulator according to numerical modelling. However, due to the use of unpolarized beam splitters, a great portion of optical energy is lost. Moreover, the spatial resolution of the modulator is reduced to half since two physical pixels are assigned for one independent gray-level pixel. The two optical paths in the PS- BPLC cell are separated by a large spatial delay (several centimeters) in the beam splitters, thus diffraction would take place as beam propagates, and the phase accumulation calculation should be more complicated. Low Voltage PS-BPLC Phase Modulator II: Peng et al. proposed an alternative approach to double the optical paths and lower the operation voltage for PS-BPLC phase modulators, but without sacrificing the optical efficiency much. [52] Moreover, a larger Kerr constant PS-BPLC material was employed to further reduce the voltage to below 24 V in the entire visible region. But the tradeoff is the slightly slower decay time 3 ms owing to the high viscosity of the large Δε host LC used. The device structure and operation principle are depicted in Figure 15(c). On top of the reflective PS-BPLC cell, there is laminated a reflective polarizer (e.g., wire grid polarizer or dual brightness enhancement film [167,168] ), which is set to transmit parallel polarization and reflect perpendicular polarization. Between the glass substrate and the reflective polarizer, there is a broadband quarter wave plate whose optic axis is orientated 45 o with respect to the transmission axis of the reflective polarizer. To realize phase modulation, the incident beam is set to be polarized parallel to the paper plane, and gets transmitted by the reflective polarizer. After passing through the quarter wave plate, the beam is converted into right-handed circular polarization before it hits the PS-BPLC layer. If there is no voltage drop between a pixel electrode and the planar electrode, the PS-BPLC in between exhibits an isotropic refractive index n iso. When there is a voltage applied, the optic axis of the induced refractive index ellipsoid mainly aligns in the vertical direction. Ignoring fringing field effect, the perpendicular and parallel components of the right-handed circular polarized beam experience the same index n o and phase. Upon reflection from the aluminum electrode, the beam remains circularly polarized but with opposite handedness. Encountering the quarter wave plate again, the left-handed circularly polarized beam is converted to perpendicular polarization, and further reflected back by the reflective polarizer as shown in the figure. After passing through the quarter wave plate the third time, the beam enters the PS-BPLC layer with left-handed circular polarization. Similarly to the first round, light transverses the BPLC layer twice, and finally gets transmitted through the reflective polarizer with parallel polarization. With such a structure, light passes through the PS- BPLC layer four times, hence the operation voltage is lowered significantly from device aspect. In order to lower the operation voltage from material aspect, a large Kerr constant PS-BPLC (PS-BPLC-7) was employed. According to Equation (7), Kerr constant is proportional to the dielectric anisotropy Δε. Thus, a LC host, JC-BP07N (from JNC, Japan), with a large dielectric anisotropy (Δε = 332 at 300 Hz) was used to obtain a large Kerr constant. With Δn sat = and E s = 2.58 V μm 1, the Kerr constant was calculated as nmv 2 for 633 nm wavelength. A 4.97 μm vertical field switching cell without an alignment layer was used, and the voltage-dependent phase change were measured for a single pixel modulation in a proof-of-concept experiment. It is found that at around 24 V, a 2π phase change is achieved using the proposed scheme. However, the host LC needs several polar groups to generate the large Δε, resulting in an increased rotational viscosity and slower response time. The rise and delay times switching between 24 V and 0 V were measured as 0.96 ms and 3.5 ms, respectively. Also measured is the voltage dependent phase change curve of a PS-BPLC cell with the same cell gap, but a different PS- BPLC material (PS-BPLC01). The saturation birefringence of PS-BPLC01 Δn sat is higher 0.17, and the Kerr constant K = 7.46 nmv 2 is about 3 times smaller than PS-BPLC-07, but the 2π voltage V 2π is only 12.5% higher. Thus, the saturation birefringence plays a more important role in determining V 2π. The authors also investigated the electro-optical performance of the proposed structure with different cell gaps, wavelengths, and PS-BPLC materials. The operation voltages of the phase modulator using PS-BPLC-07 within the entire visible range are below 24 V, which is the maximum affordable voltage in a high resolution LCoS. [169] This is an important step towards the implementation of PS-BPLC into high resolution TFT driven LCoS. The low operation voltage is achieved with efforts from both device and material aspects. The use of the polarization-selective reflective polarizer significantly reduces energy loss, but still allows the optical path to be doubled in the reflective PS- BPLC cell, and thus the operation voltage dramatically lowed. However, a small oblique angle of the incident light would result in a relatively large horizontal displacement in the PS- BPLC layer due to the thick glass substrate and wave plates, producing cross talks between pixels. Realizing submilliseond-response spatial phase modulator is of significant importance for the applications of beam steering, real time optical calibration and so on. However, up to today, no high-resolution pixelated PS-BPLC spatial light modulator has been experimentally demonstrated. The two major obstacles that have hindered it from being implemented are high operation voltage and fringing field effect. Adopting the reflective mode on silicon is a smart move since it automatically reduces voltage because of the double path inside the BPLC cells. Further attempts to reduce the voltage involve more complicated device configurations, but are important towards practical applications. The second obstacle is the fringing field effect, which is actually the byproduct of the small phase change δn = n iso -n o <Δn/3 as driven by vertical fields. To achieve the same 2π phase change, the required cell gap for BPLC is about 3 times thicker compared to its nematic counterpart. And the thicker cell gap tends to aggravate the fringing field effect between adjacent pixels, and consequently the phase profile is distorted. More work towards the practical implementation of PS-BPLC spatial phase modulators is highly demanded Resonance Condition Change of Interference Optical Filters Tunable LC optical filters based on refractive index change have found wide applications in telecommunication, [170] color generation, [171] and biomedical optical imaging [172,173] and so on. But conventional nematic LCs have relatively slow response 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (23 of 28) wileyonlinelibrary.com

24 time. With PS-BPLC as the index-modulating medium, one can conveniently tune the resonant wavelengths or the intensity of a certain wavelength using electric voltage at a rapid speed. High Q-factor Micro-Ring Resonator: Microring resonators, [ ] due to their inherent wavelength selectivity, are used as optical filters for wavelength-division-multiplexing techniques. The resonant wavelength of a micro-ring is determined by the ring structure and materials used for the core and claddings. Nematic liquid crystal based micro-ring resonators [ ] can have large tunability of the resonant wavelength owing to the large refractive index change. However, they usually suffer from problems such as slow response time and severe scattering loss. Scattering loss is caused by the long-range orientation order (large coherent length) of nematic LC materials, and would severely degrade the quality (Q)-factor of the micro-ring resonator, especially when the alignment is imperfect and when an electric field is applied. [ ] To reduce scattering loss and improve response time, Lin et al. employed a PS-BPLC as a cladding material for a micro-ring resonator. [95] The resonant wavelength could be continuously tuned by changing refractive index of PS-BPLC. With the DTC structure in PS-BPLC in the order of hundreds of nanometers, scattering loss is suppressed, and thus an ultrahigh Q-factor (>2000) is achieved both with and without an applied electric field; and response times are in the submillisecond range thanks to the short coherent length of BPLC as well. The device structure is shown in Figure 16a and b. A 16 μm SiO 2 layer was on top of a Si substrate. Then a patterned SiN layer with a thickness of 0.5 μm was formed on top of the SiO 2 layer. The width of both the straight line and the micro-ring of the SiN layer was 1.2 μm, the radius of the micro-ring was 40 μm, and the coupling gap between the line and micro-ring was 0.65 μm. With an ITO glass on the top, and the Si substrate on the bottom, a LC cell with a cell gap of 5 μm was formed. By injecting a BPLC precursor into the cell and then exposing it to UV light, a tunable micro-ring resonator with waveguide structure was fabricated. In the straight and micro-ring waveguides, the SiN layer served as the core, the SiO 2 layer and PS-BPLC layer served as claddings. Since the refractive index of SiN is close to that of the PS-BPLC, the resonant wavelength could be sensitively tuned by the change of PS-BPLC index. The device is designed for the operation of transverse magnetic (TM) mode. When a voltage is applied between the bottom silicon substrate and the top ITO electrode, a nearly uniform vertical electric field is generated in the PS-BPLC layer. As the index ellipsoids aligns in the vertical direction, for TM wave, it experiences an increased refractive index n e n iso +Δn(E)2/3, where n iso is the refractive index of the PS-BPLC cladding at voltage-off state. As the cladding index is changed by varying the voltage, the effective refractive index of the resonator n eff changes accordingly, which causes the resonant wavelength shift according to the resonance equation: λ = 2 πrn / m m eff (17) where m is the grating order, which is a positive integer, λ m is the wavelength of the mth order resonant mode, and R is the radius of the micro-ring resonator. The voltage dependent resonant wavelength of the micro-ring resonator in TM mode was measured with the aid of an infrared tunable laser and a power meter. As plotted in Figure 16c Figure 16. Principles of electrical switching of the proposed PS-BPLC resonator in a) V off and b) V on states, c) Variation of resonant wavelength as a function of driving voltage, and d) corresponding spectra at V = 0, 50, 90, 120 and 150 V. Panels (c) and (d) reproduced with permission. [95] Copyright 2014, The Optical Society (24 of 28) wileyonlinelibrary.com 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

25 and d, when voltage increases from 0 to 150 V, the resonant wavelength can be continuously tuned from nm to nm. Moreover, to evaluate the performance of the micro-ring resonator, its full width at half maxima (FWHM) and Q-factors are compared at different voltage. The FWHM at 0, 30, 90, 120 and 150 V are 0.06, 0.06, 0.064, and nm respectively, and the Q-factors at these voltages are 25892, 24274, 24275, and 24991, respectively. The good performance indicates that there is uniform refractive index change in the PS-BPLC cladding and much smaller scattering occurs. Fabry-Peort (FP) Filter: In 2011, Lin et al. experimentally demonstrated a tunable FP filter using a PS-BPLC. [94] The resonant wavelength could be tuned by nm V 1 and the free spectral range is 16 nm in the visible region; and the wavelength tunability is 0.12 nm V 1 and the free spectral range is 97 nm in the near infrared (NIR) region. The FP filter has two ITO glass substrates separated by spacers as shown in Figure 17a. On the inner surfaces of each glass substrate, there is an Aluminum-coated mirror. The cell gap is 3.8 μm and the reflectivity of the mirrors is 88% in both visible and NIR regions. The performance of the FP filter was investigated using the optical setup depicted in Figure 17b. A white light source, halogen lamp, with a spectrum range between 360 nm and 2000 nm was used to illuminate the sample, and an optical spectrum analyzer was used to examine the transmitted light. The transmission (T FP ) of a FP filter at a given wavelength λ is determined by: [187] T FP 2 T = 2 2 (1 R) + 4Rsin (2 πnd/ λ) (18) where T and R represent transmittance and reflectance of the mirrors, respectively; n and d are the refractive index and thickness of the medium filled in the FP cavity. By varying the voltage applied between the ITO electrodes, n of the PS-BPLC layer could be tuned continuously while the other parameters T, R and d are kept the same. At voltage-off state, for normally incident light that transverses the FP filter, a refractive index n iso is seen. As the voltage increases, birefringence is induced, and the refractive index is decreased to n o n iso -2Δn(E)/3 for normal incidence, resulting in a blue shift of the transmission spectrum. The transmission spectra of un-polarized visible light from 500 nm to 700 nm at different voltages are plotted in Figure 17c. At 0 V, there are 11 transmission peaks due to the relatively large cell gap. As voltage increases, the transmission spectrum shifts towards the short wavelength gradually due to the reduced index of PS-BPLC. The maximum shift 11 nm is obtained at 120 V. The free spectral range (FSR), which is the spacing between two successive transmission maxima, is determined by cell gap, wavelength, and refractive index of the cavity medium. In the visible range, the FSR is 11 nm. In the NIR region from 1350 nm to 1550 nm, covering the optical communication region, there is a similar trend of blue shift in the transmission spectrum as voltage increases. A maximum shift 12 nm is achieved at 100 V, and the FSR is 97 nm as shown in Figure 17d. To quantitatively calculate the voltage-dependent-wavelength shift due to the change of refractive index of the PS-BPLC δn, the authors measured δn using a reflective Michelson interferometer and found δn was almost linearly proportional to E 2, well following the Kerr effect. Good polarization independence was achieved in both visible and NIR regions in voltage-off state and voltage-on state (60 V) thanks to the vertical field and normal incidence in the proposed configuration. The rise time was measure to be 660 μs with the abrupt application of a 60 V voltage, and the decay time was 750 μs when the voltage was removed. The tunable optical filters using PS-BPLCs with submillisecond response and self-assembly properties are very attractive. The main bottlenecks of those devices are the limited tuning range because of the small refractive index change of BPLC, and the high operation voltage. Figure 17. a) Configuration of the PS-BPLC FP filer. b) Experimental setup for measuring the spectra of the PS-BPLC FP filter. Spectra of the FP filter transmittance at different voltages c) in the visible range and d) in the NIR region. Panels (c) and (d) reproduced with permission. [94] Copyright 2011, The Optical Society WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (25 of 28) wileyonlinelibrary.com