In this paper, a direct switching between a transparent (or reflecting) planar (P) state to an opaque (or transparent) focal conic (FC) state and vice-versa of a polymer free bistable cholesteric light shutter without any homogeneous polyimide (PI) layer, is demonstrated based on the sign inversion of dielectric anisotropy of dual frequency liquid crystal (DFLC). The direct switching was achieved by applying square wave field at low (1 kHz) and high (50 kHz) frequency. As a result, the DFLC light shutter sustains bistable bright and dark states in electric field off state and exhibits excellent electro-optic performance. The direct switching from the FC to P states not only supports more uniform P state but also significantly reduces switching voltage by eliminating the high field homeotropic (H) state required for the switching in the conventional polymer stabilized cholesteric texture (PSCT) light shutter. The driving voltage applied to make a transition from the P to FC one is relatively low (3Vp-p/µm). Further, switching time from FC to P state was reduced drastically with homeotropic PI layer. Results show that dual frequency cholesteric liquid crystal (DFCLC) light shutter holds a great promise for use in energy efficient display devices and switchable windows.
©2012 Optical Society of America
The helical structure with controlled pitch of cholesteric liquid crystal (CLC) in CLC and their composites makes them extremely promising for uses in polarizer free electro optic devices, such as electrically switchable privacy windows, light shutters [1–4], optical filters [5–9], dynamic diffraction gratings [10–12], tunable reflectors  as well as bistable cholesteric reflective displays [1–9]. CLC phase inherently exhibits selective reflection that is related to the Bragg optics associated with the helicoidal structure formed from one dimensional rotation of the director, where the wavelength of the reflected light is determined by the Bragg wavelength [14–23] and governed by a simple relation, as shown in Eq. (1).
In the CLC composite systems a small amount of monomer is dispersed in the CLC and polymerized in the liquid crystal phase to form anisotropic polymer networks [24,25]. After polymerization, a cholesteric texture is stabilized by polymer networks is known as polymer stabilized cholesteric texture (PSCT) [2,3,13,24,26] and the polymer network has an aligning effect on the LC, which tends to keep the liquid crystal parallel to it. Depending on the cholesteric pitch, polymerization condition and structure of the polymer network, PSCT commonly operated in normal and reverse mode light shutter. If the monomer is polymerized in the homeotropic (H) state of CLC, the formed polymer network is perpendicular to the cell substrates, which usually stabilizes the scattering focal conic (FC) texture, and the PSCT normal mode light shutter is obtained [24,25]. In a planar (P) texture, all the helical axes are arranged in the direction perpendicular to the substrate surfaces. If the pitch length is much larger or smaller than the wavelength of visible light, the cell will be transparent.
In the focal conic state, the helical axes are randomly arranged and texture shows strong light scattering because of the discontinuous spatial variations of the refractive indices at the domain boundaries. Effect of electric-field-driven textural transition between planar and focal conic states in polymer networks makes a base of operation of PSCT displays . Both planar and focal conic configurations are stable in the absence of external electric field. However, the switching between states can be achieved only through the H state, where the cholesteric helix is completely unwound by a dielectric coupling between LC molecules with positive dielectric anisotropy (> 0) and vertical electric field. Consequently high switching voltage is required for conventional PSCT optical devices. Conventionally, in general, CLC switching from the P state to the FC state is induced by a pulse of an ac square wave. When a high voltage beyond a critical value is applied, the CLC will go into the H state. Subsequent transition to the P state can be achieved, if the field is turned off quickly, however if the high voltage is turned off slowly, the H state of the CLC will be altered to FC state. In this driving scheme, the transition from the FC to P state is accomplished through an intermediate H state, and the transition time is very long due to the slow H to P transition . This conventional drive scheme employs indirect transition paths to switch from the bistable FC state to the P state. Anyhow, switching from either the P or the light-scattering FC state to the other has been proposed for a variety of LC applications such as cholesteric displays, reverse-mode light shutters, and other electro-optical devices . Very recently, thermally as well as electrically switchable bistable PSLC light shutters, which can maintain two optical states with the application of an additional electric field (and so called energy efficient), are reported [3,29,30]. Bao et al. utilized higher concentrations of monomers to enhance the hysteresis phenomenon of normal mode conventional PSCT, to fabricate electro-thermal switchable bistable PSCT light shutter . Ma et al. further made use of dual frequency CLC to achieve electrically switchable bistable PSCT light shutters . But still remains an unsolved problem how the reverse mode PSCT, with such outstanding electro-optical performances as fast switching speed, very small hysteresis, and selective reflection, can be made bistable [3,13,26,31]. When a sufficiently large electric field perpendicular to the cell substrates is applied to the reverse mode PSCT, the polymer network becomes distorted and switching from the stable P texture to the stable FC texture is not capable of returning to the transparent P texture. A very high electric field is required to switch the shutter from opaque to transparent state via H state of CLC.
An alternative way of switching a CLC light shutter between two stable states is to use dual-frequency nematic liquid crystals. These DFLC materials have a high dielectric dispersion where the dielectric anisotropy, is frequency dependent, resulting in a change in sign at the crossover frequency, where. In some DFLC materials occurs at a few kHz and changes significantly over the range 1–100 kHz. In a DFLC cell, the director can be driven between either homogeneous or homeotropic alignment by applying an electric field across the sample at a frequency either above or below. As the molecules of the LC have a preferred direction (unit vector) along which they tend to be oriented. When an electric field is applied to the LC it will exert a torque on the unit vector. Depending on the sign of the anisotropy, i.e. or , this torque will turn the director respectively toward being parallel or perpendicular to the field direction, as illustrated in Figs. 1(a) and 1(b), respectively.
M. Xu and D.-K. Yang reported on electro optical properties of a small size CLC reflective display by using DFLC material based on direct switching , however authors used a homogeneous polyimide (PI) alignment layer for the initial planar state, which makes the approach cost incompetitive and it needs various manufacturing process steps for the device. Further, the addressing scheme was not sufficiently fast to display dynamic images and the applied voltage across the pixel to address to the FC and P texture was very high 66 V and 100 V, respectively. Moreover, authors could not expose the retention time for the memory mode, visibility in P state and opacity in FC state, for the commercial application. More recently, Y. C. Hsiao et al also reported on the bistable cholesteric intensity modulator by using DFCLC  with homogeneous polyimide alignment layer in the planar cell, but the operating voltage was still relatively high and the scattering power of the FC state was not enough to warrant the use of the device as an ideal bistable light shutter. Here, as the authors used the homogeneous PI layer in the planar cell, however based on our study the homogeneous alignment layer can give better alignment of the LC in initial planar state (before applied a high frequency field) but it always destabilize the FC state in pure cholesteric system at 0 V and FC state is not stable for long time in absence of the low frequency applied field. Thus we conclude here that the positive effect obtained in our research is due to combined effect of differences in the physical mechanisms of texture transformations as well as by using MDA-00-3969 + R1011 as a more optimal composition as compared with MLC2048 + S811[as used in reference 33]. As the surface anchoring energy of the homogeneous PI layer (used in referred paper) and in our study (because of untreated ITO) is quite different, which has a crucial effect on physical mechanisms of texture transformations.
In this paper, we demonstrate a reverse mode bistable CLC light shutter by using dual frequency liquid crystal (DFLC) without any homogeneous PI coating and polymer network, which can be switched directly between transparent (or reflective) P state to opaque (or transparent) FC state and vice-versa by applying relatively very low electric field at different frequencies for the sign inversion of dielectric anisotropy. Figure 2 shows the schematic diagram of the configuration of the CLC and the operating principle of this DFCLC bistable light shutter for reversible transparent P and scattered FC state under low and high frequency applied field. Further, no additional voltage has to be applied for switching or to sustain the optical states, and therefore this shutter is exceptionally energy efficient for a widespread application of switchable windows.
The DFCLC used in the experiment was a mixture of an uniaxial birefringent dual frequency nematic liquid crystal (MDA-00-3969, Merck) and a chiral dopant R1011 (E. Merck) having helical twisting power (HTP) 25 µm−1. At low (≤ 1 kHz) and high (≥ 50 kHz) frequency AC electric fields, the dielectric anisotropy () is positive ( + 3.2) and negative (−2.7) with a cross-over frequency at approximately 15 kHz, as well as the liquid crystal tends to be parallel and perpendicular to the applied electric field, respectively. The optical birefringence () value of host LC is + 0.2214 with ordinary and extraordinary refractive indices no = 1.4978 and ne = 1.7192 respectively, at λ = 589.3 nm. The clearing point (Tc) and rotational viscosity (γ) of LC material are 106 °C and 310 mPas, respectively. However for this experiment to analyze the optimum condition, we used different concentration (e.g. 2.75, 4, 5 & 6 wt%) of chiral dopant. We found that for all the concentrations, the DFCLC mixture showed the similar bistable behavior by applying electric field in the range of 3-4V/µm at 1 kHz and 50 kHz. The results again show that there is no significant effect on the dielectric anisotropy (∆ε) and cross-over frequency of DFCLC mixture in this range of chiral concentration. Thus the pitch length of the DFCLC mixture was fixed at about 1.0 µm and controlled by adjusting the concentration (4.0 wt%) of R1011 from the helical twisting power (HTP) equation, HTP = 1/pC, where p is the pitch and C is the concentration of chiral dopant.
Further it’s worthy to mention that no any monomer and photoinitiator was mixed to the CLC mixture and therefore there is no need of further polymerization of the sample. The cells with an area of 2 × 3 cm2 and a cell gap of 10 μm were made using Indium Tin oxide (ITO) coated glass substrates and mixture was filled by capillary action in the isotropic phase. The sheet resistance of the ITO electrodes used in the experiment was 20 ohm/□. The ITO glass substrate surfaces were cleaned ultrasonically, dried in vacuum oven and untreated. The cell was spaced using 10 µm polymer spacer and sealed by using the hot press. The pure DFCLC textures were observed with a polarizing optical microscope (POM, NIKON LV100POL). A white light source was incident at normal to the sample cell by using LCMS 200 (Sesim Photonics Technology) for electro-optic study. The AC electric field was supplied by an arbitrary function generator (Agilent-33521A) in conjunction with a high voltage amplifier (A 400 FLC Electronics). All electro-optical measurements were carried out at the frequency of 1 kHz and 50 kHz and no polarizers were employed in the experiment.
3. Results and discussion
The POM photographs of P and FC textures of the DFCLC sample cell under crossed polarizer at a magnification of 200X in transmissive mode are shown in Fig. 3 . We observed that if sample cell is heated at its isotropic temperature and then cooled it down with a controlled cooling rate (annealing) of 1°C/min then the interaction between the LC molecules, favors the the FC state with helical structure. The shorter the pitch, the stronger the LC tends to be in the FC state. If the sample cell is cooled with a faster cooling rate (quenching) of 30 °C/min then the DFCLC molecules favors the P state. However, the cooling rate does not any effect on the bistability of the DFCLC light shutter, because bistability changes with the application of applied electric field at low (1 KHz) and high (50 KHz) frequency.
Further, when a high frequency electric field is applied across the cell, the LC tends to be aligned perpendicular to the field as the dielectric anisotropy is negative and thus the P state is favored. When a low frequency electric field is applied across the cell, the LC tends to be aligned parallel to the field due to positive dielectric anisotropy and thus the FC state is favored. Figure 3(a) shows the initial P texture at 0 volt, when the 1 kHz square wave is applied the DFCLC changes entirely into FC state at 30 Vp-p (Fig. 3(b)) which is stable at off (zero) voltage (Fig. 3(c)). Next, when a high (50 kHz) frequency field was applied to the FC texture, results in DFCLC cell reverting to the transparent stable P texture. Thus there is no need to add any polymer network to sustain the P or FC texture and no constraint to apply much higher field for switching from opaque FC state to transparent P texture contrary to the conventional PSCT light shutter which requires high field (100 Vrms) to switch back to the P state from FC texture through the homeotropic state .
Most interestingly, after applying the high frequency field, the amount of oily streaks in the primitive DFCLC cell is significantly reduced [Figs. 3(d) and 3(e)] and subsequently more uniform transparent P state is obtained and retained stable after removal of the switching field. Both, P and FC state are stable eternally and even show better uniformity as well as enhanced opacity in P and FC state respectively, at 0V as a function of time. Figures 4(a) and 4(b) show the textures of reversible direct switching from planar to focal conic and vice versa, at 30 Vp-p under low (1 kHz) and high (50 kHz) frequencies, however Figs. 4(c) and 4(d) show the textures of P and FC state at 0 V, taken after more than 100 hours. This phenomenon is not more obvious in the case of PSCT, because the doped monomers and formed polymer networks after curing become impurities. It should be noted that a strong color in the planar state, observed in a depolarized condition, is not caused by the selective reflection of the cholesteric LC but originated from the interference between ordinary and extraordinary lights propagating normal to the substrates.
The voltage dependent transmittance of DFCLC sample cell and corresponding textures are shown in Fig. 5 . Due to the fact that the sample adopted a P texture with p > λvis, the cell has a high transmittance, when no electric field is applied to it. The transmittance of sample cell decreases rapidly when the applied voltage exceeds a 10 Vp-p under the low frequency (1 kHz), as because the P texture begins to transform to FC one. On further increasing the field the transmittance decreases to its lowest value and the sample cell remains in FC state up to the critical voltages 50 Vp-p. The critical operating voltage (Vc) for bistable switching of a pure CLC light shutter is linearly proportional to the cell gap (d) and chiral concentration (X) as described by de Gennes’s theory , can be given byFig. 5, the CLC can be switched from FC state to the H state by a voltage (60 Vp-p) much higher than the critical voltage (Vc) and therefore, the transmission increases rapidly with this applied voltage. On decreasing the applied field the transmittance decreases and remains low as H texture changes to FC texture. Interestingly, preceding transition to the P state can be achieved, if the field is turned off quickly. Thus on increasing and decreasing amplitude of the low frequency field for a positive dielectric anisotropy, the DFCLC shows essentially the same electro-optic behaviors as of the conventional PSCTs. As a result, shutter can also be operated in the dynamic mode using switching between the planar and homeotropic states.
Further on applying the high frequency (50 kHz) field for a negative dielectric anisotropy, the LC molecules switched toward the back into the perfect planar state. Interestingly, after applying high frequency field, the transmittance is much higher as compare to initial planar state on removal of the field and the defects (oily streaks) are almost removed and remains in perfect planar state (Fig. 3(e)). As, when high frequency electric field is applied to the DFCLC, due to the sign of the anisotropy (<0), the dielectric torque helps the DFCLC director to move back into the P state. Moreover, our sample is pure DFCLC without any polymer network, the CLC switches from P texture to the FC texture and vice versa shows the Grandjean texture in a planar state with much reduced oily streaks and consequently higher transmittance. Further, in direct reversible switching, the switching time from P to FC state is about 110 ms when 30 V was applied to the cell at low frequency, however the FC state could be switched to the P state in about 450 ms when same voltage was applied at high frequency.
Figure 6 shows the maximum transmittance of the light shutter in field off state (at 0 volt) after switching the light shutter by applying low (1 kHz) and high (50 kHz) frequency peak to peak voltages at 20, 30 and 40 volts. The normalized transmittance (T = Tmin/Tmax) follows a simple exponential relationship as T = exp (-βd), where β is the light scattering coefficient at focal conic state and d is the cell gap. The parameter β is mainly determined by the pitch length and LC birefringence, as stated above the shorter the pitch, the stronger the LC tends to be in the scattered FC state. From above relation, the device contrast ratio is simply the inverse of T, i.e.,Eq. (2). Based on Eq. (4), the contrast ratio is critically influenced by β and d as if the pitch length gets farther away from the light wavelength (p>>λ) the light scattering efficiency decreases which is unfavorable for contrast ratio. In our experiment the contrast ratio of the light shutter was found highest at a drive voltage 30 Vp-p, when switched from planar to focal conic state and vice versa with low and high frequencies.
Figure 7 shows the photographs of the bistable DFCLC light shutter at zero field in transparent (P texture) and scattering (FC texture) states. Both states can directly transit to one another by applying an electric field 30 Vp-p with low (1 kHz) and high (50 kHz) frequency with no aid of high field homeotropic state. The scene behind the light shutter is clearly visible in transparent state and light shutter blocked the scene behind completely in scattering state. However, the images of the character “CBNU” which were placed comparatively very near to light shutter at 2.5 cm behind, is also completely blocked and the scattering state of the focal conic texture is still good.
Moreover, we also studied the sensitivity at the zero field alignment to mechanical shock and applied external pressure (P0 < P1 < P2 < P3) locally to the surface of a light shutter in the zero field P and FC bistable states. Here P0 intends for the zero (no) pressure applied to P or FC state, however P1 is the relatively low pressure at which the stable FC state changes to the transient P state. P2 and P3 are the pressures in ascending order applied to the light shutter at which transient P state changes to stable P state. In the FC state, the regions where the external pressure is applied, induces the flow of LCs and are switched to the transparent planar state in the vicinity. In the P state, the regions where the external pressure is applied are more uniform (no oily streaks at all in the vicinity). The planar state again reverts to the focal conic state completely, with an applied voltage of 30 Vp-p. Thus the proposed light shutter possibly may applicable as an input device also, as we can write text messages with a stylus pen on the proposed DFCLC device by applying an external pressure locally to switch it from the FC state to the P state. The line width of the written text and the gray scales can be controlled by the level of applied pressure . To remove the written text, a voltage of 30 Vp-p can be applied to the device to return it to the FC state. As shown in Fig. 8 , the stable FC state at zero pressure (P0) change to transient P state by applying a low pressure (P1) which finally changed to transparent stable P state [Fig. 8(d)] at relatively higher pressure (P3) through the P state [Fig. 8(c)] at medium pressure (P2). Further, the line width and image of the message can be expected to control more precisely by using a plastic substrate (due to level of applied pressure) instead of a glass substrate.
Finally, as it is observed that the switching time from P state to FC state is quite fast but the switching time from FC state to P is still relatively slow. To accelerate the response time, further we used homeotropic PI coating to demonstrate DFCLC light shutter. The cell gap was maintained 10 um for DFCLC cell with homeotropic PI layer. The surface polar anchoring energy of PI layer was observed a value of ~2.0 X 10−5 J/m2 and measured by retardation vs voltage (RV) technique [36,37]. Amusingly, the shutter still shows the good P state and bistable at 0 V with direct switching between transparent P to scattered FC state and vice-versa. Figure 9 shows the optical microtextures of the bistable direct switching with homeotropic PI layer under crossed polarizer at a magnification of 200X in transmissive mode. The voltage dependent transmittance characteristic of DFCLC with homeotropic PI layer follows the same trend as shown in Fig. 5. It is pointed here that the maximum transmittance in P state is not as higher as observed above without any PI layer, but the scattered FC state is much better and overall contrast ratio of the device is superior of ~17% (results are not shown here).
Figures 10(a) and 10(b) shows the macroscopic photographs of the bistable DFCLC light shutter with homeotropic PI layer in transparent P and scattered FC state under cross polarizer. Figures 10(c) and 10(e) and Figs. 10(d) and 10(f) are the photographs of the bistable DFCLC light shutter in field off state in transparent P and scattered FC states, respectively. Again the character “CBNU” behind the light shutter is clearly visible in P state and light shutter blocked the scene behind completely in excellent FC scattering state. The response time of the reversible switching is almost similar and switching time from FC to P state is reduced drastically however the applied electric field in this switching was found 4 Vp-p/µm. Figures 11 and 12 show the time resolved textures of the reversible switching between P and FC state. As shown in the figures, the switching time for both the states is almost similar with the pace of around 240 ms, which is much faster to our observed value (FC to P state switching time ≈450 ms) as above in case of without any PI coating and reported literature value . The fast response time of light shutter with homeotropic PI layer may be attributing the surface anchoring energy and helix (optic axis) tilt angle. It is possible that due to the homeotropic PI layer, the optic axis may consists the tilt which produced a splay-bend deformation in the plane of the plates and results in a fast switching. As the response time τ is given by, where γ is the characteristic viscosity,, and k is the cholesteric wave vector . At last, to confirm the bistability of DFCLC light shutter for different cell thicknesses (5, 10 and 20 µm), we performed the experiments and confirmed that the DFCLC light shutter still shows very good bistability at 0V for different cell gaps. The applied electric fields for bistable reversible switching between P and FC state were found 2.3, 3.0 and 4.0 Vp-p/µm of DFCLC light shutter for cell gaps 5, 10 and 20 µm, respectively.
In summary, a bistable DFCLC light shutter without any homogeneous PI coating by means of direct switching is demonstrated. The two stable-state of the DFCLC light shutter is sensitive to the low and high frequency field. Most interestingly, the direct switching between P and FC states with no need of high field H state can be achieved based on the sign inversion of dielectric anisotropy of host DFLC. The high frequency switching also reduced line defects and thus resulted in better uniformity of the P state. As a result of the direct switching, the operating voltage is significantly lower (3 Vp-p/µm) compared to the conventional PSCT light shutter, which requires high field to switch back to the P state from FC texture through the H state  as well as DFCLC light shutter reported value [32,33,39]. It should be also pointed out that the reflective mode DFCLC directly switchable between reflective P and transparent FC states by adjusting the pitch of a cholesteric LC based on the same concept of dual frequency switching. The DFCLC shutter can also applicable as an input device by applying an external pressure locally to switch it from the focal conic state to the planar state. Further, the faster response time of the reversible switching could be achieved with homeotropic PI layer by reducing the switching time of FC to P state significantly. Thus, our results further liberate new possible applications for the input and low-power-consumption DFCLC devices such as energy efficient bistable light shutters either in reflective or scattering modes and smart glass technologies.
This project was supported by Hicel Co. and also by World Class University program (R31-20029) funded by the Ministry of Education, Science and Technology.
References and links
2. H. Ren and S.-T. Wu, “Reflective reversed-mode polymer stabilized cholesteric texture light switches,” J. Appl. Phys. 92(2), 797–800 (2002). [CrossRef]
3. D.-K. Yang, L.-C. Chien, and J. W. Doane, “Cholesteric liquid crystal/polymer dispersion for haze-free light shutters,” Appl. Phys. Lett. 60(25), 3102–3104 (1992). [CrossRef]
4. M. Xu and D.-K. Yang, “Dual frequency cholesteric light shutters,” Appl. Phys. Lett. 70(6), 720–722 (1997). [CrossRef]
8. L. V. Natarajan, J. M. Wofford, V. P. Tondiglia, R. L. Sutherland, S. A. Siwecki, H. Koerner, R. A. Vaia, and T. J. Bunning, “Tuning of a cholesteric filter having a negative dielectric anisotropy,” Proc. SPIE 6654, 66540A (2007).
9. K. Lewis, G. Smith, I. Mason, and K. Rochester, “Design issues for tunable filters for optical telecommunications,” Proc. SPIE 4679, 213–224 (2002). [CrossRef]
10. R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, T. J. Bunning, and W. W. Adams, “Electrically switchable volume gratings in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64(9), 1074–1076 (1994). [CrossRef]
11. T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, and R. L. Sutherland, “Holographic polymer-dispersed liquid crystals (H-PDLCs),” Annu. Rev. Mater. Sci. 30(1), 83–115 (2000). [CrossRef]
12. A. Urbas, J. Klosterman, V. Tondiglia, L. Natarajan, R. Sutherland, O. Tsutsumi, T. Ikeda, and T. Bunning, “Optically switchable bragg reflectors,” Adv. Mater. 16(16), 1453–1456 (2004). [CrossRef]
13. Z. Li, P. Desai, R. B. Akins, G. Ventouris, and D. Voloschenko, “Electrically tunable color for full-color reflective displays,” Proc. SPIE 4658, 7–13 (2002). [CrossRef]
14. Y. Koikea, A. Mochizukia, and K. Yoshikawaa, “Phase transition-type liquid-crystal projection display,” Displays 10(2), 93–99 (1989). [CrossRef]
15. D.-K. Yang, J. W. Doane, Z. Yaniv, and J. Glasser, “Cholesteric reflective display: drive scheme and contrast,” Appl. Phys. Lett. 64(15), 1905–1907 (1994). [CrossRef]
16. D.-K. Yang, J. L. West, L.-C. Chien, and J. W. Doane, “Control of reflectivity and bistability in displays using cholesteric liquid crystals,” J. Appl. Phys. 76(2), 1331–1333 (1994). [CrossRef]
17. B. Taheri, J. W. Doane, D. Davis, and D. St. John, “Optical properties of bistable cholesteric reflective displays,” SID Int. Symp. Digest Tech. Papers 27, 39–42 (1996).
18. J. Anderson, P. Watson, J. Ruth, V. Sergan, and P. Bos, “Fast frame rate bistable cholesteric texture reflective displays,” SID Int. Symp. Digest Tech. Papers 29(1), 806–809 (1998). [CrossRef]
19. A. Khan, X.-Y. Huang, R. Armbruster, F. Nicholson, N. Miller, B. Wall, and J. W. Doane, “Super high brightness reflective cholesteric display,” SID Int. Symp. Digest Tech. Papers 32(1), 460–463 (2001). [CrossRef]
20. D.-K. Yang, “Flexible bistable cholesteric reflective displays,” J. Disp. Technol. 2(1), 32–37 (2006). [CrossRef]
21. W. St. John, W. Fritz, Z. Lu, and D.-K. Yang, “Bragg reflection from cholesteric liquid crystals,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51(2), 1191–1198 (1995). [CrossRef] [PubMed]
22. S. Shandrasekhar, Liquid Crystals (Cambridge University Press, 1992).
23. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Oxford University Press, 1993).
24. D.-K. Yang, L.-C. Chien, and Y. K. Fung, Liquid Crystals in Complex Geometries, G. P. Crawford and S. Zumer, eds. (Taylor & Francis, 1996), Chap. 1, pp. 103–142.
25. Y. K. Fung, D.-K. Yang, S. Ying, L.-C. Chien, S. Zumer, and J. W. Doane, “Polymer networks formed in liquid crystals,” Liq. Cryst. 19(6), 797–801 (1995). [CrossRef]
26. S.-T. Wu and D.-K. Yang, Reflective Liquid Crystal Displays (John Wiley & Sons, Ltd. 2001), Chap. 3, pp. 98–99 (2001).
27. T. Yamaguchi, H. Yamaguchi, and Y. Kawata, “Driving voltage of reflective cholesteric liquid crystal displays,” J. Appl. Phys. 85(11), 7511–7516 (1999). [CrossRef]
28. K.-H. Kim, H.-J. Jin, K.-H. Park, J.-H. Lee, J. C. Kim, and T.-H. Yoon, “Long-pitch cholesteric liquid crystal cell for switchable achromatic reflection,” Opt. Express 18(16), 16745–16750 (2010). [CrossRef] [PubMed]
29. R. Bao, C.-M. Liu, and D.-K. Yang, “Smart bistable polymer stabilized cholesteric texture light shutter,” Appl. Phys. Express 2, 112401 (2009).
30. J. Ma, L. Shi, and D.-K. Yang, “Bistable polymer stabilized cholesteric texture light shutter,” Appl. Phys. Express 3(2), 021702 (2010). [CrossRef]
31. Y. Huang, Y. S. Chih, and S. W. Ke, “Effect of chiral dopant and monomer concentrations on the electro-optical response of a polymer stabilized cholesteric texture cell,” Appl. Phys. B 86(1), 123–127 (2006). [CrossRef]
32. M. Xu and D.-K. Yang, “Electrooptical properties of dual-frequency cholesteric liquid crystal reflective display,” Jpn. J. Appl. Phys. 38(Part 1, No. 12A), 6827–6830 (1999). [CrossRef]
34. P. G. De Gennes, “Calcul de la distorsion d'une structure cholesterique par un champ magnetique,” Solid State Commun. 6(3), 163–165 (1968). [CrossRef]
35. K. H. Kim, D. H. Song, Z. G. Shen, B. W. Park, K. H. Park, J. H. Lee, and T. H. Yoon, “Fast switching of long-pitch cholesteric liquid crystal device,” Opt. Express 19(11), 10174–10179 (2011). [CrossRef] [PubMed]
36. X. Nie, Y.-H. Lin, T. X. Wu, H. Wang, Z. Ge, and S.-T. Wu, “Polar anchoring energy measurement of vertically aligned liquid-crystal cells,” J. Appl. Phys. 98(1), 013516 (2005). [CrossRef]
37. H. Yokoyama and H. A. van Sprang, “A novel method for determining the anchoring energy function at a nematic liquid crystal‐wall interface from director distortions at high fields,” J. Appl. Phys. 57(10), 4520–4526 (1985). [CrossRef]
38. S. T. Lagerwall, Ferroelectric and Antiferroelectric Liquid Crystals (Wiley -VCH, 1999), Chap. 4, p. 103.
39. Y.-C. Hsiao, C.-Y. Wu, C.-H. Chen, V. Y. Zyryanov, and W. Lee, “Electro-optical device based on photonic structure with a dual-frequency cholesteric liquid crystal,” Opt. Lett. 36(14), 2632–2634 (2011). [CrossRef] [PubMed]