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Photoalignment of dye-doped cholesteric liquid crystals for electrically tunable patterns with fingerprint textures

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Abstract

We present a convenient photoalignment approach to fabricate rewritable fingerprint textures with designed geometrical patterns based on methyl red doped cholesteric liquid crystals (MDCLCs). MDCLC systems with/without nanoparticles of polyhedral oligomeric silsesquioxanes (POSS) were employed to realize two types of sophisticated binary patterns, respectively. Based on the understanding of involved mechanisms related to boundary conditions and middle-layer theory, we demonstrated the precise manipulation of fingerprint patterns by varying the fingerprint grating vectors in different domains. Notably, the hybrid-aligned liquid crystal configuration induced by POSS nanoparticles, which leads to the electrically rotatable grating, can be converted into the planar-aligned configuration by the adsorption of photoexcited methyl red molecules onto the indium-tin-oxide (ITO) surface. In this manner, the dynamic voltage-dependent behavior of fingerprint gratings is altered from the rotation mode (R-mode) to the on-off mode (O-mode).

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Recently, the beyond-display applications of liquid crystals (LCs) have attracted a great deal of attentions because of the remarkable electro-optical phenomena and the abilities to control light flow [1–10]. In particular, cholesteric liquid crystals (CLCs) with helical arrangement of spatially-twisted molecules, practically obtained by doping chiral additives into nematic LCs, are known to exhibit unique optical properties. Fingerprint textures with the modulation of refractive index are facilely achieved in CLCs owing to an appropriate combination of anchoring conditions of aligning surfaces and other parameters, such as helical pitch of CLCs, cell thickness, and applied voltage [11,12]. Fingerprint textures, which can act as phase gratings in the Raman-Nath regime, possess huge potentials to be used as optical modulators [13], diffraction gratings [14,15], non-mechanical beam steering devices [16] and waveguide lasers [17], etc. Moreover, the attractive feature of dynamic behaviors is enabled by applying external stimuli, such as temperature [18], electrical field [19,20] and optical field [21–27].

As an alternative of traditional mechanical rubbing process, which might possibly cause contamination problems by dust particles and electrostatic charges, the photoalignment technique is feasible to generate high resolution aligning patterns in multi domains [28, 29]. Notably, we have demonstrated that high-quality CLC fingerprint textures were able to be successfully achieved by utilizing the pronounced photoalignment technique in SD1-coated LC cells [30]. Fascinating spatially-variant patterns with fingerprint textures, like spiral and wavy stripes, have been successfully recorded. However, as we know, SD1 is a relatively expensive azo dye and the utilization of SD1 involves a sophisticated procedure of photoreactive alignment layer. It is meaningful to further investigate other photoalignment methods to fabricate CLC textures. Compared with SD1, methyl red is a kind of uncostly azo dye, which can be facilely doped into LCs directly without the coating process of alignment layers. The dependence of the laser-induced change in pretilt angle and absorptive anisotropy of a methyl red-doped LC on illumination duration was revealed [31]. Apart from that, in our previous work, dynamic fingerprint textures in shapes of dashed curve and dashed line were generated by a one-step polarization holography process in a bulk-mediated CLC system dissolved with methyl red [32]. Furthermore, since the photoalignment approach provides a versatile route to fabricate novel material systems which could act as molecular motors/switches [33] and form long-range periodic structures of nanoparticle assemblies [34], there is still a demand to expand its application capabilities and scopes. It should be addressed that the change of alignment conditions can lead to different switch behaviors of fingerprint gratings [16,18]. Especially, to the best of our knowledge, the influence of photo-induced alignment transition (from hybrid-aligned to planar-aligned) on the conversion of fingerprint grating modes has not yet been reported.

In this paper, we proposed two types of methyl red-doped CLC (MDCLC) systems without and with nanoparticles of polyhedral oligomeric silsesquioxanes (POSS), respectively. Based on the understanding of involved mechanism related to boundary conditions [33,35,36] and middle-layer theory [14,16,36–38], we demonstrated that MDCLCs could be photoaddressed with fingerprint textures via single-step or two-step photoalignment procedure. Dynamic evolution of CLC fingerprint textures was realized by varying the applied voltage. In addition, the homeotropic alignment dominated by POSS nanoparticles can be altered into the planar alignment by the photoexcited adsorption of methyl red molecules onto the indium-tin-oxide (ITO) surface [39], resulting in the transition of boundary condition from the hybrid alignment to the planar alignment. Accordingly, the voltage-dependent behavior of CLC fingerprint gratings is altered from the Rotation Mode (R-Mode) to the On-off Mode (O-Mode). We expect the approach would provide a promising combination of CLC superstructures and photoalignment techniques to be utilized in various types of LC devices.

2. Experiment

In the experiment, two MDCLC systems, denoted as Sample I and II, were prepared without and with the incorporation of POSS nanoparticles, respectively. Sample I was a mixture of achiral nematic LC E7 (Xianhua, China), chiral dopant S811 (Xianhua, China) and azo dye methyl red (Sigma-Aldrich). And the weight concentrations of E7, S811 and methyl red are 96.17 wt%, 1.83 wt% and 2.0 wt%, respectively. The S811 molecule has a helical twisting power value of −10.9 µm−1. Sample II was obtained by doping POSS nanoparticles additionally and the concentrations of E7, S811, methyl red and POSS are 96.02 wt%, 1.83 wt%, 2.0 wt% and 0.15%, respectively. The natural pitches P0 of both samples were determined to be ~5.0 μm by the Cano Wedge method [40]. The clearing point of MDCLCs was measured to be 56.5 °C by the Differential Scanning Calorimeter (DSC, Netszch DSC 200 F3 Maia, 5K/min, air). Both MDCLC mixtures were filled into cells through capillary forces after homogeneous mixing and heating up to 65 °C. The cells used in the experiments were made from two ITO glass plates with the top plate untreated and the bottom plate coated with polyimide layer rubbed along the y axis as shown in Fig. 1(a). The thickness d of the ITO/polyimide cells was fixed to be ~4.8 μm, therefore the ratio of the cell gap to the natural pitch (d/P0) for the samples is calculated to be ~0.96.

 figure: Fig. 1

Fig. 1 The schematic LC configurations of (a) Sample I processed via the two-step photoalignment and (b) Sample II processed via the single-step photoalignment. (c) The top view of the twisted planar geometry after photoalignment. (MR and PI represent methyl red and polyimide, respectively)

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Two exposure procedures to fabricate binary MDCLC patterns, named as two-step photoalignment and single-step photoalignment, were illustrated schematically in Figs. 1(a) and 1(b), respectively. The ITO/polyimide cells filled with Sample I were processed by the two-step photoalignment. In the first-step exposure, the cell was mounted on a miniature hot stage (65 °C). The untreated top ITO plate of the cell was vertically illuminated by one collimated linearly-polarized light beam with a certain polarization direction and an intensity of ~60 mw/cm2 from a continuous-wave and single-longitudinal-mode laser (Coherent Compass 315M, 532 nm) for 5 min, whose wavelength was close to the absorption spectrum peak of methyl red. Then the cell was cooled down to ambient temperature in ~3 min before removing away from the laser beam. In the second-step exposure, a photomask with designed geometric figures was attached on the outside surface of the top ITO substrate, and the polarization direction of the incident laser beam was adjusted to another direction with the same illumination time as the first-step exposure. On the other hand, the single-step photoalignment with a photomask and a collimated linearly-polarized laser beam was also performed to photoaddress the ITO/polyimide cells filled with Sample II. The photoalignment parameters, including heating temperature, irradiation source, intensity and duration, were fixed to be the same as those used in the two exposures for Sample I.

A proper alternating current (AC) electric voltage (square wave, 1 kHz) was applied to generate fingerprint textures. A crossed polarized optical microscope (POM, PM6000, Nanjing Jiangnan Novel Optics, China) was used to observe the particulars of the textures obtained by the photoalignment process. A linearly-polarized He-Ne laser (632 nm) was used as a probe beam and the diffraction patterns were captured by a digital camera (Nikon, D7000). To investigate the dependence of diffraction power on polarization state and applied voltage, a silicon detector (Thorlabs PDA36A), a programmable function signal generator/oscilloscope (Hanetek 3064A) and an AC voltage amplifier were used to monitor the power of different diffraction orders.

3. Results and discussion

In the case of Sample I as shown in Fig. 1(a), before the photoalignment, the LC directors adjacent to the bottom polyimide surface were orderly arranged along the rubbing direction, while those LC molecules adjacent to the top ITO surface distributed messily without regular alignment. During the first-step exposure in the two-step photoalignment process, the methyl red molecules in Sample I underwent a series of trans-cis isomerizations followed by molecular reorientation, diffusion, and eventually adsorbed onto the inner surface of the ITO substrate [41]. Given suitable irradiation intensity and duration, the methyl red molecules that adsorbed on the ITO surface prefer to be reoriented with their long axes perpendicular to the polarization direction of the incident laser beam in order to minimize the photon absorption, causing the adjacent LC molecules align along the direction of their long axes [42]. The orientation of LC directors close to the bottom polyimide surface is still predominated by the rubbing direction since the anchoring energy provided by the rubbed polyimide surface is large enough to overcome any possible alignment effect induced by the photoaligned methyl red molecules. As a result, a uniform planar texture with helical axes orthogonal to both ITO and polyimide substrates was achieved. Figure 1(c) depicts the twisted planar geometry induced by the photoalignment with linear polarization, in which θ is the included angle between the polarization direction of the incident laser and the rubbing direction of the bottom plate, and the yellow arc represents the twist angle of the LC molecules from the bottom plate to the top plate. When the angle θ is in the first quadrant, θ < 0. When the angle θ is in the fourth quadrant, θ > 0. The twist angle is determined by the angle θ and the ratio of the cell gap to the natural pitch (d/P0) .

When applied with proper AC voltages, fingerprint textures characterized with uniform grating stripes induced by the well-known Helfrich deformation [22,43–45] would be generated in Sample I. According to the Helfrich theory, the threshold voltage Vth, at which grating stripes begin to emerge, is determined by the following equation [22,46]

Vth2=8d3π3(6K22K33)0.5/ΔεP,
where d is the cell thickness, P is the helix pitch, Δε is the dielectric anisotropy of LCs, K22 and K33 are the elastic constants for twist and bend deformations, respectively. It should be noticed that the Eq. (1) derived for d<<P can only describe qualitatively the general properties of Vth for dP. The Vth increases with decreasing helix pitches i.e. increases with increasing twist angles for the constant thickness of cells. On the other hand, the stripe direction is perpendicular to the director direction of the LC molecules in the middle layer [32,36–38]. Consequently, the change of angle θ with fixed d/P0, i.e., the change of twist angle would result in different threshold voltage Vth and the rotation of the fingerprint stripes [32,46,47]. Here, we set θ to be −45° for the first-step exposure in the two-step photoalignment process. According to our previous investigation, the corresponding fingerprint texture would be unstable, which appears at the threshold voltage of about 4.3 V (peak to peak value, similarly hereinafter) and begins to disappear immediately [32]. During the second-step exposure with photomask, the polarization direction of the incident laser with positive θ was adopted to obtain stable fingerprint texture with relatively low Vth. In the reexposed region of the cell corresponding to the hollowed-out part of the photomask, the methyl red molecules were reoriented, rearranging the adjacent LC molecules with their long axes perpendicular to the latter polarization direction, leading to a planar texture with a different twist angle. Meanwhile, the unexposed region remains the initial twisted planar texture induced by the first-step exposure. In this manner, the grating could be repeatedly designed with various optical patterns due to the excellent rewritable ability of methyl red molecules.

Figure 2 shows four representative patterned fingerprint textures formed in Sample I via the two-step photoalignment process. In Figs. 2(a) and 2(b), an amplitude binary grating with period of 500 µm was employed as a photomask and the angle θ of the second-step exposure was 10°. As shown in Fig. 2(a), no fingerprint texture can be observed at 0 V, and the distinguishable stripes with period of about 500 µm are attributed to the periodical refractive index modulation of the two alternating twisted planar textures formed in the first- and second-step exposures, respectively. When an AC voltage of 3.4 V was applied across the cell, the reexposed region in the second-step exposure began to convert from twisted planar texture to the developable-modulation-type fingerprint texture [11], which became distinct gradually by increasing the external voltage. In addition, photomasks with shapes of pentagram, asterisk, and triangle were adopted, and the angles θ of the second-step exposure were 20°, 40° and 50°, respectively. As shown in Fig. 2(c), patterned fingerprint textures with the same shapes as photomasks and various grating vectors were achieved. The angles between the grating stripe directions and the horizontal axis were 35°, 25° and 20°, respectively. It is necessary to clarify that the brightness difference of the fingerprint patterns might be ascribed to the difference of phase retardation by varying the voltage. In the other aspect, the texture transition was not observed in the unexposed region of the second-step exposure until the applied voltage was increased up to 4.0 V, which was corresponding to the lightproof part of photomask and expected to remain in the unstable domain. However, stable fingerprint stripes with varying direction were observed experimentally at 4.0 V. This phenomenon was further confirmed by annealing the cell at temperature of 80 °C [32]. With the prolonging heating time, the direction of grating strips tended to be perpendicular to the rubbing direction corresponding to the twist angle of 2π. It is suspected that the annealing process may lead to a different anchoring condition analogous to the “planar degenerated alignment” [48,49] in the absence of light irradiation. Hence the cells possess their intrinsic helical structures with a twist angle close to 2π to match the d/P0 of 0.96, eventually resulting in the decrease of Vth and the rotation of fingerprint stripes. We could utilize the characteristic to generate patterns with the thermal-responsive grating directions. On the other hand, the photoaligned fingerprint gratings can be modulated electrically for numerous cycles and preserved for several months at ambient temperature without any noticeable degeneration of electro-optical properties.

 figure: Fig. 2

Fig. 2 The crossed POM images of Sample I with various geometrical patterns. One-dimensional periodic stripes and the enlarged details in the white rectangle region with voltages of (a) 0 V and (b) 3.5V. (c) Two-dimensional geometric patterns with variable grating vectors, in which the insets detail the fingerprint textures in white rectangle regions and the grating directions with respect to the negative x-axis.

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With regard to Sample II as shown in Fig. 1(b), suitable amount of POSS nanoparticles dispersed in LCs could directly induce vertical alignment on the top untreated ITO surface without conventional vertical-aligning layer which may be owing to the interaction between the functional groups of POSS nanoparticles and the LC molecules [50]. Meanwhile, LCs adjacent to the bottom polyimide surface would like to be homogeneously aligned along the rubbing direction because the anchoring intensity provided by POSS nanoparticles is considerably weaker than the one provided by the rubbing process. Thus, a uniform hybrid-aligned configuration was achieved. In the single-step photoalignment process with photomask, methyl red molecules in Sample II would also adsorb onto the exposed ITO surface and induce the homogeneous alignment perpendicular to the polarization direction of the incident beam. The transition of alignment condition from POSS-dominated homeotropic state to methyl red-dominated homogeneous state in the exposed region led to a twisted planar-aligned LC configuration. And the unexposed region corresponding to the lightproof part of the photomask still remained in the hybrid-aligned state. In this manner, alternating hybrid and planar alignments were achieved in different regions within the cell.

The series of POM images presented in Figs. 3(a)-3(f) clearly display the dynamic behavior of the fingerprint textures formed in Sample II under increasing AC voltages after the single-step photoalignment. As shown in the left part of Fig. 3(c), vague fingerprint stripes appear in the unexposed hybrid-aligned area with an applied AC voltage of 1.5 V, while no stripe was found in the exposed planar-aligned area (the right parts). With the increase of voltage, the stripes in the unexposed hybrid-aligned area became distinct gradually and rotated anticlockwise as indicated in Figs. 3(c)-3(e). When the voltage reached ~3.0 V, the rotatable stripes in the unexposed hybrid-aligned area started to fade out as a result of the unwinding of helical structures. Notably, when the voltage was further increased to ~3.9 V, the developable-modulation-type fingerprint texture with horizontal grating stripes (θ = 90°) appeared in the exposed planar-aligned area. The developable-modulation-type grating started to disappear at 4.3 V. In this way, Sample II was endowed with the voltage-dependent capability of switching between the R-Mode and the O-Mode by utilizing the single-step photoalignment to induce anchoring transitions.

 figure: Fig. 3

Fig. 3 The texture evolution of Sample II observed via a POM with voltages of (a) 0 V, (b) 1.0 V, (c) 1.5 V, (d) 2.0 V, (e) 3.0 V and (f) 4.0 V after the single-step photoalignment. The left parts in figures were unexposed and the right parts were exposed.

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An amplitude binary checkerboard pattern was recorded on the cell filled with Sample II via the single-step photoalignment procedure and the diffraction behavior was investigated. After the photoalignment, we prepared the same pattern with alternating hybrid-aligned and planar-aligned regions corresponding to unexposed and exposed areas, respectively. The linearly-polarized probe beam (632 nm) was normally incident on the cell with the diameter of ~1 mm and the polarization direction was parallel to the rubbing direction. Because of the relatively large feature size of the photoaligned pattern (500 μm × 450 μm), insufficient periods in the limited irradiation area of the probe beam could not bring forth diffractions with fine details. Rotatable diffraction spots distributed along the direction of the fingerprint grating vector were observed by increasing the applied voltage. The higher order diffraction spots rotated around the 0th order spot gradually, as a result of the grating rotation. As shown in Fig. 4, the direction angle of the grating vector β (relative to the horizontal axis) increased from 95° to 120°, which means the total continuously-rotatable angle range of the R-Mode grating is 25°. The appearance and disappearance voltage values of diffractions coincide well with the previous voltage data determined by the POM observation. As the AC voltage was further increased to Vth of 3.2 V, another diffraction pattern with larger spacing, corresponding to the O-Mode grating (θ = 0°), appeared with β = 132°. The abrupt increase of ± 1st order diffraction angle is due to the smaller grating period, which is remarkably different from that of the previous R-Mode one. By modulating the applied voltage, the grating can be switched between the R-Mode and the O-mode repeatedly without fatigues. The diffraction efficiency is dependent on the external electric field and the maximum first-order efficiencies of the R-Mode and the O-Mode are about 5% and 1%, respectively. The intrinsic low diffraction efficiency is ascribed to the fact that the LC director distribution does not exactly follow the electric field and is usually smooth due to the long coherence length [16,51]. In addition, the initial electro-optical performance of the Sample II can be maintained for several weeks. The relatively short life time compared with Sample I may be due to the distortion of the original aligning configuration of LCs induced by the partial aggregation of POSS nanoparticles.

 figure: Fig. 4

Fig. 4 Diffraction behavior of Sample II photoaligned with checkerboard patterns and the voltage dependence of the direction angle of grating vector β with respect to the horizontal axis. The insets (I, II, III…IX, X) show the corresponding diffraction patterns with increasing voltages. The insets (a) and (b) present the POM images of Sample II with alternating hybrid and planar aligned checkerboard patterns, corresponding to R-Mode (2V) and O-Mode gratings (4V) respectively. (HBA and PA represent hybrid and planar alignments, respectively)

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Furthermore, we also recorded the same checkerboard patterns on the cell filled with Sample I via the two-step photoalignment process, in order to qualitatively compare the distinctions of diffraction behaviors between the two types of checkerboard patterns fabricated from Sample I and Sample II. Figures 5(a) and 5(b) present the POM images of the photoaligned pattern along with the enlarged details for Sample I. Figure 5(c) shows the diffraction pattern when the sample was applied with an external AC voltage of 3.5 V and the maximum first-order diffraction efficiency of the grating was about 2%. The black solid line in Fig. 5(d) illustrates the voltage-dependent transmittance of the probe beam through the cell in the normal direction, aka the transmittance of the 0th order diffraction. It is revealed that the transmittance of the 0th order diffraction of Sample I remained stable in the beginning and started to decrease drastically till the voltage was increased to ~3.4 V, which is equal to the Vth of the developable-modulation-type fingerprint texture (O-Mode grating). The transmittance reached the minimum at 4.4 V, then increased gradually and recovered completely at ~6.0 V due to the unwinding of helical structures.

 figure: Fig. 5

Fig. 5 (a) The POM image of checkerboard-patterned Sample I at a voltage of 3.5V. (b) The enlarged detail in the white rectangle region in (a) which is corresponding to the boundary of developable-modulation-type fingerprint and planar texture. (c) The diffraction pattern of Sample I with checkerboard pattern at 3.5V. (d) Voltage-dependent transmittance of Sample I and Sample II and the normalized power of light scattering, R-Mode and O-Mode diffraction, obtained by the peaks-fitting simulation of Sample II.

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The red dashed curve depicts the influence of voltage on the transmittance of the 0th order diffraction of Sample II processed by the single-step photoalignment, from which both transmittances of the R-Mode and the O-Mode fingerprint textures could be well distinguished. Here, we used the peaks-fitting simulation to analyze the transmittance behavior (red dashed curve, Transmittance II) by taking into consideration of both the scattered light (blue short-dashed curve, Fitted scattered light), and the diffracted light induced by R-Mode (yellow dotted curve, Fitted Peak A) and O-Mode gratings (pink dashed-dotted curve, Fitted Peak B). The light scattering was induced by the sudden change of refractive indices at the boundary of the individual square region with different anchoring conditions, which could be eliminated by applying a high voltage to completely unwind the helix. The green dashed-dotted-dotted curve (Fitted diffracted light) presents the normalized power sum of both R-Mode and O-Mode diffractions. Consequently, the purple short-dotted curve (Fitted transmittance II) simulated by means of combining the total normalized power loss due to scattering and diffraction, agrees with the experimental transmittance curve. In the R-Mode stage, the transmitted light power decreased slightly till a diffraction maximum was reached at a voltage of ~2.9 V, indicative of the initial disappearance of the rotatable grating. In the O-Mode stage, the diffraction maximum was found at 4.3 V, close to that of Sample I. The difference of voltage and diffractive efficiency of O-Mode gratings between Sample I and Sample II might be ascribed to the doping effect of POSS nanoparticles, i.e. the change of dielectric anisotropy, etc. These voltage values are basically in accordance with the investigation of POM images and the diffraction patterns revealed in Fig. 4.

4. Conclusions

In conclusion, dynamic fingerprint textures with designed geometrical patterns based on MDCLCs were achieved by single-step and two-step photoalignment procedures. MDCLC systems with/without POSS nanoparticles were chosen to realize two types of sophisticated patterns, respectively. It was demonstrated that various binary patterns with different grating vectors were facilely achieved by the irradiation through photomasks with designed patterns and precisely adjusting the polarization direction of incident laser beam. The voltage-dependent morphological evolution and the diffraction properties of photoaddressed LC patterns were investigated. It was also found that the POSS-dominated hybrid-aligned configuration of LCs, which leads to the electrically rotatable grating, could be readily changed into the methyl red-dominated planar-aligned configuration after the single-step photoalignment. In this manner, the voltage-dependent diffraction behavior of fingerprint gratings can be altered from the R-Mode to the O-Mode facilely. The work presented herein disclosed a convenient way to construct dynamic hierarchical superstructures in a considerably large scale with a rewritable manner. These CLC superstructures might hold great promise for various advanced optical applications in the future, such as beam steering, photonic switcher, and particle manipulation, etc.

Funding

National Natural Science Foundation of China (NSFC) (Nos. 61505173, and 61675172); Natural Science Foundation of Fujian Province, China (No. 2017J01124); Shenzhen Science and Technology Project (No. JCYJ20170306142028457).

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Figures (5)

Fig. 1
Fig. 1 The schematic LC configurations of (a) Sample I processed via the two-step photoalignment and (b) Sample II processed via the single-step photoalignment. (c) The top view of the twisted planar geometry after photoalignment. (MR and PI represent methyl red and polyimide, respectively)
Fig. 2
Fig. 2 The crossed POM images of Sample I with various geometrical patterns. One-dimensional periodic stripes and the enlarged details in the white rectangle region with voltages of (a) 0 V and (b) 3.5V. (c) Two-dimensional geometric patterns with variable grating vectors, in which the insets detail the fingerprint textures in white rectangle regions and the grating directions with respect to the negative x-axis.
Fig. 3
Fig. 3 The texture evolution of Sample II observed via a POM with voltages of (a) 0 V, (b) 1.0 V, (c) 1.5 V, (d) 2.0 V, (e) 3.0 V and (f) 4.0 V after the single-step photoalignment. The left parts in figures were unexposed and the right parts were exposed.
Fig. 4
Fig. 4 Diffraction behavior of Sample II photoaligned with checkerboard patterns and the voltage dependence of the direction angle of grating vector β with respect to the horizontal axis. The insets (I, II, III…IX, X) show the corresponding diffraction patterns with increasing voltages. The insets (a) and (b) present the POM images of Sample II with alternating hybrid and planar aligned checkerboard patterns, corresponding to R-Mode (2V) and O-Mode gratings (4V) respectively. (HBA and PA represent hybrid and planar alignments, respectively)
Fig. 5
Fig. 5 (a) The POM image of checkerboard-patterned Sample I at a voltage of 3.5V. (b) The enlarged detail in the white rectangle region in (a) which is corresponding to the boundary of developable-modulation-type fingerprint and planar texture. (c) The diffraction pattern of Sample I with checkerboard pattern at 3.5V. (d) Voltage-dependent transmittance of Sample I and Sample II and the normalized power of light scattering, R-Mode and O-Mode diffraction, obtained by the peaks-fitting simulation of Sample II.

Equations (1)

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V t h 2 = 8 d 3 π 3 ( 6 K 22 K 33 ) 0.5 / Δ ε P ,
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