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This work proposes a thermally rotatable grating that is based on hybrid-aligned cholesteric liquid crystals (HBA-cholesteric LCs). Experiments reveal that the HBA-cholesteric texture has a uniformly striped domain, which forms a grating, when the ratio of the cell gap to the helical pitch (d/p) is in the range of 2≤d/p≤3. The stripe direction of the HBA-cholesteric grating is predicted by the proposed vertically aligned LC layer model. The stripe direction of the HBA-cholesteric grating rotates continuously under thermal and electrical effects. Furthermore, the HBA-cholesteric grating has a larger rotational angle under the thermal effect (~101°) than under the electrical effect (~48°). Potential applications of the proposed thermally rotatable cholesteric grating for beam steering devices are emphasized.
©2012 Optical Society of America
1. Introduction
Cholesteric liquid crystals have been used in light-modulators, liquid-crystal lasers, reflective displays, and smart reflectors [1–6]. Because of their spatially twisted molecules, cholesteric LCs also can be utilized as controllable optical diffraction gratings. Cholesteric diffraction gratings have potential for use as non-mechanical beam steering devices, which are important components of various optical systems, such as in optical communications [7], optical interconnects [8], optical data storage [9], and projection displays [10]. The formation of the striped domain of cholesteric diffraction gratings depends on the surface alignment, the helical pitch of the cholesteric LCs, the cell thickness, and the applied voltage [11–17]. For a homogeneously aligned cell, a uniform striped domain of the cholesteric grating is formed when a small voltage is applied and the orientation of the stripe pattern depends on the ratio of the cell gap to the helical pitch (d/p) [11–16]. For a vertically aligned cell, a uniformly striped domain of the cholesteric grating is formed without the application of a voltage when the substrate surface is rubbed [17]. For both homogeneously and vertically aligned cells, the diffraction patterns of the cholesteric gratings are electrically and thermally tunable in only one dimension (along the grating vector) [15, 16].
A direction-tunable cholesteric grating has been developed based on vertically aligned cholesteric LCs with a patterned electrode [18]. The stripe direction is tunable by shifting the center of the cholesteric grating by applying different voltages. However, the stripe direction is tunable only in a local region of the grating and the maximum angle of rotation of the grating is small (≤ 90°). A homogeneously aligned cholesteric grating in which the stripe direction can be switched by electrically and optically controlling the d/p ratio has been proposed [19]. However, the stripe direction can be switched only between two orthogonal directions. The stripe direction of hybrid-aligned (HBA) cholesteric gratings is reportedly electrically rotatable and the dynamic rotation of their striped domain has also been studied [20]. This study investigates the characteristics of the thermal rotation of the stripe direction of the HBA-cholesteric gratings and its dependence on the d/p ratio. The stripe direction of the HBA-cholesteric grating at different d/p ratios can be predicted using the proposed vertically aligned LC (VA-LC) layer model. The morphology of the polymer network on the substrates of the HBA-cholesteric grating supports the proposed VA-LC layer model. The thermally induced rotational angle of the HBA-cholesteric grating increases with the d/p ratio. Experiment results also reveal that the maximum rotational angle of the stripe direction of the HBA-cholesteric grating that is induced by the thermal effect (>100°) exceeds than induced by the electrical effect (~48°).
2. Experiment
In the experiment in this study, a nematic liquid crystal E7 (Merck), which has a positive dielectric anisotropy Δε = 5.9 at f = 1kHz, three elastic constants K11 = 12pN, K22 = 9pN, K33 = 19.5pN (at 20°C) and refractive indices of ne = 1.75 and no = 1.52 (at 20°C and λ = 632.8nm) for extraordinary and ordinary waves, respectively, is used. In the experiment, the nematic liquid crystal is doped with a chiral agent CB15 (Merck) to form a cholesteric LC. Hybrid-aligned empty cells, which are homogeneously aligned on one of the substrates and vertically aligned on the other substrate, are filled with cholesteric LCs. The cell gap of the HBA-cholesteric texture is 5 ± 0.1μm over the entire cell to maintain the uniformity of the striped domain. The HBA-cholesteric textures are heated using a hot stage (T95-PE, Linkam) during the experiment. The HBA-cholesteric textures are observed using a polarizing optical microscope (Axio-scope A1, Zeiss). The diffraction pattern of the HBA-cholesteric grating is probed and recorded using an He-Ne laser (λ = 632.8nm) and a charged coupled device (CCD), respectively.
3. Results and discussion
Figure 1 shows the striped domains of the HBA-cholesteric texture with different d/p ratios that are observed under a polarizing optical microscope. The homogeneously aligned substrate of the HBA-cholesteric texture is the bottom substrate of the cell. The experimental results reveal a uniformly striped domain of the HBA-cholesteric texture at 2≤d/p≤3 (Figs. 1(b)-(e)). For a hybrid-aligned cell, the vertically aligned substrate provide a vertical force to reorient the helical axis of the cholesteric LC parallel to the surface of the substrate [17], yielding an HBA-cholesteric grating. Thus, the striped domain of the HBA-cholesteric grating can be observed with no applied field. When the d/p ratio is small (d/p<2), the LCs of the HBA-cholesteric texture exhibit a uniform splay-twist deformation, and no striped domain is observed (Fig. 1(a)). When the d/p ratio is large (d/p>3), the surface anchoring force of the homogeneously aligned substrate is too weak to align the stripes of the HBA-cholesteric texture, so a disordered striped domain with many disclination lines appears (Fig. 1(f)). Figure 1 also shows the stripe direction of the HBA-cholesteric grating varies for various d/p ratios in the range 2≤d/p≤3 (Figs. 1(b)-(e)). Figure 2(a) plots the stripe directions of the HBA-cholesteric gratings with different d/p ratios. From Fig. 2(a), the stripe direction of the HBA-cholesteric grating rotates through ~360° as the d/p ratio increases from two to three. The stripe direction of a cholesteric grating can be predicted using the middle-LC layer model [16, 21]. For a homogeneously aligned cell, the helical pitch of cholesteric LCs adjusts itself to satisfy the homogeneous boundary condition [21]. Thus, the middle-LC layer is always parallel or perpendicular to the rubbing direction, causing the stripe direction of the cholesteric grating also to be parallel or perpendicular to the rubbing direction, based on the middle-layer LC model [16]. In contrast, for a hybrid-aligned cell, the orientation of the LC director is arbitrary on the vertically aligned substrate, and the orientations of the LC director,ϕML for the middle- LC layer and ϕVA for the VA-LC layer, as shown in Fig. 2(b), depend on the d/p ratio. Thus, in Fig. 2(a), the stripe direction of the HBA-cholesteric grating varies with the d/p ratio. However, according to the middle-LC layer model, the stripe direction of the HBA-cholesteric grating is ϕML = (d/p)π and rotates by only 180° rather than ~360° as the d/p ratio changes from two to three (solid line in Fig. 2(a)). For HBA-cholesteric textures, the vertically aligned substrate provides a vertical force that aligns the helical axis of the cholesteric LC parallel to the surface of the substrate, forming the HBA-cholesteric grating. In contrast, the homogeneously aligned substrate tends to align the helical axis normal to the surface of the substrate, hindering the formation of the striped domain. Thus, we believe the striped domain of the HBA-cholesteric grating forms near the vertically aligned substrate and the stripe direction should be parallel to the orientation of the LC layer near the vertically aligned substrate surface, ϕVA = (d/p)2π, rather than to the orientation of the middle-LC layer. The dashed line in Fig. 2(a) represents the calculated stripe direction of the HBA-cholesteric grating, determined using the vertically aligned LC (VA-LC) layer model. This calculated result closely matches the experimental result. Notably, since the stripe direction of the HBA-cholesteric grating depends strongly on the d/p ratio, as shown in Fig. 2(a), the uniformity of the cell gap must be precisely controlled to produce HBA-cholesteric gratings with a highly uniform striped domain, as determined by comparing them with homogeneously aligned cholesteric gratings.
Fig. 1 Micrographs of HBA-cholesteric texture at different d/p ratios (a) d/p = 1.5, (b) d/p = 2.2, (c) d/p = 2.5, (d) d/p = 2.7, (e) d/p = 3.0 and (f) d/p = 4.0.
Fig. 2 (a) Stripe direction of HBA-cholesteric gratings with different d/p ratios. Stripe direction ϕ is defined with respect to rubbing direction. Dashed line is fitted using the VA-LC layer model and solid line is fitted using middle-LC layer model. Since 360° represents one period, the range of stripe directions ϕ is 0°≤ϕ≤360°. (b) Director orientation of HBA-cholesteric texture. The x -axis is defined to be parallel to rubbing direction; ϕML is orientation of middle-LC layer, and ϕVA is orientation of VA-LC layer.
To verify the VA-LC layer model, the director distribution of the HBA-cholesteric grating is studied using the polymer network method [22]. A small amount of monomer RM257 (Merck) (~4 wt%) is added to the HBA-cholesteric grating and the polymer network is then formed by UV irradiation. Figure 3 presents the scanning electron microscopic (SEM) images of the morphology of the polymer network on the substrates of the HBA-cholesteric grating after the removal of LC. Figure 3 shows that the polymer network on the vertically aligned substrate has a distinct striped profile (Fig. 3(a)) by comparing it with the polymer network on the homogeneously aligned substrate (Fig. 3(b)). The striped profile of the polymer network on the vertically aligned substrate verifies the VA-LC layer model that the striped domain of the HBA-cholesteric grating forms near the vertically aligned substrate. A three-dimensional (3D) calculation of the detailed director distribution for the HBA-cholesteric grating is underway.
Fig. 3 SEM images of morphology of polymer network on surfaces of (a) vertically aligned substrate and (b) homogeneously aligned substrate of HBA-cholesteric grating.
The stripe direction of the HBA-cholesteric grating can be thermally rotated. Figure 4 presents micrographs of the stripes of the HBA-cholesteric grating (d/p = 3), showing their directions at different temperatures. The helical pitch of the cholesteric LC in an HBA-cholesteric texture decreases continuously as the temperature increases. Figures 5(a) and (b) plot the distributions of the directors of an HBA-cholesteric texture with a long helical pitch and a short helical pitch, respectively. Since a positive chiral agent (CB15) is added to the cholesteric mixture in this study, the HBA-cholesteric texture with a short helical pitch has a larger ϕVA than the HBA-cholesteric texture with a long helical pitch, as shown in Fig. 5. As the HBA-cholesteric LC changes from having a long helical pitch (Fig. 5(a)) to having a short helical pitch (Fig. 5(b)) during heating, the stripe direction of the HBA-cholesteric grating rotates in a counterclockwise sense, as presented in Fig. 4.
Fig. 4 Micrographs of HBA-cholesteric grating with d/p = 3.0 at (a) T = 26°C, (b) 38°C, (c) 42°C and (d) 48°C.
Fig. 5 Orientations of directors of VA-LC layers of HBA-cholesteric gratings with (a) long helical pitch (p1) and (b) short helical pitch (p2), where p1 > p2.
Figure 6 plots the change of the stripe direction of the HBA-cholesteric gratings with d/p ratio at different temperatures. The hysteresis between heating and cooling is insignificant (ΔT<1°C) for the HBA-cholesteric grating. Thus, Fig. 6 presents only the results for the heated HBA-cholesteric grating. From Fig. 6, an HBA-cholesteric grating with a larger d/p ratio has a larger rotational angle (Δϕ~101° for d/p = 3 vs. Δϕ~44° for d/p = 2.2) with a change in temperature. The rotational angle of the HBA-cholesteric grating is the sum of the variations in the pitches of the cholesteric LC layers. Thus, a larger d/p ratio indicates a more cholesteric LC layer, causing the rotation of the HBA-cholesteric grating with temperature to be larger. Notably, the stripe directions of the HBA-cholesteric texture are disordered when temperature T>49°C owing to the thermal fluctuation effect, and the striped domain disappears when the temperature exceeds the clearing point (T~52°C). As the grating rotates, the stripe direction repeats every 180° rather than every 360°, so a rotatable grating is fully rotated when it has been rotated through 180°. We believe that the angle of the thermally induced rotation of an HBA-cholesteric grating can be further increased to 180° by using LC materials with a high clearing point or a helical pitch that depends strongly on temperature (large dp/dT).
Fig. 6 Change of stripe direction of HBA-cholesteric gratings with d/p ratio at different temperatures. Heating rate used in experiment is ~1°C/min.
Figure 7 shows diffraction patterns of the rotatable HBA-cholesteric grating (with d/p = 2.2) at various temperatures. Like that of other cholesteric gratings, the diffraction efficiency of the HBA-cholesteric grating depends on polarization [16]. The polarization state of the probe beam is parallel to the stripe direction to maximize the diffraction efficiency during the rotation of the diffraction pattern. As the temperature increases from 26°C to 46°C, the diffraction pattern of the HBA-cholesteric grating rotates continuously by approximately 43°, which result is consistent with the result in Fig. 6. Since the birefringence of the LC, Δn, is small at temperatures near the clearing point, the diffraction pattern of the rotatable HBA-cholesteric grating is almost invisible at high temperature (Figs. 7(e) and (f)).
Fig. 7 Diffraction patterns of HBA-cholesteric grating with d/p = 2.2 at various temperatures. (a) 26°C, (b) 30 °C, (c) 34 °C, (d) 38 °C, (e) 42 °C and (f) 46 °C.
The characteristics of the electrically induced rotation of the HBA-cholesteric grating are examined. Figure 8(a) presents micrographs of the stripes, showing the directions of the HBA-cholesteric grating (d/p = 2.4) under different applied voltages. The helical pitch of the HBA-cholesteric texture changes from short (Fig. 5(b)) to long (Fig. 5(a)) as the applied voltage increases. Since an increase in helical pitch causes a decrease in ϕVA, as shown in Fig. 5, the striped domain of the HBA-cholesteric grating rotates in a clockwise sense as the applied voltage increases (Fig. 8(a)). Figure 8(b) plots the change of the stripe direction of the HBA-cholesteric grating with d/p ratio at various applied voltages. From Fig. 8(b), the maximum angle of the electrically induced rotation of the stripes of the HBA-cholesteric grating |Δϕ| decreases as the d/p ratio increases. In an electric field, the helical pitch of a cholesteric LC increases with the strength of the field, and the helix unwinding voltage, at which the cholesteric LCs are completely unwound, is proportional to (K22/Δε)1/2/p [21]. Thus, an HBA-cholesteric grating with a smaller d/p ratio has a larger p and so is more easily electrically untwisted. Thus, in Fig. 8(b), the stripes of an HBA-cholesteric grating with a smaller d/p ratio rotate through a larger angle (|Δϕ|~48° for d/p = 2.0 vs. |Δϕ|~22° for d/p = 2.7) in an electric field. From Figs. 6 and 8(b), the HBA-cholesteric grating has a larger rotational angle under the thermal effect (~101°) than under the electrical effect (~48°). Notably, in Fig. 8(b), the striped domains of the HBA-cholesteric gratings disappear as the applied voltage increases above the phase-transition voltage. The phase-transition voltage of the HBA-cholesteric grating increases as d/p increases, because the elastic restoring force of the LC is larger for an HBA-cholesteric grating with a larger d/p (a smaller helical pitch), so the phase-transition voltage is also higher.
Fig. 8 (a) Micrographs of HBA-cholesteric grating with d/p = 2.4 at different applied voltages. (b) Change of stripe direction of HBA-cholesteric gratings with d/p ratio at different applied voltages.
4. Conclusions
A thermally rotatable diffraction grating that is based on hybrid-aligned (HBA) cholesteric textures is developed. The directions of the stripes of HBA-cholesteric gratings with different d/p ratios are predicted using the proposed VA-LC layer model, which is supported by the SEM images of the polymer network. An HBA-cholesteric grating with a larger d/p has a more cholesteric LC layer, and therefore a larger angle of thermally induced rotation. Moreover, the thermally induced rotation of the HBA-cholesteric grating is larger (~101°) than the electrically induced rotation (~48°). The thermally rotatable HBA-cholesteric grating can be used for beam-steering devices in the future.
Acknowledgments
The authors would like to thank the National Science Council of Taiwan for financially supporting this research under Contract No. NSC 98-2112-M-110-006-MY3.
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