1. INTRODUCTION

Cholesteric liquid crystals (CLCs) organized in self-assembled, periodically helical superstructures are known as a class of 1D chiral photonic crystals. In the Grandjean planar (P) state, a CLC is characterized by the so-called Bragg bandgap in a specific wavelength region, thus enabling the reflection of selective circularly polarized light with the same handedness as that of the CLC helix. This unique feature permits CLCs to be promising for the development of a variety of photonic devices such as reflective displays, reflectors, lasers, and sensors [1–4]. More attractively, dynamic control of CLC bandgap properties is attainable, permitting CLC photonic devices with variable optical properties. The center wavelength (${\lambda }_{\text{c}}$) of the CLC bandgap is determined by the helical pitch ($p$) as well as the ordinary ($n_{\text{o}}$) and extraordinary ($n_{\text{e}}$) refractive indices of the nematic host, according to the relation ${\lambda }_{\text{c}}=p·(n_{\text{e}}+n_{\text{o}})/2$ [5]. As such, a good number of studies of tunability of ${\lambda }_{\text{c}}$ or tunable reflective color in CLCs have been proposed via the control of helical pitch by external stimuli. For instance, CLCs with thermo-responsive bandgap properties have been obtained on the basis of the temperature dependency of LC phase transition [6], the helical twisting power (HTP) of the chiral dopant [7], and the mixture solubility [8]. Employment of photo-responsive chiral switches as dopants in CLCs has also been suggested for realizing variable and rewritable ${\lambda }_{\text{c}}$ by light irradiations thanks to the tunable HTP via the process of photo-induced trans–cis isomerizations [9]. On the other hand, electrical tuning of ${\lambda }_{\text{c}}$ would be preferable for practical applications because of the ease of operation and high compatibility of the CLC cell with modern optoelectronic devices. Considering a CLC cell subject to a vertical electric field, most of recent electrical-tuning approaches have been developed with negative nematic LCs—i.e., nematic LCs with negative dielectric anisotropy ($\mathrm{\Delta }ϵ<0$)—as the host material to prevent helical distortion by the applied voltage. With a direct-current (DC) voltage applied to a CLC consisting of chiral additives in negative LC, wavelength tuning has been asserted and examined in terms of the voltage-induced electrohydrodynamic instability [10], mechanical cell-gap bending [11], and defect annealing [12]. Alternatively, Choi et al. proposed to further exploit ferroelectric LC as electrically commanded aligning surfaces [13] or as dopants [14] in a negative CLC cell to achieve bandgap tuning by alternating-current (AC) voltages. However, the tunable wavelength ranges of the bandgap are quite limited, and the voltages required are generally too high ($>100\mathrm{V}$ by either DC or AC voltage) by the above-mentioned electrical-tuning approaches, thus hindering their practical uses. In a special case, Xiang et al. demonstrated electrically tunable selective reflection from ultraviolet (UV) to visible and infrared (IR) in an oblique helicoid state rather than the typical P state by doping proper amounts of the bent-shape molecules CB7CB and CB6OCB into a CLC [15].

Different from all aforementioned studies, in this work, we propose a state-of-the-art approach based on the electro-thermal effect, allowing the tunability of the reflective color in a wide wavelength range, covering the entire visible spectrum, by AC voltage applied across a negative CLC that is confined in a planar-aligned cell with indium–tin-oxide (ITO) electrodes. Here, the CLC is designed to intrinsically possess thermo-responsive bandgap properties. When the frequency of applied voltage goes beyond a critical value, our results indicated that ${\lambda }_{\text{c}}$ of the reflection band can be electrically tuned by varying either the amplitude or the frequency of the AC voltage. The results are complemented by both dielectric spectroscopy and IR thermography, thus affirming the increase in cell temperature through the induction of dielectric heating by the applied voltage. In general, dielectric heating in a dielectric medium stems from absorption of electromagnetic energy through rotation of molecular dipoles, and its efficacy becomes remarkable in the frequency regime of dielectric relaxation. Because the dielectric relaxation from molecular dipole reorientation of a typical LC does not occur in the kHz-to-MHz frequency regime, the dielectric heating effect in sandwich-type LC cells to date has only been discussed in dual-frequency LC whose relaxation frequency (viz., the crossover frequency) is about tens of kHz [16–18]. In our case, where a common negative CLC is employed, the dielectric heating is primarily governed by the pseudo-relaxation from the ITO effect due to the generation of losses from the cell comprising electrodes with nonzero resistance. As a result, the ${\lambda }_{\text{c}}$ of the proposed negative CLC with superior electro-thermal properties can vary from 780 nm at $0{\mathrm{V}}_{\mathrm{rms}}$ to 380 nm at merely $12{\mathrm{V}}_{\mathrm{rms}}$ at 2 MHz, thus manifesting a wider tunable wavelength range entailing much lower driving voltage in comparison with those by most current electrical tuning methods.

2. EXPERIMENT

The CLC used was prepared by incorporating 45 wt.% of the left-handed chiral additive S-811 (Merck) into the negative nematic host MLC-6608 (Merck) to induce the SmA–CLC phase transition so as to display thermal-responsive spectral properties in the CLC phase. MLC-6608 has birefringence $\mathrm{\Delta }n=0.083$ (measured at the wavelength of 589 nm and temperature of 20°C) and dielectric anisotropy $\mathrm{\Delta }ϵ=-4.2$ (at the frequency $f$ of 1 kHz and temperature of 20°C). The phase sequence of the mixture is SmA–21°C–CLC–39°C–isotropic, as determined by optical textures using a polarizing optical microscope (Olympus BX51) at various temperatures in a heating process. The CLC was heated to the isotropic phase and stirred for 2 h to ensure homogeneous blending, followed by its injection into an empty cell by capillary action. The empty cell is composed of two glass substrates; each substrate, bearing an ITO electrode, was spin-coated with an aligning layer (SE-2170) to promote planar alignment of LC molecules and, thus, the initial P state in the CLC phase. The cell gap and the effective electrode area of the cell are $d=5\pm 0.5\mathrm{\mu m}$ and $A=1{\mathrm{cm}}^2$, respectively. In general, an LC cell is created by sandwiching an LC between two ITO-covered substrates. When the resistivity of the ITO is not negligible, the equivalent circuit of such a sandwich-type cell geometry can be represented by resistance arising from the electrode layers and a capacitance contributed by the LC layer in series. As such, it has been found that the cell applied with voltages at specific frequencies will generate a certain amount of dielectric losses, leading to the induction of a pseudo-dielectric relaxation in the complex dielectric spectra [19]. The corresponding relaxation frequency ($f_{\text{PR}}$) can be defined as

All measurements were carried out at a given surrounding temperature ($T_s=22°\mathrm{C}$ or 23°C as designated) without using a hot stage unless specified. Spectral properties of the cell in the wavelength regime between 380 and 800 nm were monitored by transmission spectroscopy using a fiber-optic spectrometer (Ocean Optics $\mathrm{HR}2000+$) in conjunction with a halogen light source (Ocean Optics HL2000). No polarizer was employed in the spectral measurement. To investigate the dielectric heating effect and electro-thermal properties of the CLC cell, dielectric spectra, and the change in cell temperature ($\mathrm{\Delta }T$) as a function of the applied voltage ($V$) were, respectively, acquired with a high-precision LCR meter (Agilent E4980A) and a noncontact IR thermometer (precisely, IR camera FLIR ThermaCam P25). External voltages in the sinusoidal waveform with controllable amplitudes (from $0.05{\mathrm{V}}_{\mathrm{rms}}$ to $15{\mathrm{V}}_{\mathrm{rms}}$) and frequencies (from 20 Hz to 2 MHz) were specifically supplied by the same LCR meter to prevent from errors under various voltage conditions caused by different instruments.

3. RESULTS AND DISCUSSION

Figure 1 illustrates the temperature-dependent bandgap properties and optical textures at four given temperatures of the CLC cell without voltage applied. Here, the cell was placed on a hot stage (Linkam-LTS120E) to precisely control the cell temperature. The experimental data, as shown in Fig. 1(a), indicate that the reflection band blueshifted gradually with rising temperature ($T$), varying from ${\lambda }_{\text{c}}=760\mathrm{nm}$ at $T=23°\mathrm{C}$ to ${\lambda }_{\text{c}}=380\mathrm{nm}$ at $T=32°\mathrm{C}$. This led to the change in color of the reflective optical texture at various temperatures, appearing red (${\lambda }_{\text{c}}=760\mathrm{nm}$) at 23°C, orange (${\lambda }_{\text{c}}=610\mathrm{nm}$) at 23.8°C, green (${\lambda }_{\text{c}}=512\mathrm{nm}$) at 25°C, and navy (${\lambda }_{\text{c}}=397\mathrm{nm}$) at 29.4°C [see Fig. 1(b)]. When using the chiral material S-811 as the dopant to form a CLC with a SmA–CLC phase transition, similar results to those shown in Fig. 1(a) have also been obtained in CLCs with distinct nematic hosts [12,20], and this phenomenon has been interpreted by the temperature dependence of the twist elastic constant [6]. Such temperature-dependent spectral behavior can be fitted by Keating’s theory, expressed as [21]

 

Fig. 1. (a) Temperature-dependent ${\lambda }_{\text{c}}$ of the experimental (open circles) and simulated (solid line) results. (b) Optical textures of the cell in the CLC phase observed in the reflection mode at four distinct temperatures. Inset in (a) is the transmission spectra at various temperatures.

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To discuss the correlation between the “pseudo-dielectric relaxation” and the voltage-induced dielectric heating, Fig. 2(a) first displays the complex dielectric spectra of the pure LC (MLC-6608) and the CLC ($\mathrm{MLC}\text{-}6608+45\text{-}\mathrm{wt.}\%$ S-811) cells representatively at $T=23°\mathrm{C}$. Because the orientation of the LC molecules having $\mathrm{\Delta }ϵ<0$ remains unchanged in a vertical electric field, the profile of the dielectric spectrum is independent of the amplitude of the probe voltage. When the resistivity of the ITO material is nontrivial, which is truly the case, a resistance–capacitance circuit is produced in a sandwich-type cell, resulting in energy losses and, in turn, pseudo-dielectric relaxation [19]. Now that the polarization contributed by space charge is excluded at high frequencies ($>\mathrm{kHz}$), and the orientational polarization relaxation of a negative LC typically occurs beyond MHz [18], the single Debye-type relaxation detected in the complex dielectric spectra of either cell is undoubtedly attributable to the use of the ITO cell. Referring to the Debye model, the real- (${ϵ}^{\prime }$) and imaginary-part (${ϵ}^{\prime \prime }$) dielectric functions of this relaxation can be described by

 

Fig. 2. (a) Experimental and simulated complex dielectric spectra of the pure LC (MLC-6608) and the CLC ($\mathrm{MLC}\text{-}6608+45\text{-}\mathrm{wt.}\%$ S-811) cells at $T=23°\mathrm{C}$. (b) Temperature dependence of deduced static dielectric constant ${ϵ}_{\text{s}}$ and relaxation frequency $f_{\text{PR}}$ of the pseudo-dielectric relaxation of the LC cell in the CLC phase.

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Figure 3(a) depicts the $f$ dependence of the steady-state cell temperature at $V=15{\mathrm{V}}_{\mathrm{rms}}$ measured by an IR camera. Here, each IR image was taken after the application of a given voltage to the cell for 8 min to ensure that the cell temperature became saturated or time-independent. For this measurement, $T_s$ was controlled at 23°C, and the temperature increase $\mathrm{\Delta }T$ is defined as $T-T_s>0$. The control of cell temperature by applied voltage was directly confirmed by IR thermography, revealing image color changes from blue in the field off-state or at $f=1\mathrm{kHz}$ ($T=23°\mathrm{C}$) to green at $f=600\mathrm{kHz}$ ($T=32°\mathrm{C}$) and to yellow at $f=2\mathrm{MHz}$ ($T=37.7°\mathrm{C}$), as shown in the insets of Fig. 3(a). Figure 3(a) indicates that there exists a critical frequency ($f_0$) that triggers the onset of temperature increase with increasing frequency. In the case of $V=15{\mathrm{V}}_{\mathrm{rms}},\mathrm{\Delta }T$ starts to increase with rising frequency beyond 24.5 kHz, reaching $\mathrm{\Delta }T\sim 14.7°\mathrm{C}$ (i.e., $T=37.7°\mathrm{C}$) at $f=2\mathrm{MHz}$. Considering the relation between the heat generation and the dielectric properties of an LC cell, we attempt to elucidate the result of Fig. 3(a) in terms of the temperature elevation from the dielectric heating effect by the following time-varying equation [16]:

 

Fig. 3. (a) Temperature increase as a function of the frequency of an applied AC voltage of $15{\mathrm{V}}_{\mathrm{rms}}$. (b) Dynamic temperature increases of the CLC cell under the application of various voltages at a fixed frequency of 2 MHz. Note that the solid line in (a) is a simulated curve based on Eq. (6) and that the open symbols and solid lines in (b) represent experimental and curve-fitting results according to Eq. (5), respectively.

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By setting $t\to \infty$, Eq. (5) in the stationary state can be simplified as [22]

The pseudo-dielectric relaxation from the ITO effect has long been considered as a nuisance for dielectric investigations of an LC in that signals of certain relaxations from the LC material could be concealed at high frequencies [23]. Because the pseudo-dielectric relaxation can hardly be avoided in a sandwich-type cell, the direct way to suppress or shift this undesired dielectric signal beyond the investigated frequency regime is to use metal substances instead of ITO to lower the resistivity of the electrodes (e.g., silver electrode used in Ref. [16]) and/or to increase the cell gap (e.g., $d=40\mathrm{\mu m}$ used in Ref. [17]), according to Eq. (1). Some other methods based on mathematical calculations have also been proposed to eliminate the contribution of the cell-geometry-induced pseudo signal to the complex dielectric spectra so as to deduce the real dielectric behaviors of LCs [19,23]. Because the dielectric heating behavior in an LC cell has only been focused on the dielectric relaxation from dual-frequency LC molecules, the present work would be the first of its kind to confirm the contribution of the LC container to dielectric heating.

Utilizing this unique feature together with the thermal-responsive bandgap properties of a CLC, one can electrically tune the reflection band of the negative CLC through the control of cell temperature by an externally applied voltage. Figure 4 displays transmission spectra and optical textures together with the corresponding photographs of the cell submitted to various AC voltages at $f=2\mathrm{MHz}$. Taken without any polarizer, these photographs, shown as the insets, are mirror images of a piece of black paper showing white inverted letters (“NCTU LCP”) reflected from the CLC cell. To illustrate the wavelength tuning ability, we refer to Fig. 1(a) and masterly controlled $T_s=22°\mathrm{C}$ so as to allow the reflection band to lie in the near-IR region in the field off-state (${\lambda }_{\text{c}}=1392\mathrm{nm}$ at $V=0{\mathrm{V}}_{\mathrm{rms}}$). When the voltage increased to $3.5{\mathrm{V}}_{\mathrm{rms}}$, the bandgap appeared in the visible light regime (${\lambda }_{\text{c}}\sim 800\mathrm{nm}$ at $V=3.5{\mathrm{V}}_{\mathrm{rms}}$) and blueshifted further with increasing voltage, reaching ${\lambda }_{\text{c}}\sim 380\mathrm{nm}$ at $V=12{\mathrm{V}}_{\mathrm{rms}}$. The color changes of the reflective optical texture and of the cell appearance from red at $V=4.5{\mathrm{V}}_{\mathrm{rms}}$ to green at $V=6.5{\mathrm{V}}_{\mathrm{rms}}$, blue at $V=9{\mathrm{V}}_{\mathrm{rms}}$, and to violet at $V=12{\mathrm{V}}_{\mathrm{rms}}$ are consistent with the corresponding bandgap properties. Further increasing the voltage to $15{\mathrm{V}}_{\mathrm{rms}}$ resulted in the disappearance of the bandgap from the visible spectrum.

 

Fig. 4. Transmission spectra, texture images of the CLC, and photographs of the real cell driven by various voltages at 2 MHz.

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The bandgap shift to the UV region at $V=15{\mathrm{V}}_{\mathrm{rms}}$ brought about the dark appearance of the CLC phase. The results, as shown in Fig. 4, imply that the proposed electrical tuning method enables a broadband tunable wavelength range, spanning from the IR, visible, and UV light regions, for reflective color by simply regulating the applied voltage between 0 and $15{\mathrm{V}}_{\mathrm{rms}}$ at $f=2\mathrm{MHz}$.

Alternatively, Fig. 5(a) depicts the frequency dependence of tunable ${\lambda }_{\text{c}}$ of the cell under the application of various external voltages. In considering the limit of detection of the used spectrometer (i.e., 380 nm–820 nm), $T_s$ here was set at $\sim 23°\mathrm{C}$ so that ${\lambda }_{\text{c}}\sim 760\mathrm{nm}$ at $V=0{\mathrm{V}}_{\mathrm{rms}}$. It is clear that ${\lambda }_{\text{c}}$ remained unchanged and then decreased with ascending frequency beyond a critical value ($f_0$), dropping with increasing $V$ from $f_0\sim 118\mathrm{kHz}$ at $V=5{\mathrm{V}}_{\mathrm{rms}}$ and approaching a saturated value of $f_0\sim 24.5\mathrm{kHz}$ at voltages beyond $12{\mathrm{V}}_{\mathrm{rms}}$. This establishes that both the amplitude (Fig. 4) and frequency [Fig. 5(a)] of the voltage have a profound influence on ${\lambda }_{\text{c}}$ of the reflection band. The higher the amplitude (frequency) of the voltage applied across the cell gap, the lower the frequency (amplitude) required for desired ${\lambda }_{\text{c}}$ tuning [see Eq. (6)]. For instance, to achieve tunable ${\lambda }_{\text{c}}$ from 760 to 380 nm, one can vary the frequency from 24.5 kHz to 2 MHz at $V=12{\mathrm{V}}_{\mathrm{rms}}$ or from 24.5 kHz to 403.7 kHz at $V=15{\mathrm{V}}_{\mathrm{rms}}$. Furthermore, Fig. 5(b) presents the frequency dependence of $\mathrm{\Delta }T$ of the cell applied with various voltages. The $\mathrm{\Delta }T$ data, obtained by fitting the results of Fig. 5(a) into Eq. (2), well match the (solid-symbol) curves acquired by IR thermography, corroborating the change in ${\lambda }_{\text{c}}$ by voltage-induced temperature alteration. Notice that the $\mathrm{\Delta }T(f)$ curves at various voltages can be plotted by fitting the data using Eq. (6) as well (not shown in the figure). In addition, one can see from the inset of Fig. 5(b) that $\mathrm{\Delta }T$ is linearly proportional to the square of $V$, conforming to the mechanism of the dielectric heating effect, as described by Eq. (6). Furthermore, to verify that the above-mentioned results are nonspecific, we prepared another CLC cell, designated CLC-1, whose ITO resistivity (giving $R_{\mathrm{ITO}}\sim 1.6\mathrm{k}\mathrm{\Omega }$) is much larger than that of the primarily used cell ($R_{\mathrm{ITO}}\sim 310\mathrm{\Omega }$) in this study, whereas other conditions, such as $A=1{\mathrm{cm}}^2$, $d=5\mathrm{\mu m}$, and the CLC injected, for these two cells are kept identical. Figure 6 shows the dielectric spectra of CLC-1 at $T=23°\mathrm{C}$ [Fig. 6(a)] and the frequency-dependent ${\lambda }_{\text{c}}$ and $\mathrm{\Delta }T$ of this cell under the application of a $15-{\mathrm{V}}_{\mathrm{rms}}$ voltage [Fig. 6(b)]. One can still observe from Fig. 6(a) a single Debye-like dielectric relaxation, but it shifts to lower frequencies as compared with that of the results shown in Fig. 2(a). By fitting the real-part dielectric spectrum into Eq. (3), the results indicate an identical value of ${ϵ}_{\text{s}}=6.4$ and a decrease in $f_{\text{PR}}$ (from 440 kHz to 93 kHz) upon increasing the value of $R_{\mathrm{ITO}}$ (from $310\mathrm{\Omega }$ to $1.8\mathrm{k}\mathrm{\Omega }$). This confirms again that the unique dielectric relaxation in the complex dielectric spectra of our used CLC cell is attributable to the significant $R_{\mathrm{ITO}}-C_{\mathrm{cell}}$ circuit of the cell rather than the rotation of LC molecules. Moreover, electrically tunable ${\lambda }_{\text{c}}$ of CLC-1 can also be realized, but its tunable range (between 740 and 480 nm) by $15-{\mathrm{V}}_{\mathrm{rms}}$ voltage in the frequency range between 1 kHz and 2 MHz is narrower than that of the CLC with $R_{\mathrm{ITO}}\sim 310\mathrm{\Omega }$ (between 760 nm to 380 nm) even by $V=12{\mathrm{V}}_{\mathrm{rms}}$ in the same frequency range, as shown in Fig. 6(b). Similarly, we obtain $\mathrm{\Delta }T$ by the variation in ${\lambda }_{\text{c}}$ according to Eq. (2). As displayed in Fig. 6(b), the frequency-dependent $\mathrm{\Delta }T$ curve of CLC-1 can perfectly be fitted by Eq. (6) with $f_{\text{R}}=91.2\mathrm{kHz}$, which still follows the relation of $f_{\text{R}}\sim f_{\text{PR}}=93\mathrm{kHz}$. The frequency-dependent $\mathrm{\Delta }T$ also reflects a weakened efficacy of dielectric heating of CLC-1 by lowered $f_{\text{R}}$; this is again consistence with Eq. (6). Additionally, experiments using cells with various cell parameters have also been performed in our laboratory. It can be summarized based on the data that the cell gap, the electrode area, and the intrinsic dielectric anisotropy of LC materials can be used to optimize the pseudo-dielectric relaxation and the strength of dielectric heating, following Eqs. (1) and (5), respectively.

 

Fig. 5. Frequency-dependent (a) center wavelength and (b) temperature elevation at various AC voltages. The open and solid symbols in (b) represent $\mathrm{\Delta }T$ deduced from fitting of the experimental data using Eq. (2) and measured with an IR camera, respectively.

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Fig. 6. (a) Complex dielectric spectra of the CLC cell with $R_{\mathrm{ITO}}=1.6\mathrm{k}\mathrm{\Omega }$ at $T=23°\mathrm{C}$. (b) Frequency-dependent ${\lambda }_{\text{c}}$ and $\mathrm{\Delta }T$ of this cell under a $15-{\mathrm{V}}_{\mathrm{rms}}$ applied voltage.

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4. CONCLUSIONS

In summary, we have demonstrated a feasible approach enabling the electrically tunable reflective color from a CLC over the full visible spectrum. According to the thermally sensitive bandgap properties of the CLC and the cell parameters, the working principle of this approach is explicated in terms of the tunable ${\lambda }_{\text{c}}$ of the Bragg reflection band via the voltage-induced dielectric heating effect instead of the joule heat. Notably, the dielectric heating is predominated by the pseudo-dielectric relaxation originating from the use of the ITO cell with finite conductance. This heating effect is unique and demonstrated for the first time in this study, which should be carefully distinguished from the well-known dielectric heating effect in dual-frequency LCs explained by the dipole rotation of the molecules. Upon the application of AC voltage to the cell, our results validate that the tunable color ($380\mathrm{nm}\le {\lambda }_{\text{c}}\le 780\mathrm{nm}$) can be readily realized by varying either the voltage amplitude (say, $0{\mathrm{V}}_{\mathrm{rms}}\le V\le 12{\mathrm{V}}_{\mathrm{rms}}$ at $f=2\mathrm{MHz}$) or frequency (e.g., $24.5\mathrm{kHz}\le f\le 2\mathrm{MHz}$ at $V=12{\mathrm{V}}_{\mathrm{rms}}$). Because the CLC exhibits electrothermally tunable ${\lambda }_{\text{c}}$ between 1392 nm at $0{\mathrm{V}}_{\mathrm{rms}}$ and 340 nm at $15{\mathrm{V}}_{\mathrm{rms}}$ with a frequency of 2 MHz, true black color can be facilely obtained. The fabrication of the proposed negative CLC cell is of ease by virtue of all materials used, including the empty sandwich-type cells with ITO substrates, to be commercially available. In contrast with other electrical tuning methods, this study provides a new pathway to a wider tunable reflective color range with lower operating voltage, thus promoting the applicability of CLC for the design of superior color-reflective displays and electrically tunable photonic devices.