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Abstract
Light polarization rotations, created by applied optical field, are examined experimentally and theoretically in a photosensitive chiral nematic fluid. The polarization rotation of the transmitted beam is initiated by illuminating the sample with uniform UV light. The operation is tunable and reversible, depending on the UV intensity. It was revealed that the rotations can be ascribed to the optical-field-induced chirality effect, where the helical structure in chiral nematics changes in accordance with the UV intensity. The evolution of the helical structure as well as its effect on the light polarization upon illumination by uniform UV light have been monitored experimentally and compared by calculations based on the continuum theory. Our results proved that a polarization field with specific characteristics can be achieved using the remote and precise optical control.
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Corrections
11 April 2024: A typographical correction was made to the author affiliations.
1. Introduction
Apart from the intensity, frequency and phase, polarization is another important characteristic of light, which has recently extensively been concerned in the fields of optical communication, polarization imaging, biomedical analysis and materials characterization.
Some materials, such as azobenzenes or dichroic dyes, are capable of giving photosensitive response to the light polarization, which can be exploited in photonic devices to perform specific functionalities associated with polarization field [1,2]. Besides, thanks to the optical anisotropy and sensitivity to the external fields, nematics are also ideal candidates to tune the polarization state of transmitted light [3]. One famous example is the twisted nematic device, where the director rotates along a helical axis; with such a structure the electric vector of transmitted light follows the rotation of the director synchronously and the corresponding polarization state changes accordingly [4–6]. Another well-known example is an optical waveplate with desired retardation, which transforms the polarization state due to birefringence [7,8]. In the above-mentioned cases, the direction and magnitude of the polarization variation is determined by the surface alignments and the (induced) helical pitch of nematics; thus, they both are static and fixed during the device preparation, which brings about rather an inflexibility in application [9].
In order to manipulate the light polarization dynamically, recently a new system composed of a nematic and a photosensitive chiral dopant has been introduced [10]. As the helical twisting power (HTP) of our chiral dopant changes upon illumination by UV light, the induced helical structure of the system, as well as the orientation of the applied voltage induced electroconvection patterns can be controlled by the UV field [11]. Adopting a hybrid aligned cell (HAC) geometry to ensure the change of helical pitch freely, the change of pattern orientation could be made continuous, facilitating a two-dimensional beam steering [12].
In this paper, we show that the HAC system above is also capable of rotating the polarization state of transmitted light using a controlling UV field. We demonstrate an unusual linear polarization rotator, which is able to dynamically and continuously twist the plane of a linearly polarized light and can be tuned optically. It is anticipated that such effects can be generalized to fabricate fantastic photonic devices, such as polarization rotator arrays, which can define spatial polarization distributions according to custom presetting, with dynamically and in situ switchable tunability.
We are aware that the method described in this paper is not the only possibility to realize continuous polarization rotation. Recently, an alternative way with slightly different geometry (tangential – conical boundary conditions) has also been proposed to perform such operations [13]. In addition, recently a conceptionally different technique based on heliconical cholesterics with short pitch ($P\; \sim \; \lambda $) has also been suggested to achieve continuous polarization rotations [14,15]. Our method works in a completely different pitch range (P >> λ) of the light transmission, where the Mauguin limit fulfils. In addition, the optical tuning is not based on the optical torque as in the heliconical case, but rather on the molecular conformation changes induced by the illuminating UV light.
2. Materials and methods
2.1 Samples
The measurements were performed on a cholesteric liquid crystal (CLC) obtained by doping the nematic host E7 with the chiral dopant M5(R) (9-(2-methyl-2,3-dihydro-1H-cyclopenta[a]naphthalen-1-ylidene)-9H-fluorene) at weight concentration CM5. The CLC compound was filled into hybrid aligned cells with thickness d, where one substrate surface was treated by the polyimide (PI) Nissan 7511 L to obtain homeotropic alignment, while the other substrate was covered by the PI Nissan SE150, which resulted in a parallel alignment after rubbing along the direction n0.
As a photosensitive molecular switch (also called as light powered nanomotor [16]), the HTP of the chiral dopant M5(R) varies with the intensity of UV irradiation, resulting in a tunable helical pitch P(Iuv) [10,11,17]. It was found that there is a critical UV intensity Ic = 1.25 mWcm−2, where the HTP becomes zero, i.e. the helical structure fully unwinds yielding a nematic-like, compensated cholesteric state with |P(Ic)| = ∞. Initially, without UV illumination, the dopant M5(R) induced right-handed cholesteric helix; afterwards, upon UV illuminating, M5(R) molecules may undergo photoisomerisation; if the UV intensity exceeds Ic, then the helix switches to an opposite (left-handed) helical sense [12].
2.2 Photo-tuning setup
A DMD (digital micro-mirror device) - based dynamic mask photo-tuning technique was employed, where a collimated λ = 365 nm UV beam from a LED lighter (FUV-8BIT, Height-LED Opto-electronics Technology Co.), acting as command light, was reflected onto the DMD and subsequently carried a designed light intensity pattern (Fig. 1). In our experiments, a uniform (pattern free) image was uploaded into the DMD producing homogeneous UV intensity Iuv, which could be adjusted by the grey level of the image.
Fig. 1. Schematic diagram of the DMD-based dynamic mask system for photo-tuning, which integrated light emission, dynamic pattern generation, image focusing and monitor components.
After being focused by an objective, the UV beam was projected onto the sample, whose intensity was detected by an UV meter (UV-A from Bejing Shida Photoelectric Technology) placed in front of sample. A linearly polarized laser (λ=633 nm) acted as probe beam and impinged upon the sample, and the polarization state of transmitted beam was measured by a polarimeter (PAX1000 from THORLABS). Besides, in order to check how morphologies of the sample changed with varying Iuv, the 633 nm laser beam was replaced by a collimated white light, with the help of front and rear polarizers, colorful optical textures were monitored by a CCD at reflected-light mode [18]. Meanwhile, two optical color filters were installed before the polarimeter and CCD to block the UV light, respectively.
3. Experimental results
In the following experiments, samples with CM5 = 0.0075% and d = 60 µm were inspected typically, where the combination of the values of CM5 and d were selected so that to produce a π/2 rotation of transmitted light’s polarization at Iuv =0 with respect to that of the incident beam. At this concentration the initial (unilluminated) pitch is ${P_0} = 2.13\cdot d{\; } = {\; }128$ µm. A uniform UV field was used to tune the pitch and to manipulate the polarization states of the transmitted beam.
3.1 Polarization rotation of the transmitted beam
When subjected to a controlling UV light, both the pitch P and the chirality of samples changed accordingly. For the spatially uniform Iuv, the corresponding helical structure distributed homogeneously in the whole sample.
Depending on Iuv, four kinds of helical structures appeared, demonstrated in Figs. 2(a)–2(d), respectively: ① initially right-handed state with P0 > 0 at Iuv =0; ② right-handed states with P(Iuv) > P0 > 0 in the range of 0 < Iuv < Ic; ③ unwound, compensated state with P(Ic) ≈ ∞ at Iuv = Ic; ④ left-handed states with P(Iuv) < 0 in the range of Ic < Iuv, indicating a handedness inversion.
Fig. 2. Schematic illustration of the evolution of helical structures upon illumination by a uniform UV light with intensity Iuv, where (a) the sample stays in its initially right-handed state with pitch + P0 at Iuv =0; (b) the sample remains in a right-handed state with pitch + P1 (|P1|>|P0|), when Iuv < Ic; (c) the sample becomes compensated with pitch |P| = ∞ at Iuv = Ic; (d) the sample turns into a left-handed state with pitch of -P2, when Iuv > Ic.
As the helical structure was homogeneous in the cell plane, the normally incident light beam travelled through the sample directly. Due to the interaction between the helical structure and the incident beam, characteristics of the transmitted beam, such as the polarization state and the output intensity, may differ from that of the incident beam, as shown in Fig. 3. In the following, we demonstrate how a uniform Iuv affects the sample, its polarization state and the output intensity of the transmitted light.
Fig. 3. Schematic diagram of light traveling through a sample, illuminated by an additional uniform UV light. Iin and Ein, Iout and Eout are the intensity and polarization state of the incident and the transmitted beam, respectively.
3.2 Dependence of the CLC texture upon the UV intensity
Illuminated by uniform Iuv, various excited, pattern-free states were formed in the samples with crossed polarizers, characterized by different colors. It should be noted that upon enhancing Iuv, the resulting colors changed smoothly: at 0 ≤ Iuv ≤ Ic, the samples changed from the initial bright texture (Fig. 4(a)) to a dim texture (Fig. 4(b)), then an extinction texture corresponding to the unwound, compensated state with P(Ic) ≈ ∞ in Fig. 4(c); afterwards, when Ic ≤ Iuv, the samples went through the above states with reversed handedness, as shown in Figs. 4(d) - 4(f).
Fig. 4. Representative optical textures (450 µm × 290 µm) at crossed polarizer P and analyzer A, illuminated by increasing uniform UV intensity, where (a) Iuv = 0, (b) Iuv = 0.34 Ic, (c) Iuv = 1.0 Ic, (d) Iuv = 1.58 Ic, (e) Iuv = 6.68 Ic and (f) Iuv = 14.1 Ic, respectively.
3.3 Dependence of the polarization state upon the UV intensity
When the incident beam was linearly polarized with polarization along the x axis (azimuth angle of the polarization: α = 0), it was observed that during the change of Iuv, the polarization state of the transmitted beam was almost linear, while the polarization angle α varied, as illustrated in Fig. 5.
Fig. 5. Representative polarization states of the transmitted beam upon uniform UV field with (a) Iuv = 0, (b) Iuv = 0.34 Ic, (c) Iuv = 1.0 Ic, (d) Iuv = 1.58 Ic, (e) Iuv = 6.68 Ic and (f) Iuv = 14.1 Ic, respectively; α is the polarization angle.
Further inspection indicated that for the initially right-handed sample, upon enhancing Iuv, α decreased monotonically and continuously by rotating clockwise, even when the sample had turned into a left-handed one due to Iuv > Ic. Eventually, α could be adjusted between -π/2 and +π/2, thus the polarization state can sweep the whole plane, as shown in Fig. 5 and Fig. 6(a).
Fig. 6. Dependence of (a) the polarization angle α and (b) the degree of linear polarization (DoLP) of the transmitted beam on the UV intensity Iuv. The inset illustrates the rotation of the polarization state with increasing Iuv in the initially right-handed sample.
3.4 Degree of polarization of the transmitted beam versus the UV intensity
The variation of the degree of linear polarization (DoLP) of the transmitted beam was examined depending on the Iuv, as shown in Fig. 6(b). Herein, DoLP was defined as DoLP = Imajor/(Imajor + Iminor), where Imajor and Iminor are the intensities along the major and the minor axes of the elliptically polarized beam, respectively. DoLP = 1 means a perfectly linearly polarized state.
It was found that the DoLP indicates a reasonably high degree of linear light polarization during the whole adjustability range of -π/2 ≤ α ≤ + π/2.
3.5. Effect of the sample thickness on the photo-tuning operation
It was found that the thickness d is a critical factor to determine the photo-tuning results, as shown in Fig. 7. Three samples were prepared and compared, where the dopant concentration CM5 and thickness d were carefully combined in order to fix α = π/2 for the transmitted beam at the initial unperturbed state (Iuv = 0).
Fig. 7. Dependence of the polarization state of the transmitted beam on the cell thickness d at Iuv = 0. The representative thicknesses d (CM5) are (a) 9 µm (0.06%), (b) 36 µm (0.013%), (c) 60 µm (0.0075%).
Under such conditions, the polarization state of the transmitted beam in the absence of UV illumination varies significantly with d; namely, a larger d induces a higher DoLP (reduction of the ellipticity), as illustrated in Fig. 7.
4. Discussion
As the characteristics of the transmitted beam closely correlate with the pitch P of the sample, the knowledge of how P is modulated by the UV light is a precondition for understanding the tunability mechanism.
4.1 Calculation of the director field in the hybrid aligned cholesteric sample
The director field in the HAC geometry can be calculated from the continuum theory [3,19]. The director field is represented by the tilt angle ϑ and the azimuthal angle φ. It is assumed that the director is homogeneous in the x-y plane, i.e. both angles depend on the coordinate z (normal to the substrates) only:
The Frank’s free energy density f of the sample reads as
Here $\vartheta ^{\prime}$ and $\varphi ^{\prime}$ denote the first z-derivatives, K1, K2 and K3 are the elastic moduli, while q = 2π/P is the twisting power and P is the pitch. The functions ϑ(z) and φ(z) minimizing Eq. (1) are searched for by variational calculus using the Euler-Lagrange equations
As f does not depend on φ, Eq. (3) can immediately be integrated yielding
Here the integration constant was chosen as 0, in order to prevent divergence of $\varphi ^{\prime}$ at the homeotropic boundary. Eq. (4) readily shows that the twisting power of the cholesteric is changing, if the director tilts away from the planar state. As K2 < K3, a reduction of the twisting power occurs corresponding to the K2/K3 ratio, as one moves from the planar toward the homeotropic boundary.
Multiplying Eq. (2) with $\vartheta ^{\prime}$, it can be transformed into a total differential
After substituting $\varphi ^{\prime}$ from Eq. (4) the integration yields
The inverse functions z(ϑ) and φ(ϑ) can then be derived as the integrals
The integrals in Eqs. (6,7) can be calculated numerically. The integration constant B should first be iterated until the condition $z({{\vartheta_h}} )= d$ fulfils. Then ${\varphi _h} = \varphi ({{\vartheta_h}} )$ provides the total twist angle of the director in the sample. In the formulas above, ϑp and ϑh correspond to the tilt angles at the planar and homeotropic boundaries, respectively. During the calculations, the material parameters of E7 were taken from the supplier as: K1 = 11.3 × 10−12 N, K2 = 6.7 × 10−12 N, K3 = 18.6 × 10−12 N. Strong boundary conditions with a small pretilt angle (ϑp = 1°and ϑh = 89°) and rubbing along the x-axis (φp = 0) were assumed.
Figures 8(a) and 8(b) depict the numerically calculated ϑ(z) and φ(z) dependences, respectively, for different values of the helical pitch P. It can clearly be seen that the twist angle decreases, while the tilt angle increases with the growth of the pitch. Moreover, the shape of the ϑ(z) curve changes from concave at the initial (P = P0) to convex at the compensated (P → ∞) state. The convexity of ϑ(z) in the compensated state is a direct consequence of the missing twist contribution (q = 0) in Eq. (5) and the K1/K3 < 1 ratio. The twist term at q ≠ 0, mainly contributes and reduces $\vartheta ^{\prime}$ near the planar side, thus inducing the transition to concave shape at smaller P. At the same time, φ(z) preserves convexity for all pitch values, as expected from Eq. (4).
Fig. 8. Director profile across the sample for different values of the pitch P. (a) The tilt angle ϑ(z), (b) the azimuthal angle φ(z).
The simulation results in Figs. 8(a)–8(b) show only the curves for various values of the righ-handed pitch. Note, however, that the ϑ(z) curve is not sensitive to the helical sense, as Eq. (5) contains q2 only. Thus the ϑ(z) curves belonging to right-handed and left-handed helices of the same |P| should coincide. In contrast to that, the sign of φ(z) depends on the helical sense as seen from Eq. (4); thus the φ(z) curves of left-handed helices can be obtained by reflecting the φ(z) curves of right-handed ones onto the horizontal axis.
4.2 Evolution of the pitch under the UV field
Due to the photo-induced chirality effect of chiral dopant M5(R), the pitch P(Iuv) of the sample could change in spatially homogeneous manner, when the sample was submitted to uniform UV intensity.
In a usual planar geometry, with the helical axis perpendicular to the substrates, an integer number of half turns must be formed in the sample due to the boundary conditions (Grandjean-texture), i.e. the pitch can take only discrete values [11,19]. In the HAC geometry used in our experiments, however, P(Iuv) could be tuned freely by the UV intensity Iuv, due to the lack of azimuthal constraint on the director at the homeotropic surface. Moreover, due to the large pitches involved, the sample manifested as a slightly twisted system. Consequently, the total twist angle ${\varphi _h}({{I_{uv}}} )= \varphi ({z = d} )$ changed smoothly depending on the small ratio of d/P(Iuv) [12,20].
According to the UV intensity dependence of P(Iuv) [11], we distinguished two intensity regions separated by the critical intensity Ic : ① In the low UV intensity region of 0 < Iuv < Ic, the handedness of the helical structure was the same as that in the unilluminated (Iuv = 0) state. Increasing Iuv resulted in the enlargement of the pitch |P(Iuv)|, and hence in diminishing ${\varphi _h}$. ② At Iuv = Ic, one had a compensated cholesteric structure, where there is no twist of the director and hence ${\varphi _h}$ = 0. ③ In the high UV intensity region of Ic < Iuv, the handedness experienced a reversal, while |P(Iuv)| decreased and $|{{\varphi_h}} |$ increased accordingly with growing Iuv. Thus, the rotation of ${\varphi _h}({{I_{uv}}} )$ at the border of the low and the high intensity regions was monotonic and smooth.
4.3 Characteristics of the transmitted light
In Fig. 6(b), we have seen that a smaller rotation of the polarization corresponded to a higher DoLP of the transmitted beam. Similarly, Fig. 7 depicts that in a thicker cell one finds a higher DoLP. These two observations fully coincide with the expectations from the Mauguin theorem for light transmission in twisted liquid crystal systems, which predicts an optical waveguiding mode (rotation of the light polarization with the director) if the condition $2\mathrm{\;\ \pi \;\ }\Delta n{\; }d/\lambda \gg {\varphi _h}$ is satisfied [21]. One has to take into account, however, that the hybrid aligned structure may cause complications, as the increasing tilt angle reduces the effective optical anisotropy (Δn in the above formula) and hinders the fulfilment of the Mauguin condition near the homeotropic substrate.
To explore the consequences of the twisted hybrid aligned director structure, characteristics of the transmitted light have numerically been simulated using the Jones-matrix method [3,22]. To calculate the Jones-matrix of the cell, we split it into thin slabs of thickness $dz$ along the z-direction. If $dz$ is small enough, the twist and tilt angles can be regarded constant in a slab with a good approximation. Each slab is then a birefringent waveplate with a retardation $\mathrm{\Delta }{\Phi _i}$ and the direction of its slow axis at the angle ${\varphi _i}$ with respect to the x-axis. The retardation for the ith slab coming from its birefringence can be calculated as
The refractive indices of E7 from supplier were ne = 1.741 and no = 1.517. It was found that the outgoing light is nearly linearly polarized, though it possesses a small ellipticity. The direction of the polarization (i.e. the direction of the slow axis of the ellipse) makes an angle α with the x axis, with α being slightly smaller than the maximal twist angle ${\varphi _h}$, as illustrated in Fig. 9(a). Our simulations agree well with the experiments. The rightmost end of the simulated data in Fig. 9(a) corresponds to the smallest pitch (P0 = 2.13 d), which was actually used in the experiments. The difference between the simulated and the measured value (${\approx} $90°) of α is less than 15°, which is plausible since we used the elastic constants and refractive indices of the pure nematic E7 in the simulation, not taking into account the changes in the material parameters caused by the photosensitive dopant. Little adjustment of the material constants, e.g. either purely decreasing ${K_2}$ by about 19% or purely increasing ${K_3}$ by 23% leads to $\alpha \approx 90^\circ $.
Fig. 9. (a) Comparison of the total twist angle ${\varphi _h} = \varphi ({z = d} )$ and the azimuth angle of the output light’s polarization ellipse (α) as a function of the thickness to pitch ($d\; 2\pi /P)$ ratio. (b) The degree of linear polarization (DoLP) versus $d\; 2\pi /P$. The simulation was performed at fixed $d = 60\; \mu $m.
One expects that the transmitted light will become more linearly polarized at smaller d/P. Surprisingly, the ellipticity does not vary monotonically with the pitch; instead it exhibits a damped oscillation upon enlarging P, as depicted in Fig. 9(b). This behavior reminds to that of the thickness dependence of the transmission of a twisted nematic cell [23,24]. Note that theoretically, at normal incidence, DoLP depends on the angles ϑ and |φ|, i.e. it should not be sensitive to the sign of the pitch. Nevertheless, the experiment shown in Fig. 6(b) depicts a slight asymmetry. It can be attributed to UV light induced change of the material parameters (e.g. elastic moduli) or slight misalignment of the optical setup.
As a conclusion, under the photo-tuning operation, the cholesteric sample forms an optical waveguiding structure; thereby the transmitted beam becomes a guided-wave, even when the pitch and the chirality of sample varies with Iuv. Consequently, our device acted as a polarization rotator that allowed the transmitted beam to be linearly polarized with a fixed intensity and controlled polarization direction.
4.4 Response time of the polarization changes
As we described earlier [11], the UV illumination induces a conformational transition of the chiral dopant to an excited state, which possesses a different sign of its helical twisting power. This excited conformer returns to its initial, unexcited state via thermal relaxation. Therefore, in order to ensure a desired rotation angle of the light polarization, illumination by a proper UV intensity should permanently be maintained.
Figure 10 exhibits an example of how the polarization angle α behaves upon UV intensity transients. It can be figured out that our sample responded with a response time of about 15 minutes, both on switching the UV on or off. One can identify at least two different mechanisms, which determine the response times: (a) the conformational transitions of the dopants and (b) the adjustment of the director structure corresponding to the altered value of the pitch. We assume that the molecular processes (excitation by UV light and the thermal back relaxation) occur at a shorter time scale, so the response time is basically governed by the director relaxation time which is proportional to the square of the sample thickness. This assumption is supported by the fact that former measurements on the light induced rotation of electroconvection patterns (which reflect the underlying rotation of the director) in d = 6 µm thick samples (in contrast to the d = 60 µm used here) yielded a response time in the order of a few seconds [11].
Fig. 10. Temporal variation of the polarization angle upon switching the UV illumination on and off.
We note that the reason of using large sample thickness was our aim to realize polarization rotation with large DoLP. Reducing the sample thickness in order to speed up the device at the same concentration of the dopant would constrain the range of the polarization rotation angle to lower values. If the angle range has to be maintained, the dopant concentration has to be increased (as was done for the samples shown in Fig. 7) in order to shorten the pitch, but then the Mauguin condition might be less fulfilled, increasing the ellipticity of the transmitted beam. Thus, we conclude that having large DoLP (≈ 1) and fast response implies contradictory requirements.
5. Conclusion
We reported that the output polarization state of light can be manipulated continuously by applying a UV field, depending on the intensity of the uniform UV illumination.
In addition to the continuous rotation of the linear polarization, where the rotation angle could sweep the whole horizontal plane (-π/2 ∼≤ α ≤ +π/2) for the transmitted beam, it should be stressed that our prototype could work in a dynamical manner. It is based on bulk effect of the self-assembled helical structure being either compressed or dilated in response to the strength of the controlling UV field. In contrast, conventional linear polarization rotators only perform inflexibly, as are usually based on surface effects, where the surface alignments have been permanent since the devices were fabricated [25,26].
Funding
Hungarian National Research (NKFIH FK142643); Guangdong Provincial Science and Technology Plan (2022A0505050072, 2022A1515010777); Grantová Agentura České Republiky (22-16499S); National Key Research and Development Program of China (2020YFE0100200); Guangzhou Science and Technology Program key projects (202201000008); Fundamental Research Funds for the Central Universities (2023FRFK06011); Magyar Tudományos Akadémia (22-16499S); Guangdong Provincial Key Laboratory of Optical Information Materials and Technology (2017B030301007).
Acknowledgments
This work was supported by Guangdong Provincial Science and Technology Plan (2022A1515010777 and 2022A0505050072); Hungarian National Research, Development, and Innovation Office under Grant NKFIH FK142643, EIG CONCERT-Japan project FerroFluid (2023-1.2.1-ERA_NET-2023-00008); Czech project, Czech Science Foundation (22-16499S); National Key R&D Program of China (2020YFE0100200), Science and Technology Projects in Guangzhou (202201000008) and Guangdong Provincial Key Laboratory of Optical Information Materials and Technology (2017B030301007); Fundamental Research Funds for the Central Universities (2023FRFK06011). P.S. was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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