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Abstract
Linear polarization rotators have been widely used in optical systems. Commonly used polarization rotators are still beset by strong dispersion and thus restricted spectral bandwidth of operation. This leads to the development of achromatic or broadband alternatives, but most of them incorporate multiple waveplates for retardation compensation, which comes at the cost of increased complexity and reduced flexibility in operation and system design. Here, we demonstrate a single-element achromatic polarization rotator based on a thin film of dual-frequency chiral liquid crystal. The angle of polarization rotation is electrically tunable from 0° to 180° with low dispersion (±3°) in the entire visible spectrum, and a high degree of linear polarization (>95%) at the output.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The modulation of optical polarization has been widely applied in neoteric optical devices, instruments, and techniques for biosensing, communication, image optimization, and material detection and display [1–15]. The phase difference between two orthogonal components of light (such as TE/TM and right/left circular polarization) determines the output polarization state. Typically, most polarization modulators play phase retardation to manipulate an optical polarization, such as conventional waveplates and Faraday rotator [16–21]. The phase retardation is expressed as δ = 2πd Δn / λ, where d is the thickness of the medium, Δn is the linear or circular birefringence, and λ is the operation wavelength. The phase retardation is wavelength dependent, so the polarization modulation by conventional modulators is inevitably dispersive. To broaden the operation bandwidth of conventional polarization rotators, multi-component rotators are developed, which typically comprise a series of waveplates for dispersion compensation so that the effective δ is nearly constant within a broad targeted range of wavelengths [22–24]. However, these broadband rotators are cumbersome and less tunable. Many of them are either fixed at a designed angle of rotation or limited in the maximum angle of rotation, which ultimately limits their flexibility in system design or the range of applications. Liquid crystals (LC) have been a good candidate as a tunable retarder for dynamically controlling polarization owing to their birefringence and high dielectric anisotropy. For instance, twisted nematic liquid crystals (TN LCs) in which LC directors in-plane rotate from one substrate to the other can achieve achromatic linear polarization rotation by a single element. For a TN LC fulfilling Mauguin’s condition (dΔn >>$\mathrm{\lambda }$), a linearly polarized light passing through the TN LC undergoes (nearly) achromatic polarization rotation with the angle same as the twisted angle of the TN LC [25–27]. However, the rotation angle is fixed once the device is fabricated, and the device only permits the switch between the state of no rotation and the state that allows the incident linear polarization to be rotated by a predetermined angle.
Thus far, the LC devices that allow continuous and (nearly) achromatic tuning of the rotation angle are the hybrid splay-twist LC and the in-plane switching TN LC [28,29]. However, they are limited to at most 90° of rotation [30,31]. Since a linear polarization is often considered to be a headless vector in most optical applications, the tuning range should be at least 180° to cover all possible polarization rotations. Polarization imaging, for example, usually requires four polarization rotation angles: 0°, 45°, 90°, and 135° [8–10]. In this work, we demonstrate, by experiments and simulations, a LC mode called hybrid-aligned super-twist (HAST) that enables 180°-tunable and nearly achromatic rotation of linear polarization with high degree of linear polarization at the output. Note that, although the LC mode is called hybrid-aligned super-twist for simplicity, splay and bend deformation are also present in range of applied field strengths.
Figure 1 illustrates the proposed operating concept. We fabricate a hybrid cell that have asymmetric boundaries (planar alignment [PA] and vertical alignment [VA]) and chiral dopant-doped dual-frequency LC (DF LC). The LC directors are initially arranged from a low tilt angle (planar alignment) to a high angle (vertical alignment) gradually in the direction of the cell thickness (represented as θ), with a twist deformation from 0° to 180° (represented as φ) due to the interplay between the boundaries’ anchoring force and the LCs’ elasticity. Thus, the initial state without an applied field is TN LC with a twist angle of 180°. Note that, the high tilted angle of the vertical boundary changes the working range of the birefringence. Because of the high tilted angle, the directors close to the VA substrate in the cell thickness direction act as a homogeneous material with a single refractive index of ${n_o}$ and does not contribute the phase retardation. Thus, the director twist from 0° to 180°, acting as TNLC with an effective optical polarization rotation angle (represented as ΦPR=∡PinPout) of Φinitial. With the application of a low-frequency electric field, the LC is positively dielectric and reorient parallel to the direction of the external field, thus expanding the effective length where directors have the high tilted angles; the twist angle is maintained from 0° to 180°. The optical polarization rotation angle decreases gradually from Φinitial to 0° under external fields of different strengths. Through the application of an external field with a high frequency, the LC exhibits negatively dielectric anisotropy and aligns perpendicularly to the external field. Consequently, the effective length with the high tilted angle is reduced and the twist angle remains from 0° to 180°. In addition, the optical polarization rotation angle increases from Φinitial to 180°.
Fig. 1. Operation concept of HAST-LC; $\theta $ represents the polar angle between the director and substrate, and $\varphi $ represents the twist angle between the director and direction of incident polarization.
2. Demonstration of 180° polarization rotation
In this study, we use the DFLC HEF967100-100 (Δn = 0.196, Δε = 2.74 at 100 Hz and −2.81 at 30k Hz respectively; HCCH, China) with a chiral dopant of R811 (HCCH, China) of 0.05wt%. The cell gap is 75 μm and the substrates are coated by PI-5291 for PA alignment and PI-5661 for VA alignment (Nissan, Yokohama, Japan), respectively. The detail of the mixture and cell condition please see supplementary information. To verify our design and demonstrate the continuously polarization rotation effect under applied fields of low and high frequency, we probe a linearly polarized laser beam at 632 nm (the direction of linear polarization is parallel to the rubbing direction) through the HAST-LC from the PA side, and monitor the transmittance variation at output beam by an analyzer of different transparent axes. To determine the rotation angle with respect to an incident linear polarization, we define the rotation angle ΦPR as the angle between the incident polarization and the orientation of an analyzer allowing the maximum transmittance at output. Note that, the rubbing direction of the entrance window (the substrate coated by planar alignment) is set as 0°. The degree of linear polarization (DOLP) is defined as DOLP = (Tmax – Tmin) / (Tmax + Tmin), where Tmax and Tmin represent the maximum and minimum transmittance when an analyzer rotates round, respectively. A DOLP equal to 1 represents 100% pure linear polarization. With the measured transmittance under different analyzer angles, we transform the polarization states under different external fields into Stokes parameters as follows: S1 = IP cos2ψ cos2χ, S2 = IP sin2ψ cos2χ, and S3 = IP sin2χ, where IP is equal to 1 when the incident beam is fully polarized by the polarizer, ψ is the angle value of ΦPR, and χ = tan-1(Tmin / Tmax).We then plot each point under different applied fields onto the Poincaré sphere illustrated in Fig. 2(a). The initial polarization state without an external field is located at 102°. Upon the application of an electric field of 100 Hz, the rotation angle ΦPR begins to decrease and the polarization state on the Poincaré sphere moves clockwise. The rotation angle ΦPR gradually decreases (from 102°) with an increasing electric field until ΦPR reaches 0° when the applied field is 0.4V/μm. Thus, continuous polarization rotation from 102° to 0° is realized. When the field of 30 kHz is applied, the rotation angle ΦPR increases with the increasing strength of an external field and the polarization state moves counterclockwise on the Poincaré sphere. The rotation angle ΦPR increases to 180° at Eac = 0.27 V/μm, realizing polarization rotation from 102° to 180°. Figure 2(b) shows the rotation angle ΦPR and DOLP functioning as an electric field; the blue and red circles represent the field is operated at 100 Hz and 30k Hz, respectively. We also examines the polarization rotation property by simulation (represented by gray triangle), showing the variation in the polarization angle under different applied fields perfectly matching experiments. Moreover, the DOLPs in both the experiment and simulation are higher than 0.95 under all modulation conditions, which indicates a high degree of linear polarization. As shown in Fig. 2(c), we capture polarized optical microscope (POM) images under parallel polarizers and analyze the polar graphs under applied fields of 100 Hz and 30 kHz. With the initial polarization state of 102°, the POM image shows a gray appearance. Through application of the 0.027 V/μm field at 100 Hz, the appearance turns dark because the output polarization is tuned to 90°. With the increasing strength of the field at 100 Hz after 0.027 V/μm, the POM image becomes bright as a result of the decreasing rotation angle. With the increased field at 30k Hz, the POM image becomes dark because the polarization modulation is between 102° and 180°. The polar graphs under 100 Hz and 30k Hz fields illustrate the continuously control of the polarization rotation angle and high degree of the linear polarization.
Fig. 2. (a) Polarization state under different applied fields at 100 and 30k Hz on a Poincaré sphere. (b) Relation among the applied field, ΦPR, and DOLP. (c) Polarized optical micrographs (POMs) with parallel polarizers and polar graphs under different applied fields.
3. Simulation and director distribution
To provide the mechanism underlying the HAST-LC, we employee the LC simulation software TechWiz LCD 3D [Vector Education TRN] (Sanayi System, Incheon, South Korea) to reveal the LC directors’ configuration under different applied fields. We control the dielectric anisotropy Δε and elastic constants k11, k22, and k33 to enable the fitting of the experiment and simulation results. However, the simulation software imposes restriction on our simulation parameters. The major limitation is that the polar and azimuthal anchoring strength on the top and bottom substrates are indivisible; thus, we cannot separate and control them individually. For this reason, there will be difference between the experiment and simulation parameters. However, we maintain that the structural behavior of the two processes fit (considering the variation in the polarization rotation angle ΦPR and DOLP at different fields Eac) and that the simulation result can be regarded as indicating the same process as that of the experiment. In the simulation, we use 75 layers and the mesh size of 1 μm. The simulation cell has the cell gap of 75 μm, which comprised a PA substrate (pretilt angle of 5° and azimuthal angle of 0°) and VA substrate (pretilt angle of 88.9° and azimuthal angle of 180°); the anchoring strength is set to 1 × 10−3 N/m. To simulate the DFLC, we use two materials with different dielectric anisotropies, Δε = +2.14 and −3.07 (to simulate the positively and negatively dielectric anisotropy under 100 Hz and 30 kHz, respectively). Both materials are designed to have the following parameters: k11 = 19 pN, k22 = 8.5 pN, k33 = 28 pN, and p = 212 μm. The optical performance is obtained using the Jones matrix, with the director distribution calculated by TechWiz. The director distribution under different fields is detailed in Fig. 3. The effective birefringence can be presented as:
Fig. 3. (a) (b) Distribution of the effective birefringence, polar angle, and azimuthal angle in the cell thickness direction of $\hat{z}$ with positive and negative dielectric anisotropic.(b) Director profiles of simulation results under different applied field strengths ${E_{ac}}$. (c) Polar graphs under different applied fields at 632 nm.
The director profiles of the simulation result under different applied field strengths Eac are depicted in Fig. 4(a), illustrating the director orientation under the decreasing and increasing polarization rotation angle ΦPR. The polar graphs in Fig. 4(b) and 4(c) describe the continuous controlling of the output polarization under different applied fields Eac at a wavelength of 632 nm with negative dielectric anisotropic (high frequency) and positive dielectric anisotropic (low frequency).
Fig. 4. (a) Director profiles of simulation results under different applied field strengths ${E_{ac}}$. (b) Polar graphs under different applied fields at 632 nm with negative dielectric anisotropic and (c) with positive dielectric anisotropic.
4. Achromaticity of HAST-LC
Herein, we discuss the achromaticity of the HAST-LC under different applied fields ${E_{ac}}$, with operation wavelength ranging from 400 to 700 nm. To obtain the polarization rotation angle ΦPR under different wavelengths and Eac, we measure the transmittance spectrum under various analyzer transmittance angles using a spectrometer USB4000 (Ocean Optics) with a white light source (a tungsten halogen lamp from Ocean Optics). We obtain the analyzer angle at its maximum transmittance as the polarization rotation angle ΦPR for each wavelength. To verify that the modulated output linear polarization remains a high degree of linearity, the DOLP is also examined at each wavelength. The results are presented in Fig. 5 where Fig. 5(a) and 5(c) are the experimental results and Fig. 5(b) and 5(d) are simulation results. As detailed in Fig. 5(a) and 5(b), the simulated ΦPR is perfectly matched to the experimental one, with the largest variation being ±3° in both the experiment and simulation. As depicted in Fig. 5(c) and 5(d), the DOLP is greater than 0.95 under all external field conditions. The achromaticity of the HAST-LC is ±3°, indicating low dispersion. Note that, enhanced achromaticity requires a larger cell gap or greater birefringence of the LC. An increase in cell gap size produces the fingerprint texture mentioned in supplementary information and Fig. S2, thus, a DFLC with a high birefringence would be the more favorable solution.
Fig. 5. (a) and (b) Polarization rotation angle ΦPR; (c) and (d) DOLP at different wavelengths under different applied fields in the experiment and simulation.
5. Conclusion
In summary, in this study, we design a linear polarization rotator with a continuously tunable polarization angle from 0° to 180° and low dispersion using the HAST-LC. This system consists of DFLC with a chiral dopant and hybrid-aligned substrates with an antiparallel rubbed direction. Without an applied field Eac, polarization rotation of 102° occurs. When an external field at 100 Hz is applied on the HAST-LC, the LC directors reorient owing to the positive dielectric anisotropy, and the polar angle rise in the direction of thickness. In addition, the polarization angle decrease with the strength of the electric field to realize continuous polarization control from 102° to 0°; the rotation angle can be modulated from 102° to 180° with an external field at 30 kHz, which causes the LC to reorient due to the negative dielectric anisotropy. The simulation fitting is also analyzed, in which the operating mechanism of the HAST-LC is described by the director distribution obtained using the simulation software. Achromaticity and the DOLP at different wavelengths ranging from 400 to 700 nm under electric fields of different strengths is also examined. The largest variation in the polarization rotation angle at different wavelengths is ±3°, and the DOLP is always higher than 0.95 under all applied field strengths. Enhanced achromaticity can be achieved with DFLC with high birefringence. For most applications in optical designs and systems, linear polarization modulation from 0° to 180° is essential for devices such as the spatial light modulator controlling polarization in spatial distribution and polarization imaging for capturing the light intensity with different angles to the optical axis. This study extends the possibility for more innovative applications in optical techniques.
Funding
Ministry of Science and Technology, Taiwan (MOST 110-2223-E265 110-001, MOST 109-2112-M-110-013-MY3).
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.
Supplemental document
See Supplement 1 for supporting content.
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