Electrically Active Terahertz Liquid-Crystal Metasurface for Polarization Vortex Beam Switching

Abstract

Polarized vortex waves have attracted widespread attention in investigations of light–matter interactions and the augmentation of information capacity owing to their distinctive characteristics. Nevertheless, the reconfigurable generation of vector beams, especially at terahertz (THz) frequencies, remains challenging. In this study, a tunable THz polarization vortex beam generator based on a liquid-crystal metasurface is proposed. A unit cell featuring reconfigurable linear polarization selectivity is developed. A general methodology for designing metasurfaces to generate customized and reconfigurable polarization patterns is introduced. Furthermore, the electrically tunable generation of polarized patterns and cylinder vector beams is experimentally demonstrated. The findings of this study can open up opportunities for wireless communication and super-resolution imaging applications.

Introduction

Vector beams are light beams with spatially varying polarization vectors.^[^{1, 2}^] They allow for distinct spatial polarization, offering a wide variety of fascinating phenomena, and have garnered significant attention. For example, polarization vector beams, which carry spin angular momentum,^[^3-5^] are essential for investigations of primary physical effects such as light–matter interaction and classical-quantum coupled systems.^[^6-8^] Vector beams offer distinctive advantages, including enhanced resolution,^[^{9, 10}^] improved sensitivity, expanded data capacity,^[¹¹^] and versatile functionalities beyond the capabilities of conventional light beams. The exploration and harnessing of vector beams at terahertz (THz) frequencies^[^12-15^] hold vast potential for transformative advancements in fields such as wireless communications,^[^16-18^] imaging,^[^{9, 10}^] and sensing.

A reconfigurable and versatile platform for generating and manipulating vector beams in the THz band is highly desirable. However, generating vector beams^[^19-21^] in the THz band is challenging due to the lack of efficient and compact sources and modulators capable of locally manipulating the polarization. Most existing methods for generating vector beams require bulky and complex optical components, such as q-plates^[^22-24^] and polarization converters.^[^25-28^] However, their insufficient tunability limits their applications in complex and dynamic scenarios, especially in telecommunication.

Incorporating liquid crystals (LCs) into metasurfaces is an effective approach for the dynamic control of THz waves. In recent years, significant progress has been made in terms of achieving a reconfigurable and programmable THz amplitude^[^29-34^] and wavefront control.^[^35-39^] LC metasurfaces have been widely used for realizing a variety of tunable functional devices, including beam deflectors,^[^35-39^] holograms,^[^40-44^] and lenses.^[^45-47^] LC devices can generate a range of vortex light fields by utilizing the spatially varying LC orientation to form spiral phase patterns^[^{48, 49}^] and geometric phase lenses.^[^{50, 51}^] Previous studies have demonstrated the potential of LCs in facilitating the tunable THz polarization devices.

In this paper, we propose a method for dynamically manipulating the polarization state of THz waves locally based on an LC metasurface. We developed a polarization-selective unit cell that can be switched dynamically. By arranging the unit cells with different orientations in a specific way, we developed reconfigurable devices capable of generating polarization patterns and cylindrical vector beams (CVBs). This study offers a general route to reconfigure vector light fields.

Concept of Polarization Vector Beam Generator

The proposed metasurface-based reconfigurable THz vector beam generator is shown in Figure 1. Unit cells with anisotropic response are oriented in a specific pattern to generate a CVB.^[^{52, 53}^] The CVB is a polarization vortex state whose polarization direction angle (φ) can be expressed as^[⁵⁴^]

\begin{equation}\varphi \ \left( \alpha \right) = \ P \cdot \alpha + {{\varphi }_0}\end{equation}

(1)

where α is the azimuthal angle, P is the topological charge of the vortex beam, and ??₀ is the initial polarization orientation. When the external voltage bias is removed, the reflected wave is radially polarized. When the bias is applied, the reflected wave transforms into an azimuthally polarized state. Their corresponding positions in the first-order Poincaré sphere are (0, 0) and (π, 0).^[¹^] Thus, the reflected THz wave can switch from a zeroth-order scalar polarization state to a first-order vector polarization vortex state.

Design of Unit Cells

The metasurface consists of periodic hexagonal unit cells. As shown in Figure 2a, each unit cell has a metal–insulator–metal structure, and the side length (P) is 186 µm. Two metallic layers are fabricated onto the quartz substrates. The dual-frequency LC layer (Jiangsu Hecheng Display Technology, DP002-016) is sandwiched between two metallic layers, which functions as a tunable dielectric medium. The metallic structure on the top layer is a circular patch with a diameter of 260 µm. The metallic pad with a cross-slit in the center on the bottom layer functions as the ground, as shown in Figure 2b. The two axes of the cross-slits have different lengths. The long and short axes of the cross-slits are L₁ = 135 µm and L₂ = 90 µm, respectively. It results in a difference in the resonance frequency for the orthogonal polarization waves. Thus, the unit cell has an anisotropic response.

Figure 2

Diagram of the unit cell and simulated THz absorption spectra. a) Exploded view of the structure of a unit cell. The top and bottom layers are 500 µm-thick quartz substrates. The 200 nm-gold film structure is fabricated onto the quartz substrates, and the middle layer is 25 µm-thick LC. b) Schematic of the cross-slit on the bottom metallic layer with a rotation angle of θ, where ? stands for the clockwise angle between the long-axis of the cross-slit and the y-axis. c) Simulated co-polarized absorption spectra under x and y polarized incidence in ON and OFF states. d) Simulated co-polarized absorption spectra with different rotation angles of the cross-slit. e) Simulated and calculated co-polarization absorption spectra as a function of θ at 0.409 THz.

We numerically simulated the reflection spectra of the unit cells using the electromagnetic simulation software. The metallic layers are made from gold film, and its conductivity in the simulation is 4.561 × 10⁷ S m⁻¹. We define the permittivity of LC in OFF and ON states as 2.7 and 3.4, respectively (see Note S1, Supporting Information, for details). Figure 2c shows the simulated absorption spectra under x- and y-polarized incidence. In the OFF state, the absorption peak under x-polarized incidence is obtained at 0.409 THz, and the peak value reaches 0.98, while the absorption peak frequency under y-polarized incidence is 0.430 THz, and the peak value is 0.945. When switching to the ON state, the resonance frequencies under x- and y-polarized incidence are red-shifted. The peak absorption coefficients are 0.817 at 0.37 THz and 0.96 at 0.409 THz, respectively. Based on the above simulation results, the device can switch from the y-polarized to the x-polarized polarizer at 0.409 THz with the change of LC permittivity.

The polarization-selective absorption is related to the orientation of the cross-slit on the lower metallic layer. As shown in Figure 2b, we define the long-axis direction of the cross-slit in the bottom unit cell as ${\mathrm{\vec{L}}}$ , and the short-axis direction as ${\mathrm{\vec{S}}}$ . When the cross-slit is rotated, the orientation angle of ${\mathrm{\vec{L}}}$ deviating from the y-axis is defined as the rotation angle (θ). The absorption spectra at different θ values for the case when the x- and y-polarized waves are incident on the device along the normal direction are shown in Figure 2d. When θ changes from 0° to 90°, the resonance frequency under x-polarized incidence shifts from 0.409 to 0.431 THz, while the resonance frequency under y-polarized incidence red-shifts from 0.431 to 0.409 THz.

The rotation of the cross-slit induces the alteration of the co-polarized absorption coefficient at 0.409 THz, which follows the vector decomposition theorem, as displayed in Figure 2e. The polarization-selective absorption direction in the OFF state is parallel to the direction of

{\mathrm{\vec{L}}}

and changes synchronously with the rotation of the cross-slit. When switching to the ON state, the polarization-selective absorption direction changes to the direction of

{\mathrm{\vec{S}}}

. According to the above simulation results, we can derive the Jones matrix of this THz tunable polarization absorption metasurface as follows

\begin{equation}{{G}_{{\mathrm{psm}} - {\mathrm{lc}}}} = \left[ { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} {{\mathrm{cos}}\theta }&{{\mathrm{sin}}\theta }\\[4pt] { - {\mathrm{sin}}\theta }&{{\mathrm{cos}}\theta } \end{array} } \right]\ \left[ { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} {{{r}_{xx}}}&0\\[4pt] 0&{{{r}_{yy}}} \end{array} } \right]\left[ { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} {{\mathrm{cos}}\theta }&{ - {\mathrm{sin}}\theta }\\[4pt] {{\mathrm{sin}}\theta }&{{\mathrm{cos}}\theta } \end{array} } \right]\end{equation}

(2)

where r_xx and r_yy are the co-polarization reflection coefficients of the x- and y-polarized waves, respectively (see Note S2, Supporting Information, for detailed derivation). As shown in Figure 2e, the simulation results agree well with the theoretical calculations. In the OFF state, r_xx = 0, and the device acts as a y-polarizer. When rotating the cross-slit, the coordinate system is rotated synchronously. The device maintains absorption for the linear polarized waves. When switching to the ON state, r_yy = 0, and the device functions as an x-polarizer.

The designed metasurface, composed of periodic unit cells with ?? = 0 reflects the y-polarized wave in the OFF state and the x-polarized wave when it switches to the ON state when a circularly polarized wave is incident. The polarization trajectory of the reflected wave on the zeroth-order Poincaré sphere is shown in Figure 3a. To demonstrate the function of the switchable polarization selectivity of the designed unit cell, we fabricated the reconfigurable device composed of the periodically arranged unit cells (see Experimental Section for fabrication process). Figure 3b shows the microscopic image of the fabricated device.

Details are in the caption following the image — **Figure 3**
Electrically tunable THz polarizer and measured reflection spectra. a) Polarization switching of the reflected THz wave on the zeroth-order Poincaré sphere. b) Microscopic images of the metallic structures on the upper and lower layers. c,d) Measured co-polarization reflection spectra with the bias voltage change under x-polarized (c) and y-polarized (d) wave incidence.

Electrically tunable THz polarizer and measured reflection spectra. a) Polarization switching of the reflected THz wave on the zeroth-order Poincaré sphere. b) Microscopic images of the metallic structures on the upper and lower layers. c,d) Measured co-polarization reflection spectra with the bias voltage change under x-polarized (c) and y-polarized (d) wave incidence.

We used THz time-domain spectroscopy (THz-TDS) to measure the reflection spectra under x- and y-polarized wave incidence, as shown in Figure 3c,d. For the x-polarized wave incidence, as the applied voltage increases from 0 to 20 V, the absorption peak frequency red-shifts from 0.409 to 0.38 THz, and the reflection coefficient at 0.409 THz increases from 0.27 to 0.87. When switching to y-polarized incidence, the absorption peak frequency gradually drops from 0.435 to 0.409 THz, and the reflection coefficient at 0.409 THz drops from 0.67 to 0.11. The experimental and simulation results are consistent, proving that the proposed device can switch the polarization-selective absorption direction by electric control. Though the experimentally obtained absorption for the x-polarized wave is high, it does not reach near-perfect absorption at the working frequency. It is mainly attributed to the parameter deviation, such as the substrate thickness and the material loss between the experimental and simulation results.

Electrical Switching of Polarization Patterns

We can generate different polarization patterns on a 2D plane by arranging the unit cells with different θ in a specific distribution. We fabricated a device with a predefined unit cell distribution, as shown in Figure 4a. The top layer has isotropic circular patches, and θ of the cross-slits in the bottom layer has a predefined distribution. The bottom layers are divided into different pixels, and each pixel consists of one of the unit cells with θ = 0°, 90°, and ±45°. Thus, a specific polarization pattern can be formed, as shown in Figure 4b. Applying the voltage bias will cause the switching between two complementary polarization patterns.

Figure 4c shows the measured electric field strength distribution at 0.409 THz. The external voltage bias is a 1 kHz square wave with a 20 V peak–peak voltage. In the OFF state, when the incident polarization wave is x-polarized, the electric field strength at the letter regions of “N, J, U” and the cross-pattern region is higher over other regions, the electric field strength of these patterns is the weakest, and the electric field strength in the “X” pattern in the lower right corner is intermediate. When switching to y-polarized wave incidence, the measured electric field strength pattern is complementary to that under x-polarized wave incidence. The complementary polarization patterns before and after switching conform to the polarization channel distribution in Figure 4b. The results verify that we can electrically generate polarization patterns and switch them to the orthogonal ones. The intensity distribution of the pattern has a grayscale, indicating that the change in its polarization absorptance agrees with the vector decomposition theorem. Therefore, the proposed metasurface can achieve a highly flexible polarization control and pattern generation.

Electrically Tunable Cylindrical Vector Beams

We further develop a tunable THz polarization vortex beam generator. The device comprises the LC unit cells with a specific orientation distribution, as shown in Figure 1. The orientation of the cross-slits in the surrounding unit cells was arranged based on their coordinate position. For the unit cell with a position of (x, y), the long-axis orientation of the cross-slit satisfies $\alpha \ =\ \textit{arct}\textit{an}(y/x)$ . As we have verified, the polarization direction of the unit cell in the OFF state is along the long-axis direction, which means that the polarization direction in the whole plane satisfies $\varphi \ ( \alpha ) = \ \alpha$ . When it is in the ON state, the polarization direction of each unit cell switches to the short-axis direction, and the polarization direction in the whole plane satisfies $\varphi \ ( \alpha ) = \ \alpha + \frac{\pi }{2}$ . We built an experimental setup, as shown in Figure 5a, to image the spatial electric field distribution. We fabricated the device consisting of unit cells with the above orientation distribution, as displayed in Figure 5b.

We experimentally measured the electric field distribution of reflected THz waves. When the linear polarizer is polarized at x-, y-, and ±45° direction, the measured distribution pattern at 0.409 THz is shown in Figure 5c. When the polarizer is rotated counterclockwise, the measured electric field distribution rotates counterclockwise synchronously, which means that the device generates a cylindrical polarization vortex wave. In the OFF state, the electric field strength is strong along the detection polarization directions and weakens on both sides. They reach the minimum at the direction perpendicular to the polarization direction, which indicates that the reflected THz wave is radially polarized. When switching to the ON state, the electric field strength is the weakest along the detection polarization directions and weakens on both sides. They reach the maximum at the direction perpendicular to the polarization direction, which indicates that the reflected THz wave is converted to an angular polarization wave.

Based on Figure 5c, we compute the polarization extinction ratio (PER) of two polarization vortices using the following equation

\begin{equation}{\mathrm{PER}}\ = \ 10{\mathrm{lg}}\ \frac{{{{P}_{{\mathrm{max}}}}}}{{{{P}_{{\mathrm{min}}}}}} = \ 10\lg \left( {\frac{{E_{{\mathrm{max}}}^2}}{{E_{{\mathrm{min}}}^2}}} \right)\end{equation}

(3)

where P_max and P_min are the maximum and minimum power values, respectively, and E_max and E_min are the maximum and minimum electric fields, respectively. The calculated PER is 7.38 and 8.17 dB in the OFF and ON states, respectively.

We also calculated the electric field strength distribution of two CVBs under different polarization directions, as shown in the upper right inset of the corresponding experimental results. As shown in Figure 5c, the amplitude distribution of the two is in good agreement. It indicates that the device can generate a polarization vector beam and switch it electrically. We note that the theoretical amplitude distribution charts are usually finer than the experimental ones. It is mainly because the size of the THz beam spot in the experiments exceeds the size of a unit cell, so the value of a single pixel is the average reflection intensity of several unit cells. The experimentally measured intensity distribution is not uniform due to defective unit cells in the fabrication process.

The proposed THz LC devices have demonstrated the capability of generating vector beams in a reconfigurable manner, which is critical for various applications, such as optical communication,^[^16-18^] manipulation,^[^29-38^] and sensing. By changing the preset arrangement, we can generate vector vortex beams with different topological charges. Recently, a THz programmable device based on an LC metasurface has been developed. The capability of manipulating the THz wavefront and amplitude of each pixel enriches the functions of metasurfaces and broadens their application prospects. If the unit cell capable of arbitrary and individual polarization control is developed, it will enable more complex and flexible vector beam manipulation. The programmable vector beam generators will have vast potential for enhancing the information capacity of the THz communication systems.

Conclusion

We demonstrated an LC-based metasurface for manipulating the polarization state of THz waves in a reconfigurable manner. A tunable THz absorber that could selectively reflect x- and y-polarized waves was experimentally demonstrated. We further proposed a general method for designing a metasurface that can realize customized tunable 2D planar polarization patterns by specifically distributing the unit cells with different orientation angles. We experimentally demonstrated a reconfigurable polarized pattern and CVB generators as a proof of concept. Our work may offer a tool for generating the THz vector beams and open new possibilities for imaging, sensing, communication, and energy harvesting.