# Multi-Band High-Efficiency Multi-Functional Polarization Controller Based on Terahertz Metasurface

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}dielectric layer-metal backboard, which could be used as a dispersion-free half-wave plate or quarter-wave plate in a broad bandwidth [28]. Quader et al. demonstrated a graphene-based metasurface that exhibited a dynamically tunable feature and could generate broadband and efficient linear-to-circular polarization conversion [29].

## 2. Theory and Structure Design

_{u}= 240 μm, r

_{v}= 56 μm, t = 65 μm, the angle between the u-axis and x-axis is 45°, the permittivity of polymer dielectric plate is 2.324 + 0.003 * i, the metal cladding is made of gold with a thickness of 0.2 μm and a DC conductivity of 4.56 × 10

^{7}S/m. The simulations were performed using the commercial finite element simulation software CST Microwave Studio 2021 (Darmstadt, Germany). In the simulations, periodic boundary conditions are applied along the x-axis and y-axis directions. The open boundary condition is applied along the z-axis direction, and the linear polarization incident wave propagates along the z-axis direction. For the incident x-polarization wave (

**E**

_{i}= E

_{0}

**e**

_{x}), the reflected wave is ${\mathit{E}}_{R}={E}_{x}{\mathit{e}}_{x}+{E}_{y}{\mathit{e}}_{y}={R}_{xx}{E}_{0}{e}^{j{\phi}_{xx}}{e}_{x}+{R}_{yx}{E}_{0}{e}^{j{\phi}_{yx}}{e}_{y}$, where ${R}_{xx}={E}_{x}/{E}_{0}$ and ${R}_{yx}={E}_{y}/{E}_{0}$ represent coefficients of the co-polarization and cross-polarization reflection components, respectively, and ${\phi}_{xx}$ and ${\phi}_{yx}$ represent phases of the corresponding components. When $\mathsf{\Delta}\phi ={\phi}_{xx}-{\phi}_{yx}=2n\pi -\pi /2$ or $\mathsf{\Delta}\phi =2n\pi +\pi /2$ (n is an integer), if ${R}_{xx}={R}_{yx}$, the reflected wave will be a right-handed or left-handed circularly polarized wave, respectively.

## 3. Results and Discussion

_{yx}are over 0.95 in the frequency range of 0.36–1.0 THz, while co-polarization reflection coefficients R

_{xx}are less than 0.32, indicating that the x-polarized wave is efficiently converted to y-polarized wave in this frequency range, and the relative bandwidth reaches 94%. In addition, the same polarization conversion effect can also be observed at the frequencies of 1.20 THz and 1.31 THz. The reflection coefficients of co-polarization and cross-polarization components are the same at the frequencies of 0.32 THz, 1.03 THz, 1.18 THz, 1.21 THz, 1.29 THz, and 1.32 THz, and the phase differences between the co-polarization and cross-polarization components shown in Figure 2b are 0.5 π, −0.5 π, −1.5 π, −0.5 π, −1.5 π, −0.5 π, respectively. This means that, at the corresponding frequencies, the outgoing wave is a left-handed circularly polarized wave, right-handed circularly polarized wave, left-handed circularly polarized wave, right-handed circularly polarized wave, left-handed circularly polarized wave, and right-handed circularly polarized wave, respectively. Meanwhile, the reflection coefficients ($\sqrt{{R}_{xx}^{2}+{R}_{yx}^{2}}$) of the circularly polarized wave are over 0.97. These facts imply that the designed metasurface can realize the high-efficiency multi-band linear-to-circular polarization conversion.

_{0}, S

_{1}, S

_{2}, and S

_{3}represent the total reflection ratio of reflection wave, horizontal or perpendicular linear polarization state, +45°or −45° linear and circular polarization state, respectively. According to Stokes Parameters, the ellipticity is defined as:

_{RR}are over 0.95 in the frequency range of 0.36–1.0 THz and near the frequencies of 1.20 THz and 1.31 THz. While the coefficients of the cross-polarization reflection component R

_{LR}are less than 0.32 with the polarization conversion efficiency being less than 10% (Figure 5b). These facts indicate that the reflection wave is still right-handed circularly polarized wave at the corresponding frequency range. Thus, the designed metasurface can be regarded as a chiral preserving meta-mirror. The reason for generating the above phenomenon is that the rotation direction of the circularly polarized wave will change when it is reflected at the interface. That is, right-handed (left-handed) circularly polarized wave will be converted to left-handed (right-handed) circularly polarized wave. Since the metasurface can function as a half-wave plate at the corresponding frequency, it can also convert the right-handed (left-handed) circularly polarized wave to a left-handed (right-handed) circularly polarized wave. The above two factors result in the chirality of incident circularly polarized wave unchanged after being reflected from metasurface. Additionally, as the metasurface can also act as a quarter-wave plate at frequencies of 0.32 THz, 1.03 THz, 1.18THz, 1.21 THz, 1.29 THz, and 1.32 THz, the incident circularly polarized wave will thus be converted to linear polarization wave.

_{vv}and R

_{uu}, are approximately equal in the whole frequency range except for the frequency of 1.21 THz, and the reflection coefficients are very close to 1. It can be seen in Figure 7b that the phase difference $\mathsf{\Delta}\phi $ between the two major axes approximately maintains ± π in the frequency range of 0.36–1.0 THz and at the frequencies of 1.20 THz and 1.31 THz. Due to this feature, the designed metasurface can function as a high-efficiency half-wave plate. In addition, as the phase difference between two major axes is $\mathsf{\Delta}\phi =2n\pi \pm \pi \u20442$(n is an integer) at the frequencies of 0.32 THz, 1.03 THz, 1.18 THz, 1.21 THz, 29 THz, and 1.32 THz, the metasurface can therefore also achieve the function of multi-band quarter-wave plate.

**E**

_{0}impacts on the metasurface, it will excite dipole oscillation

**p**primarily along the major axis (u-axis) of metal elliptical blade, which can be decomposed into two oscillations p

_{x}and p

_{y}along the two orthogonal directions. In addition, the co-polarized scattered field is determined by

**E**

_{0}and p

_{x}, while the cross-polarized scattered field depends on p

_{y}. The multiple reflection caused by the Fabry–Pérot-like cavity may result in the interference effect of polarization couplings, which may enhance or weaken the whole co-polarized and cross-polarized reflected field. The Fabry–Pérot-like cavity with suitable length may induce a constructive interference for the cross-polarized field, with a destructive interference for the co-polarized field, and the cross-polarization conversion effect can thus be obtained. Similarly, the linear-to-circular polarization conversion can also be achieved via a Fabry–Pérot-like cavity with a certain length.

_{0}k

_{0}d, where n

_{0}is the refractive index of dielectric spacer, k

_{0}is the wave number in free space, and d is the thickness of dielectric spacer. The total reflected field can be expanded by ${\mathit{E}}_{r,\sigma}={\displaystyle \sum _{j=1}^{\infty}{\mathit{E}}_{r,\sigma j}}(\sigma =x,y)$, where j−1 denotes the roundtrip within the dielectric spacer. The m-th term is given by [48]:

_{Bσ;Aσ’}and r

_{Bσ;Aσ’}represent the transmission and reflection coefficients when wave is incident from medium

**A**with polarization σ’ and propagates to medium

**B**with polarization σ. Figure 8b depicts the simulated and calculated results of the proposed metasurface. The theoretical calculation results on the basis of tracking the various Fabry–Pérot-like scattering processes show excellent agreement with the simulated in addition to the slight deviations, demonstrating the interference effect presented above. Therefore, we can conclude that the polarization conversion functions of the designed metasurface indeed originate from the interference effect of Fabry–Pérot-like cavity.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**(

**a**) The reflection spectra and (

**b**) phase curves of the designed metasurface for incident x-polarized wave.

**Figure 3.**(

**a**) The ellipticity and (

**b**) AR of the designed metasurface for incident x-polarized wave. The purple dashed line denotes the AR of 3 dB.

**Figure 4.**The polarization conversion efficiency of terahertz metasurface. The purple region indicates the PCR greater than 90%. The red dots denote the frequencies of 0.32 THz, 1.03 THz, 1.18 THz, 1.21 THz, 1.29 THz, and 1.32 THz, respectively.

**Figure 5.**(

**a**) The reflection spectra and (

**b**) polarization conversion efficiency for the incident right-circularly polarized wave.

**Figure 6.**The reflection spectra of the designed metasurface vary with the incident angle for the linear polarization incidence. (

**a**) α = 10°, (

**b**) α = 20°, (

**c**) α = 30°, (

**d**) α = 40°.

**Figure 7.**The simulation results of incident u- and v-polarization wave. (

**a**) Reflection spectra, (

**b**) Phases.

**Figure 8.**(

**a**) Schematic of multiple reflection in the Fabry–Pérot-like cavity. (

**b**) Simulation and calculation results of reflection spectra of the designed metasurface.

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**MDPI and ACS Style**

Chen, H.; Zhao, W.; Gong, X.; Du, L.; Cao, Y.; Zhai, S.; Song, K.
Multi-Band High-Efficiency Multi-Functional Polarization Controller Based on Terahertz Metasurface. *Nanomaterials* **2022**, *12*, 3189.
https://doi.org/10.3390/nano12183189

**AMA Style**

Chen H, Zhao W, Gong X, Du L, Cao Y, Zhai S, Song K.
Multi-Band High-Efficiency Multi-Functional Polarization Controller Based on Terahertz Metasurface. *Nanomaterials*. 2022; 12(18):3189.
https://doi.org/10.3390/nano12183189

**Chicago/Turabian Style**

Chen, Huaijun, Wenxia Zhao, Xuejian Gong, Lianlian Du, Yunshan Cao, Shilong Zhai, and Kun Song.
2022. "Multi-Band High-Efficiency Multi-Functional Polarization Controller Based on Terahertz Metasurface" *Nanomaterials* 12, no. 18: 3189.
https://doi.org/10.3390/nano12183189