## Abstract

Polarization coding is of great importance because of its applicability to information processing, storage, and security devices. In this paper, we numerically demonstrated a binary and ternary polarization coding scheme using a cross-shaped graphene/Au hybrid metasurface with two-dimensional (2D) electrical tunability. The C_{4} symmetry broken of the cross-shaped structure, caused by different lengths of Au bars in *x-* and *y-* directions, allows 2D tunability for *x*- and *y*-polarized waves at one biasing condition. For *x*-polarized wave incidence, the proposed structure generates near-zero or near-unit absorption by switching the graphene’s Fermi energies, corresponding to the binary codes of ‘0’ and ‘1’. Due to 2D tunability, the combination of two absorptions excited by *x*- and *y*-polarized waves at 2.45 THz are encoded into ternary codes with the states of ‘−1’, ‘0’, or ‘1’ by gating voltages. The compatibility for binary and ternary coding in the tunable metasurface opposes huge potentials in artificial intelligent devices.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Recently, digital circuit develops very fast because of its low-power consumption and the development of computational circuit in quantum computer and artificial intelligence (AI) [1]. Nowadays, binary coding is in general use since computation and the technology of binary processing is already established. However, the ternary cods with three states with yes (1), no (−1) and unknown (0) is much closer to human thinking logic, which extremely facilitates the autonomous learning in AI. Also, ternary codes possess the advantages of reducing the complexity of interconnects, smaller chip area and the reducing number of cells [2]. To adapt to the technology transition from binary to ternary codes, the encoding scheme’s compatibility for binary and ternary codes are highly desired.

Metamaterials with effective medium parameters or gradient phases have been enabled plenty of emerging functions in the applications of beam steering [3], focusing [4], hologram [5], polarization conversion [6], and cloaking [7] etc.. These metamaterials are usually characterized by continuously macroscopic media with effective permittivity and permeability. In contrast to the ‘continuous’ feature, the concept of ‘coding metamaterial’ has been proposed in [8]. Based on the discrete concept, the phases of 0 and π in a static coding metamaterial mimic the ‘0’ and ‘1’ elements for binary codes [8,9]. Similarly, the polarization state of left circular polarization (LCP) and right circular polarization (RCP) states are used to represent binary codes in [10,11]. Also, the 2-bit logic codes are realized by the fast amplitude switching between unit and zero at a certain frequency [12,13]. However, most of these coding metamaterials are static structures, and only a few tunable metamaterials are reported [11,13,14]. To gain the compatible scheme for binary and ternary coding, one needs to control the responses of structure in *x*- and *y*-directions separately, which is named as 2D tunability. Despite the multiple-layer stacked structures with 2D tunability have been achieved by applying two different voltages [15,16], the complex construction of two voltage set limits its further development and applications.

Here, we numerically achieved 2D tunability using a gate voltage in a cross-shaped Au/graphene array, which enables binary and ternary coding simultaneously. The Au/graphene bar in *x*- or *y*-direction enables binary coding due to the absorption switching between near unity and zero at 2.45 THz, which is caused by one-dimensional frequency tunability. Due to the 2D tunability in the cross-shape structure, resonant frequency switching of the polarization-dependent absorptions achieves three absorption combinations by controlling graphene’s Fermi energies, which represents the three states of ternary codes ‘−1’, ‘0’, and ‘1’. Further, by designing the coding sequences of ‘−1’, ‘0’ and ‘1’ in the proposed coding array, we can realize 2-bit or multi-bit ternary coding. The coding metasurface with 2D tunability enabling binary and ternary coding offers more potentials in computing, security, data storage, and information processing, etc..

## 2. Design and simulations

To gain 2D tunability, we first achieve tunable polarization-dependent absorptions by an Au/graphene bar array by tuning graphene’s Fermi energies, as shown in Fig. 1(a). An is placed on the top of a 1.7 µm thick dielectric spacer separated by 1nm hexagonal boron nitride (hBN) film, and the back of dielectric spacer is Au supporting layer. Note that the design of combining graphene with hBN could improve the quality of graphene in experiment [17,18]. The combination of graphene and hBN significantly improves the purity of graphene in experiment due to their lattice matching [19,20], so the graphene in contact with hBN has superior electrical/optical properties. The measured mobility of graphene on hBN substrate ranges from 1.5×10^{4} to 6×10^{4} cm^{2}/Vs at 300 K in [19], but the reported mobility of graphene on SiO_{2} substrate is between 2×10^{3} and 2×10^{4} cm^{2}/Vs [19–21]. The lengths of Au and graphene bars are 34 µm and 40 µm respectively, and the width of Au and graphene bars are 6 µm. The Au/graphene bar array supports the plasmon excitation for normally incident waves with electric field parallel to the *x*- or *y*- direction. To show the polarization-dependent plasmon resonance, the absorption spectra of the Au/graphene bar array under the excitations of *x*- and *y*-polarized light are numerically calculated in Fig. 1(c). The absorption of normally incident *x*-polarized light reaches 0.98 at 2.45 THz, while the one of *y*-polarized light is zero. Furthermore, vectoral electric field excited by *x*-polarized incident light at 2.45 THz is confined inside dielectric spacer with opposite directions as shown in Fig. (b), which also demonstrates plasmon resonance. Also, the polarization dependent absorption can be qualitatively understood by the modeling system as a one-port resonator within the framework of coupled mode theory (CMT) [15,22,23]. The one-port CMT model assumes that an incident light can be reflected from the metasurface through two channels: non-resonant channel and resonant scattering channel. For *y*-polarized light incidence, the total reflected light is only through non-resonant channel, because Au substrate serves as a high impedance mirror that reflect the incident light directly. So, the absorptions are almost zero in the whole waveband as the blue and red dash lines shown in Fig. 1(c). However, upon illumination with *x*-polarized light, since Au/graphene bar resonators exhibit plasmon resonance, the total reflected light are from both non-resonant and the resonant scattering channel. When the reflection coefficients from both channels have the same reflection amplitude and 180° phase difference, critical coupling is achieved with the characters of near zero reflection and near unit absorption.

In addition, the absorption peak under the excitations of *x*-polarized light is frequency tunable by switching gate voltages. As shown in Fig. 1(c), the absorption peak of *x*-polarized wave shifts to higher frequency from 2.45 THz to 2.89 THz as Fermi energy increases from 0 eV to 0.42 eV. The tuning of graphene’s Fermi energy can be realized in experiment via gate voltage in the field-effect transistor (FET) structures [24], which is shown in Fig. 2(b). While the absorptions of *y*-polarized wave are near zero at the whole waveband, where is no tunability at all. Therefore, the frequency tunability is limited to *x*-polarized light due to the one-direction plasmon resonance in the *x*-direction bar array. The higher frequency shift results from the changes in graphene’s conductivity induced by the rises of Fermi energies. Different conductivities bring different disturbed fields, which affect plasmon resonances at various degree when the metallic microstructures are fabricated close to graphene sheet. Concretely, the changes in resonant frequency can be interpreted using perturbation theory as [25,26],

*W*and

_{e}*W*are the total electric and magnetic energies. The frequency shift value of Δω not only relies on the material perturbation caused by graphene $\Delta \overleftrightarrow \varepsilon $, but also the local enhancement of optical fields generated by dielectric array ${\overrightarrow E _0}$. The frequency shift (Δ

_{m}*ω*) is large when a perturbation encounter with strong plasmon resonances, because the enhanced fields will make great contribution in frequency-tunability as described in Eq. (1).

To tune *x*- and *y*-direction responses of a certain structure simultaneously, we combine two group Au/graphene bars with 90°twisted angles. In order to gain the two high absorptions of *x*- and *y*-polarized light with different Fermi energies at the same frequency, the length of the bar in *x*-direction is fixed at 34 µm, and the length of the bar in *y*-direction is optimized. Figure 2(a) shows the optimized structure with the following geometry: the period is 40 µm in *x* and *y*-directions, the widths of graphene and Au bars in *x*- and *y*- directions are 6 µm, and the lengths of Au bars in *x*- and *y*-directions are 36 and 34 µm, respectively. Since the working frequency is closely related to structure’s geometric parameters, we break structure’s C_{4} symmetry by using different-length Au bars to construct the cross-shape unit cell. So, when graphene’s Fermi energy is 0 eV, the two absorption peaks of the asymmetric cross-shape Au/graphene array in *x* and *y-*directions are at 2.45 THz and 2 THz, respectively, corresponding to the excitation of normally incident *x*- and *y*-polarized waves in Fig. 3. To gain the near unity absorptions at a frequency for both the different-length Au bars in *x*- and *y*-directions, we use different graphene’s carrier density to compensate the difference in length. The absorption of *x*-polarized wave with 0 eV Fermi energy appears at the same spectral position (2.45 THz) as the absorption of *y*-polarized wave with 0.42 eV Fermi energy in Fig. 3. Because the absorption peaks of both *x*- and *y*- polarized light shift to higher frequency with the increasing of Fermi energies, which is consistent with the Drude-like model [27]. The higher Fermi energy, the higher conductivity. The conductivity of graphene, from free-carrier response, has a Drude-like frequency dependence [27]. Though the absorption amplitude fluctuates slightly with the variation of Femi energy, the smallest absorption is above 0.75, which will not affect the scheme of polarization coding.

The absorption spectra are simulated using a frequency domain solver based on a finite element method in 3D electromagnetic simulation software (CST Microwave Studio) [28]. The boundary conditions are periodic in *x*- and *y*- directions (transverse to light propagation direction) and open for ± *z* directions in free space. The adaptive tetrahedral mesh for frequency domain solver in CST is used. The optical constants of gold are taken from [29]. The permittivity of dielectric spacer is 2.25. Graphene is modeled as surface impedance $Z(\omega ) = {1 \mathord{\left/ {\vphantom {1 {\sigma (\omega )}}} \right.} {\sigma (\omega )}}$, and the surface conductivity of graphene $\sigma (\omega )$ is calculated using Random Phase Approximation [25,26],

*H*(

*ω*) = sinh (

*ω/ω*)/[cosh(

_{T}*ω*) + cosh (

_{F}/ω_{T}*ω/ω*)], ${\omega _F} = {{{E_F}} \mathord{\left/ {\vphantom {{{E_F}} \hbar }} \right.} \hbar }$, ${\omega _T} = {\kappa _B}T/\hbar $,

_{T}*e*and ${\kappa _B}$ are the electron charge and Boltzmann constant, and $\hbar$ is the reduced Planck constant. According to Eq. (2), graphene’s in-plane conductivity depends on angular frequency

*ω*, temperature

*T*, Fermi energy ${E_F}$ and relaxation time

*τ*. The relaxation time τ and mobility are related by [30,31]

*µ*

_{DC}of graphene on hBN substrate is 40000 cm

^{2}V

^{−1}s

^{−1}at 300 K [19,21], ${v_F}$ is the Fermi velocity (

*v*

_{F}= 1 × 10

^{6}m/s), and Fermi energy ${E_F}$ ranges from 0 eV to 0.42 eV. Generally, the Fermi energy of graphene can be tuned over a wide range in experiment (typically from −1 eV to 1 eV) [15,24]. Hexagonal boron nitride (hBN) is a van der Waals crystal with two kinds of infrared active phonon modes relevant to hyperbolicity: (1) out-of-plane phonon modes, which have $${\omega _{TO,\bot}} = 23.38\;\textrm{THz}$$, ${\omega _{LO,\bot}} = 24.88\;\textrm{THz}$; and (2) in-plane phonon modes, which have ${\omega _{TO,\parallel}} = 41.07\;\textrm{THz}$, ${\omega _{LO,\parallel}} = 48.27\;\textrm{THz}$. The hBN permittivity is given by

*m*=⊥, //. The other parameters are ${\varepsilon _{\infty,\bot}} = 4.87$, ${\varepsilon _{\infty,\parallel}} = 2.95$, ${\Gamma _ \bot } = 0.15\;\textrm{THz}$, and ${\Gamma _\parallel } = 0.12\;\textrm{THz}$ [21,26]. The frequency region of 1.5-3.5 THz is far away from the frequencies of out-of-plane and in-plane phonon mode, so here hBN does not show its hyperbolicity. The permittivities of hBN in plane and out of plane are set as ${\varepsilon _ \bot } = 3$ and ${\varepsilon _\parallel } = 2.4$ at the region of 1.5-3.5 THz in the simulation.

## 3. Binary and ternary coding

#### 3.1. Binary coding with x- or y-polarized incident light

We achieved binary coding using the polarization-dependent absorption by encoding signals into *x*- or *y*-polarized light at 2.45 THz as is shown in Fig. 4. For *x*-polarized incident wave at 2.45 THz, the absorption with the graphene’s Fermi energy of 0 eV is near unity and the absorption with the Fermi energy of 0.42 eV is below 0.05, where the near-one and near-zero absorptions at 2.45 THz represent the on and off states in the binary codes (1, 0). Alternatively, the signals can also be encoded into binary codes by *y*-polarized THz wave. The absorption under the excitation of *y*-polarized wave is near zero with 0 eV Fermi energy and above 0.75 with 0.42 eV Fermi energy at 2.45 THz in Fig. 3, which also allows the binary coding for off and on states (0,1). As the encoding scheme shown in Fig. 4, x- or *y*-polarized light allows electrically controlled binary coding by achieving near one or near zero absorptions at fixed frequency by controlling graphene’s Fermi energy. Therefore, by designing coding sequences of ‘0’ and ‘1’ elements in coding metamaterials, we can realize 2-bit or multi-bit binary coding.

#### 3.2. Ternary code with x- and y-polarized incident light

The binary calculation rules are very simple but cannot fully express the human mind. Mathematically, ternary coding is more efficient than binary coding, because ternary logic is closer to the human brain's way of thinking. In ternary logic, the symbol ‘1’ stands for true; The symbol ‘−1’ stands for false; The sign ‘0’ stands for unknown. The logical expression of ternary codes is more consistent with the development trend of computer in artificial intelligence. In the proposed cross-shaped structure, signals can be encoded by controlling graphene’s Fermi energies. Figure 5 shows the polarization absorption spectra under the excitations of *x*- and *y*-polarized light with graphene’s Fermi energies of 0 eV, 0.21eV and 0.42 eV. At the frequency of 2.45 THz, when the Fermi energy is 0 eV, the absorption of *x*-polarized light is near unity, while the absorption of *y*-polarized light is near zero; When the Fermi energy is tuned to 0.21 eV, the absorption of *x*- and *y*-polarized light are both near zero; When the Fermi energy is 0.42 eV, the absorption of *x*-polarized light is near zero, while the absorption of *y*-polarized light is near unity. Thus, the absorption peak of *x*-polarized light (0 eV) and the absorption peak of *y*-polarized light (0.42 eV) are in the same frequency. We need to use *x*- and *y*-polarized light to excite the plasmon resonance of the Au/graphene cross-shape array in sequence, and then encode the ternary signals (−1, 0, 1) into three combined absorption of (≈1, ≈0), (≈0, ≈0) and (≈1, ≈1) by controlling graphene’s Fermi energies. For example, the signal code “0” representing the logic ‘unknown’ can be achieved by gating graphene’s Fermi energy at 0.21 eV in Fig. 6. The absorption in sequence under the excitation of *x*- and *y*-polarized light (≈1, ≈0), (≈0, ≈0), (≈1, ≈1) represents three states of ‘−1’, ‘0’, and ‘1’ of ternary codes. Therefore, each Fermi energy of 0 eV, 0.21eV, and 0.42 eV is corresponding to one state of ternary codes (−1, 0, 1). Also, the dynamic switching of absorption combinations caused by gating graphene enables 1-bit ternary coding with three signals of −1, 0, and 1. A group of the proposed arrays can be arranged into a coding system, where the arrays behave as independent elements representing various codes. A 2- and more-bit ternary coding metamaterial consisting of two and more cross-shape arrays can be achieved by manipulating each cross-shape array individually by Field-Programmable Gate Array (FPGA). Compared with binary codes, ternary codes offer more storage capacity. This is because *N*-bit ternary codes represent *N*^{3} kinds of information, while *N*-bit binary codes represent *N*^{2} kinds of information. Take a 2-bit element as an example, the ternary coding carried with nine kinds of information is much better than the binary coding with 4 kinds of information. Therefore, the ternary codes have great potential in information communication, data storage, encryption, dynamic hologram, artificial identification and intelligent devices.

## 4. Summary

We obtained 2D tunable polarization-absorptions at THz waveband using asymmetric cross-shaped graphene/Au structure. The proposed structure enables binary polarization coding by switching the absorption between 0 and 1 states at a certain frequency by gating graphene. Under the excitation of *x*- and *y*-polarized wave, the resonant frequency shift of the cross-shape structure both in *x* and *y-*directions leads to 2D tunability. Thus, the proposed cross-shaped structure can be encoded ternary codes with three states (−1, 0, 1) by electrically switching graphene’s Fermi energies among 0 eV, 0.21eV and 0.42 eV. The proposed coding scheme in this paper is compatible for binary and ternary coding. The proposed coding metasurface supporting for both binary and ternary codes without changing geometric parameters, holds great potentials in future intelligent devices with reconfigurable and programmable functionalities.

## Funding

Guangdong University of Technology (22041332901); Harbin Institute of Technology (2019KYCXJJZD01).

## Disclosures

The authors declare that there are no conflicts of interest related to this article.

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