Reconfigurable graphene-based metamaterial polarization converter for terahertz applications

This study proposes a high-gain polarization converter using a graphene-based metamaterial array, a rectangular array comprising 20 periodic unit-cell elements. Each graphene-based metamaterial unit-cell element contains a rectangular patch with four triangular-shaped graphene parts at its four corners placed over a rectangular substrate backed with a perfect electric conductor and has a relative permittivity of εsub = 3.38. The metamaterial characteristics of the proposed graphene-based metamaterial unit-cell element are obtained over frequencies of 1.5–2.2 terahertz (THz). The graphene-based metamaterial array is placed over a linearly polarized slot antenna operating at 1.8 THz, with a maximum gain of 5.5 dBi. The linearly polarized wave radiated from the slot antenna can be converted into reconfigurable right-handed or left-handed circular polarizations according to the graphene parts’ biasing states. Moreover, the slot antenna’s operating − 10 dB bandwidth (BW) is increased by 22.2%, and the gain is enhanced to 8 dBi at the same operating frequency. A reconfigurable polarization conversion for the slot antenna can be obtained over a wide 3 dB axial ratio BW from 1.75 to 1.92 THz (20%–3 dB BW).

The MM surface is designed as a periodic structure from the unit-cell elements satisfying metamaterial electromagnetic properties (ε, µ, and n). MM surfaces' operating frequency can be tuned geometrically by changing the dimensions of one or all constituent parts of the unit-cell element, changing its conductance and capacitance (Meng et al. 2020;Askari et al. 2021;Askari and Bahadoran 2022;Askari and Hosseini 2020;Tsakmakidis et al. 2007;Dani et al. 2011). The performance of the MM unit-cell elements can be changed electrically, thermally, chemically, or optically according to the material used in the proposed design Smith et al. 2005). It can also be changed using positive intrinsic negative diodes, varactor diodes, or microelectromechanical systems (Yang, et al. 2021).
In this study, a graphene-based MM (GMM) unit-cell element is designed at an operating frequency of 1.8 THz. The GMM properties (ε, µ, and n) and the 3 dB axial ratio (AR) are calculated and figured. This unit-cell element is arranged in an MM-based surface to obtain a reconfigurable polarization dipole antenna in the THz band. A 4 × 4 GMM-based array is used as a reflector for the proposed dipole antenna to convert its LP wave to LHCP or RHCP through the biasing state of each two opposite graphene triangles. The proposed constructions are designed and analyzed using a computer simulation technology (CST) microwave (MW) studio based on the finite integration technique. Section 2 presents the design and analysis of the GMM-based unit-cell element. Section 3 introduces the design and analysis of the reconfigurable polarization slot antenna. Section 4 concludes this study.

Design and analysis of GMM unit-cell element
The GMM-based unit-cell element comprises a rectangular PEC patch of a side length (L P = 26.84 µm), with four triangular-shaped graphene parts at its coroners. Each graphene triangle has two equal sides of length (a = 10.93 µm) and a base of length (b = 15.46 µm) ( Fig. 1). Two are placed oppositely at 45°, and the other two at − 45° concerning the positive x-axis. The copper patch and four graphene triangles are placed over a square-shaped substrate of side length (L S = 29.82 µm), height (H S = 7.57 µm), and relative permittivity (ε rsub = 3.38), backed by a square perfect electric conductor (PEC) ground plane of the same side length.
Graphene's controllable conductivity (σ(ω)) is a critical property for antenna reconfigurability applications. Unlike most popular materials, graphene conductivity can be altered in diverse ways, such as applied electric field, applied direct current (DC) voltage, or chemical doping. The Kubo formula represents the graphene conductivity as a frequencydependent complex value according to Eq. (1) (Hu and Wang 2018).
where inter ( ) is the inter-band contribution corresponding to electron-hole pair generation and recombination events. intra ( ) is the intra-band contribution corresponding to the conductivity of free carriers. Each inter-band and intra-band is represented as: and where is the angular frequency, c is the chemical potential (between 0 and 2 eV), Γ is the scattering rate ( Γ = 1∕ ), T is the temperature (K), is the time of relaxation, q e is the electron charge, K B is the Boltzmann's constant, and ℏ is the reduced Plank's constant.
For operating frequencies below 8 THz, graphene conductivity can be represented in terms of the inter-band only where the intra-band can be neglected (Hu and Wang 2018). The most well-known technique used to control graphene conductivity is by varying the applied DC voltage (Hu and Wang 2018). In this study, we apply the graphene conductivity inter-band because it is designed for applications below 8 THz. According to Eq. (2), the graphene functions as a dielectric if it is unbiased with the DC voltage value equivalent to c = 0 (unbiased state). However, it functions as a conductor if it is biased with the DC voltage value equivalent to c = 2eV (unbiased state). In this study, we discuss the biased and unbiased states of graphene to achieve the polarization conversion property, as discussed below. (1) The reflection and transmission coefficient variations versus the GMM unit-cell element frequency when a the two opposite graphene triangles directed to θ 1 = + 45° are biased and b directed to θ 2 = − 45° are biased Also, the resistivity of graphene monolayer has a large dependency on the temperature. According to several measurements, it was found that for temperatures lower than 150 K, the graphene monolayer resistivity is linearly dependent on temperature. For higher temperatures degrees the dependency of graphene resistivity on temperature is strongly increased. This may be as a result of ripples in the graphene monolayer or coupling between it and the remote interfacial phonons (RIPs) at the SiO 2 surface (Price et al. 2012).
Using a Floquet port in the CST-MW software, the unit-cell element's dimensions are optimized and analyzed. The two opposite graphene triangles directed to θ 1 = + 45° are biased, and those directed to θ 1 = − 45° are unbiased (case 1). Figure 2a shows the magnitudes of reflection (S 11 ) and transmission (S 21 ) coefficients of the GMM unit-cell element. Conversely, in case 2, the two opposite graphene triangles directed to θ 2 = − 45° are biased, and those directed to θ 2 = + 45° are unbiased. Figure 2b shows the magnitudes of reflection (S 11 ) and transmission (S 21 ) coefficients of the GMM unit-cell element. Note that S 11 and S 21 have the same value at 1.8 THz. Figure 3 shows the variation of the reflection (P 11 ) and the transmission (P 21 ) phases and their differences in the two cases. From the results, the phase difference in both cases is (φ = 90°) at the operating frequency, and the proposed GMM unit-cell element satisfies the AMC requirements at the operating frequency of 1.8 THz (Sofi et al. 2019). Figures 3c, and d presents the electric field map and the distribution of the charge distribution, respectively, for the proposed GMM unit-cell element case (2) resonance excitation and concentration through the patch area of the unit-cell at the frequency of 1.8 THz. The charges are mainly concentrated at the tips of the biased graphene triangles only (case 2) like in Ahmadivand et al. (2016). The reflection S 11 and transmission S 21 coefficients are used to calculate the MM parameters (ε, µ, and n) for the unit-cell element. First, the impedance z and the refractive index n are calculated using Eqs. (4) and (5), respectively (Zheludev 2015).
n is the refractive index, k is the incident wave's wavenumber, and H is the MM unit-cell element's overall thickness. These two equations are used to calculate the electrical permittivity, ε, and the magnetic permeability μ as in Eqs. (6) and (7), respectively [31,232].
Figures 4, 5, and 6 show the variations of real and imaginary parts of the unit-cell element's parameters (ε, µ, and n) versus frequency, respectively. The real parts of ε, µ, and n of the MM unit-cell elements must be negative at the operating frequency of 1.8 THz in this study. In Fig. 4a, the real part of the relative permittivity ε has negative values through a wide band of frequencies from 1.5 to 2.2 THz for case 1 and 1.6 to 2.1 THz for case 2.
Case 1 Case 2 Case 1 Case 2 Fig. 4 The variations of a the real part and b the imaginary part of permittivity versus the GMM unit-cell element's frequency for cases 1 and 2, respectively Figure 5a shows that the real part of the relative magnetic permeability µ has negative values over the frequency band from 1.5 to 2.2 THz for case 1 and 1.6 to 2.2 THz for case 2.
Also, the proposed GMM unit-cell element has negative values for the refractive index n through the frequency band from 1.6 to 2.2 THz for cases 1 and 2 (Fig. 6a). Here, the proposed unit-cell element is valid to be an MM unit cell.
From the results, the proposed GMM unit-cell element can be used for polarization conversion at 1.8 THz. For case 1, because the reflection phase P 11 is greater than the Case 1 Case 2 Fig. 6 The variations of a the real part and b the imaginary part of the refractive index versus the GMM unit-cell element's frequency for cases 1 and 2, respectively transmission phase P 21 by 90° (Fig. 3a), the transmitted wave's polarization is RHCP. For case 2, because the transmitted phase P 21 is greater than the reflection phase P 11 by 90° (Fig. 3b), the transmitted wave's polarization is LHCP (Dani et al. 2011).
In summary, the proposed GMM unit-cell element converted the incident LP to RHCP or LHCP according to the biasing state of the graphene triangles as in cases 1 and 2. The 3 dB AR bandwidth (BW) from 1.78 to 1.86 THz (4.4% 3 dB BW) is achieved for case 1 (Fig. 7a). The 3 dB AR BW from 1.76 to 1.84 THz (4.44% 3 dB BW) is achieved for case 2 (Fig. 7b). The AR is calculated using Eq. (8) (Price et al. 2012).

Reconfigurable polarization slot antenna using a GMM array
The proposed GMM unit-cell element is arranged in a 4 × 4 array to perform polarization conversion for an LP slot antenna comprising a square PEC sheet of a side length L ps = 119.82 µm and a rectangular slot of length L s = 62.6 µm and width of W s = 6 µm. The PEC sheet with the rectangular slot is placed over a square substrate of the same side length (height of H s = 2.5 µm) and relative permittivity ε rs = 3.38 (Fig. 8a). The slot antenna is radiated through a stripline placed at the bottom of the substrate with length L st = 96.5 µm and width W st = 6.5 µm (Fig. 8b). An array of 4 × 4 GMM unit-cell elements with a surface area of 119.82 × 119.82 µm 2 is used as a polarization converter for the proposed slot antenna (Fig. 9a). This array is placed under the proposed dipole antenna at an optimized distance h = 25 µm, equivalent to λ/4. The reflected wave from the MM array is of a high gain with a maximum value of 6.18 dBi (a) (b) Fig. 11 The AR of the overall construction with biased GMM array for a cases 1 and b 2

(a) (b)
ERHCP ELHCP ERHCP ELHCP Fig. 12 The E R and the E L of the overall construction with biased GMM array for a cases 1 and b 2 along the positive z-axis (Fig. 10b), with a wide BW from 1.5 to 2.1 THz (30.93%, − 10 dB BW) (Fig. 11a). Note that the − 10 dB BW and the gain of the proposed dipole antenna are enhanced considerably. Figure 10a shows that the reflection coefficient of the overall construction is enhanced to − 22 dB instead of − 2 dB of the slot antenna when the graphene triangles are biased in case 1 and enhanced to − 44 dB when the graphene triangles are biased in case 2 (Fig. 10b). The enhancement of the reflection coefficient of the proposed slot antenna at the operating frequency (1.8 THz) means increasing the matching level between the antenna and the GMM array. As a result of the enhanced matching level, the antenna gain is also increased in both cases 1 and 2 as shown in Fig. 11.
Moreover, the transmitted wave from the GMM array is converted to RHCP and LHCP waves for cases 1 (Fig. 11) and 2 (Fig. 12), respectively.
The slot antenna's LP wave is converted to RHCP when the GMM array's graphene is biased according to case 1. This is confirmed by the results of Fig. 11a, where a wide 3 dB BW of 10.55% and from 1.74 to 1.93 THz is achieved. Also, the ERHCP component of the radiated field is greater than the ELHCP component by 18 dB at the operating frequency of 1.18 THz (Fig. 12a). Biasing the GMM array's graphene according to case 2 produces an LHCP wave with a 3 dB AR BW of 13.3% from 1.73 to 1.96 THz (Fig. 11b). The difference between the ERHCP and LHCP components of the radiated field for this case is 19 dB at the operating frequency of 1.8 THz (Fig. 12b).
Compared with similar studies (Tsakmakidis et al. 2007;Dani et al. 2011), the proposed configuration exhibits an electrical polarization conversion with a wider BW, better CP conversion, more simplicity, and a wide 3 dB AR bandwidth.

Conclusions
A GMM unit-cell element was designed and analyzed at 1.8 THz. A high gain with a reconfigurable polarization antenna was introduced using a GMM array. The GMM array comprised 20 GMM unit-cell elements arranged over the proposed slot antenna. Using the GMM array increased the − 10 dB BW by 22.2%, and the gain of the proposed slot antenna was enhanced to 8 dBi instead of 5.8 dBi. Moreover, the GMM polarization converter switched the slot antenna's LP wave between RHCP and LHCP waves according to the graphene materials' biasing states of cases 1 and 2 with a high 3 dB AR BW (10.55% and 13.3%, respectively). are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.