1 Introduction

Terahertz (THz) waves are used for many applications. In medicine, THz radiation can detect differences in water content and tissue density. THz waves are used in airports for security to detect hidden illegal substances with passengers. In communication, because of their higher carrier frequency, higher data rates are achieved (up to 1000’s Gbit/s data rates). In manufacturing processes, THz waves are used for imaging and sensing, quality control, and monitoring (Mukherjee and Gupta 2008). Metals, such as copper and gold, are used for antenna applications in this band (Tamagnone et al. 2012). Copper is the most used metal for antenna applications in the THz band (Keller et al. 2014), but copper-based antennas suffer high propagation losses and low radiation efficiency. These disadvantages exist as conductivity because copper’s skin depth is decreased. These facts encourage using carbon-based materials, such as graphene and carbon nanotubes for THz antennas. Graphene is a two-dimensional carbon membrane with a one-atom thickness arranged in single or multiple layers (Yi and Wei 2017). Graphene material has unique characteristics. It has high electron mobility that at room temperature, approaches 20 m2/V∙s. Graphene, compared with other materials, is the strongest because of its lattice configuration, and its breaking strength is 100 times that of steel. Graphene is the stiffest material ever studied, with mechanical stress of 100 GN/m2 (1 × 1011 N/m2) and an elastic modulus of 1 TN/m2 (1 × 1012 N/m2) (Sharma et al. 2021). Despite high mechanical properties, graphene has impressive flexibility (Obeng and Srinivasan 2011).

The antenna’s property reconfigurability has attracted researchers’ attention in wireless communications, especially mobile and satellite (Haider et al. 2013; Priya et al. 2020; Ojaroudi Parchin et al. 2020; Costantine et al. 2014). The most popular reconfigurable antenna properties are operating frequencies, the radiation pattern, and polarization (Shakhirul et al. 1019; Costantine et al. March 2015). The propagation link’s budget is primarily affected because of polarization mismatch at the receiving end in most wireless communication applications, indicating that the linearly polarized (LP) wave in satellite communication might be rotated while transferring between the transmitting and receiving sides. The LP wave’s rotation is the Faraday rotation, increasing the propagation link’s budget (Khan and Eibert 2019). This issue decreases LP wave usage in wireless applications. Also, from the drawbacks of LP wave multipath fading during transmission and the antenna’s orientation at the receiving side. Therefore, the need for circularly polarized (CP) waves became necessary because of their advantages over LP waves (Lin et al. 2020; Qi et al. 2020; Fahad et al. 2020).

The most vital advantage of CP waves is their high immunity against transmission medium effects (Baghel et al. July 2019; Tao et al. 2019; Chen and Zhang 2018). To convert an LP wave to a CP wave, researchers have designed an aided construction obeying that conversion, i.e., polarization converters. The antenna performing such conversion is a reconfigurable polarization antenna (Li et al. 2020). Reconfigurable polarization is the antenna’s ability to switch between LP to left-hand circular polarization (LHCP) or right-hand circular polarization (RHCP) or between LHCP and RHCP, solving the single polarization issue in the antenna field (Liu et al. 2016; Zhang et al. 2020). Different structures can be used to convert the LP wave to the CP wave. These surfaces might be designed based on artificial magnetic conductors (AMCs) (Malhat et al. 2020) or frequency selective surfaces (Mabrouk et al. 2019). Other surfaces are based on metamaterials (MM), which are artificial structures with negative real parts of electrical permittivity (ε), magnetic permeability (µ), and refractive index (n) at the antenna’s operating frequency (Zheludev 2015). 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 (Askari et al. 2022; 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.

2 Design and analysis of GMM unit-cell element

The GMM-based unit-cell element comprises a rectangular PEC patch of a side length (LP = 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 (LS = 29.82 µm), height (HS = 7.57 µm), and relative permittivity (εrsub = 3.38), backed by a square perfect electric conductor (PEC) ground plane of the same side length.

Fig. 1
figure 1

A 3D diagram of the graphene-based metamaterial (GMM) unit-cell element

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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 frequency-dependent complex value according to Eq. (1) (Hu and Wang 2018).

$$\sigma \left(\omega \right)={\sigma }_{inter}\left(\omega \right)+{\sigma }_{intra}\left(\omega \right)$$
(1)

where \({\sigma }_{inter}\left(\omega \right)\) is the inter-band contribution corresponding to electron–hole pair generation and recombination events. \({\sigma }_{intra}\left(\omega \right)\) is the intra-band contribution corresponding to the conductivity of free carriers. Each inter-band and intra-band is represented as:

$${\sigma }_{inter}\left(\omega ,{\mu }_{c},\Gamma ,T\right)\approx j\frac{{q}_{e}^{2}}{4\pi \hslash } ln\left(\frac{2\left|{\mu }_{c}\right|-\left(\omega +j{\tau }^{-1}\right)\hslash }{2\left|{\mu }_{c}\right|+\left(\omega +j{\tau }^{-1}\right)\hslash }\right)$$
(2)

and

$${\sigma }_{intra}\left(\omega ,{\mu }_{c},\Gamma ,T\right)\approx -j\frac{{q}_{e}^{2}{ K}_{B} T}{\pi {\hslash }^{2} \left(\omega -j2\Gamma \right)} \times \left(\frac{{\mu }_{c}}{{ K}_{B} T}+ln{\left({e}^{-{\mu }_{c}/{ K}_{B} T}+1\right)}^{2}\right)$$
(3)

where \(\omega \) is the angular frequency, \({\mu }_{c}\) is the chemical potential (between 0 and 2 eV), \(\Gamma \) is the scattering rate (\(\Gamma =1/\tau \)), T is the temperature (K), \(\tau \) 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 \({\mu }_{c}=0\) (unbiased state). However, it functions as a conductor if it is biased with the DC voltage value equivalent to \({\mu }_{c}=2 eV\) (unbiased state). In this study, we discuss the biased and unbiased states of graphene to achieve the polarization conversion property, as discussed below.

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 SiO2 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 θ1 =  + 45° are biased, and those directed to θ1 =  − 45° are unbiased (case 1). Figure 2a shows the magnitudes of reflection (S11) and transmission (S21) coefficients of the GMM unit-cell element. Conversely, in case 2, the two opposite graphene triangles directed to θ2 =  − 45° are biased, and those directed to θ2 =  + 45° are unbiased. Figure 2b shows the magnitudes of reflection (S11) and transmission (S21) coefficients of the GMM unit-cell element. Note that S11 and S21 have the same value at 1.8 THz. Figure 3 shows the variation of the reflection (P11) and the transmission (P21) 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).

Fig. 2
figure 2

The reflection and transmission coefficient variations versus the GMM unit-cell element frequency when a the two opposite graphene triangles directed to θ1 =  + 45° are biased and b directed to θ2 =  − 45° are biased

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Fig. 3
figure 3

The reflection and transmission phase variations and their difference versus the MM unit-cell element frequency when a the two opposite graphene triangles directed to θ1 =  + 45° are biased, b directed to θ2 =  − 45° are unbiased, c Electric field map, and d the charge distribution for the GMM unit-cell element case 2

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The reflection S11and transmission S21coefficients 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).

$$z = \pm \sqrt{\frac{{\left(1+{T}_{xx}\right)}^{2}-{{T}_{xy}}^{2} }{{\left(1-{T}_{xx}\right)}^{2}-{{T}_{xy}}^{2}}}$$
(4)
$$n=\frac{1}{kH}{\mathrm{cos}}^{-1}\left[\frac{1}{2{T}_{\mathit{xy}}}(1-{{T}_{\mathit{xx}}}^{2}+{{T}_{\mathit{xy}}}^{2})\right]$$
(5)

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].

$$\varepsilon ={n}/ {z}$$
(6)
$$\mu =n\times z$$
(7)

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.

Fig. 4
figure 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

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Fig. 5
figure 5

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

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Fig. 6
figure 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

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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 P11 is greater than the transmission phase P21 by 90° (Fig. 3a), the transmitted wave’s polarization is RHCP. For case 2, because the transmitted phase P21 is greater than the reflection phase P11 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).

$$AR=\sqrt{\frac{1+{\beta }^{2}+\sqrt{{\left(1-{\beta }^{2}\right)}^{2}+4{\beta }^{2}{cos}^{2}\varphi }}{1+{\beta }^{2}-\sqrt{{\left(1-{\beta }^{2}\right)}^{2}+4{\beta }^{2}{cos}^{2}\varphi }}}$$
(8)

where \(\beta =\frac{{|T}_{xx}|}{{|T}_{xy}|}\) and φ is the phase difference between Txx and Txy.

Fig. 7
figure 7

The variations of the axial ratio (AR) versus frequency for a the RHCP GMM unit-cell element (case 1) and b the LHCP GMM unit-cell element (case 2)

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3 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 Lps = 119.82 µm and a rectangular slot of length Ls = 62.6 µm and width of Ws = 6 µm. The PEC sheet with the rectangular slot is placed over a square substrate of the same side length (height of Hs = 2.5 µm) and relative permittivity εrs = 3.38 (Fig. 8a). The slot antenna is radiated through a stripline placed at the bottom of the substrate with length Lst = 96.5 µm and width Wst = 6.5 µm (Fig. 8b).

Fig. 8
figure 8

a The top view and b the bottom view of the LP slot antenna

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An array of 4 × 4 GMM unit-cell elements with a surface area of 119.82 × 119.82 µm2 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 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.

Fig. 9
figure 9

4 × 4 GMM unit-cell elements array over the proposed slot antenna for graphene biasing states for cases a 1 and b 2, and c is the side view of the overall construction

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Fig. 10
figure 10

Variations of the reflection coefficient versus the slot antenna’s frequency against that of the overall construction with biased GMM array for a cases 1 and b 2

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Fig. 11
figure 11

The AR of the overall construction with biased GMM array for a cases 1 and b 2

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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.

Fig. 12
figure 12

The ER and the EL of the overall construction with biased GMM array for a cases 1 and b 2

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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.

4 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).