Circularly polarized tunable graphene-patch over SiO2 substrate for THz applications

In this communication, a graphene-based radiator is designed and analyzed at THz frequency. A tilted dumbbell-shaped aperture is loaded on a graphene patch for creating degenerated orthogonal mode with 90° phase shift, which in turn produces circularly polarized (CP) waves. Graphene patch is placed over SiO2 substrate. Slot loading in graphene patch shifts the frequency band due to a reduction in effective permittivity. Another important feature of the proposed antenna is to provide a tunable feature in the frequency response and axial ratio by changing the chemical potential. The proposed antenna operates from 5.85 to 6.05 THz. 3-dB axial ratio is obtained from 5.85 to 5.95 THz. Good value of gain, as well as left-handed circular polarization characteristics, makes the proposed THz antenna in sensing applications.


Introduction
The modern world of wireless communications moves towards the THz spectrum because it provides a higher data rate with wider impedance bandwidth (Federici and Moeller 2010). The main challenge to designing an antenna at THz frequency is the metallic losses in the case of printed radiators and non-planarity in the dielectric resonators (Akyildiz et al. 2014). These challenges can be overcome by 2D materials such as graphene. It can also provide reconfigurability to the antenna characteristics by simply varying its chemical potential (Ariza and Ortiz 2010).
Polarization is one of the most important parameters in any radiator. A circularly polarized antenna makes the transmitter and receiver orientation independent and reduces the effect of multipath fading (Balanis 2005). Very few research articles are available on circularly polarized THz antenna. Varshney et.al. proposed a ceramicbased nano-cylindrical ceramic antenna, which supports the CP waves from 188.5 to 199.6 THz. However, there is no tunable feature in this radiator (Varshney et al. 2019 (Ansha et al. 2021).
This article explains the design of a tunable tilted dumbbell-shaped aperture loaded graphene patch, which supports the circular polarization feature. This antenna operates from 5.85 to 6.05 THz. Change in chemical potential of graphene patch provides the tunable feature inside the radiator. The sense of polarization can easily be controlled by simply changing the orientation of the slot. For better understanding, the article is divided into sub-categories i.e. antenna design layout, antenna analysis, optimized antenna outcome, and conclusion.

Antenna design layout
The structural layout of the proposed graphene-based THz antenna is displayed in Fig. 1. A tilted dumbbell-shaped slot is etched from the graphene patch. SiO 2 substrate, having permittivity 3.9, is used to design the proposed antenna. SiO 2 behaves as a lossy dielectric. Its thermal conductivity is 1.3 W/m K and resistivity is around 1e + 023 Ω-m. The ground plane along with the microstrip line is made up of a conductor. Gold and silver are two choices for the same. The use of gold gives better performance because of its better conductivity as well as lower oxidation rate. However, it is very costly. Therefore, silver can be used. It cannot oxidize rapidly. The optimized antenna dimension is given in the caption of Fig. 1. Drude's model is used to obtain the dispersive features of silver. It is mathematically given by the following formula (Varshney et al. 2019): In Eq. (1), 'ε' shows the permittivity; ' ε ∞ ' real part of the dielectric constant, f P and f cl is the plasma frequency and collision frequency respectively. The value of ε ∞ , f P and f cl is taken as 5, 2175 THz, and 4.35 THz respectively (Varshney et al. 2019). The dispersive feature of exciting structure can be selected in such a way that transmission losses are minimum at THz frequency. In the proposed antenna design, proximity coupling is used. In this type of feeding mechanism, spurious radiation is less and wider impedance bandwidth is achieved due to stacking of dielectric material (Balanis 2005).

Antenna analysis
In this section, step by step analysis of the proposed circularly polarized THz antenna is described. CST-MWS simulation software is used to design and analyse the proposed antenna. CST software is based on FDTD technique. In CST-MWS, Mesh Size is taken as 20 cells per wavelength and open add space boundary conditions boundary condition is used to simulate the proposed antenna design. At the THz frequency range, spatial distribution in the graphene-based patch is expected to be absent (Cabellos-Aparicio et al. 2015). Now, with the assistance of Kubo's formula, the thickness of the graphene layer i.e. 0.34 nm is placed over the SiO 2 -based substrate. In the THz frequency range, the energy of a photon is negligible as compared to Fermi energy (Varshney et al. 2018). Therefore, the value of interband conductivity of graphene is quite low as compared to intraband conductivity. Its intraband conductivity can be mathematically given as follows (Falkovsky and Pershoguba 2007): In CST-MWS simulation software, graphene material is placed with relaxation time = 1 ps, temperature T = 300 k (Mohammadreza Razavizadeh 2017). Figure 2 shows the  Fig. 2 is that the conductivity of graphene alters with variation in chemical potential. This indicates the tunable feature can be achieved in a graphene-based patch with the alteration of chemical potential. Figure 3 displays the variation in |S 11 | with and without a tilted dumbbell-shaped slot. From Fig. 3, it can be observed that the loading of the slot over the graphene patch shifts the resonance peak to a higher frequency range. It is due to a reduction in the effective permittivity of the radiator (Bharti et al. 2020). The proposed dumbbell-shaped aperture is the diagonally perturbed circularshaped aperture. Figure 4 shows |S 11 | optimization of the radius of the circular-shaped aperture. From Fig. 4, it can be observed that as the radius of the slot increases, resonant frequency shifts in a forward direction. It is due to a reduction in effective permittivity. On the other hand, impedance matching degrades with radius increases. The optimum value of R is taken as 2.0 um. Figure 5 displays the axial ratio variation with and without a tilted dumbbell-shaped slot. It is perceived from Fig. 5 that CP waves are obtained with the loading of the proposed slot within the desired frequency band i.e. 5.85 THz to 5.95 THz. To produce the CP feature in any radiator, two conditions must be fulfilled: (i) creation of degenerated orthogonal modes; and (ii) 90° phase shift between the modes (Balanis 2005). For satisfying this condition in the proposed radiator, a circular aperture is loaded first. It can create two orthogonal degenerated modes with the same amplitude. After that, the circular aperture is perturbed diagonally. The degree of perturbation creates the path delay between the orthogonal components, which in turn creates the desired phase difference i.e. 90°. Figure 6 shows the optimization of a degree of perturbation of the circular aperture. From  Fig. 6, it can be observed that the optimum value of AR is obtained, when the circular aperture is perturbed diagonally with an angle of 45°. In other words, it can be said that the dumbbell-shaped slot is tilted at an angle of 45°. Figure 7 displays the magnitude of E-field variation on graphene patch with and without slot at 5.9 THz. From Fig. 7, it can be observed that the variation of the E-field is uniform about the X-axis in the absence of a slot, while it is distorted after loading the dumbbellshaped slot. It is allied diagonally. This phenomenon indicates the creation of CP waves. TM 41 mode is supported by the proposed graphene-shaped aperture (Varshney et al. 2020).
Another important significance of the graphene patch is its capability of tuning by simply varying the chemical potential. Figures 8 and 9 show the reflection coefficient and axial ratio variation with change in chemical potential (u C ). As the value of chemical potential increases, resonance frequency shifts towards the higher frequency band. By change of the chemical potential, blueshift occurs. AR values also change in the same way. Change in chemical potential does not create many effects on orthogonal mode formation. However, some small changes may occur in the amplitude of the modes, which will create a small effect on the value of AR.
Easy controlling of the sense of circular polarization is also an important feature of the proposed antenna. Figure 10 displays the LHCP and RHCP pattern in the XZ plane at 5.9 THz with a proposed aperture as well as a mirror image of the proposed aperture. From

Optimized outcomes of proposed radiator
In this section, the optimized outcome of the proposed radiator is discussed and compared with the HFSS EM simulator. Figure 11 displays the |S 11 | variation of the proposed antenna with CST-MWS and HFSS EM simulator. There is good agreement between the |S 11 | variations obtained from both the software. From Fig. 11, it is confirmed that the proposed antenna works from 5.85 to 6.05 THz. Figure 12 displays the axial ratio variation with HFSS and CST-MWS software. From Fig. 12, it is confirmed that the proposed antenna supports the CP waves from 5.85 to 5.95 THz. There is good agreement between the results obtained from HFSS and CST-MWS.  Figure 13 shows the gain variation of the proposed antenna. From Fig. 13, it is perceived the gain value is around 5.5 dBi in the operating frequency band. Figure 14 displays the 2D LHCP and RHCP radiation pattern in XZ and YZ planes at 5.9 THz. From Fig. 14, it is concluded that the proposed antenna acts as a left-handed circularly polarized antenna. Table 1 shows the performance comparison of proposed antenna with other circularly polarized THz antennas. From Table 1, it is confirmed that the overall performance of proposed antenna is better as compare to existing radiators.
Fabrication and measurement of such type of Nano antennas is one of the future possibilities. Some fabrication methods available in literature for antennas at Nano scale i.e. ion beam milling and electron-beam lithography (Novotn and Hulst 2011).

Conclusion
In this article, a tunable graphene-based radiator is designed and analyzed at THz frequency. Loading of tilted dumbbell-shaped patch incorporates the circular polarization feature in the proposed antenna. The proposed antenna works from 5.85 to 6.05 THz with supporting TM 41 mode. The proposed antenna shows a good gain value i.e. 5.5 dBi along with broadside radiation characteristics. A feature of CP waves at THz frequency makes the proposed radiator suitable for sensing applications.