Frequency reconfigurable antipodal Vivaldi 2-port antenna based on graphene for terahertz communications

A graphene-based two ports antipodal Vivaldi antenna with improved gain for THz applications is introduced. The single antenna is composed of an antipodal Vivaldi antenna with a graphene radiator on the top and copper ground plane on the back with a total size equal to 108 µm × 84 µm to achieve reconfigurable performance from 3 to 4.5 THz. The reconfigurability is validated by changing the external DC Volt which in turn changes the graphene chemical potential and then changes the operating frequency. As well, to enhance the antenna gain, frequency selective surfaces (FSS) with a metallic patch are utilized to enhance the antenna gain. The FSS performance is investigated and optimized using a finite integral technique (FIT) software to achieve a reflective feature with band rejection from 2 up to 5 THz within the operating bands of the suggested antenna. The FSS is inserted below the MIMO antenna to reflect the antenna radiation and then enhance the antenna gain. The antenna gain is increased from 6 dB (single antenna without FSS) to 10.8 dB (with FSS) at 3.4 THz. The MIMO antenna is operated from 3.2 to 4.45 THz with S11 ≤ − 10 dB, isolation ˃ 20, gain from 8 to 10.8 dB, and efficiency higher than 80%. Finally, the MIMO parameters outcomes achieved good values which suggested the antenna to be employed in IoT THz applications.


Introduction
graphene 2-port MIMO patch antenna with metamaterial cell to enhance the isolation between ports and with RIS structure for beam steering is displayed in Khaleel et al. (2022b).
In this work, a 2-port antipodal Vivaldi MIMO antenna with a graphene radiator, high gain, and isolation is discussed. The graphene radiator of the antipodal Vivaldi antenna is utilized to reconfigure the frequency band within 3-4.45 THz by changing the external Volt which in turn changes the graphene chemical potential and then changes the operating frequency. The 6 × 9 FSS cells are used to enhance the antenna gain by 4 dBi within the operating frequency band and loaded below the MIMO antenna to operate in band-stop mode to reflect the back radiation of the antenna. The MIMO antenna with FSS has a total dimension of 120 × 180 × 13.2µm 3 . The MIMO antenna is operated from 3.2 4.45 THz with S 11 ≤ − 10 dB, isolation ≥ 20, gain from 8 to 10.8 dB, and efficiency higher than 80%. The novelty of this work can be summarized as: first, 2 ports antipodal Vivaldi MIMO antenna with graphene radiators and compact size to tune the frequency band of the antenna from 3.2 to 4.45 THz and with isolation higher than 20 dB. Second, increasing antenna gain by using the FSS layer in working in band-stop mode to reflect radiation and enhance the antenna radiation features.

Graphene material
The graphene material is a carbon atom one layer thick which is sorted into hexagonalshaped cells. It has an electrical and thermal conductivity higher than the copper material, especially at THz bands. Also, it has high charge mobility which enables electrons to pass with lower resistance in graphene materials which means faster speed than other conductors Hafez et al. 2018;Dakhlaoui et al. 2021). So, these features of the graphene material at the THz band enable it to be utilized in several applications (Geim and Novoselov 2007). The graphene material has a conductivity that is calculated using the Drude model (Beiranvand et al. 2020). As shown in Eq. (1), the graphene conductivity equals the summation of the intra-band and the inter-band conductivity parameters.
where ℏ, q e , K B , τ, ω, T, c , Γ and are the reduced Planck's constant, the charge of the electron, Boltzmann's constant, relaxation time, angular frequency, temperature, and chemical potential, reflection coefficient respectively. In our MIMO antenna, the intra-band conductivity is more dominant at THz frequency than the other part so the inter-band conductivity can be neglected and the total conductivity can be calculated using Eq. (4) From Eq. (4) it can be seen that the conductivity can be adjusted using the µ c parameter. The µ c parameter of the graphene can be controlled by using electric and magnetic fields, external gate voltage, and chemical doping. The µ c parameter calculation in terms of external gate voltage can be extracted from Eq. (5) (Khaleel et al. 2022b;Gómez-Díaz and Perruisseau-Carrier 2013).
where, ε o , ε r , V g , t, and v f are the permittivity of free space, the relative permittivity of substrate material, gate voltage, the thickness of the substrate, and the Fermi velocity in graphene. The graphene material is modeled in a time domain FIT software with a 10 nm thick conductive sheet and with a surface impedance of Malhat et al. (2020).

Suggested single antipodal Vivaldi structure
The side view of the antenna is illustrated in Fig. 1a. A SiO 2 layer with εr = 4 and a thickness of 5 nm is inserted between the graphene layer and a substrate with εr = 4.5 and a thickness of 2.27 µm to control the graphene conductivity by utilizing the external voltage (Vg) (Dash et al. 2019). The antenna bands are not affected by this layer because of its thin thickness. In measurements, based on Eq. (5), to change the µc from 0.4 eV, 1 eV, 1.5 eV, and 2 eV, the external voltages (Vg) of = 2.7 V, 16.8V, 38V, and 67.5V are applied. The designed steps of the suggested antenna are illustrated in Fig. 1b. The Vivaldi antenna is selected due to its advantages such as high gain, wide bandwidth, linear The suggested antenna evolution polarization, and radiation patterns stability. The first step is the Vivaldi antenna with a graphene tapered slot which is curved exponentially using a well-known function (Dixit and Kumar 2020;Yousaf et al. 2020) and the antenna is fed with a transmission line with copper material on the back of the substrate as illustrated in Fig. 1b antenna 1. As illustrated in Fig. 2 the red dotted line, the antenna is operated around 5 THz with narrow bandwidth. Fig. 1b antenna 2 is modified by cutting two circular slots from the radiators but the matching of the antenna is affected as illustrated in Fig. 2 blue dashed line. Finally, to achieve the desired wide bandwidth, the second radiator is moved to the back of the substrate with copper material to form the suggested antipodal Vivaldi antenna as shown in Fig. 1b antenna 3. The top radiator is composed of graphene and the back one is composed of copper and treats with the ground. Fig. 2, the black solid line show that the antenna worked from 3.2 to 4.45 THz with S 11 ≤ − 10 dB. The final suggested antenna 2D layout and 3D configuration with total dimensions are illustrated in Fig. 3.The antenna is an antipodal Vivaldi antenna with a graphene radiator on the top and copper ground plane on the back. The antenna's total size is equal to 108µm × 84 µm. Two slots are cut from the upper and lower slots with equal radii R1 = R2 = 38 µm and two small circular slots R3 = 5 µm and R4 = 8 µm. These slots affected the antenna bandwidth. So, these parameters should be adjusted carefully to achieve the desired frequency band. As we discussed earlier the top layer is composed of graphene material and its conductivity of it can be controlled by using external gate voltage which in turn changes the chemical potential. The effect of changing the chemical potential on the antenna impedance bandwidth is shown in Fig. 4. When the µc = 0.4 eV the antenna is operated with S 11 ≤ 10 dB from 3 up to 3.2 THz. When the µc is increased to 1eV the antenna is worked from 3 to 3.55 THz. By increasing the µc to 1.5 eV the antenna is operated from 3 up to 4.23 THz. Finally, by increasing it to 2 eV, the antenna is operated from 3.2 to 4.45 THz which confirms the ability of the suggested antenna to reconfigure its frequency band by changing the external voltage To know the effect of antenna dimensions on its performance, parametric investigations are performed. As sown in Fig. 5 the effect of the R1 on the antenna bandwidth is illustrated at µc = 2 eV. The lower frequency band is affected when the R1 is changed from 35 to 40 µm and the best value is R1 = 38 µm when all antenna dimensions are the same. Also, R3 and R4 have a critical influence on antenna matching as illustrated in Figs. 6 and 7. The values of R3 and R4 should be properly chosen to achieve the desired frequency

Two ports antipodal Vivaldi structure
The suggested single antenna is copied and added close to the first antenna to form the proposed 2-port MIMO configuration. Fig. 8 displays the top and back 2D configuration of the 2-port MIMO antenna. The two elements are placed with side by side configuration. The wireframe of the configuration is illustrated in Fig. 8 to illustrate the top and back views on the same figure. To reduce the structure complexity, the decoupling elements aren't employed. The antenna has a total size of 102µm×168µm. Also, it is seen from Fig. 8 that the configuration is a symmetry which means the same results are achieved from the two ports. So, only the outcomes from port 1 are displayed. The S-parameters outcomes at port 1 are presented in Fig. 9. The antenna worked from 3.2 to 4.45 THz with S 11 ≤ − 10 dB and isolation ≤ 25 dB from 3.2 3.6 THz and ≤ 30 dB from 3.6 to 4.45 THz.

FSS structure
The graphene material as we mentioned above can achieve frequency reconfigurability but the gain of the antenna can't be enhanced. So, FSS cells can be utilized to enhance the antenna gain. The FSS cells in this work are placed below the antenna to reflect the antenna radiation and improve the antenna gain. The same substrate of the antenna is used in the FSS design. A copper patch with 0.035 µm height and two slots is forming the FSS unit cell without adding any layer at the back of the substrate as illustrated in Fig. 10. The S-parameters of the FSS unit cell are displayed in Fig. 11. It is seen that the FSS has bandrejection area with S 21 from 2 up to 5 THz with the deepest level at 3.4 THz which covers the antenna operation with S 11 close to 0 dB which validate the idea of reflection.

Suggested high gain antipodal Vivaldi structure
The number of the FSS cells and the FSS cell separation(s) affect the antenna performance. So, the number of its cells and separation are investigated and introduced. First, two FSS cell configurations with 6 × 9 and 7 × 10 cells are investigated at S = 8.7 µm. we chose the number of cells that cover the whole antenna and the distance lower than 0.25λ at 3.4 THz as illustrated in Fig. 12. It is noticed from Fig. 13 that number of cells affects the antenna gain but the antenna matching and isolation are slightly affected. So, the number of cells with lower elements is utilized to keep the compactness of the antenna size. Second, the 6 × 9 FSS array is selected and added below the antenna. To show the effect of the separation (S) on the antenna performance three different spaces S = 5 µm, S = 8.7 µm, and S = 10 µm are introduced as illustrated in Fig. 14. It is clear from Fig. 14 that FSS Separation (S) affects the antenna gain, the antenna matching and isolation. So, S = 8.7 mm is utilized to keep the compactness of the antenna size.
After finishing the parameter investigation on the cell numbers and separation, the FSS with 6 × 9 cells and S = 8.7 mm are chosen to achieve an antenna total size of 120 × 180 × 13.2 µm 3 . As well, the effects of changing the chemical potential on the 2-port MIMO antenna S 11 and S 21 are illustrated in Fig. 15. When the µc = 0.4 eV the antenna is operated with S 11 ≤ 10 dB at 3 THz and S 21 ≤ 30. When the µc is increased to 1 eV the antenna is worked from 3 to 3.55 THz and S 21 ≤ 25. By increasing the µc to 1.5 eV the antenna is operated from 3 up to 4THz and S 21 ≤ 25. Finally, by increasing it to 2 eV, the Fig. 12 The configuration of the two ports antipodal Vivaldi structure loaded with FSS antenna is operated from 3.2 to 4.45 THz and S 21 ≤ 20 which confirms the ability of the suggested antenna to reconfigure its frequency band by changing the external voltage. Figure 16 shows the single antenna 2 D radiation pattern in the two planes at 3.4 THz and 4 THz in comparison with the MIMO antenna at port 1 loaded with FSS. It is seen that the FSS cells reflect the back radiation and enhance the antenna gain. The co and crosspolarization at port 1 at 3.4 THz and 4 THz are shown in Fig. 17. The antenna is linearly polarized with a value of more than 10 dB between the two components is achieved as illustrated in Fig. 17. Figure 18 illustrates the 3D gain at port 1 at 3.4 THz and 4 THz. The gain equals 10.8 dBi, 7.57 dBi at the selected two frequency bands.
As well, Fig. 19a shows the single antenna peak gain with frequency in comparison with the MIMO antenna at port 1 loaded with FSS. It is seen that the single antenna has a peak gain from 3 dBi to 6 dB with a maximum peak gain of 6 dB at 3.4 THz. However, the antenna with FSS has a peak gain from 7.5 dBi to 10.8 dB with a maximum peak gain of 10.8 dB at 3.4 THz. This means the ability of FSS cells to increase the antenna gain by 4.8 dB. Fig. 19b shows the single antenna efficiency with frequency in comparison with the MIMO antenna at port 1 loaded with FSS. It is seen that the single antenna has Fig. 13 The S-parameters and gain outcomes at different cell sizes @ port1 at S = 8.7 mm a S 11 , b S 21 , c gain Fig. 14 The S-parameters and gain outcomes at FSS spacing (S) @ port1 and at cell size 6 × 9 a S 11 , b S 21 , c gain Fig. 15 The suggested S-parameters outcomes loaded with FSS @ port1 a S11, b S21 radiation and total efficiency of from 78 to 93% and from 70 to 90%, respectively while the antenna with FSS has radiation and total efficiency of from 70 to 82% and from 69 to 80%, respectively.

MIMO investigation
There are several parameters such as envelope correlation coefficient (ECC), diversity gain (DG), channel capacity loss (CCL), mean effective gain (MEG), and multiplexing efficiency is employed to judge the MIMO performance. These parameters can be calculated and extracted from equations used in Ali (2021, 2022), Aboelleil et al. (2021), . The ECC parameters of the MIMO antenna calculated from both the S-parameters and radiation patterns outcomes are plotted in Fig. 20a. The ECC has a value lower than 0.001  The MIMO parameters @port 1 a ECC, b DG, c CCL using the two formulas. As well, the DG is illustrated in Fig. 20b with values around 10 dB. The CCL is calculated and displayed in Fig. 20c with values lower than 0.4(bit/s/Hz). The MEG = − 3 dB within the operated band as shown in Fig. 21a. Finally, the multiplexing efficiency ranges from − 1.5 to −1 dB as illustrated in Fig. 21b. From the outcomes displayed in Figs. 20 and 21, it is noticed that all outcomes have values lower than the standard limits.
Finally, the suggested antenna is compared with others to judge the contribution and novelty as tabulated in Table 1. It is seen that the suggested antenna has wider bandwidth, higher gain, compact size, and suitable MIMO performance which suggested the antenna to be employed in IoT THz applications.

Conclusion
A reconfigurable two ports graphene antipodal Vivaldi MIMO antenna with a total size equal to 120 µm × 180 µm to achieve reconfigurable performance from 3 up to 4.5 THz has been introduced and discussed. The band stop from 2 up to 5 THz FSS with a metallic patch has been employed below the antenna to enhance the antenna from 6 to 10.8 dB at 3.4 THz. The MIMO antenna has been worked from 3.2 to 4.45 THz with S 11 ≤ − 10 dB, isolation ˃ 20, gain from 8 dBi up to 10.8 dB, and efficiency higher than 80%. The MIMO analysis outcomes have obtained competitive values which presented the antenna to be employed in high speed and data rates IoT indoor applications such as smart homes which require such performance. Finally, the suggested antenna has achieved good outcomes as compared to other works discussed in the literature section.