Numerical investigation of graphene-based metamaterial microstrip radiating structure

Recent advancement in antenna technology is directed to achieve reconfiguration of radiating structure parameters. In this paper, we propose graphene-based reconfigurable and high gain microstrip radiating structure for multiband wireless communication applications. The circular copper patch is used as a radiating element of the radiating structure. Graphene layer with circular holes is applied to this microstrip based radiating structure to tune the radiating structure parameters. The radiating structure is stacked with superstrate layers to improve the gain of the design. Frequency reconfiguration and gain enhancement are achieved by varying the chemical potential of graphene. Radiating structure analysis in terms of the reflection coefficient, radiation pattern and gain polar plot is obtained. The proposed reconfigurable radiating structure can be used for L and S-band applications.

There are various designs available with split ring resonator structure. Some of the basic structures of SRR are a single ring with one cut, single ring with two cut and SRRs with multiple splits rings. Change in electromagnetic characteristic depends on the structure of split ring [11].   Reconfigurable and high gain antennas are used widely nowadays because of its applications in radar, satellite, mobile, etc, [12][13][14][15][16][17][18][19][20][21]. Two symmetric U-slots are added in an antenna to achieve reconfiguration. This reconfigurable antenna is applicable in radar applications [12]. The reconfigurable patch antenna is presented to have polarization agility. Reconfigurability is achieved by using p-i-n diodes [13]. Pattern reconfigurable patch antenna with parasitic elements is presented in [14,15]. The reconfigurable and high gain antenna is designed and reconfiguration is achieved by using switching. Different switching states are activated to tune the frequency and improve the gain of the antenna [16]. Corrugated split ring resonators are added to improve the gain of microstrip based antenna [17]. Lumped capacitors are added in the microstrip patch antenna to achieve reconfiguration [18]. Frequency and polarization reconfiguration are possible with the addition of split ring resonators to microstrip patch antenna [19,20]. Multiple band frequency reconfigurations are achieved with PIN diode switches [21].
The reconfiguration is very important and required phenomenon in antennas nowadays and there are very few antennas which give broadband behaviour and frequency reconfiguration both. So we have proposed here, a  . 2D geometry of microstrip antenna having applied external biasing with chemical potential (μ c ) to the graphene layer. Here 'h' represents the height of substrate, 'g' represents the height of the ground, 'e' represents the air gap between ground plane and graphene layer, 'c' represent the height of the copper patch. Graphene chemical potential is applied through different pads to cover the whole geometry and V DC1 ==V DCN . new radiating structure design using graphene material which is targeted to achieve frequency reconfiguration and broadband behaviour both by changing the graphene chemical potential. This frequency reconfiguration can be used in many applications and is presented in section 3.

Design and modelling
The proposed graphene antenna is designed using a 40 mm square substrate. The FR4 material is used as a substrate with permittivity ε r = 4.4. Figure 1 represents the design of graphene antenna along with its stack layer defining separate stack layer in the right side. Figure 2 represents the structure of 3D microstrip antenna. In figures 1 and 2, the antenna has (FR4) substrate having a length of 40 mm, the width of 40 mm and height of 0.8 mm. The height (g), length and width of the ground plate made of copper material is kept the same as that of the substrate material. The radius of the circular patch placed above the substrate is denoted by 'd1' is 18 mm. The height which is denoted by 'c' is 0.5 mm. The width of the feed line(f) is 7 mm. Here 'e' represents the air gap between the ground plane and the graphene layer that is 0.8 mm which is beneath the substrate. In figure 1, the right side represents stack layer of the antenna with a cross made of copper material with the same length, width and height. Figure 2 represents a circular patch antenna and figure 3 shows the stack layer structure placed above a circular patch antenna. The antenna consists of a circular copper patch, FR4 substrate and copper ground layer as represented in figure 2. Microstrip line feed is made up of copper material. The antenna is superstrated with stack layer consisting of FR4 superstrate as represented in figure 3. The radius of the circular patch is 18 mm. Width and length of the FR4 substrate are 40 mm as shown in figures 2 and 3. The height of the substrate is 1.6 mm. The ground plane is having 40 mm length and width with 1 mm thickness. The dimension of the feed line is set as 7 mm length, 2 mm width and 0.5 mm height. Table 1 show different dimension values of the microstrip patch antenna. Substrate area is 40×40 mm 2 . The copper stack area is 18×8 mm 2 . Copper patch thickness is taken 0.5 mm with its radius 18 mm. Feed line is placed at 7 mm. Ground plane and substrate thickness is 0.8 mm.
Top view of the microstrip patch antenna is presented in figure 3. The shorting pins are represented by black dots. The distance from the centre of the antenna to the shorting pins is denoted by d2 which is equal to 8 mm. The shorting pins are used to connect ground plane and patch. Figure 4 represents the honeycomb lattice structure of graphene material layer sheet The circular shape is subtracted from this sheet to create metamaterial behaviour. The radius of the circular shape R1 is 3 mm. The distance between the centres of the two circles is denoted by R2 having  10 mm. (grey colour represent the graphene layer). Figure 5 is showing the different voltage pads provided to the graphene sheet to give equal chemical potential to the graphene layer.

Graphene conductivity model
The surface conductivity of graphene has been considered as the Kubo formula [22]. ⎡ Where, the first term is due to intraband contributions, and the second term due to interband contributions, electron charge is represented as e, ω is radian frequency, μ c is chemical potential, Г is a phenomenological scattering rate that is assumed to be independent of energy ε, T is temperature and ħ is the reduced Planck's constant. In equation (1), ( ) ( ) is the Fermi-Dirac distribution where k B is Boltzmann's constant [23]. The reflectance mainly depends on the graphene chemical potential and frequency. The wave-vector component when the wave is incident with angle θ i is given by k=ω sin θ i /c. The reflection coefficient is given by [24]: Optical conductivity of graphene material is denoted by σ and given by the following equation: from all the above equations, the relationship between the conductivity and reflectance is given by: The relationship between the conductivity and reflectance is changed if the complex part is considered and is given by:   Now if θ i =k=0, The reflectance for the incident wave is given by: From the equations (2)- (7), it is clear that the graphene chemical potential and its conductivity closely related to reflectance [24].

Results and discussions
The design presented in section 2 is analyzed using COMSOL Multiphysics RF module and results achieved through this simulation is presented in figures 5-14).
The reflection coefficient is tuned by changing the graphene chemical potential in figure 5. When chemical potential (μ c ) 0 eV is applied, then three bands of reflection coefficient are obtained. From these three bands, the first band is obtained at 1.  resonant frequency with a reflection coefficient of −25.12 dB and the bandwidth of 60 MHz. The third band is obtained at 3.46 GHz of resonant frequency with a reflection coefficient of −20.43 dB and bandwidth of 220 MHz. The comparison of graphene chemical potential, frequency and bandwidth for graphene sheet with circular slots is presented in table 2 and graphene sheet without circular slots is presented in table 3. From the comparison, it is evident that the design with circular slots graphene sheet has better bandwidth and tuning compared to the graphene sheet without circular slot design. Figure 6 shows the Voltage Standing Wave Ratio(VSWR) of the microstrip antenna at different graphene chemical potential. Figure 7 represents reflectance at a different chemical potential (μ c ) (0.01 eV,0.03 eV, 0.06 eV and 0.09 eV) for 1 GHz to 4 GHz frequency range. In this, the colour bar indicates normalized reflectance where a blue colour corresponds to minimum reflectance and red colour indicates maximum reflectance. From this figure, it is observed that with applied different chemical potential, the resonant frequency is tuned. 3.87 70 Table 4. Gain of the antenna with and without plus shaped superstrate layer. No.

Resonant Frequency (GHz)
Gain (dB) 2D radiation pattern ( figure 11(A)) and 3D polar plot( figure 11(B)) with applied μ c of 0.03 eV at frequency 2.14 GHz with achieved gain of 5.12 dB. 2D radiation pattern (figure 11(C)) and 3D polar plot(figure 11(D)) with applied μ c of 0.03 eV at frequency 2.81 GHz with achieved gain of 6.28 dB. 2D radiation pattern (figure 10(E)) and 3D polar plot(figure 11(F)) with applied μ c of 0.03 eV at frequency 3.38 GHz with achieved gain of 2.41 dB. Figure 12 show the radiation pattern and polar plot for 0.06 eV graphene chemical potential. The highest gain of 7.63 dB is achieved for 3.05 GHz. Figure 13 show the radiation pattern and polar plot for 0.09 eV graphene chemical potential. The highest gain of 9.42 dB is achieved for 2.25 GHz frequency. Electric field response to different chemical potential is presented in figure 14. Table 2 shows the results in terms of the reflection coefficient, gain, bandwidth for different graphene chemical potential. The tuning of the frequency with respect to different chemical potential is also presented in the table. The maximum reflection coefficient, gain, bandwidth of −30.39 dB, 9.42 dB, 240 MHz are achieved respectively. The maximum tuning of 240 MHz is achieved by changing the graphene chemical potential from 0 eV to 0.03 eV.
The comparative results in terms of reflection coefficient, graphene chemical potential, gain, bandwidth are presented in table 5. The comparison clearly shows that maximum gain of 9.42 dB and a maximum bandwidth of 240 MHz is achieved.

Conclusion
The graphene-based microstrip antenna is presented to improve the gain and tune the frequency spectrum. The analysis in terms of the reflection coefficient, bandwidth, radiation pattern, and the gain polar plot is obtained. Multiband and tunable frequency response are observed and tuning is achieved by changing the graphene chemical potential. Designed antenna results into highest gain of 9.42 dB at 3.25 GHz and μ c =0.09 eV with −25.12 dB reflection coefficient value. The tunability of frequency is observed with different chemical potential of graphene. The maximum tuning of 240 MHz is achieved by changing the graphene chemical potential from 0ev to 0.03 eV. It is also observed that the bandwidth of the proposed antenna increases with an increase in the chemical potential. The maximum bandwidth of 240 MHz is achieved with 0.06 eV graphene chemical potential at 3.46 GHz frequency. The proposed reconfigurable antenna can be a potential candidate for various RF and microwave application in L and S bands.