Terahertz frequency range is the band from 0.1 THz to 10 THz of the electromagnetic spectrum which has not been explored completely. This regime has many applications in imaging, networking, medical field, wireless network, short distance communication, astronomy, and space science applications [5, 7, 9, 20]. Terahertz range can be beneficial for increasing the bandwidth and data rate in wireless communication [19]. In wireless communication systems antenna is a very important component. Some manners including increasing the substrate thickness or the patch size, were used to broaden the bandwidth and to get better the gain of the microstrip patch antenna. But thicker substrate reduces the radiation efficiency because of surface wave losses. To defeat this problem THz patch antenna utilized a photonic crystal slab or Photonic Band Gap (PBG) structure with multi slotted ground as a microstrip substrate [6] because of being able to reduce the surface wave propagation and improve the electrical performance of the antenna. For the reduction in size the By two dimensional photonic crystals are utilized to beat the microstrip patch antenna limitations such as low efficiency, low antenna gain (≤ 2dB) [10]. Monolayer Graphene [15] whose conductivity depends on the Fermi level can be dynamically tuned by a gate voltage, i.e. by electrical biasing. The optical conductivity of graphene depends upon both interband and intraband transitions. At Fermi level of above half of the photon energy, the interband transitions are stopped, and intraband transitions govern in the optical conductivity. Intraband transitions are highly responsive to the charge carrier concentration in the graphene, hence the graphene optical conductivity (s) and permittivity [ε = 1 + (iσ(ω)/ωε₀)] give one an idea 0 about a strong variation on the gate voltage, which decides graphene a capable electrically tunable plasmonic object [8, 21]. Graphene can be very useful for the design of efficient antenna in the THz range with versatile nature.

The past work lacks for the terahertz antenna with good performance parameters (antenna gain, antenna directivity, and antenna radiation pattern), good gain and good directivity leads to better radiation efficiency. The present work discusses about the importance of utilization of graphene properties in antenna field. Here graphene with slotted ground PBG structure is used to give improved results for antenna in terahertz regime. Previous researches lack high gain and good radiation efficiency [18]. The Microstrip antennas are low profile antennas and are generally found applications in satellites and missiles due to its benefits of conformal to planar and non planar surfaces [4]. Section 1 of the paper describes the objective. Section 2 of the paper discusses about the conductivity of the graphene and parametric details of the proposed antenna. In section 3, proposed graphene based various antenna designs and analysis of simulation results are included. Finally the paper is concluded.

Terahertz frequency range (from 0.1 THz to 10 THz) which is not fully utilized, has attracted many researchers because of extreme possibility of applications in the unused band. This work shows the inclusion of graphene with Photonic Band Gap (PBG) in antenna and its effect in the performance of the proposed antenna. Here graphene exceptional properties are utilized in terahertz regime antenna for wireless network applications. Good gain and good directivity of the proposed antenna shows better radiation efficiency of the antenna in the THz regime. Graphene as patch material provides a new set of tools to the engineering community to design nanoscale components with unprecedented possibilities. Design of antennas in terahertz regime demands for efficient design methodologies as miniaturization limits the performance in terms of higher geometric uncertainty, improper characterization of the antenna leading to fabrication difficulties. Graphene plays an important role in reducing the limitations for miniature antenna while maintaining the key antenna parameters like return loss, gain, directivity, radiation pattern, and radiation efficiency. Moreover, graphene antennas support SPP (Surface Plasmon Polaritons) modes, and this enables miniaturization and increase in efficiency of antenna in micro scale in terahertz frequency regime. Hence graphene is an effective alternative to metal for the THz antenna offering simplicity in design.

Few designs of THz antenna are proposed here. Graphene patch antenna on simple substrate, graphene patch antenna with slotted ground and graphene patch antenna with PBG substrate are presented. Here graphene properties are utilized and the performance of with PBG substrate, with simple substrate, with and without ground slot are analyzed. The parametric detail of all the designs are same except the inclusion of slot and PBG structure in proposed designs. The proposed graphene based PBG terahertz patch antenna is shown in Figure 1. Antenna consists of PBG structure on a substrate of Arlon (AR-100) having length L_s , width W_s , and thickness T_s with graphene as patch material, patch has a length and width L_p and W_p ,  respectively and is excited by discrete port on the middle of the antenna. The necessary parametric detail of the proposed design are given in tabular form (Table 1).

Figure 1. Top View of Proposed Graphene Based Photonic Band Gap (PBG) Terahertz Antenna

Table 1. Parametric Detail of the Proposed Antenna

Graphene plays very important role as a radiator in the THz range. The conductivity of graphene has been calculated by Kubo's formula as given in [1, 11, 14]. The conductivity varies on the chemical potential μ_c, temperature T, frequency ω₂, and transport relaxation time τ. Graphene quality strongly depends upon relaxation time and here in all simulation cases the standard value of relaxation time is 10^-12 s^-1. Antennas with graphene are contemplated to have dimensions of a few micrometers, for a graphene sheet with dimension larger than few hundred nm, the edge effects on the graphene conductivity can be nullified, so the surface conductivity model can be used to build up the graphene sheet.

With the Drude-like intraband contribution, the surface conductivity can be given as [13],

(1)

While the surface conductivity because of interband contribution, can be represented as [13],

(2)

The total conductivity is given by,

(3)

In this work, the authors have analyzed graphene based terahertz antennas with modification in substrate and modification in ground to improve the performance of the terahertz antenna. First case of the proposed design of simple graphene based terahertz patch antenna is shown in Figure 2 (a).

The proposed antenna is simulated using electromagnetic solver (HFSS), and the MATlab codes are used to generate and utilize the exceptional properties of the graphene. Graphene's exceptional properties are used to enable antenna to radiate in terahertz range and by so increasing the capacity of information exchange between inter and intra chip networks. This paper utilizes graphene's outstanding properties for the extension of antenna operating frequency range with better performance parameters. In very first case, they have presented a basic terahertz patch antenna that is tuned at terahertz regime and the same is showing multi frequency operation. The configuration details are same as given in Table 1. The return loss plot of basic patch terahertz antenna is shown in Figure 2 (b). Four resonances, i.e. -15.09 dB at 0.341 THz, -19.9 dB at 0.421 THz, -13.1 dB at 0.501 THz, and -10.4 dB at 0.591 THz are reported here.

The 3D gain and directivity plots for the simple terahertz patch antenna is shown in Figure 2 (c) and 2 (d), respectively. The maximum value of the gain in this case is 5.61 dB and the maximum value of the directivity is 5.94 dB. The distribution of gain and directivity are also good for the depicted antenna.

Figure 2. (a) Simple Graphene Based Terahertz Antenna, the Proposed Antenna is Excited by Lumped Port, (b) Return Loss Plot of the Proposed Simple Terahertz Antenna shows Four Resonant Conditions, (c) Gain Plot of the Proposed Simple Graphene Based Terahertz Antenna, the Maximum Value of the Gain 5.61db is reported here, (d) Directivity of the Proposed Simple Graphene Based Terahertz Antenna, the Maximum Value of Directivity 5.94 Db is reported here

Another case of the proposed antenna is graphene based terahertz antenna with one slot on the ground as shown in Figure 3 (a). In this case ground has a slot in the center position causing some shift in resonant frequency conditions. There are four resonant conditions in terahertz antenna without ground slot and the same is reported with ground slot case, but there is a shift in first resonant condition, i.e. frequency is shifted from 0.341 THz to 0.201 THz and so a decrease of 0.14 THz can be observed, also first resonant impedance matching is reduced by 4 dB value which can be seen as lesser matched condition, in second resonant condition is shifted from 0.421 THz to 0.341 THz and the amount of frequency shift is 0.08 Thz. This resonant condition is better matched by 8 dB value approximately with ground slot case. In third resonant condition resonant frequency is shifted from 0.501 THz to 0.421 THz so a decrease of same amount of 0.08 THz frequency shift can be observed, but impedance matching is again improved by about 14 dB. The last and fourth resonant frequency is shifted from 0.591 THz to 0.511 THz so the amount of frequency shift is again same as 0.08THz and the impedance matching is good in fourth resonant condition with ground slot and without ground slot terahertz antenna.

From profound analysis it can be noted that except first resonant condition the amount and nature of resonant frequency shift is same for all resonant conditions with slot in the ground of the terahertz antenna. So it is an important finding of the proposed antenna in terms of static reconfiguration of the antenna. Another aspect of the slotted ground antenna is the improvement of the impedance matching in the terahertz regime. Summarizing the findings, there are four resonant conditions, i.e. - 10.9 dB at 0.201 THz, -15.8 dB at 0.341 THz, - 27.2 dB at 0.421 THz, and -11.1 dB at 0.511 THz for graphene patch terahertz antenna with ground slot as depicted in Figure 3 (b) and impedance matching is also improved approximately in all resonant conditions.

3D gain pattern and directivity pattern of the proposed terahertz antenna with ground slot is as shown in Figure 3 (c) and 3 (d), respectively. The maximum value of gain and directivity is 5.74 dB and 6.57 dB, respectively. On comparing the values of gain and directivity of the proposed terahertz antenna with ground slot and without ground slot there is increase in the maximum value of the gain and directivity by the amount of 0.13 dB and 0.63 dB respectively. This can be taken as a benefit in addition to static frequency reconfiguration and better impedance matching.

Figure 3. (a) Simple Graphene Based Terahertz Antenna with One Slot on the Ground, (b) Return Loss Plot of the Simple Graphene Based Terahertz Antenna With One Slot on the Ground, Four Resonant Conditions are reported here, (c) Gain Plot of the Simple Graphene Based Terahertz Antenna with One Slot on the Ground, the Maximum Value of Gain 5.74 dB is reported here, (d) Directivity Plot of the Simple Graphene Based Terahertz Antenna with One Slot on the Ground, Maximum Value of Directivity is 6.57 dB

Another design of same dimensions with same materials as used in proposed antennas of (Figure 2a and Figure 3a) excluding slot in the ground, graphene based patch terahertz antenna with photonic band gap structure is presented in Figure 4 (a).

This design shown in Figure 4 (a) utilizes the properties of graphene in addition with photonic band gap structure to reduce the surface wave propagation and improve the electrical performance of the antenna. The presented design shows multi resonant frequencies, i.e. taking into account -8 dB threshold consideration, total of seven resonant conditions (-11.14 dB at 0.431 THz, -13.39 dB at 0.521 THz, -13.55 dB at 0.691THz, -10.76 dB at 0.741 THz, and -11.1 dB at 0.831 Thz, -9.1 dB at 0.220 THz, and -9.5 dB at 0.615 THz) as shown in Figure 4 (b) can be observed, and on changing the threshold to -10 dB level would count total of five resonant conditions (-11.14 dB at 0.431 THz, -13.39 dB at 0.521 THz, -13.55 dB at 0.691THz, -10.76 dB at 0.741 THz, and -11.1 dB at 0.831 THz) as shown in Figure 4 (b) can be seen. This multi resonant operation can be very beneficial for applications of multi resonant operation. Figure 4 (c) and Figure 4 (d) represent the gain and directivity plot of the PBG terahertz antenna. The maximum value of the gain and directivity are 5.78 dB 6.26 dB respectively. The distribution of both (gain and directivity) the parameters are better distributed.

Figure 4. (a) Photonic Band Gap Structure Based Terahertz Antenna, (b) Return Loss Plot of the PGB Antenna, Total of Five Resonant Conditions are Reported, (c) Gain Plot of the PBG Terahertz Antenna, Maximum Value of the Gain Is 5.78 dB, (d) Directivity of the PBG Antenna, Maximum Value of Directivity is 6.26 dB

Comparing the gain and directivity, proposed antenna has improved performance and shows that PBG structure with graphene radiates the power in better way. Comparison table of the work reported in this paper and the work reported in the previous papers are depicted in Table 2. Resonant frequency, gain, directivity and radiation efficiency are given for comparison purpose. This comparison reveals better performance of the proposed paper.

Table 2. Comparison of Performance Parameters of the Proposed Antenna and Work Reported Earlier

The proposed antenna discusses about basic graphene patch antenna, graphene patch antenna with ground slot and PBG substrate based graphene patch antenna and compared the performance among them. The work states about the effect of graphene in patch antenna, effect of ground slot, and influence of PBG substrate in terahertz antenna. And also reports multi resonance operation with seven resonant frequencies (for -8 dB level of threshold) and five resonant frequencies (for -10 dB level of threshold) for PBG substrate THz antenna. Gain and directivity of proposed graphene patch antenna with ground slot and PBG substrate based graphene patch antenna are 5.74 dB, 6.57 dB, and 5.78 dB, 6.26 dB, respectively. The proposed antenna can be useful in wireless sensor networks and for high speed inter and intra chip networks in wireless sensor networks.

Acknowledgement

I convey sincere thanks for the support provided by Thapar University, Patiala, Punjab, IKGPTU, Jalandhar, Punjab and IIT Indore, India. I also convey my sincere thanks to Dr. Mukesh Kumar, Asst. Professor, IIT Indore, for his valuable support and guidance.