Introduction

In recent years, one of the significant concerns for modern photonic and electronic devices is closing to the terahertz (THz) gap which is located between the highest frequencies of photonics and the lowest frequencies of electronics. Furthermore, the equipment which generated and detected the electromagnetic (EM) radiation in that region is called an optoelectronics device [1].

Nowadays, the optoelectronics research field has become so interested in plasmonic nano-antennas, which radiate in multiple band frequencies. The experts continuously work to create a novel plasmonic antenna that successfully connects the free space radiation and concentrated subwavelength energy of restricted electromagnetic (EM) radiation [2]. Plasmonic antennas are being widely implemented in a number of new applications, including sensing, spectroscopy, nonlinear optics, nanophotonic circuitry, optical metasurfaces, photodetection, and better photoemission [3].

The terahertz range from (0.1 to 10) THz, and it is placed between the infrared (IR) and millimeter (mm) wave. It is provides wide bandwidths in the hundreds of gigahertz range, extremely high data rate, and smaller attenuation than optical signals [4,5,6]. Nevertheless, in this frequency band, conventional metallic conductors are unable to be appropriate as a result of the presence of low conductivity and high skin effect, which causes a high loss in the antenna radiation performances, due to low electron mobility in the metallic structure at the THz frequency band [7, 8]. However, the low skin effect, permanent tunability through the electrostatic gating, and chemical potential of graphene make it a good alternative conductor material, which is mostly interesting for designing and fabricating antenna in THz applications [9]. Graphene is widely employed in many different kinds of industry sectors, including photonics, telecommunications, and electronics [10]. Moreover, it plays an important role for the development of planar adaptable antennas having multi-functional manners for determining the state of electromagnetic (EM) waves in terms of polarization, operating frequency, and antenna radiation patterns [11,12,13].

Therefore, these properties of graphene encouraged researchers to develop many different types of graphene-based antennas having currently observed performance in the terahertz range. For instance, in [14], a Vivaldi antenna is developed using graphene layers to improve the antenna bandwidth as the Fermi energy level is increased. In [15], the graphene material capability was implemented to design microstrip antennas of square patch shapes to regulate and control antenna polarization. Moreover, a tunable graphene antenna which consist of a radiating graphene patch and a non-radiating graphene ring was suggested and investigated in transverse magnetic (TM22) mode by [16]. Additionally, the effect of size and repetition of the photonic crystal on the antenna radiation characteristics in the THz frequency bands was also studied by [17]. Furthermore, a number of multi-beam tunable graphene-based dipole antennas incorporating reflector-transmission and reflector-director windows techniques for modulation were investigated in the THz band. On the other hand, in [18,19,20], a different microstrip antenna–based graphene having polarization variance was proposed by changing the chemical potential of the graphene patch to achieve linear polarization, right-hand circular polarization (RHCP), and left-hand circular polarization (LHCP) in the antennas far-field radiation pattern.

In this article, plasmonic microstrip antennas based on graphene with different dielectric substrates are designed and simulated to operate in the frequency band ranges from 0.1 to 5 THz. In addition, the dielectric substrate thickness is also modified to allow the antenna to operate at multi-band frequency operations. The simulation procedure was performed by implementing a full-wave electromagnetic model based on the finite integration technique (FIT) technique. The remaining part of the present work is organized as follows. In the “Material Method” section, the graphene properties and configuration of the plasmonic microstrip antenna are described. Outcomes of the proposed antenna simulation are mentioned in “Results and Discussion” section. Afterward, the “Conclusion” section shows the conclusions.

Material Method

The proposed plasmonic microstrip antenna based on graphene is designed, simulated, and optimized using an electromagnetic (EM) simulator named computer simulation technology (CST), which is based on a finite integration technique (FIT) [21]. In its simple construction, the microstrip antenna is composed of a dielectric substrate sandwiched between two conductor materials as illustrated in Fig. 1.

Fig. 1
figure 1

Schematic diagram shows the designed graphene microstrip antenna

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In this figure, the substrate thickness is denoted by h, while the width and length of patch and ground plane conductor material dimensions are represented by Lp, Lg, Wp, and Wg, respectively. The characteristic and properties of graphene material and its construction are explained in the following sub-section.

Properties of Graphene

Graphene is a new nanomaterial made of a very thin two-dimensional (2D) carbon atom layer within a hexagonal honeycomb lattice. It is a unique material in which the relationship between the energy and momentum of electrons is linear instead of quadratic during a variety of energies [22]. This behavior led to the creation of very high carrier mobility at room temperature. Also, this extraordinary characteristic of graphene allows it to be extremely attractive for supporting and promoting surface plasma polaritons (SPPs)’ mode, particularly in the range of terahertz (THz) band, where its resonance plasma frequency is perfectly placed in this spectrum [23].

Furthermore, the surface conductivity of graphene (σs) is dependent on the frequency that can be determined by its values approximately using Kubo’s equation, which consists of two parts, interband conductivity and intraband conductivity, as given by [24]:

$${\sigma }_{\mathrm{s}}\left(\omega ,{\mu }_{\mathrm{c}}\right)= {\sigma }_{\mathrm{intra}}\left(\omega ,{\mu }_{\mathrm{c}}\right)+{\sigma }_{\mathrm{inter}}\left(\omega ,{\mu }_{\mathrm{c}}\right)$$
(1)

The graphene intraband conductivity (\({\sigma }_{\mathrm{intra}}\)) term can be represented as [25]:

$${\sigma }_{\mathrm{intra}}\left(\omega ,{\mu }_{c}\right)= -j\frac{2 {\mathrm{e}}^{2} {K}_{\mathrm{B}}T}{\pi {\mathrm{\hbar }}^{2}}\mathrm{ln}\left(2\;\mathrm{cosh}\left(\frac{{\varphi }_{c}}{2}\right)\right).\frac{1}{\omega -j{\tau }^{-1}}$$
(2)

The graphene interband conductivity (\({\sigma }_{\mathrm{inter}}\)) term can be represented as [25]:

$$\sigma_{\mathrm{inter}}\left(\omega,\mu_{\mathrm c}\right)=\frac{e^2}{4\hbar}\left(H\left(\frac\omega2\right)+j\frac{4\omega}\pi\int_0^\infty\frac{H\left(\varepsilon\right)-H\left(\frac\omega2\right)}{\omega^2-4\varepsilon^2}d\varepsilon\right)$$
(3)

where \(H\left(\varepsilon \right)=\frac{\mathrm{sinh}\varphi }{\mathrm{cosh}{\varphi }_{c}+\mathrm{cosh}\varphi }, {\varphi }_{c}= \frac{{\mu }_{c}}{{K}_{B}T}\;and\;\varphi =\frac{\mathrm{\hbar }\varepsilon }{{K}_{B}T}\)  

where \({\mu }_{\mathrm{c}}\) is the chemical potential, \(T\) is temperature, \({K}_{\mathrm{B}}\) is a Boltzmann’s constant,\(\omega\) is the angular frequency, ℏ = reduced Planck’s constant, τ is relaxation time, and e is the charge of the electron. In this article, the value of \({\mu }_{\mathrm{c}}\) is assumed to be equal to 0.1 eV, KB = 8.62 eVK−1, T = 300 K, τ = 1 ps, ℏ = 6.582 × 10−16 eVs, and e = 1.6 × 10−19 C. According to the Pauli exclusion principle, the intraband surface conductivity leads the total value of surface conductivity (σs) at low frequency in the range of THz. Meanwhile the interband component experiences no influence on the overall surface conductivity (σs) and, therefore, can be neglected [26].

Antenna Configuration

The proposed antenna was constructed from a single rectangular patch of graphene is putted at the upper part of the dielectric substrate. The opposing side of the substrate comprises a graphene layer of identical dimensions to the substrate that is used to create the antenna ground plane. The height of the ground plane and radiating patch is assumed to be equal to (0.34 nm). As the graphene patch is excited using electromagnetic waves (EM), the electrons inside it are moving back and forth at (THz) frequencies, and this phenomenon is referred to as surface plasma polariton (SPP) [27, 28]. The dispersion relation of possible maintained (TM) mode of plasmons or the SPP wavenumber (kSPP) of the graphene layer is expressed in free space as [29]:

$${k}_{\mathrm{SPP}}={k}_{\circ }\sqrt{1-{\left(\frac{2}{{\eta }_{eff} {\sigma }_{g}}\right)}^{2}}\approx \frac{\mathrm{\hslash }{\omega }^{2}}{2\alpha {\mu }_{c} c}$$
(4)
$${\eta }_{\mathrm{eff}}=\sqrt{1-\frac{4{\mu }_{\circ }}{{\varepsilon }_{\circ } {\left({\sigma }_{g}\right)}^{2}}}\approx \frac{\lambda }{{\lambda }_{SPP}}$$
(5)

where ηeff and k0 are effective intrinsic impedance of free space and wavenumber of graphene material, respectively. Furthermore, the effective intrinsic impedance of graphene sheet is associated with both the free space permittivity (ε0) and permeability (μ0). The dimensions of a plasmonic microstrip antenna are determined from the equations presented by [30] as:

$${W}_{p}=\frac{(2M+1)}{\sqrt{{\varepsilon }_{r}}}\times \frac{{\lambda }_{\circ }}{2}$$
(6)
$${L}_{p}=\frac{(2N+1)}{\sqrt{{\varepsilon }_{eff}}}\times \left(\frac{\lambda spp}{2}\right)-2\Delta L$$
(7)

where N and M are positive integers (in this paper are regarded as, N = M = 1); λspp and λ0 are the operating and free space wavelengths; ΔL is the patch length extension as a result of the fringing effect; and (εr) and (εeff) are relative dielectric constant and the effective dielectric constants, respectively. The width of the feeding line (Wf) is determined from the antenna total input impedance (Za) which can be obtained by:

$${Z}_{a}=\frac{11.96 {\lambda }_{\circ }}{{W}_{f}}$$
(8)

Furthermore, Za is matched in accordance with the accepted standard of 50 Ω impedance through the feeding line length (Lf) with the characteristic impedance, which is expressed as Z0 = 50 × Za. Consequently, the physical dimensions of the ground and substrate are determined using the equation that follows the expression:

$${W}_{\mathrm{s}}={W}_{\mathrm{g}}={W}_{\mathrm{p}}+2{L}_{\mathrm{f}}$$
(9)
$${L}_{\mathrm{s}}={L}_{\mathrm{g}}={L}_{\mathrm{p}}+2{L}_{\mathrm{f}}$$
(10)

where Ls is the length while Ws is the width of the dielectric substrate, respectively. The optimized dimensions of the proposed antennas are illustrated in Table 1.

Table 1 Optimized dimensions of the proposed microstrip antenna dimensions
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Besides, selecting an appropriate dielectric substrate material plays an essential role to graphene antennas since the substrate’s height (h) and dielectric constant (εr) significantly impact impedance characteristics and, therefore, the antenna operating frequency. Moreover, the substrate material can be attributed to changing charge carrier density in the graphene patch, which affects the carrier mobility numbers and supports graphene’s tuned capabilities. Therefore, in this work, various substrate materials are chosen such as RT5800, polyimide, quartz, silicon dioxide (SiO2), FR4, mica, silicon nitride (SiO3N4), and gallium arsenide (GaAs), each of which has its own thermal, electrical, and mechanical properties as summarized in Table 2.

Table 2 Electric, thermal, and mechanical characteristics of various substrate materials
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The above-mentioned dielectric substrate materials are implemented for designing a plasmonic microstrip antenna operating at 1.0 THz using CST simulation techniques.

Results and Discussions

In the present work, radiation characteristics of the plasmonic microstrip antenna based on graphene are analyzed for various dielectric substrate materials using (CST) microwave studio simulation software at the resonate frequency of 1.0 THz. The performance of the recommended antenna is studied in terms of return loss (S11), voltage standing wave ratio (VSWR), impedance bandwidth (BW), efficiency, gain, and antenna radiation pattern such as E-plane and H-plane, and the results are presented and discussed in the form of graphs and tables in the following sub-sections.

Single and Dual Band Antenna

One of the most important antenna parameters is return loss (S11), and it should be less than − 10 dB for appropriate impedance matching. Figure 2 shows the return loss (S11) according to operating frequency near 1.0 THz, which is − 15.903 dB for RT5880 at 0.995 THz, − 40.059 dB for polyimide at 1.010 THz, − 45.674 dB for quartz at 1.00 THz, − 40.283 and − 37.508 dB for SiO2 at 0.990 THz, and − 36.045, − 29.435, − 22.199, and − 21.144 dB for FR-4, mica, SiO3N4, and GaAs at 0.985, 0.935, 0.870, and 0.825 THz, respectively.

Fig. 2
figure 2

Variation of S11 of proposed plasmonic antenna based on graphene with various substrates

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In addition, the voltage standing wave ratio (VSWR) is also another important factor that should be taken into account during assessment of an antenna performance. A lower value of VSWR indicates that the antenna is properly matched to the transmission line feed, and this means a greater amount of power that is transmitted to the antenna terminal. Besides, the antenna bandwidth, gain, and antenna efficiency for each dielectric substrate materials are computed, and the results are presented in Table 3.

Table 3 Performance comparison of proposed antenna for various substrate materials
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This table says that each of the considered dielectric substrates maintains a reliable VSWR values near to unity and among which the quartz and SiO2 provide lower S11 and VSWR values. Moreover, the antennas with both silicon nitrate and gallium arsenide substrate material are resonating at another band frequencies, which are 4.134 and 3.674 THz with S11 values of − 13.536 and − 13.703 dB and VSWR values of 1.531 and 1.520, respectively, as indicated in Figs. 2 and 3.

Fig. 3
figure 3

Variation of VSWR of proposed plasmonic nano-antenna based on graphene with various substrates

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In addition, the 2-dimensional electric (E) and magnetic (H) plane radiation patterns for the first exaction mode (TM10) of the advised antenna with each assumed substrate materials are also calculated and the results are displayed in Fig. 4. It is clearly seen from these figures that the antennas’ gain varies from 2.540 to 3.150 dB at their operating frequencies. The results also imply that the quartz substrate material provides peak values of antennas’ gain and efficiency with acceptable antenna bandwidth. Consequently, the fundamental antenna parameters that are derived from the proposed antennas using RT5800, polyimide, quartz, SiO2, FR4, mica, SiO3N4, and GaAs substrate materials, as presented in Table 3 can be regarded as a baseline comparison for identifying a suitable substrate for antenna designing in terahertz region.

Fig. 4
figure 4

2D view of the proposed antennas radiation pattern. a E-plane and b H-plane with different substrates for the first exaction mode (TM10)

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Triple Band Antenna

In this section, the impact of substrate thicknesses on the antenna performances for GaAs substrate material is analyzed due to its wide usage in the solar cell applications and it also provides multi-band operation which makes it reliable for designing novel smart antennas operating at multi-operational frequencies. For this, the thickness of the GaAs substrates is varied from 4 to 8 µm, and the computation results for the antenna bandwidth, gain, and efficiency are demonstrated in Table 4. This table displays that the proposed antenna is operated with a dual resonance frequency at 0.825 and 3.674 THz and 0.810 and 3.605 THz, respectively, for the substrate thickness 4 µm and 5 µm. Moreover, when the substrate thickness is raised to 6, 7, and 8 µm, a third resonance frequency occurs at 4.720, 4.510, and 4.340 THz, respectively. This behavior can be attributed to the creation of more fringing filed lines that arise at the edge of the dielectric substrates as the height of the substrate is increased. Therefore, the energy stored in the microstrip antenna resonator decreases. Hence, the quality (Q) factor drops, and hence, the bandwidth (BW) of the proposed antenna is improved.

Table 4 Antenna performance with the use of GaAs material of various substrate thickness
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Commonly, the graphene patch works exactly as a parallel plate transmission line, resonating between the feeding line and the ground plane. As a result, the basic vibration mode is TM10 [18]. Meanwhile, when the substrate thickness becomes thicker, enough space is formed inside the antenna substrate for a further higher-order vibration mode, such as TM11, TM20, and TM30 to propagate. The aforementioned mode will produce resonance equivalent to TM10 but with various frequencies because of a different phase constant. Therefore, the antenna substrate thickness can be adapted to provide triple-band operating frequencies. The optimum substrate thickness for triple-band resonance seems to occur at 7 μm and 8 μm. However, when the substrate thickness is raised to higher than this limitation, the capabilities of the antenna will be decreased with regard to surface wave propagation in the antenna resonator. In general, a proposed plasmonic microstrip graphene patch antenna is operated with a dual-band operating frequencies when the substrate thickness is of the order of 4 to 5 µm and beyond which it operates with triple-band frequencies as shown in Figs. 5 and 6.

Fig. 5
figure 5

Change of S11 as a function of frequency with various GaAs substrate thicknesses

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Fig. 6
figure 6

Change of VSWR as a function of frequency with various GaAs substrate thicknesses

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Moreover, the 3D and 2D views of the far-field radiation pattern for the triple-band antenna for a GaAs substrate with a substrate thickness of 7 µm is calculated, and the results are displayed in Fig. 7. Additionally, the realized gains for the plasmonic antenna with the optimized GaAs substrate thickness values of 7 μm is also calculated as a function of frequency, and the results are shown in Fig. 8. This figure again displays that our proposed antenna is operated at three band frequencies of 0.766, 3.285, and 4.51 THz with a gain value of 2.51, 2.73, and 6.56 dB, respectively.

Fig. 7
figure 7

3D radiation pattern at a 0.766 THz, b 3.285 THz, c 4.510 THz, and d E-plane and H-plane patterns at 4.510 THz (TM20) mode with the substrate thickness of 7 μm

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Fig. 8
figure 8

Realized gain versus frequency of the proposed antenna built up on GaAs substrate with thicknesses of 7 μm

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Finally, the computed antenna gain, bandwidth, and antenna size of the present work at the single band (1 THz) for quartz substrate, dual-band (0.825 and 3.674) THz, and triple-band (0.766, 3.285, and 4.510) THz, frequency operation for GaAs substrate material, and those obtained by other researchers are summarized in Table 5. One clearly observes from this table that the size, gain, and bandwidth parameter values obtained for the proposed antennas are in a reliable agreement with those previously achieved by other research workers at single-, dual-, and triple-band operational frequencies. Additionally, our results are better than most of the available data presented in this table, especially regarding the antenna size and bandwidth values.

Table 5 Performance of the suggested antenna in comparison to state-of-the-art works
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Conclusion

This work deals with the design of a plasmonic microstrip graphene patch antenna supporting dual- and tri-band resonance in the low THz frequency ranging from 0.1 to 5 THz. The analysis procedure is performed by implementing CST with the use of different dielectric substrate materials of the same thickness. The simulation result displays that the quartz substrate material maintains a minimum S11 value of − 45.674 dB with a suitable VSWR of 1.010 at the frequency of 1.0 THz with the gain, bandwidth, and efficiency values of 3.150 dB, 310 GHz, and 92.65%, respectively. In addition, the computed results also reveal that the GaAs and SiO3N4 operate at dual-band frequency with a reliable gain and bandwidth values.

Moreover, the simulation outcome indicates that, as the GaAs substrate thickness increased beyond 6 µm, the proposed antenna operates with a tri-band operational frequency. However, a better value of gain of 2.510, 2.730, and 6.560 dB is attained for a 7-µm substrate thickness, corresponding to the frequencies of 0.766, 3.285, and 4.510 THz, respectively. On the other hand, this technique of using a graphene patch to develop milt-band resonance frequency can be regarded as an easy technique for modulation, low profiles, simple, and alternative to complexities compared to implementing conducting material slots, stacks, or extensions along the patch radiating borders techniques. Finally, the radiation performance of the proposed antenna seems to be better than most of the previously performed by other research workers, especially in terms of antenna size and bandwidth.