1 Introduction

Terahertz (THz) frequency spectrum is being investigated for the implementations of future wireless systems due to its feature that it has the capability of providing wide bandwidth (Akyildiz et al. 2014). The wide bandwidth offered by THz spectrum can provide the higher data transfer rate which is the main requirement of future wireless technology (He et al. 2020; Burford and El-Shenawee 2017). It can offer the properties of radiation like microwave and infrared frequency spectrum (Varshney and Giri 2021; Khan et al. 2021). The application sectors of THz spectrum are being expected as medical, defense and communication in imaging and sensing (Mumtaz et al. 2017; Tekbıyık et al. 2019; Son et al. 2019; Forsythe et al. 1991; Roggo et al. 2005; Zhang et al. 2020). Also, THz spectrum can offer its significant usability in food technology for the detection of viruses and toxicity (Afsah-Hejri et al. 2019). The advancements in wireless systems require antennas with reconfigurability in radiation pattern and frequency response (Varshney 2020a; Varshney et al. 2019a). A recent article had briefed about the latest developments in THz antennas that these can be implemented with the usage of metal, dielectric and graphene material-based radiators (Varshney 2020b). The usage of dielectric radiator-based antennas are efficient but their operation is restricted due to they offer large height (Gupta et al. 2021; Varshney and Sahana 2021; Sahana and Varshney, 2022; Gotra et al. 2020). They may not be compatible with small-scale systems and they do not offer the inherent tunability. Another category of THz antennas is based on the graphene material which can provide the tunable antenna response (Varshney 2020a; Farman et al. 2021; Varshney et al. 2020). The ability of graphene material in offering the tunable electronic properties can provide the tunable antenna response (Cao et al. 2016; Hanson 2008a; Chen et al. 2013; Wang et al. 2015; Correas-Serrano et al. 2015; Naghdehforushha and Moradi 2017). The limitation of antennas with graphene-based resonating unit is that they are a poor radiator (Hosseininejad et al. 2018; Abadal et al. 2013, 2019; Kiani et al. 2020; Naghdehforushha and Moradi 2019). Third category is about the utilization of metal-based radiators in THz antennas (Naik et al. 2021; Murali et al. 2021; Singhal 2019a; Keshwala et al. 2020). The microstrip technology has been serving the wireless technology around for last more than four decades specially at microwave spectrum (Losada et al. 1999; Richards et al. 1981; Lee and Tong 2012). The microstrip-based antennas can offer efficient radiation performance along with the small size which can overwhelm the future THz technology as well (Lee and Tong 2012; Michalski and Zheng 1992; Sharma 2020; Das and Varshney 2022).

Furthermore, the focus of researchers in current time is to implement the THz antenna with ultra-wideband (UWB) response (Keshwala et al. 2021; Varshney 2020c; Sharma et al. 2020, 2022; Singhal 2021a, 2021b). Here, the term UWB is being referred for defining the feature of any antenna providing the bandwidth more than few giga hertz (GHz). The usage of UWB systems in communication technology can allow the long-distance transmission with short duration pulses. This feature of UWB systems can be suitable in radar systems. The recent developments in THz radar systems can seek the advanced antennas with UWB response (Forsythe et al. 1991). THz UWB antennas can have advanced features if they are able to offer the inbuilt filtering capability (Srivastava et al. 2021). The inbuilt filtering characteristics in antenna response can prevent the usage of external filters (Srivastava et al. 2021). There are a number of techniques available in microwave antennas which suggest the technique of generation of tunable stop band in antenna response like usage of switches, diodes and relays (Srivastava et al. 2021). The small dimensions of THz antenna do not allow to use these switching devices in the circuit. The recent development in THz UWB antennas shows that graphene strips can provide the band notch characteristics in UWB response (Sharma et al. 2020). The alteration in electronic properties of graphene material can offer the tunability in achieved band notch over frequency. However, this is still a challenging task.

Based on the above discussions, current research issue can be summarized as; implementing the THz antenna with tunable filtering response which has been followed here in this article and a simple solution is reported. A graphene disc is placed beneath the substrate in opposite to the radiating patch which confines the localized surface plasmons and thus anti-resonance is created in the specific frequency range for achieving the filtering characteristics. The alteration in electrical properties of graphene material can provide the tunability in the created notched frequency band. The proposed research work reports a simplest technique for obtaining the filtering characteristics in UWB response of THz antenna. The simple antenna geometry can allow it to be used in the implementation of antenna arrays with UWB response and engraved filtering characteristics. Also, this geometry can allow the implementation of multiport antennas with UWB response along with the filtering characteristics.

2 Antenna design and evolution

The final antenna structure is shown in Fig. 1. The antenna structure contains the simple metal-based radiator of diameter \(d\) connected to a microstrip feedline of width \({w}_{f}\) at one side of the substrate of height \({h}_{s}=1.6 \mu m\) and half ground plane structure at its another side. The substrate of polyimide with the relative permittivity \({\epsilon }_{s}=3.5\) having dimensions \({l}_{s}\times {b}_{s}\) is used for implementing the antenna structure. Fabrication of antenna can be done with the substrate having metal coating at its both sides which can be grown using sputtering technique. The metallic coating can be patterned to form the shape of radiator and ground plane using electronic beam lithography (Suñé 2008). The antenna contains the ground plane of size \({l}_{g}\times {w}_{g}\) which covers the half-size of the substrate. The structure of this antenna is shown in Fig. 2a and mentioned by the name as antenna-1 and it provides the UWB response as plotted in Fig. 2b. The dimensions of this antenna have been selected using the traditional approach used for designing the microstrip antennas (James and Hall 1990). This antennas structure is then modified with the engravement of graphene disc of outer and inner radius as \({r}_{o}\) and \({r}_{i}\), respectively beneath to the substrate in opposite to the circular metallic radiator. This antenna structure is mentioned by antenna-2 with its top and bottom view in Fig. 2a. The application of graphene disc with chemical potential \({\mu }_{c}=0 eV\), relaxation time \(\tau =1 ps\) at temperature \(T=300 \mathrm{K}\) provides the antenna response as similar as antenna-1. Antenna starts providing the band notch characteristics with the application of graphene with \({\mu }_{c}=0.8 eV\). The antenna structure is implemented using CST microwave studio. The dimensions of antenna are mentioned in Table 1. Figure 2c shows the impedance plot of antenna-2 with \({\mu }_{c}\) as \(0\) and \(0.8 \mathrm{eV}\). The impedance plot shows the generation of multiple resonances in the antenna structure for providing the UWB response. Also, the mode pattern is drastically disturbed in the region of frequency where band notch is achieved. It can be seen that antenna with \({\mu }_{c}=0 eV\) operates with three resonances \({m}_{1}\), \({m}_{2}\) and \({m}_{3}\). For \({\mu }_{c}=0.8 eV\), two more resonances are also generated \({m}_{{g}_{1}}\) and \({m}_{{g}_{2}}\) at the center frequency and merged with the resonance of circular patch. Varying the chemical potential of graphene can tune the resistivity and hence the impedance matching at the generated surface plasmon resonance due to the addition of the graphene ring. Thus, the impedance matching at the frequency of the generated surface plasmon resonance can be tuned to generate the band notch. A discussion about the surface conductivity and its electrical properties is reported in the next section of this manuscript. The performance of antenna-1 and 2 is reported in Table 2. The antenna operation is verified with the electrical equivalent circuit model shown in Fig. 3. The electrical circuit model is prepared with five parallel RLC circuits for representing it with \({\mu }_{c}=0.8 \mathrm{eV}\). The resistance of the two tank circuits corresponding to \({{m}_{g}}_{1}\) and \({m}_{{g}_{2}}\) is represented by the variable resistance due to the fact that surface conductivity and hence the resistivity of graphene can be set using an external electrostatic voltage. Thus, the impedance matching of these two central tank circuits can be set accordingly and hence the antenna operation without and with the band notch can be verified. All the circuit parameters have been calculated using circuit theory approach as already reported in the case of a graphene antenna and mentioned in Table 3 (Varshney 2020a).

Fig. 1
figure 1

Top (left) and bottom (right) view of antenna structure

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Fig. 2
figure 2

a Antenna evolution containing the structure of antenna-1 and 2, their b reflection coefficient and c impedance plot

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Table 1 The dimensions of antenna structure \((\mathrm{all dimensions in \mu m}\))
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Table 2 The performance of antenna-1 and 2
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Fig. 3
figure 3

a Equivalent electrical circuit model and its S11 parameter response with \({\mu }_{c}=\) b \(0\) and c \(0.8 \mathrm{eV}\)

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Table 3 The circuit parameters of equivalent circuit model
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Figure 4 shows the effect of varying the physical parameter of antenna, \({r}_{o}\) and \({r}_{i}\). The best values of these parameters by maintaining the appropriate impedance matching in the passband and with the highest value of reflection coefficient is 16 and 8 \(\mathrm{\mu m}\), respectively. The upper passband can be contracted to the small impedance bandwidth for lower values of \({r}_{i}\). In fact, there are certain values of \({r}_{o}\) with which antenna does not provide the filtering action. Figure 5 shows the antenna response with variable radius of the radiating patch and width of the feedline. The radius of radiating patch can be set to provide the desired bandwidth of the created notched band. Also, the impedance matching is only affected by the width of the feedline, as expected.

Fig. 4
figure 4

S-parameter response with variable a \({r}_{o}\) b \({r}_{i}\) with \({\mu }_{c}=0.8 \mathrm{eV}\)

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Fig. 5
figure 5

S-parameter response with variable a \(d/2\) and b \({w}_{f}\)

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3 Tunability in notch band

The alteration of Fermi energy using the applied electrostatic voltage on it can provide the tunability in the antenna response (Gale et al. 2012; Taghioskoui 2009; Warner et al. 2013). The surface conductivity of graphene can be represented in two parts; intraband and interband (Hanson 2008b). The intraband part of the surface conductivity is greatly affected in the lower THz frequency ranges with insignificant alteration in its interband part. The surface conductivity of graphene can be represented using the Drude’s model and Kubo’s formalism. The dependency of intraband surface conductivity of graphene on \({\mu }_{c}\) and applied electrostatic voltage is given in Eq. (1) and (2), (Hanson 2008b; Wang et al. 2019; Varshney et al. 2018a, 2019b).

$${\sigma }_{intra}\left(\omega ,{\mu }_{c},\Gamma ,T\right)=-j\frac{{e}^{2}{K}_{B}T}{\pi {\hslash }^{2}\left(\omega -j2\Gamma \right)} \left(\frac{{\mu }_{c}}{{K}_{B}T}+2ln\left({e}^{-\frac{{\mu }_{c}}{{K}_{B}T}}+1\right)\right)$$
(1)
$${V}_{g}=\frac{e{\mu }_{c}^{2}{h}_{s}}{\pi {\hslash }^{2}{v}_{f}^{2}{\epsilon }_{o}{\epsilon }_{r}}$$
(2)

Here, the terms\(e\),\(T\),\({K}_{B}\),\({\mu }_{c}\),\(\Gamma\),\({v}_{f}\),\({\epsilon }_{o}\), \({\epsilon }_{r}\) respectively, stand for the electron's charge of electron, temperature,the Boltzmann constant, the chemical potential of graphene, scattering rate, the reduced Plank's constant, the Fermi velocity of the charge in the graphene layer, the free space permittivity, and the relative permittivity of the spacer between the graphene sheet To adjust the electrical properties of graphene, a DC voltage called \({V}_{g}\) is provided to the graphene loop which is inserted to back side of substrate. The response of the proposed antenna with the variation in chemical potential of graphene is reported in Fig. 6. The S11 parameter response shows that the created band notch in the antenna response can be tuned over the frequency by keeping the lower 10 dB cut-off points approximately fixed. Thus, the proposed antenna can provide the response with the tunable band notch characteristics.

Fig. 6
figure 6

a and b S-parameter response with variable \({\mu }_{c}\)

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The operation of creation of the stop band can be analyzed using the electric field distribution on the antenna structure as illustrated in Fig. 7. The magnitude of the electric field is drawn at the frequency of passband and stopband without and with the graphene applied in the antenna structure. The difference in the electric field distribution is clear specifically at the frequency of the band notch. It can be seen that there is no field confinement at the bottom of the substrate at frequency 3.14 THz which is the band notch frequency. The application of graphene disc can provide the heavy confinement of electric field on it which results in mitigating the radiating resonant modes at this frequency. This may be due to the fact that the generated surface plasmon resonance can be in opposite phase to the resonant modes on the antenna radiator at this frequency which leads to provide the filtering action. The combined effect of graphene and metal radiator can be understood from the impedance plot which shows the large imaginary part of the reactive impedance at the frequency of filtered band. This confirms that the resonance of adverse phase has been generated in the filtered frequency band due to the placement of graphene in antenna.

Fig. 7
figure 7

Electric field distribution on antenna a 1 (first row) b 2 at \({\mu }_{c}=0.8 \mathrm{eV}\) (second row)

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The far-field performance of antenna is studied by drawing the 3D gain pattern as illustrated in Fig. 8. The gain pattern has been drawn in the case of antenna without and with graphene. The antenna offers the radiation pattern like a monopole antenna with the high value of gain in the passband. Also, antenna provides inferior radiation behavior at band notch frequency confirming the sharp filtering response is being obtained from the antenna. Moreover, the plot of gain and radiation efficiency is drawn in Fig. 9. The comparison of gain plot of antenna-1 and 2 (with different values of \({\mu }_{c}\)) is reported in Fig. 9a. This clearly represents that antenna-2 with \({\mu }_{c}=0.8 \mathrm{eV}\) follows the pattern of gain as antenna-1 in the passband but its gain is drastically reduced in the filtered bands, as expected. The sharp roll-off rate of decay of gain in the stopband makes the proposed technique proficient if THz antenna is required to be implemented with tunable filtering response. The antenna without graphene provides the radiation efficiency around more than 90% in the passband and similar is maintained in the case of when graphene disc is applied with \({\mu }_{c}=0 \mathrm{eV}.\) Setting the value of \({\mu }_{c}\) as \(0.8 \mathrm{eV}\) provides the band notch operation and hence the low value of radiation efficiency is obtained in the frequency region of the created band notch. Also, the application of graphene reduces radiation efficiency of antenna to level of 80% in the case the graphene disc is applied with \({\mu }_{c}=0.8 \mathrm{eV}\). The reduction in the radiation efficiency is due to the absorbing nature of the graphene material.

Fig. 8
figure 8

3D gain pattern of antenna a 1 b 2 at 2.02 (left), 3.45 (middle) and 5 THz (right) with \({\mu }_{c}=0.8 \mathrm{eV}\)

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Fig. 9
figure 9

a Gain and b radiation efficiency of all the antennas

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A comparison of the proposed antenna with others available THz UWB antennas is reported in Table 4. This shows that the proposed antenna can provide a way of implementing the THz UWB antenna with the tunable filtering response. Most of other antennas are not providing the filtering response (Poorgholam-Khanjari et al. 2020; Varshney et al. 2018b; Varshney 2020d). In fact, the antenna which is providing the tunable response is not efficient (Varshney et al. 2018b). The antenna which is providing the tunable filtering response is also less efficient (Sharma et al. 2020). Thus, one can conclude the proposed antenna as simple and suitable for THz communication where tunable filtering response is required.

Table 4 Comparison with other UWB antennas
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4 Conclusion

A THz antenna with metallic radiator has been designed to provide the monopole like radiation characteristics and UWB response. A graphene disc has been applied beneath the substrate of antenna opposite to the metal radiator. The confinement of electric field in the area covered by the graphene disc has been varied using the chemical potential of graphene. This leads to generate the surface plasmons which suppressed the resonating modes of antenna at certain frequencies for specific value of chemical potential of graphene. Thus, band notch characteristics in UWB response has been obtained. The tunability in the created band notch has been obtained with the variation in the chemical potential of graphene. The antenna can be utilized in THz communication systems which require to guard the specific frequency ranges by preventing the external filters.