1 Introduction

The term "medical imaging" encompasses a wide range of techniques used to get visuals of the human body for the purposes of diagnosis, monitoring, and treatment. Several medical technologies provide unique insights about the health of a certain body part, the severity of an injury, or the efficacy of a therapy [1]. Many imaging techniques include X-ray radiography, X-ray CT, MRI, ultrasonography, elastography, optical imaging, radionuclide imaging (Scintigraphy, PET and SPECT, thermography, and terahertz imaging [2]. Terahertz medical imaging is found to be comparatively safer for the biological tissues as compared to other medical imaging techniques due to nonionizing radiations [3], The terahertz region (THz = 1012), as specified by the International Telecommunications Union (ITU), occupies the electromagnetic spectrum from 0.3 to 10 THz [4]. Since it lies in between the infrared and microwave regions, it exhibits characteristics of both. THz has shown to have a tremendous amount of potential in various domains such as high- speed communication [5], medical imaging, material determination [6] and sensing. THz radiation can permeate various materials because of the long wavelength of the THz photons, and it is especially sensitive to the vibration modes of water. It also has some drawbacks, like THz detectors have a low signal to noise ratio and a slow processing speed. The emitters only generate incoherent and dim THz radiation. THz sources require freezing temperatures and a low contrast between healthy and unhealthy tissues [2].

The patch antenna is a prominent form of antenna that has been explored for THz applications. Microstrip antennas have numerous advantages like its compact and light weight patches, high efficiency, operating at short wavelengths, reconfigurability, and dependability. Return loss (which depends on the matching of port and antenna), dielectric loss (depends on the type of material of the substrate used in the antenna) and conductor loss (depends on the type of material used for the conducting patch) are three main factors for designing the microstrip patch antenna [7]. Microstrip patch antennas have some limitations also such as narrow bandwidth, lower gain, low efficiency, back radiation etc. Antenna properties such as gain, bandwidth, and efficiency strongly depend on the material used in the patch, substrate and ground. Employing metamaterials significantly reduces antenna size while simultaneously enhancing bandwidth, gain, and multiband operating frequencies. The concept of a metamaterial was initially proposed by Veselago in 1968 [8]. Many researches have been conducted on the improvement of antenna performance with the introduction of metamaterials, and some encouraging results have been obtained [9]. THz region metamaterial-based antennas have the potential to be useful because of their great penetration with minimal attenuation, nonionizing nature, and remarkable resolution imaging potential [10]. All three antennas are suitable for usage in biomedical applications. Figure 1a illustrates the arrangement of antennas for detecting cancer tumor [11], whereas Fig. 1b demonstrates how an array of antennas may not only detect the tumor but also determine its precise location [12].

Fig. 1
figure 1

a antennas arrangement for breast tumor detection [11] b Antenna array arrangement around the breast [12]

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A novel DNA shaped fractal antenna with partial ground is designed and proposed for sub-terahertz and terahertz band applications [13]. A plant shaped wideband antenna with partial ground is presented for THz applications [14]. The design of a Vinayak slotted rectangular microstrip patch antenna that offers a quad band resonance with significant characteristics to serve applications including radio determination, satellite, mobile, and space research is proposed in [15]. The improvement in the performance of a novel microstrip patch antenna through added stages of a fractal geometry and a circular split ring resonator for multiband operation is presented in [16]. The design and a detailed discussion of the results of a novel multi band microstrip patch antenna intended to serve several applications is presented in [17]. A novel Vivaldi antenna for THz medical application in the range of 0.5–2 THz is suggested in [18].

In this paper microstrip patch antennas with three different materials (gold, silver and graphene) are analyzed and compared in the terahertz range. Antennas are designed for the medical imaging applications. In section 2, the design of the antenna has been presented this section is further subdivided into three sections (2.1) Structure and dimensions of the antenna, (2.2) Equivalent circuits and equations of microstrip patch antenna and SRR unit cell. In Sect. 3, Material properties of gold, silver and graphene microstrip antenna, their advantages and limitations of antennas with different materials are discussed. This section is sub divided into three sections, i.e., (3.1) gold microstrip patch antenna (3.2) silver microstrip patch antenna (3.3) graphene microstrip patch antenna. Advantages and limitations of all the three antennas has also been discussed in this section. In Sect. 4, Previous other models are compared with the proposed work. In Sect. 5, Comparison of characteristics of all the three antennas have been presented. Section 6, concludes the paper.

2 Design methodology of the proposed antenna

2.1 Structure and dimensions of the antenna

The proposed structure of antenna has been designed and simulated in CST microwave studio 2019. In the antenna structure, silicon dioxide substrate with the dielectric value of 3.9 and thickness ts, length Ls and width Ws, is sandwiched between the metal radiating patch of thickness tp, length Lp and width Wp and an array of 3 × 3 SRR with ground of thickness tg. To reduce the back radiation and increase the efficiency, an array of SRR is used. Figure 2 depicts the structure of the proposed antenna.

Fig. 2
figure 2

Design of the antenna a patch antenna b side view of the antenna c enlarged view of the backside

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The distance between each SRR in the array is 70 μm. The antenna structure is designed for the medical imaging range 0.1 THz to 5 THz. The dimensions of the proposed antenna are tabulated in the Table 1 given below.

Table 1 Dimensions of the proposed antenna
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Resonant frequency can be calculated by Eq. (1) [19]:

$${f}_{r}=\frac{{v}_{0}}{\sqrt{2 \times {\varepsilon }_{eff}}}\frac{4.6\times {10}^{-14}}{g} +\frac{f}{1.01}$$
(1)

fr is resonant frequency, εeff is effective dielectric constant, v0 is the electromagnetic wave velocity i.e., 3 × 1011 mm/s, g is the width of the gap or notch, f is the frequency of operation.

$${\text{ts}}\ge 0.06 \frac{{\lambda }_{air}}{\sqrt{{\varepsilon }_{r}}}$$

ts is the thickness of the substrate, εr is dielectric constant of the substrate.

$${W}_{p}=\frac{{v}_{0}}{2{f}_{r}}\sqrt{\frac{2}{{\varepsilon }_{r}+1}}$$
(2)

where, Wp is width of the patch,

$${\varepsilon }_{reff}=\frac{{\varepsilon }_{r}+1}{2}+\frac{{\varepsilon }_{r}-1}{2}\left[1+12 \frac{{t}_{s}}{{W}_{p}}\right] (\mathrm{where }\frac{{W}_{p}}{{t}_{s}}>1)$$
(3)
$$\frac{\Delta L}{{t}_{s}}=0.412\frac{\left({\varepsilon }_{reff}+0.3\right)\left(\frac{{W}_{p}}{{t}_{s}}+0.264\right)}{\left({\varepsilon }_{reff}-0.258\right)\left(\frac{{W}_{p}}{{t}_{s}}+0.8\right)}$$
(4)

where, ΔL is the normalized extension of length,

$${L}_{p}=\frac{{v}_{0}}{2{f}_{r}\sqrt{{\varepsilon }_{reff}}}-2\Delta L$$
(5)

where Lp is the length of the patch, Notch width or width of the gap can be obtained from the following equation,

$${f}_{r}=\frac{{v}_{0}}{\sqrt{2\times {\varepsilon }_{eff}}}\frac{4.6\times {10}^{-14}}{g}+\frac{f}{1.01}$$

For obtaining the preferred resonance at the operating frequency (\({f}_{r}=f\)),

$$f=\frac{{v}_{0}}{\sqrt{2\times {\varepsilon }_{eff}}}\frac{4.6\times {10}^{-14}}{g}+\frac{f}{1.01}$$
$$f-\frac{f}{1.01}=\frac{{v}_{0}}{\sqrt{2\times {\varepsilon }_{eff}}}\frac{4.6\times {10}^{-14}}{g}$$

Or, \(f\left(1-\frac{1}{1.01}\right)=\frac{{v}_{o}}{\sqrt{2\times {\varepsilon }_{eff}}}\)

$$\frac{0.1f}{1.01}=\frac{{v}_{0}}{\sqrt{2\times {\varepsilon }_{eff}}}\frac{4.6\times {10}^{-14}}{g}$$
$$g=\frac{{v}_{0}}{\sqrt{2\times {\varepsilon }_{eff}}}\frac{4.6\times {10}^{-12}}{f}$$
(6)

2.2 Equivalent circuits and design equations of microstrip patch antenna and SRR unit cell

Equivalent circuits of microstrip patch antenna with inset feed and SRR unit cell are discussed below.

2.2.1 Equivalent circuit and equations of microstrip patch antenna

Figure 3 given below depicts the microstrip patch antenna and its equivalent circuit.

Fig. 3
figure 3

Patch antenna and its equivalent circuit [19]

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Equivalent of the feed line impedance Z0 can be calculated by the following Eq. (7):

$${Z}_{0}={R}_{in}{cos}^{2}\left(\frac{\pi }{{L}_{p}}{L}_{ps}\right)$$
(7)
$${G}_{1}=\frac{1}{120{\pi }^{2}} {\int }_{0}^{\pi }{\left[\frac{sin\left(\frac{{k}_{0} {W}_{p}}{2} cos\theta \right)}{cos\theta }\right]}^{2} {sin}^{3}\theta d\theta$$
(8)

Mutual conductance can be calculated by the following Eq. (9):

$${G}_{12}=\frac{1}{120{\pi }^{2}} {\int }_{0}^{\pi }{\left[\frac{sin\left(\frac{{k}_{0} {W}_{p}}{2} cos\theta \right)}{cos\theta }\right]}^{2} \times {J}_{0}\left({k}_{0}{L}_{p}sin\theta \right){sin}^{3}\theta d\theta$$
(9)

Here, J0 is the Bessel function of the first kind of order zero. Resonant input impedance can be obtained by the following equation:

$$R_{in} = \frac{1}{2(G1 + G12)}$$

The inset feed causes the formation of a gap or notch, which in turn results in the formation of a junction capacitance. The resonance frequency is affected by this gap or notch and its concomitant junction capacitance.

Here Y is the admittance, G is the conductance and B is the susceptance.

2.2.2 Equivalent circuit and design equations of SRR unit cell

Equivalent circuit of SRR unit cell is shown in the Fig. 4 and design equations for SRR unit cell are discussed below [20].

Fig. 4
figure 4

SRR unit cell and its Equivalent circuit

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$$\rho =\frac{(N-1)(W+S)}{1-(N-1)(W+S)}$$
(10)
$$k=\frac{s/2}{w+s/2}$$
(11)
$${C}_{0}={\varepsilon }_{0}\frac{k(\sqrt{1-{k}^{2}})}{k(k)}$$
(12)
$${L}_{SRR}=4{\mu }_{0}\left[L-\left(N-1\right)\left(S=W\right)\right]\left[ln\left(\frac{0.98}{\rho }\right)+1.84\rho \right]$$
(13)
$${C}_{SRR}=\frac{N-1}{2} [2L-\left(2N-1\right)\left(W+S\right)]{C}_{0}$$
(14)
$${f}_{SRR}=\frac{1}{2\pi \sqrt{{L}_{SRR}{C}_{SRR}}}$$
(15)

There are two SRR rings, L1 and L2 measuring 190 μm and 110 μm, respectively. The width of each ring is 5 μm. The gap between the slots was 70 μm, and the formulae were used to obtain the capacitance and inductance values for the CSRR and LSRR. The fSRR can determined, for N = 2. A 50-ohm impedance microstrip line inset feed is used to excite the antenna because it offers better impedance matching.

3 Microstrip patch antennas with different materials

Dimensions of all the three antennas are same. Silicon dioxide is used as the substrate in all the antennas. Material properties of gold, silver and graphene microstrip antenna, their advantages and limitations of antennas with different materials are discussed in this section.

3.1 Microstrip patch antenna with gold

In this antenna gold has been used as metal patch at the front side as well as in the array of 3 × 3 SRR and ground. Substrate is of silicon dioxide which has been sandwiched between both of them.

Gold used in microwave devices due to its high electrical conductivity and simple processing; both of the reasons are facilitated by the fact that it is chemically inert in ambient environments. The amount of current needed to charge a circuit with a constant capacitance value increases as the operating frequency increases [21]. Gold is preferred in terahertz antenna as it does not change its properties in higher terahertz range also. Gold is opted as the radiating material for the antenna in order to make it resistant to corrosion and chemically stable. Gold possesses a significant electrical conductivity at THz frequencies despite having a lesser skin depth (~ 75 nm at 1 THz). Conventional methods of deposition, including as sputtering, evaporation, and electroplating with a high melting point, can be employed without much complication to deposit it on a surface [22]. Using Electron beam lithography THz antenna can be fabricated. After the sanitizing the sample, the photoresist is spun onto the wafer as part of the fourth phase of the manufacturing process. The design is then imported employing the EBL then the last phase is the metal rollout [23]. Properties of gold is depicted in Table 2 given below.

Table 2 Material properties of gold
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3.1.1 Advantages and limitations of gold

Advantages of Gold:

  • Good conductivity: Gold is highly conductive, allowing for efficient signal propagation and enhancing overall antenna performance.

  • Thermal stability: Gold exhibits excellent thermal stability, making it suitable for terahertz applications where temperature variations can occur.

  • Low Ohmic Losses: Gold exhibits relatively low ohmic losses in the terahertz frequency range. This characteristic minimizes the absorption and dissipation of the electromagnetic energy, leading to higher radiation efficiency and reduced signal attenuation.

  • Compatibility with Terahertz Frequencies: Gold's material properties make it well-suited for operation in the terahertz regime, where it offers good impedance matching and resonance characteristics. It can facilitate the design and optimization of terahertz microstrip patch antennas.

Limitations of gold:

  • Cost: Gold is an expensive material compared to other metals, potentially increasing the overall manufacturing cost.

  • Increased Surface Roughness Effects: In the terahertz regime, surface roughness becomes more critical as the wavelength decreases. Gold, being a relatively soft material, can have surface roughness effects that impact the antenna's performance.

  • Fabrication Challenges: Fabricating microstrip patch antennas with high precision in the terahertz regime can be challenging. The small dimensions and intricate structures required for terahertz operation pose difficulties in accurately depositing and patterning gold on the substrate, potentially affecting the antenna's performance.

3.2 Microstrip patch antenna with silver

This antenna is made up of silver metal patch and silver 3 × 3 SRR array and a ground. Substrate is of silicon dioxide which is sandwiched between both of them.

Silver is widely used THz antennas because of its high conductivity and highly conductive materials ensures the enhancement of gain, bandwidth, efficiency etc. [24]. Use of silver in metamaterials at the ground reduces the back radiation hence improving the efficiency of the antenna [25]. Properties of silver is depicted in Table 3 given below.

Table 3 Material properties of silver
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3.2.1 Advantages and limitations of silver

Advantages of silver:

  • Excellent conductivity: Silver is highly conductive, even at terahertz frequencies. Its high conductivity allows for efficient signal propagation, minimizing losses and enhancing the overall antenna performance.

  • Low ohmic losses: Silver exhibits low ohmic losses in the terahertz frequency range. This characteristic helps to reduce absorption and dissipation of the electromagnetic energy, resulting in higher radiation efficiency and lower signal attenuation.

  • Wide bandwidth: The use of silver in the microstrip patch antenna with SRR array can contribute to wider operating bandwidth. Silver's conductivity and surface properties enable improved impedance matching and resonance characteristics, allowing for broader frequency coverage.

  • Compatibility with Terahertz Frequencies: Silver is well-suited for terahertz operation due to its material properties. It offers good impedance matching and resonance characteristics, facilitating the design and optimization of terahertz microstrip patch antennas.

  • Fabrication Flexibility: Silver is a relatively robust and durable material, making it easier to work with during the fabrication process. It can withstand higher temperatures and mechanical stresses, simplifying manufacturing steps such as soldering, bonding, or etching.

Limitations of silver:

  • Cost: While silver is generally less expensive than gold, it is still more costly than other commonly used metals like copper or aluminum. The higher cost of silver may impact the overall manufacturing expenses, particularly in large-scale production.

  • Surface roughness effects: In the terahertz regime, surface roughness can significantly affect antenna performance. Silver, being a relatively soft material, may have surface roughness effects that contribute to scattering losses and reduced radiation efficiency.

  • Environmental sensitivity: It is sensitive to environmental factors such as moisture or harsh conditions. Additional protective measures or coatings may be necessary to ensure long-term stability and reliability in challenging environments.

3.3 Graphene microstrip patch antenna

This antenna is made up of graphene patch and graphene 3 × 3 SRR array and a ground. Substrate is of silicon dioxide which is sandwiched between both of them.

The propagation of surface plasmon polariton (SPP) wave is graphene's most interesting new characteristic when measured at THz frequency [26]. Graphene is often characterized as an infinitely thin conductive sheet with a complicated surfaces conductivity for terahertz frequencies [27]. The surface conductivity of graphene may be altered by varying either the electrostatic bias or the chemical doping, which optimizes the graphene THz antennas characteristics [28]. Properties of the graphene are depicted in Table 4 given below.

Table 4 Material properties of graphene [29]
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3.3.1 Advantages and limitations of graphene

Advantages of graphene:

  • High carrier mobility: Graphene's exceptional electron mobility allows for fast and efficient electron transport, improving signal response and reducing losses.

  • Broadband operation: Graphene's electrical properties enable microstrip patch antennas with wide operating bandwidths, offering greater frequency coverage.

  • Tunability: The conductivity of graphene can be adjusted, allowing dynamic control of the antenna's performance, such as changing resonant frequency or adjusting impedance matching.

  • Low weight and flexibility: Graphene's ultrathin and lightweight nature make it suitable for weight- conscious and flexible antenna designs.

  • Compatibility with CMOS technology: Graphene can be integrated with CMOS technology, enabling the development of integrated antenna systems on a single chip.

Limitations of graphene:

  • Limited conductivity: Graphene's intrinsic conductivity is lower than traditional metals, potentially resulting in higher resistive losses and reduced radiation efficiency.

  • Fabrication challenges: Fabricating high-quality graphene films and transferring them onto substrates with precise control can be complex and challenging.

  • Environmental sensitivity: Graphene's properties can be influenced by factors like moisture, temperature, and contaminants, requiring proper encapsulation or protective coatings.

  • Cost: Graphene production and processing can be expensive, potentially limiting its practicality for some applications or industries.

4 Comparison the proposed antenna with previous models

The comparison between the operating frequency, material used, gain, bandwidth, and type of the antenna with previous designed antenna is the THz spectrums are presented in the Table 5 given below. As it can be observed from the table given below that max. gain and bandwidth is obtained in the current wok.

Table 5 Comparison table
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5 Comparative analysis of the characteristics of the three antennas

Visual and tabulated comparative analysis of the characteristics like return loss, gain, radiation efficiency, VSWR, 2D and 3D radiation pattern of all the three antennas (gold, silver and graphene) are given below.

Above Fig. 5 depicts the return loss (S11) for all the three materials i.e., gold, silver and graphene. It can be observed that all the three antennas are ultra-wideband band antennas, so the range of operation is very large. Gold microstrip patch antenna has a bandwidth of 181.97% and minimum return loss is obtained at − 37.27 dB at 1.72 THz. Silver microstrip patch antenna has a bandwidth of 182.02% and minimum return loss is obtained at − 49.43 dB at 4 THz. Whereas graphene has a bandwidth of 180.72% and minimum return loss is obtained at − 60.5 dB at 1.08 THz.

Fig. 5
figure 5

Return loss of gold, silver and graphene microstrip patch antenna

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Above Fig. 6 depicts the gain for all the three materials i.e., gold, silver and graphene. The gain of the gold microstrip patch antenna obtained is 23.16 dBi. The gain of the silver microstrip patch antenna obtained is 22.42 dBi. Whereas the gain of the graphene antenna obtained is 21.79 dBi.

Fig. 6
figure 6

Gain of gold, silver and graphene microstrip patch antenna

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Above Fig. 7 depicts the radiation efficiency for all the three materials i.e., gold, silver and graphene. It can be observed that the radiation efficiency of the gold microstrip patch antenna is 85%. The radiation efficiency of the silver microstrip patch antenna is 78%. Whereas the radiation efficiency of the graphene microstrip patch antenna is 78.1%.

Fig. 7
figure 7

Radiation efficiency of gold, silver and graphene microstrip patch antenna

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Above Fig. 8 depicts the VSWR for all the three materials i.e., gold, silver and graphene. It can be observed that VSWR of all the three microstrip patch antenna is below 2.

Fig. 8
figure 8

VSWR of gold, silver and graphene microstrip patch antenna

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Above Fig. 9a shows the 3D radiation pattern of the gold microstrip patch antenna at 4.5 THz. Whereas 2D radiation of the microstrip patch antenna at 4.5 THz (constant phi) is depicted in Fig. 9b. From the above fig it can be depicted that the side lobe level is at − 14.3 dB and the half power beam width is 17.5 degree (3 dB).

Fig. 9
figure 9

a 3D radiation pattern of gold patch antenna, b 2D radiation pattern of gold microstrip patch antenna

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Figure 10a shows the 3D radiation pattern of the silver microstrip patch antenna at 4.5 THz. Whereas 2D radiation of the microstrip patch antenna at 4.5 THz (constant phi) is depicted in Fig. 10b. From the above fig it can be depicted that the side lobe level is at − 13.9 dB and the half power beam width is 17.5 degree (3 dB).

Fig. 10
figure 10

a 3D radiation pattern of silver patch antenna, b 2D radiation pattern of silver microstrip patch antenna

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Figure 11a shows the 3D radiation pattern of the graphene microstrip patch antenna at 4.5 THz. Whereas 2D radiation of the microstrip patch antenna at 4.5 THz (constant phi) is depicted in Fig. 11b. From the above fig it can be depicted that the side lobe level is at − 10.4 dB and the half power beam width is 20.7 degree (3 dB).

Fig. 11
figure 11

a 3D radiation pattern of graphene patch antenna and b 2D radiation pattern of graphene microstrip patch antenna

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6 Conclusion

The designs and analysis of all three antennas have been done, and a comparison of their various characteristics can be observed in Table 6 given above. As it can be observed from the aforementioned table, graphene has the lowest return loss in comparison to gold and silver; the bandwidth of silver is larger in comparison to gold and graphene; gold has the maximum gain and efficiency of 23.16 dBi and 85% respectively; VSWR is below 2 in all three cases; the half-power beam width of gold and silver is the same; and graphene has the minimum side lobe level, which is − 14.3. Considering the above-discussed advantages, limitations and characteristics obtained after simulation, the selection of gold, silver, or graphene for a terahertz microstrip patch antenna with SRR arrays should be based on specific application requirements, cost considerations, and the desired trade-offs between performance and fabrication complexity. Since there is a trade-off between the characteristics of the three antennas, any antenna can be utilized as long as it meets the requirements and is appropriate for the medical imaging application.

Table 6 Comparison table
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