A New Compact Split Ring Resonator Based Double Inverse Epsilon Shaped Metamaterial for Triple Band Satellite and Radar Communication

Abstract

This study presents a double-inverse-epsilon-shaped, triple-band epsilon-negative (ENG) metamaterial with two split ring resonators (SRRs). The proposed unit cell comprises a single slit two SRRs with two inverse-epsilon-shaped metal bits. Rogers RT6002, of dimension 10 × 10 × 1.524 mm³, is used as a substrate. An electromagnetic simulator CST microwave studio is used to investigate the effective medium parameters of the material. The proposed metamaterial shows three resonance peaks that are demarcated at the frequencies 2.38 GHz, 4.55 GHz and 9.42 GHz consecutively. The negative permittivity of the metamaterial is observed at the frequency ranges of 2.39–2.62 GHz, 4.55–4.80 GHz and 9.42–10.25 GHz. The goodness of the material was presented by the effective medium ratio (EMR) of the unit cell at 12.61. In addition, the simulated results are authenticated by using different electromagnetic simulators such as HFSS and ADS for the equivalent circuit model, which exhibits insignificant disparity. The anticipated scheme was finalised through some parametric analyses, together with configuration optimisation, different unit cell dimensions, several substrate materials, and altered electromagnetic (EM) field transmissions. The proposed triple band (S-, C- and X-bands) with negative permittivity (ε) metamaterial is practically used for numerous wireless uses, for instance, far distance radar communication, satellite communication bands and microwave communication.

1. Introduction

The materials that are found surrounding us from nature can attain positive permittivity (ε) and permeability (µ). Perversely, an artificial engineered structure that can achieve some exotic characteristics, which are not found in nature, is called a metamaterial (MM). When a metamaterial exhibits negative permittivity or negative permeability, then it is termed as a single-negative (SNG) metamaterial, and if attains both negatives, then it is named as a double-negative (DNG) metamaterial [1]. The characteristics of a metamaterial not only depend on its elements, but rather, it is quietly subjected to its configuration [2], i.e., dimension, pattern, etc. A theoretical metamaterial with negative permittivity (ε) and negative permeability (µ) called a double-negative (DNG) metamaterial or left-handed metamaterial (LHM) was introduced by Russian physicist Victor Veselago in 1968 [3]. Metamaterial researchers are fascinated by the metamaterials’ cloaking, absorbing, blocking or meandering for their exotic electromagnetic properties [4,5]. A metamaterial structure embossed metal element showed the effect of temperature with the thickness of the metal [6]. This metamaterial is used for sensitive microwave sensor. A Greek-key pattern metamaterial of dimension 10 × 10 mm² was fabricated using Rogers RT5880 that showed triple peaks of frequencies 2.4 GHz, 3.5 GHz and 4 GHz [7]. In ref. [8], Afsar et al. presented an epsilon-negative modified hexagonal-resonator-shaped metamaterial with EMR 11.53. Numerical analysis showed triple band resonance that covered the S-, X- and Ku-bands. In 2018, an experimental 3D metamaterial was demonstrated by Smith et al. [9] based on thin wire assemblies with an SSR that showed LHM characteristics with wide bandwidth. For the advancement of technology, SNG metamaterials and LHM have great contributions. Metamaterials with synthetic dielectric substrates started to be used after the Second World War for microwave applications.

In 2020, Dalgac et al. [10] designed a rectangular SSR-shaped metamaterial based on sensor structure to detect the influence of humidity on concrete materials in open space. Another study presented an S-shaped metamaterial of EMR 4.8 [11]. This L-band metamaterial was dedicated to the application of microwave sensors. A substrate with a dimension of 12.5 × 10 × 1.5 mm³ that was synthesised using a nickel-aluminate with a concentration of 42% aluminum [12] was designed for microwave application with the X- and Ku-bands. Gua et al. proposed a metamaterial with negative permittivity (ENG) to enhance the horizontal gain of patch antenna [13]. In 2016, Liu et al. [14] proposed a dual- band metamaterial (5 × 5 mm² in dimension) with a reformed circular electric resonator (RCER) with an EMR 5.45 covering frequency ranges from 9.70 GHz to 10.50 GHz and 15 GHz to 15.70 GHz. In another study, a three-layered wide metamaterial in the terahertz frequency was designed for heavy solar radiation absorption [15]. Metamaterials that reveal a vigorous localisation and boost of field may deliver novel tools to significantly enhance the sensitivity and tenacity of sensors. Abdolrazzaghi et al. designed an ultrasensitive microwave sensor to monitor the glucose in blood serum concentration [16]. Meanwhile, Kazemi et al. [17] recently introduced a reflective sensor that organises coupled split ring resonators as the front-end sensing element to be used in dielectric medium categorisation. It can used in dielectric medium categorisation. Meanwhile, a composite LR-handed based microfluidic sensor [18] exhibited resonance by surface capacitance and inductance.

On the other hand, an NRI metamaterial that was based on SRR with wire strips is a 2D array of repeated unit cells [19]. Moreover, Pendry et al. designed a non-natural magnetic metamaterial using different types of SRRs which were printed on the dielectric substrate [20]. An open-delta-shaped negative permittivity (ε-negative) MM based on a square ring resonator [21] indicated three resonance peaks at 4.32 GHz, 7.55 GHz and 9.76 GHz that covered the C- and X-bands. Meanwhile, in 2015, Liu et al. offered a tunable metamaterial comprising an SRR [22] used for sensing, filtering and cloaking. A triple-band metamaterial with a pie-shaped resonator centred with SSR (8 × 8 mm² in dimension) covered the S-, C- and X-bands [23]. In a recent study, a polarization-dependent, circular-shaped, triple-band metamaterial was designed using a Rogers RT6002 substrate base MM (8 × 8 mm² in dimension) resonated at 3.924 GHz, 7.254 GHz and 14.832 GHz [24]. To enhance the antenna gain for satellite communication, a Minkowski-fractal-shaped metamaterial was discussed in another study [25]. The triple-band metamaterial designed with two circular rings and one rectangular SRR exhibited a two-resonance frequency of 2.56 GHz and 5.6 GHz, which was used for Wi-MAX and WLAN networking [26]. Additionally, Reddy et al. [27] in 2020 proposed a penta band based on complementary OSRR, which combined five resonance peaks that were suitable for Wi-MAX, WLAN, Satellite band and X-band applications. Meanwhile, H. Sakli et al. [28] proposed a new two-element, ultra-wideband (UWB) MIMO antenna to yield the miniaturisation and performance using two antennas and ensure proper operation of the multiple-input–multiple-output system.

This study offered a compact and innovative metamaterial muster whose unit cell comprised two SRRs with double inverse-epsilon-formed metal strips. This design established three resonance frequencies covering the S-, C- and X-bands (2–4 GHz, 4–8 GHz and 8–12 GHz) in the microwave spectra, in addition to an indication of the epsilon-negative and negative refractive indices (n) at the same frequencies. Moreover, for the consistency of its performance, the numerical results were verified by using different validation processes. The results attained from the HFSS and from the equivalent circuits designed by ADS were used to compare with the CST simulated results. Different important parameters, including permittivity (ε), permeability (µ) and refractive index (n), along with S₁₁ and S₂₁, were analysed to characterise the metamaterial. To compare the performance, the EMR-based table was discussed in the results segment. The doubleinverse-epsilon-shaped SRR-based metamaterial designed in this study was very much compact because a << λ/4 [for 2.38 GHz λ/4 = 31.51 mm, whereas size a = 10 mm]. This design produces three resonance peaks at 2.38 GHz, 4.55 GHz and 9.42 GHz with −29.40 dB, −39.65 dB and −43.35 dB, respectively. The EMR indicated the goodness of the unit cell material at 12.61.

2. Schematic Description of Unit Cell and Simulation

The parametric description of the proposed unit cell demonstrated in Figure 1a is a new arrangement of two square ring resonators with double-epsilon-shaped metal strips. Figure 1b illustrates the perspective view of the unit cell while Figure 1c shows the simulation setup.

A square-shaped dielectric Rogers RT6002 material with a thickness (t) of 1.524 mm was used as substrate. The dimensions of the substrate were 10 × 10 mm² with a dielectric constant of 2.94 and a loss tangent of 0.0012. The dimensions of the outer and inner SRR were 4.6 × 4.6 mm² and 3.5 × 3.5 mm², respectively. Copper (annealed) of conductivity is 5.96 × 10⁷ Sm⁻¹ was utilised for all resonators of the top and bottom layers. Split gaps (G) of the each SRR was 0.20 mm, whereas the thickness of the copper strips were 0.035 mm. The split gap between the two epsilon-shaped resonators was also maintained at 0.20 mm. All metal strips were of same width (b) 0.50 mm except the epsilon-shaped bar in the centre of the unit cell. The outer radius (r₁₎ and the inner radius (r₂) of both the epsilon-shaped metals are 2.5 mm and 1.9 mm, respectively. The width (c) of the epsilon-shaped metal was 0.60 mm, whereas the length of each middle arm of the epsilon shape (e) was 1.50 mm with a thickness (d) of 0.50 mm.

Table 1. Parametric description of the unit cell.

Parameter	Dimension (mm)	Parameter	Dimension (mm)
a	10	G	0.20
L	10	r1	2.5
b	0.50	r2	1.9
c	0.60	H	4.6
d	0.50	h	3.5
e	1.50	t	1.524

summarises all the parametric magnitudes and the dimensions.

To achieve the expected results from the proposed unit cell an electromagnetic wave is incident to the Z-axis while perfect electric condition (PEC) and perfect magnetic condition (PEM) along the X-axis and Y-axis, consecutively.

Extraction Method of Effective Medium Parameters

CST microwave studio based on finite integration technique was used to differentiate the combined symmetrical erection and integration of arbitrary distribution of material and their physical characteristics. The frequency-domain solver with a tetrahedral mesh of CST was used to simulate the expected research.

As mentioned earlier, the PEC and PEM boundary conditions were applied along the X-axis and Y-axis, while the EM radiation was applied to the Z-axis to simulate the unit cell within the frequency range of 1 GHz to 12 GHz. Three vital material characteristics—permittivity (${\mathsf{\epsilon }}_{\mathrm{r}}$), permeability ${(\mathsf{\mu }}_{\mathrm{r}})$ and refractive index (n_r)—were derived through the Nicolson–Ross–Weir (NRW) technique [29] to realize the EM properties of the MMs. Popularly used MATLAB code is established in the context of Equations (1)–(5). After the execution, the attained results were verified with the CST results:

$$\mathrm{Permittivity}, {\mathsf{\epsilon }}_{\mathrm{r}}=\frac{\mathrm{c}}{\mathrm{j}\mathsf{\pi }\mathrm{fd}}.\frac{\left(1-{\mathrm{S}}_{21}\right)-{\mathrm{S}}_{11}}{(1+{\mathrm{S}}_{21})+{\mathrm{S}}_{11} }$$

(1)

$$\mathrm{Permeability}, { \mathsf{\mu }}_{\mathrm{r}}=\frac{\mathrm{c}}{\mathrm{j}\mathsf{\pi }\mathrm{fd}}.\frac{\left(1-{\mathrm{S}}_{21}\right)-{\mathrm{S}}_{11}}{\left(1+{\mathrm{S}}_{21}\right)-{\mathrm{S}}_{11} }$$

(2)

$$\mathrm{And} \mathrm{refractive} \mathrm{index}, {\mathrm{n}}_{\mathrm{r}=}{({\mathsf{\epsilon }}_{\mathrm{r}}{\mathsf{\mu }}_{\mathrm{r}})}^{1/2}$$

(3)

$$\mathrm{Or}, {\mathrm{n}}_{\mathrm{r}}=\frac{\mathrm{c}{\left[\left\{1-\left({\mathrm{S}}_{21}+{\mathrm{S}}_{11}\right)\right\}\left\{1-\left({\mathrm{S}}_{21}-{\mathrm{S}}_{11}\right)\right\}\right]}^{1/2}}{\mathrm{j}\mathsf{\pi }\mathrm{fd} {\left[\left\{1+\left({\mathrm{S}}_{21}+{\mathrm{S}}_{11}\right)\right\}\left\{1+\left({\mathrm{S}}_{21}-{\mathrm{S}}_{11}\right)\right\}\right]}^{1/2}}$$

(4)

$$\mathrm{Or}, { \mathrm{n}}_{\mathrm{r}}=\frac{\mathrm{c}{[{\left({\mathrm{S}}_{21}-1\right)}^2-{\mathrm{S}}_{11}{}^2]}^{1/2}}{\mathrm{j}\mathsf{\pi }\mathrm{fd}{[{\left({\mathrm{S}}_{21}+1\right)}^2-{\mathrm{S}}_{11}{}^2]}^{1/2}}$$

(5)

3. Parametric Studies

3.1. Design Procedure

To achieve the desired goal, the prime design was selected from the trial designs to yield optimal performance. An iterative method was applied to assess the response of the unit cell. The length, width and distance between the SRRs together with the sizes of the slits were changed on a trial-and-error basis. Figure 2 depicts some of the trial designs. Figure 2a contains two square rings with a uniform width of 0.50 mm. The dimension of the outer and inner square ring is 9.2 × 9.2 × 0.035 mm³. Following the simulation, 2 major response peaks at 5.92 GHz and 10.67 GHz were observed. Next, a split gap of 0.20 mm in each square ring was introduced into the design in Figure 2a to produce SRR. The design in Figure 2b yielded 3 resonance frequencies at 2.38 GHz, 4.72 GHz and 9.55 GHz for S₂₁. Figure 2c illustrates the introduction of two epsilon-shaped metal strips into design 1. The outer and inner radii of each epsilon were 2.5 mm and 1.9 mm, respectively, with a width of 0.60 mm. This altered design exhibited two resonances at 5.82 and 9.60 GHz. The placement of the two-epsilon shaped metals inside the second design yielded an excellence response satisfying our desired frequency band by producing three resonance peaks at 2.38 GHz, 4.55 GHz and 9.42 GHz with good bandwidth. Therefore, the proposed design in Figure 2d was selected as our final structure.

Table 2. Response of S₂₁ for various designs.

Arrangement	Resonance Frequency (GHz)	Types Structure	Resonance Peak (dB)	Covering Bands
Design-1	5.92, 10.67	Two square ring resonator	−48.79, −50.58	C-, X-
Design-2	2.38, 4.72, 9.55	Two split ring resonator	−31.02, −41.89, −45.98	S-, C-, X-
Design-3	5.82, 9.60	Two square ring resonator with two epsilon	−49.50, −44.57	C-, X-
Proposed design	2.38, 4.55, 9.42	Two SRR with two epsilon	−29.40, −39.65, −43.35	S-, C-,X-

summarises the numerical results of different steps of design optimisation. The proposed final structure exhibited three resonance frequencies with negative permittivity (ε) and negative index (n) simultaneously. The simulated results for the different designs are depicted in Figure 3.

3.2. Unit Cell Size Optimisation

Different sizes of unit cell were also investigated to select the best dimension. The unit cell of three different sizes (10 mm, 11 mm and 12 mm) with the same thickness (1.524 mm) as the substrate (Rogers RT6002) were designed by keeping other components unaltered. The numerical results are demonstrated in Figure 4. It is evident from Figure 4 that the sizes of 11 mm and 12 mm exhibited 3 resonances at nearly the same frequency with a lower bandwidth, which is quite low compared to the 10 mm unit cell. On the other hand, the 10 mm unit cell exhibited 3 major resonances at 2.38 GHz, 4.55 GHz and 9.42 GHz. Therefore, finally the 10 × 10 × 1.524 mm³ dimension was selected for the projected metamaterial unit cell.

3.3. Effect of Substrate Materials

An analysis is carried out to select the appropriate dielectric for the substrate of the metamaterial unit cell, which is shown in Figure 5. Two Rogers dielectrics, namely, RT 5880 and RT 6002, together with a flame-retardant dielectric FR4, were separately investigated to observe their responses. RT5880 and FR4 produced three resonance peaks with narrow bandwidths. Contrarily, Rogers RT6002 (dielectric constant 2.2 and loss tangent 0.0012) yielded tri-resonance peaks and adequate bandwidth covering the S-, C- and X-bands with higher EMR 12.61. Hence, the proposed unit cell was designed on Rogers RT6002 (lossy) substrate.

4. The Effect of Changing the Electromagnetic Field Propagation Direction

A regular technique was also employed to assess the effect of the changing transmission coefficient (S₂₁) for varying field propagations. The simulation setup for the changed electric and magnetic fields is depicted in the Figure 6. The electric field (E_y) was applied along the Y-axis while the magnetic field (H_x) was applied along the X-axis. Two resonances that were recorded around 6 and 10 GHz.

However, if the fields were interchanged with each other, i.e., the electric field (E_x) is applied towards the X-direction and the magnetic field (H_y) is applied towards the Y-direction, 3 major resonances would be observed at 2.38 GHz, 4.55 GHz and 9.42 GHz as depicted in Figure 7.

5. Electromagnetic Fields and Surface Current Analysis

Ampere’s law of electromagnetic induction predicted that moving the charged particle can generate a magnetic field. According to Faraday’s laws of induction, the electromagnetic interface turns it into an electric field. The EM fields produced by time-varying charged particles can be expressed using Maxwell’s curl equation [30]:

$$\overrightarrow{\nabla }\times \overrightarrow{\mathrm{H}}= \overrightarrow{\mathrm{J}}+\frac{\overrightarrow{\partial \mathrm{D}}}{\partial \mathrm{t}}$$

(6)

$$\overrightarrow{\nabla }\times \overrightarrow{\mathrm{E}}=\frac{\overrightarrow{\partial \mathrm{H}}}{\partial \mathrm{t}}$$

(7)

where the operator is:

$$\nabla =[\frac{\partial \mathrm{x}}{\partial \mathrm{t}},\frac{\partial \mathrm{y}}{\partial \mathrm{t}},\frac{\partial \mathrm{z}}{,\partial \mathrm{t}}]$$

(8)

Equations (6) and (7) are insufficient to describe the correlation between the produced fields and the material. The following equations can be used to alleviate this drawback:

$$\mathrm{E}\left(\mathrm{t}\right)=\frac{\mathrm{D}\left(\mathrm{t}\right)}{\mathsf{\epsilon } \left(\mathrm{t}\right)}$$

(9)

$$\mathrm{H}\left(\mathrm{t}\right)=\frac{\mathrm{B}\left(\mathrm{t}\right)}{\mathsf{\mu } \left(\mathrm{t}\right)}$$

(10)

The three important features that can be described using the aforementioned equations include the electric field, magnetic field and surface current. Figure 8 and Figure 9 represent the electric field distribution and magnetic field distributions, respectively, for the 3 resonance frequencies of 2.38 GHz, 4.55 GHz and 9.42 GHz. The current flow changes with a change in frequency. Two SRRs of the unit cell are more influenced by surface current flow than the other resonators, which are depicted in Figure 10. Thus, it can be noted that the first 2 frequencies, 2.38 GHz and 4.55 GHz, belong to the 2 SRRs, whereas the two epsilon-shaped resonators, which are placed in the middle of the unit cell, produced a low current flow with a frequency of 9.42 GHz.

The induced magnetic field intensity (B) depends on the current flow (I) or charge flow and the distance (r) of the conductor, which can be expressed using Biot–Savart’s law, $\mathrm{B}=\frac{{\mathsf{\mu }}_0\mathrm{I}}{2\mathsf{\pi }\mathrm{r}}$ [31], where ${\mathsf{\mu }}_0$ is the permeability in free space. With the increase in the current flow, the strength of the magnetic field also increases. The same effect is also observed in the E field, as presented in Figure 8. When the electric field pattern (Figure 8) is compared to that of the H field presented in Figure 9, it can be observed that the electric field (E) decreases when the magnetic field becomes positive. This changing pattern of the H and E fields support Equations (6) and (7). Moreover, it is also found that the electric field intensity was high in the split gaps as the splits in the resonator function as of capacitors.

Equivalent Circuit Model of the Proposed Metamaterial Unit Cell

An equivalent circuit was implemented for the proposed metamaterial unit cell to authenticate the results. The unit cell comprises two SRRs and two epsilon-shaped metal strips which contain both capacitive and inductive elements. Each metal strip functioned as an inductor, while every split gap was a capacitor. Consequently, the whole unit cell can be presented by an LC resonance circuit. If L and C represent the inductance and capacitance of the inductor and capacitor, respectively, then the resonance frequency (n) for the LC circuit can be determined using the Equation (11) [32]:

$$\mathrm{n}=\frac{1}{2\mathsf{\pi }{\left(\mathrm{LC}\right)}^{1/2}}$$

(11)

The capacitance of the capacitor formed by the slits can be calculated using Equation (12):

$$\mathrm{C}={\in }_{\mathrm{r}}{\in }_0\frac{\left(\mathrm{F}\right)\mathrm{A}}{\mathrm{d}}$$

(12)

where ${\in }_{0 }\mathrm{and} {\in }_r$ are the permittivity in free space and the relative permittivity, respectively, while A is the cross-sectional area of the conducting strip and d is the split gap:

$$\frac{\mathrm{L}\left(\mathrm{nH}\right)}{\mathrm{l}}=2\times {10}^{-4}\left[\ln \left(\frac{\mathrm{l}}{\mathrm{w}+\mathrm{t}}\right)+1.193+0.02235\left(\frac{\mathrm{w}+\mathrm{t}}{\mathrm{l}}\right)\right]{\mathrm{k}}_{\mathrm{g}}$$

(13)

Here, ${\mathrm{k}}_{\mathrm{g}}$ is the correction factor, w is the width, l is the length and t is the thickness of the strip.

Figure 11 represents a predictable equivalent circuit for the proposed metamaterial unit cell. In the equivalent circuit L₁, L₂, L₃, L₄, L₅, L₆ and L₇ depict the inductors while C₁ to C₉ represent the capacitors. The equivalent circuit for the proposed unit cell was performed using the advanced design system (ADS) software. The first SRR is represented by the inductors L₁, L₂ and capacitors C₁, C₂, respectively, which belong to the first resonance frequency of 2.375 GHz. Similarly, L₃, L₄ and C₃, C₄ are used for the second SRR, contributing to the second frequency of 4.52 GHz. Meanwhile, the two epsilon-shaped resonators are replaced by the inductors L₅ to L₇ and the capacitors C₅ to C₇, which are responsible for the third resonance frequency of 9.35 GHz, where C₈ and C₉ are the coupling capacitors. The values of all inductors and capacitors are tabulated in

Table 3. The values equivalent circuit components.

Component	Value (nH)	Component	Value (nH)	Component	Value (pF)	Component	Value (pF)
L1	1.95	L6	0.50	C1	0.06	C6	0.53
L2	0.10	L7	0.50	C2	0.10	C7	0.62
L3	1.04			C3	1.35	C8	10
L4	14.54			C4	8.195	C9	3.54
L5	7.625			C5	0.69

. The two transmission coefficients (S₂₁) for the unit cell extracted from CST and ADS are presented in the Figure 12. Based on Figure 12, the 3 resonance frequencies that were attained by ADS simulation are 2.375 GHz, 4.52 GHz and 9.35, whereas the CST-simulated frequencies were 2.38 GHz, 4.55 GHz and 9.24 GHz, indicating very negligible disparity.

6. Results and Discussion

Finite Integration Technique (FIT)-based electromagnetic simulator CST microwave studio was used to analyse the S-parameter and the various material characteristics parameters. Figure 13 illustrates the CST results of the reflection coefficient and transmission coefficient. The simulated result of S₂₁ exhibited triple band resonance at 2.38 GHz, 4.55 GHz and 9.42 GHz with the magnitudes of −29.40 dB, −39.65 dB and −43.35 dB, respectively. Meanwhile, S₁₁ is observed at 2.64 GHz, 5.65 GHz and 11.2 GHz with magnitudes of −34.85 dB, −27.38 dB and −17.19 dB, respectively. The bandwidths of three resonance peaks for the concerned bands are shown in Figure 13: These are 0.124 GHz at S-band, 0.597 GHz at C-band and 1.288 GHz at X-band. Figure 13 indicates that the first resonance of the reflection coefficient (S₁₁) pursued by the minimum value of transmission coefficient (S₂₁). Every minimum frequency of S₁₁ is lower than that of the corresponding S₂₁ maximum frequency, where each resonance of the unit cell was addressed as an electrical resonance. Meanwhile, Figure 14, Figure 15 and Figure 16 represent the three important material characteristics, namely, the permittivity (ε_r), permeability (µ_r) and refractive index (n) derived using NRW method via MATLAB programming code. According to Figure 14, the is noticed that resonance of transmission coefficient (S₂₁) just started while the values of ε changes from highest to the lowest. The smallest value of permeability (µ) was achieved when the value of the reflection coefficient (S₁₁) was the lowest (Figure 15). At the positive permeability, the value of permittivity shifted from positive to negative. The refractive index (n) of a material is also regarded as a function of frequency. It denoted a negative value when permittivity (ε) was negative, as demonstrated in Figure 16. The permittivity of the proposed metamaterial was negative for a certain frequency range. Therefore, it can be termed as an ε-negative (ENG) metamaterial. The Drude equation can be used to explain the negative permittivity [33]:

$$\mathsf{\epsilon }\left(\mathsf{\omega }\right)=\frac{\mathsf{\omega }\left(\mathsf{\omega }+\mathrm{i}\mathsf{\Gamma }\right)-{\mathsf{\omega }}_{\mathrm{p}}^2}{\mathsf{\omega }\left(\mathsf{\omega }+\mathrm{i}\mathsf{\Gamma }\right)}$$

(14)

where Γ and ${\mathsf{\omega }}_{\mathrm{p}}$ denote the energy disintegration attenuation function in the plasmons and plasmon frequency, respectively. If the losses Γ ≈ 0 and ω < ω_p, then the permittivity ε becomes negative. This artificial characteristic of the projected MM is utilised in many types of wireless communication such as antenna bandwidth development [34]. Furthermore, the other NRI properties can numerously be used to enhance the antenna gain, cloaking and application.

6.1. Array Metamaterial Results

A unit cell itself cannot satisfactorily function independently. To obtain the expected electromagnetic properties from a metamaterial, an array of the unit cell was used. The 1 × 2 and 2 × 2 arrays of the proposed unit cell with the same substrate material are illustrated in the Figure 17a,b. To investigate the coupling effect among the proposed unit cell for different orientations of an array, a parametric study was performed whereby it generated an almost similar response as S₂₁ to the unit cell. Therefore, the efficiency of the array was also observed. Figure 18a,b present the statistical results of S₁₁ and S₂₁, respectively, by CST of arrays with the proposed unit cell. By assessing the simulated results of the arrays, a change in the resonance frequencies was observed for the new array metamaterial. A comparative view of three resonance frequencies of two arrays in addition to the unit cell is shown in

Table 4. Variation in resonance frequencies for different arrays with the PMA unit cell.

Types of Simulation	Unit Cell	1 × 2 Array	2 × 2 Array	Max. Shift of Frequency (%)
First resonance (GHz)	2.38	2.36	2.40	0.84
Second resonance (GHz)	4.55	4.54	4.60	1.09
Third resonance (GHz)	9.42	9.34	9.60	1.9

. The third frequency (9.42 GHz) is shifted nearly 2%, while the other 2 frequencies (2.38 GHz and 4.55 GHz) shifted only by 1%.

A, B, C, and D are the four positions of unit cell in the 2 × 2 array. If the two elements of the diagonal BD rotate at an angle of 90° compared to another two diagonal elements of the Figure 17b, as shown in Figure 19a, interesting and magical changes are observed in the numerical result. Four resonance peaks were observed at 2.27 GHz, 4.46 GHz, 7.76 GHz and 9.21 GHz for the S₂₁ result at the new orientation, whereas, for Figure 17b, the simulated result shows three resonance peaks at 2.40 GHz, 4.60 GHz and 9.60 GHz. Figure 19b compares the two settings.

6.2. Validation by Using HFSS

The CST result of S₂₁ for the unit cell was also validated using the FEM based software HFSS. The proposed metamaterial unit cell exhibited 3 resonance peaks with almost similar magnitude at 2.40 GHz, 4.50 GHz and 9.40 GHz, whereas the CST yielded resonances at 2.38 GHz, 4.55 GHz and 9.42 GHz. Therefore, the CST and HFSS results were in excellent harmony (Figure 20).

Table 5. Verification of some previously reported MM with the offered configuration.

Author Name and Ref.	Shape of MM	Size (mm3)	Metamaterial Type	EMR (λ/L)
Mallik et.al. [35]	U	25 × 25 × 1.6	LHM	1.99
Hossain et al. [36]	Double dumbbell	9 × 9 × 1.6	ENG	11.5
Islam et al. [37]	H	30 × 30 × 1.6	LHM	3.65
Islam M et al. [38]	SRR	16 × 12 × 1.6	NRI	5.35
Hasan et al. [39]	Z	10 × 10 × 1.6	LHM	8.6
Proposed MM	Inverse epsilon shape	10 × 10 × 1.524	ENG	12.61

represents the EMR of some previously reported metamaterials based on dimension, resonance frequency and frequency band.

7. Conclusions

A triple-band, ε-negative, double-epsilon-shaped metamaterial was designed in this study. The presented work deliberated a metamaterial (10 × 10 × 1.524 mm³) on Rogers RT6002 (lossy) substrate. The unit cell of the proposed MM was simulated using the CST microwave and exhibited three resonance peaks at frequencies 2.38 GHz, 4.55 GHz and 9.42 GHz covering S-, C- and X-bands. The simulated results were authenticated using different validations such as equivalent circuit model, HFSS and array orientation. The significant material characteristics, namely, permittivity, permeability and refractive index, were extracted using the NRW-method-based MATLAB software. To investigate the response and activities of different resonators for the incident EM wave, an analysis was executed to assess the electric field, magnetic field and surface current. The 1 × 2 array and 2 × 2 arrays were simulated to compare the performance of the metamaterial. A good harmony was observed among the performance of ADS, HFSS and array. The designed unit cell yielded an EMR of 12.61 at the lower frequency of 2.38 GHz confirming compact size based on the compact metamaterial standard, L < λ/4. In conclusion, the proposed metamaterial can be used to boost the performance of different microwave devices for their n-negative and epsilon-negative characteristics. Since the S-, C- and, X-bands are frequently deployed for satellite and radar applications, the proposed MM may be a good candidate to improve the performance of satellite and radar communication devices.