## 3 Methodology  
For numerical analysis of the proposed unit cell, the finite integration technique-based CST Microwave Studio has been used. In the simulation technique, the unit-cell structure is placed between two waveguide ports, and the electromagnetic waves are set to propagate in the z-directions. Perfect electric and magnetic boundaries are considered in the x- and y-directions shown in Figure 4. A frequency-domain solver with a tetrahedral mesh is utilized for simulation from 2-14 GHz.  
The reflection (\(S_{11}\)) and transmission (\(S_{21}\)) coefficients are analyzed to realize the electromagnetic properties of the anticipated structures [24,25]. However, \(S_{11}\) and \(S_{21}\) can be written as,  
\[S_{11}=\frac{\left(1-\Gamma^{2}\right)z}{1-\Gamma^{2}z^{2}}, \tag{1}\]  
Figure 4: Simulation setup with boundary condition in CST-MWS.  
Figure 3: Fabricated 150 \(\times\) 200-mm\({}^{2}\) (15 \(\times\) 20 unit cells) array prototype of the proposed meta-atom structure.  
\[S_{21}=\frac{\left(1-x^{2}\right)\Gamma}{1-\Gamma^{2}z^{2}}, \tag{2}\]  
The effective permittivity (\(\varepsilon\)) can be calculated by,  
\[\varepsilon_{r}=\frac{2}{jkd}\times\frac{\left(1-S_{21}-S_{11}\right)}{\left(1 +S_{21}+S_{11}\right)},\]  
\[\varepsilon_{r}=\frac{c}{j\pi fd}\times\frac{\left(1-S_{21}-S_{11}\right)}{ \left(1+S_{21}+S_{11}\right)}, \tag{3}\]  
The effective permeability (\(\mu\)) can be obtained from,  
\[\mu_{r}=\frac{2}{jkd}\times\frac{\left(1-S_{21}+S_{11}\right)}{\left(1+S_{21} -S_{11}\right)},\]  
\[\mu_{r}=\frac{c}{j\pi fd}\times\frac{\left(1-S_{21}+S_{11}\right)}{\left(1+S_{ 21}-S_{11}\right)}, \tag{4}\]  
Therefore, the refractive index (\(n\)) can be expressed as follows,  
\[n_{r}=\frac{2}{jkd}\times\sqrt{\left\{\frac{\left(S_{21}-1\right)^{2}-S_{11} ^{2}}{\left(S_{21}+1\right)^{2}-S_{11}^{2}}\right\}},\]  
\[n_{r}=\frac{c}{j\pi fd}\times\sqrt{\left\{\frac{\left(S_{21}-1\right)^{2}-S_{1 1}^{2}}{\left(S_{21}+1\right)^{2}-S_{11}^{2}}\right\}}, \tag{5}\]  
where \(k=\omega/\)C and the angular frequency \(\omega=2\pi\)f. Measurement of the meta-atom is performed by the two horn antenna (frequency range from 700 MHz-18 GHz) in a semi-anechoic chamber, placed 1 m apart to satisfy the far-field condition. For measurement purposes, the fabricated prototypes utilize a horn antenna. A fabricated 150 \(\times\) 200-mm\({}^{2}\) (15 \(\times\) 20 unit cells) array prototype, displayed in Figure 3, is placed within two horn antennas (from 700 MHz-18 GHz) in a semi-anechoic chamber. The chamber is surrounded by a wedge tapered absorber. The incident electromagnetic waves travel over the prototype similar to the simulated geometry. The horn antennas are connected to the Agilent N5227A vector network analyzer to obtain the reflection and transmission coefficient of the I-shaped meta-atom unit cell. Moreover, for additional experimental accuracy, the designed structure is also measured by the waveguides method [26]. The measured results of the both methods are almost similar to the proposed meta-atom structure. In addition, in the waveguide method, the fabricated 10 \(\times\) 10-mm\({}^{2}\) unit cell is placed between the waveguide ports, which work as transmission and receiving terminals. A set of (WR284 (frequency range from 2-3.95 GHz), WR187 (frequency range from 3.95-5.85 GHz), WR137 (frequency range from 5.85-8.20 GHz), WR90 (frequency range from 8.20-12.40 GHz), WR62 (frequency range from 12.40-18 GHz)) waveguides to coaxial adapters is connected to the Agilent N5227A vector network analyzer via a semi-rigid cable for measuring the S-parameters of the operating frequency from 2-18 GHz. The waveguide experiment is performed in an open-space environment, and the measurement is performed accurately with an Agilent N4694-60001 for calibration and an Agilent N5227A as a vector network analyzer. The experimental setup for measurement purposes is shown in Figure 5.