## 5 Results Analysis
### Unit Cell Analysis  
In Figure 8a,b, both the numerical and experimental reflection (\(S_{11}\)) and transmission (\(S_{21}\)) coefficients are shown. In Figure 8a, the simulation and experimental resonance frequencies of the reflection coefficient are almost the same at 3.7 GHz and 8.6 GHz of the unit cell. In addition, the measured resonance of the reflectance of the array structure at 4.21 GHz (magnitude of 23 dB) and 8.60 GHz (magnitude of 12 dB) is shown in the same Figure 8a. Figure 8b shows the triple-band resonance of the simulation at 3.48 GHz, 7.60 GHz and 12.84 GHz in the transmittance curve. The measured results exhibit resonance at 3.53 GHz (S-band), 7.54 GHz (C-band) and 12.94 GHz (Ku-band) in Figure 8b for the unit cell. The values of the resonances at 3.53 GHz, 7.54 GHz  
Figure 7: Surface current at 12.94 GHz of: **(a)** single unit cell and **(c)** 1 \(\times\) 2 array structure. Numerical electric field distribution in the XY plane at 12.94 GHz for: **(b)** single unit cell and **(d)** 1 \(\times\) 2 array structure. and 12.94 GHz are \(-\)14.95 dB, \(-\)17.56 dB and \(-\)29.91 dB, respectively. Moreover, the measured transmittance of the array structure exhibits the resonance frequency peaks at 4.0 GHz (magnitude of 16 dB), 7.41 GHz (magnitude of 21 dB), 8.10 GHz (magnitude of 17.50 dB), 10.30 GHz (magnitude of 12 dB) and 12.41 GHz (magnitude of 23 dB) in Figure 8b. However, owing to the measurement or fabrication errors, the measured result frequencies are slightly shifted and the magnitude extended compared with the simulated results. Figure 9 shows the unit cell amplitudes of the permittivity, permeability and refractive index at 0-degree, 90-degree, 180-degree and 270-degree rotations. Figure 9a demonstrations the negative permeability from 7.85-14 GHz (bandwidth of 6.15 GHz), negative permittivity from 4.60-7.70 GHz (bandwidth of 3.10 GHz) and 8.30 to 10.36 GHz (bandwidth of 2.06 GHz) and negative refractive index from 4.50 to 7.50 GHz (bandwidth of 3.0 GHz), 7.80 to 10.10 GHz (bandwidth of 2.30 GHz) and 12.60-14 GHz (bandwidth of 1.40 GHz) at zero-degree rotation. In addition, Figure 9b displays the permeability from 7.79-14 GHz (bandwidth of 6.21 GHz), permittivity from 4.11-7.53 GHz and 8-10.20 GHz. However, the refractive index is from 3.96-7.25 GHz and 7.68-9.60 GHz at 90-degree rotation. Furthermore, in Figure 9c, the unit cell at 180-degree rotation exhibits permeability from 7.90-14 GHz, permittivity from 4.66-7.12 GHz and 8.38-10.39 GHz and a refractive index from 4.53-7.47 GHz and 7.80-10.13 GHz. Additionally, permeability from 7.80-14 GHz, permittivity from 4.11-7.53 GHz and 8.03-10.17 GHz and a refractive index from 3.59-7.25 GHz and 7.68-9.59 GHz are shown in Figure 9d for 270-degree rotation of the proposed meta-atom unit cell. Here, it is revealed that there is a variation between the effective medium parameters because the properties of the effective medium parameters are mostly affected by the polarization owing to the internal architecture of the mate atom. Figure 8: Magnitude (in dB) of: (**a**) the reflection coefficient (\(S_{11}\)) and (**b**) the transmission coefficient (\(S_{21}\)). According to the left-handed or double-negative characteristics, the refractive index will be negative, if the unit cell permittivity and permeability appear negative simultaneously. From Figure 9, the unit cell structure exhibits left-handed characteristics at every rotation angle at 9.20 GHz, which are shown in Table 2. There is a variation of the effective medium ratio between zero-degrees and 90-degrees. Actually, the electric and magnetic fields are closely related and propagate as an electromagnetic wave. The electromagnetic wave is applied to the proposed meta-atom in the \(Z\)-direction. After application of the electromagnetic wave, the inner particles of the meta-atom structure start oscillating up and down, as well as toward the vibration.