## 6 Results and Discussion
### Electric Field, Magnetic Field, and Surface Current Analysis  
With the help of mathematics and physics, the electric field distribution at resonance frequencies of 2.4 GHz, 5.6 GHz, 8.9 GHz, and 11.5 GHz was investigated. The propagation constant (\(\gamma\)) of the medium is responsible for frequency (\(\omega\)), permittivity (\(\varepsilon\)), permeability (\(\mu\)), and conductivity (\(\sigma\)). The propagation constant of the medium is adopted by E-field propagation. For the E-field, we may obtain the Helmholtz equation [40] from Equation (14). \[\
abla^{2}E_{m}-\gamma^{2}E_{m}=0 \tag{14}\]  
Figure 7: S21 of the proposed metamaterial unit cell based on the **(a)** split gap variation of gl; **(b)** split gap variation of g3; **(c)** length variation of I1; **(d)** length variation of I2. \(\mathrm{E_{m}}\) indicates the propagation of electric field and \(\gamma\) indicates propagation constant. \[\left|\gamma^{2}\right|=\omega\mu\sqrt{\sigma^{2}+\omega^{2}\epsilon^{2}} \tag{15}\]  
Equation (14) can be generated by combining the given parameters and form to Equation (16), where it is satisfied with a linear homogeneous differential equation. \[\left[\frac{d^{2}}{dz^{2}}-\gamma^{2}\right]E_{xm}(z)=0 \tag{16}\]  
At a resonance frequency, Equation (16) gives the properties to the electric field. In Figure 8, the E-field distribution over the outer SRRs is seen while simulating wave propagation along the \(z\)-axis. The properties of electric fields are also observed in the inner double C shape area of the metamaterial unit cell. At different resonances, for the proposed quad resonance frequencies, a high-intensity E-field produces a significant dipole moment when mutual coupling occurs, and this moment is shared equally by the symmetric and asymmetric parts of the structure. We adjusted the planned unit cell with a connecting slab based on the E-field. The introduced copper metallic slab inductor was placed in the gap between the outer two SRR areas at 1.7 mm from the left and 4.9 mm from the right of the outer SRR. We also introduced another metallic stripe at 4.9 mm from the left and 1.7 mm from the right of the outer cell between the two outer SRR gap. Fortunately, the feedback is produced by the electric field and resonance frequencies after connecting the two outer SRRs. There is another connecting slab used between the inner SRR and double C shape gap, which also shows effective results on electric field distribution. This modifying technique of the metallic part in the unit cell is inspired by [PERSON] et al. [41]. The resonance frequencies are implemented in this design at 2.4 GHz, 5.6 GHz, 8.9 GHz, and 11.5 GHz; the bandwidth was observed at or below \(-10\) dB and achieves distinguished results, which can be discussed further in the study. Figure 8: Electric field distribution at **(a)** 2.4 GHz; **(b)** 5.6 GHz; **(c)** 8.9 GHz; **(d)** 11.5 GHz. The electric field (E-field), magnetic field (H-field), and surface current distribution of the proposed metamaterial were analyzed for quad resonance frequency and are shown in Figures 8-10. At the resonance frequency of 2.4 GHz, a strong electric field is seen at the top-right area of the metallic part of the structure, including two outer SRRs; there is an electric field also observed in the inner split of the outer SRRs at the bottom-left area due to the capacitive effect in Figure 8a. At the same time, the magnetic field is observed in the inner double C shape area on the left side of the structure in Figure 9a, where it indicates the opposite reaction from the electric field. Figure 10a shows that a higher surface current is observed in those areas where the magnetic field is present. These characteristics fulfill the criteria of [PERSON]'s equation. At the resonance frequency of 5.6 GHz in Figure 8b, there is a strong electric field observed at both the top-right and bottom-left outer SRR area. At the same resonance frequency, the magnetic field is also observed strongly at the top-left area where the two outer SRRs are connected in Figure 9b.