## 2 Design Parameters of the Metamaterial and Simulation Setup
### Analysis of Electromagnetic Field and Surface Current  
The upper layer of the proposed metamaterial unit cell contains resonant assemblies composed of split gaps and metallic conductors. The split gaps and conductors play the roles of capacitors and inductors, respectively. Electromagnetic force is exerted on the resonators due to the interaction between time-varying EM fields and the unit cell. The induction current flows from one resonator to another through the capacitive split gaps, which are smaller than the wavelength of the incident EM wave. Produced electric and magnetic moments influence the transmission ability and change the material characteristics such as permittivity and permeability. The surface current distribution of the presented MM is illustrated in Figure 8, predicting that at a low-resonance frequency of 2.35 GHz, the outer ring subsidizes a higher amount of current. At the lower frequency, the inductive reactance is also low because the outer ring contributes a low impedance route. A significant amount of current flow decreases in the first outer ring at the second resonance frequency of 7.72 GHz because an increase in impedance occurs with the increase in frequency. At this frequency, non-uniform and random movement of current is detected in bars connecting the octagons, which eventually reduces the overall current flow. In the two inner octagons, current flow is reduced because of the neutralization of two opposite flows. For the same reasons, current flow becomes insufficient at a resonance frequency of 9.23 GHz, and high current flow is observed through the edges of all horizontal sides of all rings compared to the previous two positions. It is also noteworthy that a substantial amount of current is contributed by the two horizontal sides of the outer ring, owing to lower impedance applied by the split gap at a resonance frequency of 10.68 GHz. Figure 6: Application of changing electric and magnetic field directions: (**a**) ExHy; (**b**) EyHx. Figure 7: Transmission coefficient (\(S_{21}\)) with interchanging field propagation. Time-varying charge flow is mainly responsible for generating magnetic field according to the Amperes law in association with [PERSON]'s law of induction, which, in turn, produces an electric field due to electromagnetic interaction [36]. The induced E field and H field can be inspected using the [PERSON]'s curl Equations (8)-(12), as presented in [37]. Horizontal magnetic field component:  
\[\
abla\times H=J+\frac{\partial D}{\partial t} \tag{8}\]  
Produced electric field related to the magnetic field:  
\[\
abla\times E=\frac{\partial H}{\partial t} \tag{9}\]  
where the vector operator is expressed as:  
\[\
abla=i\frac{\partial x}{\partial t}+i\frac{\partial y}{\partial t}+k\frac{ \partial z}{\partial t} \tag{10}\]  
Equations (8) and (9) are not sufficient to explain why the two fields interact with materials. Two more equations are required to overcome these limitations [38]. \[\varepsilon\left(t\right)=\frac{D(t)}{E\left(t\right)} \tag{11}\]  
\[\mu\left(t\right)=\frac{B(t)}{H(t)} \tag{12}\]  
The material properties of permittivity \(\left(\varepsilon\right)\) and permeability \(\left(\mu\right)\) in Equations (11) and (12) are complex parameters and real in the case of isotropic lossless material. A vivid observation magnetic field \(\left(H\right)\) and electric field \(\left(E\right)\) for the four resonance frequencies (2.35, 7.72, 9.23 and 10.68 GHz) are illustrated in Figures 9 and 10, respectively. The intensity of the magnetic field and polarity depend on the amount of current and its flow direction. The H-field distribution in Figure 9 shows that at locations in the unit cell where the current density is high, the magnetic field is also high. As shown by the patterns of H-field and E-field distribution in Figures 9 and 10, if the magnetic field changes towards an increment, then the electric field changes inversely. The changing tendency of magnetic and electric fields is determined according to Equations (8) and (9).