## 3 Metamaterial Working Principle  
To observe the proposed metamaterial behavior and understand the physical phenomena of how it works when it is located in an electric and magnetic field region, the surface current distributions are analyzed and discussed for different frequencies. The surface current distributions of the proposed MTM unit cell at 2.4, 3.5, 5.5, and 10 GHz are shown in Figure 2a-d. The arrows represent the current distribution direction in the overall structure, and the colors indicate the current intensity. A visible surface current distribution at 2.4 GHz resonant frequency is illustrated in Figure 2a. However, more intensive surface current can be observed clearly at 3.5 GHz in Figure 2b, especially at the edge of outer symmetric C-shaped portions, whereas it perturbed the overall unit cell structure. In Figure 2c,d, the surface current distribution behavior is relatively in fluctuation mode at the symmetrical C-shaped outer, middle, and inner rings, whereas currents flow in different directions with a stronger current at 10 GHz. Due to this mechanism, an effective negative permeability is observed, although the current distribution flows in opposite side directions of the down and upper C-shaped etching strips, which nullify the current and generate a stopband. Figure 1: Metamaterial unit cell: (**a**) unit cell structure with g = 0.5 mm, \(r_{1}\) = 2.9 mm, \(r_{2}\) = 1.9 mm, \(r_{3}\) = 0.9 mm; (**b**) simulation set-up in the x-axis; (**c**) simulation set-up in the y-axis. The simulated transmission coefficient (S21) and reflection coefficient (S11) results of the x- and y-directions are shown in Figure 3a,b, respectively. For the x-direction, it shows the resonance frequency band in the range of 2-8.6 GHz, which is a part of UWB as well as covering several bands in the ranges of 9.8-10, 13.5-15, and 17-19.6 GHz. The outer and inner split-ring-shaped resonators are considered as the effective cause of the achieved multiband range, whereas the higher resonance at 10 GHz is shown by the blue dotted line. Furthermore, several bands are considered in the case of MTM located in the y-direction, where the S21 is in the range of 2-4.6, 5.5-6.5, 9.8-11.2, and 12-16.9 GHz. Figure 3: Simulated metamaterial reflection and transmission coefficients: (**a**) x-axis, (**b**) y-axis. Figure 2: Surface current distribution at (**a**) 2.4; (**b**) 3.5; (**c**) 5.5 and (**d**) 10 GHz. The simulated relative imaginary and real parts of the effective permittivity, permeability, refractive index, and impedance of different unit cell array structures are plotted in Figures 4-6. In these figures, the dark brown color is used to show the negative indexed zone for double-negative metamaterial (DNG) or single-negative metamaterial (SNG); however, light brown color indicates a near-zero refractive index (NZRI) and both Epsilon/Mu near-zero (ENZ/MNZ) metamaterial. The wide DNG real value of the refractive index is exhibited in the range of 2-8.5 GHz in x-axis wave propagation as shown in Figure 4a, whereas a narrow portion of NZRI is achieved with a 255 MHz bandwidth. However, it is remarkable that a greater than 2 GHz bandwidth can be achieved with an NZRI property in y-axis wave propagation, as shown in Figure 4b. This has potential applications for electromagnetic cloaking operation and high gain antenna design. For the \(1\times 1\) unit cell, as shown in Figure 5, real negative values of permittivity (\(\varepsilon\)) and permeability (\(\upmu\)) are exhibited for frequency ranges from 2.6 to 8.8 and from 2 to 6.4 GHz, respectively. Thus, the unit cell behaves as a double-negative metamaterial (DNG). Moreover, X band and KU bands are covered using the proposed metamaterial only in x-axis wave propagation with MNZ property. In Figure 6, it is apparent that several bands are exhibited with negative real values of SNG permittivity, whereas SNG permeability in the range of 2-4.3 GHz is realized, which works for S-band applications and can cause NZRI in the same range.