Objective Metamaterials have several advantages compared to natural materials. As they are produced by the artificial synthesis of periodic unit structures, metamaterials can achieve special electromagnetic phenomena, including electromagnetically induced transparency (EIT), near-zero refractive index, and photonic band gap. Therefore, improving the performance of metamaterials has become a hot topic in the industry. If metamaterial devices offer a rational selection of materials and structural parameter adjustment, their wide application in the field of terahertz technology would be possible. EIT is an optical quantum interference cancellation effect that makes opaque media transparent to light detection. It has substantial application value for the realization of slow light. In the atomic field, the conventional EIT effect requires strict experimental conditions, such as ultra-low temperature and strong light pumping. However, when using metamaterials to achieve the EIT effect, only light and dark mode structures are needed. Their resonant absorption frequencies are quite similar. After an electromagnetic wave incident, light and dark mode structures are coupled with each other, and their transmission peak appears. Many researchers have studied and designed two-dimensional metamaterials, with a variety of different media and structures, and they have achieved ground-breaking results. However, only few studies have focused on three-dimensional (3D) metamaterials with the multi-band slow-light effect. In order to solve this critical problem, a 3D metamaterial model comprising of a square closed loop and split ring resonators is designed based on relevant principles. Moreover, the proposed structure shows a multiband EIT effect in the terahertz range.

Methods To design metamaterials with optimum performance, we first designed the unit structure, in which four split ring resonators were vertically arranged on the quartz substrate. In addition, the square closed loop was placed horizontally on the quartz substrate. The parameters of these four split ring resonators were the same, and the opening positions were forward and reverse. Next, we used CST to simulate an EIT metamaterial structure and study its mechanism. For analyzing the mechanism of its electromagnetic response and EIT effect, we split the metamaterial structure into reverse and forward double-split ring resonator unit structures that were then simulated and compared. In addition, to further explore the mechanism of resonance peaks, the electric and magnetic field distributions (at each resonance peak) were analyzed. The structural parameters, including the width, opening size, and square closed loop size, were analyzed and studied. Finally, the optical buffer was studied, and the proposed structure was applied to the refractive index sensor.

Results and Discussions The designed metamaterial structure has four transmission peaks at 1.21THz, 1.46THz, 1.61THz, and 1.98THz. The coupling bodies of the bright mode and dark mode in the structure are forward and reverse double split ring resonators, respectively with a square closed loop, respectively, and the resonance intensity is about 0.90 (Fig. 2). Compared with the customary structure, the proposed structure achieves a four-band, high-intensity EIT effect. The first resonance transmission peak appears at 1.21THz, which infers that the forward and reverse double split ring resonators and the square closed loop are light and dark modes of one another. It can also be inferred that they are coupled after the magnetic wave incident (Fig. 3). The second transmission peak appears at 1.46THz, which is obtained by the coupling of the forward double split ring resonators and the square closed loop as light and dark modes of each other (Fig. 3). The third transmission peak is pinpointed at 1.61THz, which is obtained by the coupling of four split ring resonators and the square closed loop, also as bright and dark modes of each other (Fig. 3). The last transmission peak appears at 1.98THz, which indicates that it is obtained by the coupling of the reverse, double split ring resonators, and the square closed loop. In the discussion of broadband EIT characteristics, by differentiating the absorption peaks, the split ring resonators are sharper than the square closed loop, so the electromagnetic resonance is more intense and the value is also elevated. The forward double split ring resonators and the square closed loop are of mutual light and dark modes, and they are coupled to form two transmission peaks with a bandwidth of 0.25THz. In the same way, the reverse double split ring resonators and the square closed loop are also coupled, forming two transmission peaks with a bandwidth of 0.52THz and 0.41THz. The simulation results show that the broadband characteristics have clear advantages over the 0.1THz bandwidth of the traditional narrow-band structure (Fig. 4). For the opening size of the split ring resonators, the resonance intensity of the EIT transmission peak decreases simultaneously with the increase of parameters, and the bandwidth also decreases (Fig. 5). For the size of the square closed loop, the resonance intensity of the transmission peak gradually increases along with the successive increase of the transmission peak. This reveals a small blue shift of the transmission peak, and the bandwidth also increases (Fig. 6). For research in the field of optical buffering, with the rapid increase of refractive index and dispersion, the group refractive index also increases in the EIT effect. The values are 67.6, 37.5176.4, and 57.8289.4 (Fig. 7). Finally, when the proposed structure is applied to the refractive index sensor, the refractive index sensitivities of four bands are 235.2, 39.2, 65.8, and 29.4 GHz/RIU, respectively. In contrast with the conventional EIT structure, the designed metamaterial structure not only presents multiband refractive index sensing performance but also presents its own high sensitivity (Fig. 8).

Conclusions The results show that the EIT effects of 1.21THz, 1.46THz, 1.61THz, and 1.98THz can be achieved in the three-dimensional structure model of metamaterials in terahertz band; the resonance intensity can reach 0.90, 0.89, 0.90, and 0.87, respectively. The mechanism of the multiband EIT resonance was studied by differentiating the coupling response of forward and reverse double split ring resonators, and a square closed loop. By adjusting the structural parameters, the influence of the size of the opening of the split ring resonators and the size of the square closed loop on the strength and bandwidth of the EIT (in the metamaterial) is discussed. Compared with the traditional design, the metamaterial 3D structure indicates a multiband EIT effect, and it shows an escalating refractive index sensitivity in multiple bands. This can produce a strong slow-light effect at multiple frequency points. Therefore, it is satisfactory for the application and promotion in the field of refractive index sensing and optical buffer.