Surface plasma polaritons (SPPs) have been greatly promoted in recent years in the field of nano-photonology. There have been many studies which show that the SPPs can be generated on the surface of graphene and dielectric, and plasma induced transparency (PIT) effect due to the interaction between the incident light and the structure as an abnormal transmission phenomenon has been studied generally. With the advantage of dynamic modulation, the graphene has greater advantages than the precions metal materials in PIT effect, which has been proven to play a key role in the next generation of photonic devices such as photoelectric switches, sensors, and slow-light devices. The PIT effect based on patterned graphene metamaterials has evolved towards multi-layered complex structures that can achieve very excellent electromagnetic properties. However, complex patterned graphene is difficult to be produced and put into use limited by the development of nanomanufacturing technology. It is very significant to study the simple structure and high quality PIT effect for the manufacture and application of PIT devices in experiment and real life. At the same time, designing simple, manufacturable structures to produce high-quality multi-mode PIT is of great significance to the development of the SPPs field. It will also greatly promote the rapid development and application of photonic devices based on PIT effect.

In this paper, the PIT effect of monolayer patterned graphene metamaterials is studied by combining numerical simulation of electromagnetic field via finite-difference time-domain (FDTD) and theoretical calculation via coupled-mode theory (CMT). We design a single-layer metamaterial structure composed of graphene blocks and graphene strips, use FDTD solution for electromagnetic field simulation calculations to observe the transmission and power field local, and thus analyze the interaction between the light-dark mode and the incident light. Next, by deducing the theoretical formula of graphene surface conductivity, the effect of gate voltage applied changing with the Fermi level of graphene on the dielectric constant of graphene is obtained. By studying the effect of different Fermi level graphene on the PIT effect, the relevant application design scheme is proposed. CMT is widely regarded as two or more time model and spatial coupling electromagnetic wave general law of the most effective theory in recent years. In this paper, the structures of bright and dark models are used as two resonators for the analysis of mode coupling effect, through rigorous formula derived theoretical material transmittance formula. Finally, we compare numerical simulation results and theoretical calculation results to verify the rationality and correctness of the simulation calculation.

In this paper, a simple monolayer patterned graphene metamaterial is designed to achieve high quality PIT effect (Figs. 1 and 2). By changing the size of the gate voltage to dynamically regulate the Fermi level of graphene, we find that with the increase of Fermi level, the PIT spectral pattern has an obvious blue shift phenomenon, and the resonance effect of each resonance point is also significantly enhanced. Meanwhile, the simulation results obtained by FDTD are highly consistent with the theoretical calculation results obtained by CMT (Fig. 4). Dynamic adjustment of the PIT spectrum is realized by adjusting the Fermi level of graphene, multimode synchronous and asynchronous switches can be designed at the frequencies of 2.16, 3.01, and 3.84 THz, the amplitude modulations of three frequencies are 95.77%, 83.42%, and 95.58%, respectively, and the extinction ratio is up to 13.73 dB (Fig. 5). Through cross-sectional comparison with different kinds of metamaterial photoelectric switches, it is found that the switch designed can realize a high amplitude modulation system with a simpler structure (Table 1). Finally, by calculating the group refractive index, we obtain the slow light characteristics of materials at different Fermi energy levels. The materials can achieve the highest group refractive index of 180 (Fig. 6) which provides a new scheme and guidance for simple slow light devices.

In this paper, we propose a simple graphene metamaterial structure to achieve high quality PIT effect. The dynamic tuning of PIT effect is achieved by using the properties of graphene with applied gate voltage to change the Fermi level. By analyzing the PIT effect at different Fermi levels, it is not difficult to find that as the Fermi level of graphene increases, PIT effect has obvious blue shift and resonance enhancement. At the same time, we also put forward the theory of a synchronous asynchronous photoelectric switch design, which can reach 95.77% in 2.16 THz switch modulation amplitude. The realization of high quality photoelectric switch with simple structure provides a new scheme and idea for the development of nano photoelectronic devices. At the end of the article, we discuss its slow light effect through calculating the group refractive index of the metamaterial. The maximum group refractive index of 180 can be achieved, which provides a scheme and guidance for the design and application of slow optical devices.