Plasmon-induced transparency (PIT) refers to an atypical transmission phenomenon that results from the coupling of various resonance modes with the near-field electromagnetic wave. This usually results in a slowdown of the speed of light at the transmission peak due to significant dispersion, which is known as slow light performance. Numerous studies have demonstrated that slow light performance can be achieved in optical fibers, waveguides, and metasurfaces, which has led to wide-ranging applications in areas such as optical storage and optical modulation. Metasurfaces offer several advantages over optical fibers and waveguides, including small size, ease of fabrication, and excellent electromagnetic properties. Moreover, the addition of graphene to metasurfaces provides high-quality properties such as high transmittance, low loss, and dynamical adjustability. As a result, graphene-based metasurfaces hold significant potential in the study of slow light performance. However, the production and utilization of complex patterned graphene are limited by the current state of nanomanufacturing technology. Therefore, studying the PIT effect in simple structures with high quality is crucial for the practical production and application of PIT devices in experiments and real-life settings. Moreover, designing simple and manufacturable structures that produce high-quality multi-mode PIT is of great significance to optical device fabrication. This will significantly promote the rapid development and application of photonic devices based on the PIT effect.

In this paper, we investigate the PIT effect in monolayer patterned graphene metasurfaces using numerical simulations of the electromagnetic field. The simulations are performed using the full-wave electromagnetic software, namely CST Microwave Studio 2019, which utilizes the finite integration technique (FIT) to solve the discrete Maxwell equations. The metasurface structure consists of a split ring resonator (SRR) laterally coupled by metal-graphene-metal. Initially, we analyze the transmission spectrum and electric field distribution to gain insights into the PIT effect of the structure. Additionally, we derive a theoretical formula for graphene surface conductivity and investigate the effect of bias voltage on the dielectric constant of graphene by changing the Fermi level. Subsequently, we study the impact of different Fermi levels on amplitude modulation. Finally, we demonstrate the dynamic modulation of slow light performance by varying the bias voltage and graphene width.

In this paper, we present the design and analysis of a monolayer patterned metal-graphene metasurface that achieves a high-quality PIT effect (Fig. 1). We observe that as the Fermi level of graphene increases, the transmittance at resonance points also increases. Specifically, we achieve amplitude modulations of 96.05% and 65.40% at two different resonance points (Fig. 5). To quantify the relationship between the bias voltage and the Fermi level of graphene, we propose an equivalent capacitive coupling model, which shows that graphene primarily modulates the amplitude and has low sensitivity to frequency. Resonance frequency modulation can be achieved by changing the structural parameters such as the width of graphene (Fig. 7). We evaluate the performance of the slow light effect using parameters such as group delay, group refractive index, and delay bandwidth product (DBP). We find that the bias voltage is positively correlated with these parameters, while the graphene width is negatively correlated with them. For instance, when the bias voltage is set to 50 V, and the graphene width is stable, we obtain group delay, group refractive index, and DBP values of 44.11 ps, 276.19, and 3.66, respectively (Table 1). By reducing the graphene width, we further optimize these parameters, resulting in group delay, group refractive index, and DBP values of 93.12 ps, 756.67, and 9.31, respectively (Table 2). The Q value characterizes the loss of the device, with a higher Q value indicating a lower loss. When no bias voltage is applied, we obtain the largest Q value of 42.33. However, the Q value gradually decreases as the bias voltage increases, or the graphene width decreases. This suggests that high dispersion and low loss characteristics cannot be simultaneously achieved and need to be balanced in practical applications. Finally, we compare our device with relevant studies and demonstrate its significant advantages.

The study proposes a metal-graphene coupling structure to achieve a dynamically adjustable PIT effect, which results from the interference cancellation of the bright-bright mode. By adjusting the Fermi level of graphene, amplitude modulation can be achieved at 0.929 THz and 1.037 THz, with maximum modulation depths of 96.05% and 65.40%, respectively. By using the equivalent capacitive coupling circuit, the relationship between the bias voltage and Fermi level is calculated, and it is found that a bias voltage drop of Vg=30V and graphene width of w₂=2 μm can result in group delay, group refractive index, DBP, and Q values of 93.12 ps, 756.67, 9.31, and 10.19, respectively. These results hold significant value in slow optical device fabrication, THz communication, and detection research.