A dynamically tunable multiband plasmon-induced transparency (PIT) effect in a series of rectangle cavities coupled with a graphene nanoribbon waveguide system is investigated theoretically and numerically by tuning the Fermi level of the graphene rectangle cavity. A single-PIT effect is realized using two different methods: one is the direct destructive interference between bright and dark modes, and the other is the indirect coupling through a graphene nanoribbon waveguide. Moreover, dual-PIT effect is obtained by three rectangle cavities side-coupled with a graphene nanoribbon waveguide. Results show that the magnitude of the dual-PIT window can be controlled between 0.21 and 0.74, and the corresponding group index is controlled between 143.2 and 108.6. Furthermore, the triple-PIT effect is achieved by the combination of bright–dark mode coupling and the cavities side-coupled with waveguide mechanism. Thus, sharp PIT windows can be formed, a high transmission is maintained between 0.51 and 0.74, and the corresponding group index is controlled between 161.4 and 115.8. Compared with previously proposed graphene-based PIT effects, the size of the introduced structure is less than 0.5 μm2. Particularly, the slow light effect is crucial in the current research. Therefore, a novel approach is introduced toward the realization of optical sensors, optical filters, and slow light and light storage devices with ultra-compact, multiband, and dynamic tunable.

In order to reduce power, realize ultrafast response time and dynamic tunability, a plasmonic waveguide system based on four disk resonators is designed. A plasmon induced transparency effect is theoretically analyzed using two different methods:one is the direct destructive interference between bright and dark mode resonators, and the other is the indirect coupling through a plasmonic waveguide. Due to the giant effective nonlinear Kerr coefficient of the graphene-Ag composite material structure and the enhancement characteristics of slow light response to optical Kerr effect, the pump intensity of PIT system to change the phase shift of transmission spectrum is greatly reduced. An ultrafast response time of 1 ps is achieved. 0.4π, 0.8π, 1.2π, 1.6π and 2π-phase shift of the transmission spectrum in the plasmon induced transparency system are achieved with the intensity of the pump light as low as 2.34, 4.68, 7.02, 9.36 and 11.7 MW/cm^-2. In this paper, two small disk resonators directly coupled with a plasmonic waveguide is employed, and the reason is that two small disk resonators play the role of the slit between the waveguide and the resonators, and also acts as two separate resonators side-coupled with a plasmonic waveguide, which leads to the more efficient coupling of electromagnetic energy in the waveguide into the big disk resonators to form resonance and easier storage of light in the resonator. The triple-band plasmon induced transparency (PIT) effect and slow light properties of the model are analyzed by the expression of the deduced theoretical transmittance based on the coupled mode theory, which are very consistent with the finite-difference time-domain simulations. The results show that the transmission peak of the system is over 80% and the maximum group index is as high as 368. What's more, the disk resonators are easy to fabricate and the size of the entire PIT structure is <0.5 μm², which is benefit for design of optoelectronic devices on-chip integration. The research results have important application prospects in highly integrated optical circuits and networks, and also provide ideas for the design and fabrication of multi-channel optical filter and light storage devices with low power consumption, ultrafast nonlinear responses ultracompact and dynamically tunability.