Analytical Study of TM-Polarized Surface Plasmon Polaritons in Nonlinear Multi-Layer Graphene-Based Waveguides

This paper presents an analytical study of transverse-magnetic-polarized surface plasmon polaritons (SPPs) in nonlinear multi-layer structures containing graphene sheets. In the general structure, each graphene sheet has been sandwiched between two different nonlinear magnetic materials. To show the richness of the proposed general waveguide, two novel nonlinear structures have been introduced and investigated as special cases of the general structure. It will be shown that the propagation features of these structures can be tuned by changing the chemical potential of the graphene and the incident mode power. A large value of the effective index, i.e., $${n}_{\mathrm{eff}}=240$$ for the chemical potential of $${\mu }_c=0.2 ev$$ and the incident power of $$\alpha {\left|{H}_y,0\right|}²=3$$ is obtained for the second structure at the frequency of 40 THz. The analytical results confirm that the integration of nonlinear magnetic materials with graphene sheets can control and enhance the propagating features and the self-focused of the field in the nonlinear layer. This integration gives more degrees of freedom to the designer to propose new THz components such as lasers and switches in the THz region.