  This paper presents an analytical study of TM-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. 240 for the chemical potential of 0.2 ev and the
incident power of 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.
