Bifurcation Analysis of Nonlinear, Parametric Interactions of Electromagnetic Waves with Graphene Nanostructures at Photonic Frequencies

A rigorous mathematical model of nonlinear, parametric interactions of electromagnetic waves (EMWs) with graphene-based nanostructures is developed. The nonlinear diffraction boundary problem is solved for the nonlinear Maxwell's equations with electrodynamical boundary conditions simultaneously with a model of graphene surface conductivity as a nonlinear function on the time-varying electric field. The numerical approach is based on the projection method using the decomposition algorithm on autonomous blocks with Floquet channels. The instability of parametric excitation process of EMWs in multilayer graphene-dielectric nanostructure is simulated using the numerical method of bifurcation analysis of the nonlinear Maxwell's operator, taking into account the constrained geometries.