Bifurcation analysis of the thresholds of parametric generation of terahertz waves in nonlinear multilayer graphene nanostructures

Background. The purpose of this work is to develop a method for mathematical modeling of nonlinear effects (parametric generation, parametric excitation of waves, and instabilities) arising from the interaction of electromagnetic waves with strongly nonlinear multilayer graphene nanostructures based on the solution of a nonlinear diffraction problem for Maxwell's equations, taking into account geometries. Materials and methods. A method has been developed for the bifurcation analysis of nonlinear effects (parametric generation, parametric excitation of waves) arising in graphene nanostructures in the terahertz (THz) frequency range. The method consists in finding the bifurcation points of the nonlinear Maxwell operator using the developed computational algorithm, improved by a qualitative analysis method based on the Lyapunov stability theory. Results. A numerical method has been developed for the bifurcation analysis of nonlinear effects (parametric generation, parametric excitation of waves) arising in graphene nanostructures in the terahertz (THz) frequency range. The method consists in finding the bifurcation points of the nonlinear Maxwell's operator using the developed computational algorithm, improved by a qualitative analysis method based on the Lyapunov stability theory. Conclusions. It follows from the results of rigorous mathematical modeling that the thresholds of THz wave generation depend on the value of the chemical potential, the characteristics of parametric THz generators based on the multilayer graphene nanostructures can be tuned by an external bias electric field, and also controlled by the configuration and sizes of nanostructures.