Numerical Analysis of Electromagnetic Wave Instability in Nonlinear Ferrite Structures Using Bifurcation Points of the Nonlinear Maxwell´s Operator

A new approach based on the bifurcation theory to develop mathematical models of nonlinear electromagnetic waves and oscillations in waveguiding and resonator structures, containing a strongly nonlinear bounded gyromagnetic medium, is proposed. A new method for rigorous modeling of nonlinear phenomena due to the instability in the three-dimensional ferrite structures was developed based on the numerical analysis of the bifurcation points of the nonlinear Maxwell´s operator. The bifurcation points were determined by our computational algorithm, using the eigenvalues of the matrix resulting from the linearized Maxwell´s operator. The onset and the breakdown of self-oscillations in the ferrite resonator structure, caused by the instability, were modeled. The transition regime from regenerative parametric amplification to parametric generation, depending on the magnitude of the pumping wave and resonator detuning, was simulated infinitesimally close to the bifurcation points