Bifurcation Analysis of Parametric Interaction of Magnetostatic and Electromagnetic Waves in Nonlinear 3-D Ferrite Film Structures

A rigorous mathematical model of nonlinear, parametric interactions of microwave magnetostatic dipole-dipole waves and electromagnetic waves in 3-D ferrite films in waveguiding structures is developed. The 3-D nonlinear diffraction boundary problem of the full nonlinear Maxwell´s equations with electrodynamical boundary conditions, complemented by the Landau-Lifshitz equation (without the exchange term) is solved. The instability of parametric excitation process of magnetostatic waves in 3-D ferrite structures is simulated by the numerical method of bifurcation analysis of the nonlinear Maxwell´s operator for the 3-D boundary problem. The results show discrete maxima in the magnitude of reflected electromagnetic waves for distinct ferrite thickness values in the 1 mum to 1 mm range. The mode profiles were obtained. The instability regions, depending on the bifurcation parameters, were determined, and shown to be more sensitive to the pumping power than the parametric excitation of electromagnetic waves alone