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The vector field bifurcation approach and its numerical implementation for the rigorous mathematical simulation of nonlinear phenomena in microwave and mm-wave ferrite or composite semiconductor/ferrite devices are developed. The bifurcation points of nonlinear Maxwell's operator for the three-dimensional boundary problems, stated and solved rigorously (i.e., considering the full Maxwell's equations together with the nonlinear equations of motion for magnetization in ferrites and transport carriers in semiconductors) are analyzed using numerical methods. The electromagnetic field is represented as decomposed into a series of weakly nonlinear wave fields. The solutions of a linearized Maxwell's operator matrix equation are determined. The propagation constants of weakly nonlinear waves in waveguiding structures (WGS) or eigenfrequencies of weakly nonlinear oscillations in resonator structures (RS) are found. Using the bifurcation dynamics of Maxwell's equations the nonlinear wave interactions in the strongly nonlinear planar ferrite insert, loaded into strip-slot RS, are analyzed (from the harmonic frequency terms at the ‘soft’ non-linear stage into the region of ‘hard’ non-linearity). The nonlinear propagation of electromagnetic waves in the strip-slot ferrite RS are modeled. The nonlinear wave phenomena, including the parametric excitation of oscillations and the wave instability process are investigated taking into account constrained geometry WGS and RS. [ABSTRACT FROM AUTHOR]

A rigorous mathematical model of nonlinear, parametric interactions of microwave magnetostatic dipole-dipole waves and electro-magnetic 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 ~m 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]