Mathematical modeling of nonlinear waves and oscillations in gyromagnetic structures by bifurcation theory methods

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' nonlinearity). 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.