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

摘要

A new approach, based on the bifurcation theory [1], to develop mathematical models of nonlinear electromagnetic waves or oscillations in waveguiding (WGS) and resonator structures (RS), containing a strongly nonlinear bounded gyromagnetic medium, is proposed. The physical meaning of the bifurcation points of the nonlinear Maxwell's operator is that these are the values of the parameters at which qualitative modifications of nonlinear processes occur, caused by instabilities, such as the onset or breakdown of self-oscillations, the transition from periodic to chaotic behavior. The rigorous statement of a nonlinear boundary problem for waveguiding structures, containing a nonlinear gyromagnetic medium, requires to solve the full set of non-linear Maxwell's equations complemented by the equation of motion of the magnetization vector in a ferromagnet [2]. Earlier theories of the instability of magnetostatic or spin waves were developed using an approximate analysis based on the equation of motion of the magnetization for 1-D ferrite structures [3].