Modal Hybrid Analysis of a Spherical Resonator With a Ferrite Load

The modal analysis of structures containing ferrite materials is one of the greatest challenges of computational electrodynamics and goes beyond the scope of commercial software’s capabilities. The reason for this is the strong dependence of the ferrite parameters on frequency. From a numerical point of view, the task boils down to a nonlinear eigenproblem (NLEVP), the solution of which is not trivial. In particular, if the problem involves more complex structures (modeled using discrete techniques), NLEVP contains matrices of enormous dimensions and its solution seems impossible. The method proposed in this paper is based on the projection of the NLEVP onto a smaller subspace obtained by hybridizing finite element method (FEM) and the mode matching (MM) technique. This approach reduces the size of the problem, which directly improves the efficiency of the algorithm, but also allows solving NLEVP using methods whose results can be verified with controlled accuracy (unlike previous attempts to use Beyn’s method). The effectiveness of the proposed technique has been validated through numerical simulations and experimental results demonstrating a complex mode structure of a microwave spherical cavity strongly coupled to a yttrium iron garnet sphere. The results pave the way for rigorous electrodynamic modeling of spin-to-electromagnetic coupling with emerging applications in magnonic and quantum technologies. Finally, it is worth mentioning that NLEVPs are not exclusively used for electromagnetic problems and an effective algorithm for solving them could also find application in other fields of technology.