Modal analysis of non-separable outer-boundary cavities via spherical vector wave functions

A three dimensional Mode Matching/Collocation technique is proposed in the current work for the analysis of a general cavity loaded with a spherical inhomogeneity. Analytical electromagnetic field eigen-solutions expressed in terms of spherical wave functions are utilized for the field expansions. The boundary conditions on the spherical surface are enforced through the collocation method. Analytical results are obtained for both the source driven problem and the corresponding eigen-problem, i.e. the eigenfunctions of the whole inhomogeneous geometry. The proposed theory will be utilized modelling in biomedical structures and especially in microwave ablation. The contribution of the current work is the use of entire domain basis functions that provide performance improvements especially for electrically medium to large domains. Results, including finite domains, following coordinate or non-separable surfaces, inside spheroids, paraboloids and elliptic cones, have been extracted and the performance of the method with respect to computational resources will be reported.