Three dimensional Mode Matching for inhomogeneously loaded spheroidal cavity

In this paper a three dimensional Mode Matching technique is proposed for the analysis of a spheroidal cavity loaded with a spherical inhomogeneity around one of its focuses. Analytical electromagnetic field eigen-solutions expressed in terms of spheroidal and spherical wave functions are utilized for the field expansions. The boundary conditions on the spherical surface are enforced through a coordinate transformation and the related Hankel functions addition theorem. Analytical results are obtained for both the source driven problem and the corresponding eigen-problem, i.e. the eigenfunctions of the whole inhomogeneous geometry are obtained. The proposed theory will be utilized in the modelling of biomedical structures and especially in microwave ablation.