Analysis of Multilayered Gyroelectric Spherical Cavities by Weak Form VIE Formulation

In this paper, the volume integral equation (VIE) is employed to rigorously formulate the electromagnetic theory inside spherical metallic cavities loaded by highly multilayered isotropic, uniaxial, and gyroelectric-type permittivities. First, the VIE is constructed inside the cavity. However, a modified dyadic Green's function (DGF) must also be constructed, which takes into account the electric boundary condition on cavity's perfect electric conducting surface. This modified DGF is not used to solve the VIE. However, its procedure of construction lets to construct a new tensorial expansion for Green's function. Employing the weak form VIE formulation allows to evaluate the integrals analytically and reduce the VIE to an algebraic form. Rigorous analysis reveals that the weak form formulation arrives exactly to the solution governed by separation of variables method. Among other validations presented, the theory is also validated by HFSS. The eigenfrequencies of highly multilayered cavities and results showing the very different effects in the characteristic modes due to change of the permittivity type and inhomogeneity are discussed.