Axisymmetric modes of cylindrical resonators with cascaded inhomogeneous dielectrics

A generic numerical scheme is developed to calculate the resonant frequency of axisymmetric modes in an inhomogeneous cylindrical dielectric resonator. The resonator consists of sections of cylindrically stratified dielectrics within a cylindrical waveguide. In each section, the TM_0m and TE_0m waveguide modes are solved by expanding the H_φ and E_φ components in terms of the eigenmodes in an empty waveguide. The fields in each section are then expanded in terms of these TM_0m and TE_0m modes. The transverse resonance technique is then applied to obtain the resonant frequencies. Comparison with literatures validates the effectiveness of this approach. Results with continuous dielectric profiles are also obtained