Normal modes and quality factors of spherical dielectric resonators: I — shielded dielectric sphere

Electromagnetic theoretic analysis of shielded homogeneous and isotropic dielectric spheres has been made. Characteristic equations for the TE and TM modes have been derived. Dielectric spheres of radii of the order of μm size are found suitable for the optical frequency region whereas for the microwave region radii of the order of mm size are found suitable. Parameters suitable for their application in the optical and microwave frequency ranges have been used to compute the frequencies corresponding to the normal modes for the TE and TM modes. Expressions for the quality factors for realistic resonators, i.e., for a dielectric sphere with a non-zero conductivity and a metal shield with a finite conductivity have also been derived for the TE and TM modes. Computations of the quality factors have been made for resonators with parameters suitable for the optical and the microwave regions.