The natural resonant singularity expansion method (SEM) poles for a dielectric sphere in various environments

When one computes the natural resonant singularity expansion method (SEM) poles for a dielectric sphere composed of different materials, one is surprised to observe that these SEM poles do change too much with corresponding changes in the value of the permittivity and permeability. This article provides an analytical solution as to why it is so. The Mie's series is applied to solve for the resonant frequencies of a dielectric sphere composed of different materials and embedded in various dielectric materials. The variations in the resonant frequencies related to the poles are tabulated along with the material parameters to illustrate the nature of the variation.