Broken azimuthal degeneracy with whispering gallery modes of microspheres

We consider a system of two eccentric spheres, wherein an inclusion sphere is embedded in a larger sphere with a different refractive index. We demonstrate broken azimuthal degeneracy for non-axisymmetric illumination resulting in splittings in extinction peaks. The mode splitting and mixing effects are shown to be nonresonant, valid for all modes having sufficient quality factors. We demonstrate strong dependence of the splittings on the polarization of the incident light to the extent that one can diagnose the polarization characteristics of the whispering gallery mode. We show how a set of quantum numbers can be assigned to a given peak of the split resonances. We further investigate the field distribution in suitable coordinate planes in order to bring out the close relation between the magnetic quantum number, the polarization of the bisphere modes and that of incident light.