Optical resonances in graded index spheres: A resonant-state-expansion study and analytic approximations

Recent improvements in the resonant-state expansion (RSE), focusing on static mode contribution, have made it possible to treat transverse-magnetic (TM) modes of a spherically symmetric system with same efficiency as their transverse-electric (TE) counterparts. We demonstrate here that efficient inclusion RSE results its quick convergence exact solution regardless set used. then apply systems continuous radial variations permittivity. show TM polarization, spectral transition from whispering gallery Fabry-Perot is characterized by peak losses and an additional compared TE polarization. Both features are explained quantitatively Brewster angle surface reflection which occurs this frequency range. Eliminating discontinuity at sphere using linear or quadratic profiles permittivity modifies increases losses, qualitative agreement reduced reflectivity. These also provide nearly parabolic confinement for modes, analytical approximation Morse potential presented. result TE-TM splitting, shown be further suppressed choosing profile radially extending fields. Based concepts ray optics, phase analysis secular equation, effective quantum-mechanical wave we developed number useful approximations shed light physical phenomena observed spectra graded-index systems.