Unified theory of whispering gallery multilayer microspheres with single dipole or active layer sources

The development of a fast and reliable whispering gallery mode (WGM) simulator capable of generating spectra that are comparable with experiment is an important step forward for designing microresonators. We present a new model for generating WGM spectra for multilayer microspheres, which allows for an arbitrary number of concentric dielectric layers, and any number of embedded dipole sources or uniform distributions of dipole sources to be modeled. The mode excitation methods model embedded nanoparticles, or fluorescent dye coatings, from which normalized power spectra with accurate representation of the mode coupling efficiencies can be derived. In each case, the emitted power is expressed conveniently as a function of wavelength, with minimal computational load. The model makes use of the transfer-matrix approach, incorporating improvements to its stability, resulting in a reliable, general set of formulae for calculating whispering gallery mode spectra. In the specific cases of the dielectric microsphere and the single-layer coated microsphere, our model simplifies to confirmed formulae in the literature.