Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere

Coupled-mode theory is used to numerically calculate the coupling coefficients between the modes of a tapered fiber and those of a fused-silica microsphere. In the visible and near-infrared wavelength ranges, typical tapered fibers are multimode. To maximize the photon tunneling from the fundamental fiber mode to the microsphere whispering-gallery mode and to minimize the tunneling from the sphere to higher-order fiber modes, the optimal fiber radius is found to be somewhat smaller than that for phase matching. Also calculated are whispering-gallery mode spectra that take into account the eccentricity of the microsphere and the fact that in an experiment the tapered fiber is not necessarily perfectly aligned with the equatorial plane of the microsphere.