A general model for taper coupling of multiple modes of whispering gallery resonators and application to analysis of coupling-induced Fano interference in a single cavity

In this paper, we give a general model for analysis of multimode Whispering Gallery Mode (WGM) resonators coupled to multimode tapered fibers based on the coupled-mode theory. Such formulation takes into account the asymmetry of the taper-resonator coupling. Simulations for a microsphere show that the tapered fiber coupling mechanism induces cross-coupling between coherent orthonormal WGMs. We show that the degree of such cross-coupling depends basically on the fiber diameter, air-gap between the taper and resonator, intrinsic losses and eccentricity. The WGM cross-coupling affects the total transmission and spectral line-shape of the internal powers resulting in a controllable transformation of the line-shape to non-Lorentzian spectra. This analysis can be utilized to precisely determine the output and intra-cavity intensity of multimode microresonators, which is important in lasers, nonlinear optical signal generation and realization of optical delays