Theory of nonlinear whispering gallery mode dynamics in a cylindrical microresonator with a radius variation

We propose a comprehensive model describing the Kerr nonlinear dynamics of an electric field in a cylindrical microresonator with an effective radius variation, coupled to a radiation source. The proposed system of equations for coupled azimuthal modes takes into account full azimuthal dispersion as well as the influence of the radiation source on the field in the microresonator with the coupling coefficients determined experimentally. The model appears a powerful tool to study nonlinear effects, generation axial-azimuthal modes and optical frequency combs. We illustrate the power of the model with optimization of the coupling point of the light source, getting two order of magnitude improvement for the nonlinear threshold.