Analytical approach to the design of microring resonators for nonlinear four-wave mixing applications

An analytical approach for obtaining linear and nonlinear design parameters of microresonators is presented. The
eigenmode/eigenfrequency problem of planar resonators is considered in detail, with an analytical closed-form
approximation derived for resonators possessing a large radius to width ratio. The analysis permits the resonant
frequencies and mode profiles to be determined together with the dispersion properties. The dependence of the
effective nonlinear Kerr coefficient on the mode volume is further considered, and also the waveguide coupling
together with estimates of the Q-value. Examples, which are in good agreement with numerical simulations, are
presented for silicon resonators. The approach can be used for designing planar microring resonators for nonlinear
four-wave mixing applications, such as optical Kerr frequency comb generation.