Finesse and four-wave mixing in microresonators

We elaborate a comprehensive theory of the sharp variations four-wave-mixing (FWM) threshold happening with tuning pump frequency along dispersive tails nonlinear resonance in driven Kerr microresonators high finesses and finesse dispersions. Our leads to explicit estimates for difference powers required excitation one sideband pair momenta $\pm\mu$, simultaneous two neighbouring pairs $\pm(\mu+1)$. This power also measures depth Arnold tongues pump-frequency pump-power parameter space, associated aforementioned variations. A set select frequencies powers, where instabilities come first, forms complexity, which is followed by sequence conditions specifying critical three, four so on pairs. formally link dispersion density states notion borrowed from condensed matter context report value mode number signalling transition low- high-contrast tongue structure. demonstrate that large makes possible surprising multimode resonators regime bistability without FWM.