Frequency comb generation beyond the Lugiato–Lefever equation: multi-stability and super cavity solitons

The generation of optical frequency combs in microresonators is considered without resorting to the mean-field approximation. New dynamical regimes are found to appear for high intracavity power that cannot be modeled using the Lugiato–Lefever equation. Using the Ikeda map, we show the existence of multi-valued stationary states and analyze their stability. Period doubled patterns are considered, and a novel type of super cavity soliton associated with the multi-stable states is predicted.