Walk-off controlled self-starting frequency combs in χ⁽²⁾ optical microresonators

Investigations of frequency combs in χ⁽³⁾ optical microresonators are burgeoning nowadays. Changeover to χ⁽²⁾ resonators promises further advances and brings new challenges. Here, the comb generation entails not only coupled first and second harmonics (FHs and SHs) and two dispersion coefficients but also a substantial difference in the group velocities - the temporal walk-off. We predict walk-off controlled highly stable comb generation, which is drastically different from that known in the χ⁽³⁾ case. This includes the general notion of antiperiodic states; formation of localized coherent antiperiodic steady states (solitons), where the FH and SH envelopes move with a common velocity without shape changes; characterization of a new vast family of antiperiodic solitons; and the dependence of comb spectra on the pump power and the group velocity difference.