Soliton and quasi-soliton frequency combs due to second harmonic generation in microresonators

We report how a doublet of the symmetric oppositely tilted bistable resonance peaks in a microring resonator with quadratic nonlinearity set for generation of the second harmonic can transform into a Kerr-like peak on one side of the linear cavity resonance and into a closed loop structure disconnected from the quasi-linear resonance on the other. Both types of the nonlinear resonances are associated with the formation of the soliton combs for dispersion profiles of a typical LiNbO$_3$ microring. We report bright quasi-solitons propagating on a weakly modulated low intensity background when the group velocity dispersions have the opposite signs for the fundamental and second harmonic. We also show exponentially localized solitons when the dispersion signs are the same. Finally, we demonstrate that the transition between these two types of soliton states is associated with the closure of the forbidden gap in the spectrum of quasi-linear waves.