Transitional dynamics of collapsed snaking to multiple resonances in Kerr cavities with parabolic potential: dark and bright solitons

We investigate the dynamics of Kerr cavity solitons in the normal dispersion regime, under the influence of intracavity phase modulation. When increasing the strength of the parabolic phase modulation, dark solitons undergo a transformative shift into high-order bright solitons. We characterize this phenomenon and show that it is associated with a transition from a collapsed snaking bifurcation structure for dark solitons, to a multimode resonance structure for the high-order bright solitons case. This study may offer a comprehensive exploration of cavity dynamics, unveiling an avenue to access new multi-stable states by controlling the phase modulation.