Azimuthal Turing Patterns, Bright and Dark Cavity Solitons in Kerr Combs Generated With Whispering-Gallery-Mode Resonators

We investigate the formation of cavity solitons in crystalline whispering-gallery-mode disk resonators that are pumped in different dispersion regimes. In the Fourier domain, these dissipative structures correspond to specific types of mode-locked Kerr optical frequency combs. Depending on the sign of the second-order chromatic dispersion and on the pumping conditions, we show that either bright or dark cavity solitons can emerge, and we show that these two regimes are associated with characteristic spectral signatures that can be discriminated experimentally. We use the Lugiato-Lefever spatiotemporal formalism to investigate the temporal dynamics leading to the formation of these azimuthal solitons, as well as the emergence of Turing patterns. The theoretical results are in excellent agreement with experimental measurements that are obtained using calcium and magnesium fluoride disk resonators pumped near 1550 nm.