Soliton combs mediated by phonons and thermo-optic effects in Kerr optomechanical microresonators

Optomechanical microresonators have attracted particular attention in the recent past, due to their possible applications in a broad range of optical metrology contexts. Experimental studies have established that in addition to modifying the microresonator’s refractive index through the so-called thermal-lensing process, the heat stored in the microresonator cavity during roundtrips of the optical field also induces thermal expansion of the cavity, promoting mechanical excitations (phonon modes). In the present study, we examine the emergence of soliton trains in the anomalous dispersion regime of a Kerr optomechanical microresonator subjected to thermal-lensing processes, combined with phonon radiations from thermally-induced expansion of the optomechanical microresonator. The model consists of the Lugiato-Lefever equation with two extra detunings accounting for optomechanical and thermo-optic effects, coupled to the phonon equation and to a two-level equation accounting for the temporal variation of the temprature difference within the microresonator cavity. By solving numerically the model equations using a sixth-order Runge-Kutta algorithm, it is shown that a strong optomechanical coupling can inflict severe impairements on soliton-comb structures in the optomechanical microresonator. Phonon-mode amplitudes emerge to be enhanced with an increase of the optomechanical coupling coefficient, while time variation of the cavity temperature is marked by an exponential rise and saturation in an oscillating regime. Relatively high phonon characteristic frequencies favor optical soliton-crystal patterns as well as regular periodic anharmonic structures for phonon modes.