Kerr optical frequency comb generation using whispering-gallery-mode resonators in the pulsed-pump regime

Kerr comb generation is usually based on the nonlinear dynamics of the intracavity field in a whispering-gallery-mode resonator pumped by a continuous-wave laser. However, using a pulsed instead of a continuous-wave pump opens an alternative research avenue from both the theoretical and experimental viewpoints, as it permits us to tailor the spectral properties of ultrashort pulse trains with a single passive nonlinear element. In this article we study the dynamics of Kerr optical frequency combs when the whispering-gallery-mode resonator is pumped by a synchronous pulse train. We propose a model that is based on an extension of the Lugiato-Lefever equation, which accounts for both the pulsed nature of the pump and the mismatch between the free-spectral range of the resonator and the repetition rate of the pulse train. We lay a particular emphasis on the effect of pump-cavity desynchronization on the spectral shape of the output combs. The numerical simulations are successfully compared with experimental measurements where the optical pulses are generated via time-lens soliton compression, and the resonator is a millimeter-size magnesium fluoride resonator with a billion quality factor at the pump wavelength.