Soliton synchronization in microresonators with a modulated pump

Microresonator frequency comb generation from Kerr solitons has become a cutting edge technology, but challenges remain in creating, maintaining, and controlling the solitons. Pump modulation and dual pumping are promising techniques for meeting these challenges. Here we derive the equation of motion of solitons interacting with a modulated pump in the framework of synchronization theory. It implies that the soliton repetition rate locks to the modulation frequency whenever the latter is within a locking range of frequencies around an integer multiple of the free spectral range of the microresonator. We calculate explicitly, numerically, and in perturbation theory the width of the locking range as a function of the amplitude and frequency of the pump and the modulation phase. We show that a highly red-detuned, strong pump that is amplitude-modulated provides the best conditions for entrainment, and that the width of the locking range is proportional to the square of the modulation frequency, limiting the effectiveness of RF modulation as an entrainment method.