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We present a method to deterministically obtain broad bandwidth frequency combs in microresonators. These broadband frequency combs correspond to cnoidal waves in the limit when they can be considered soliton crystals or single solitons. The method relies on moving adiabatically through the (frequency detuning)×(pump amplitude) parameter space, while avoiding the chaotic regime. We consider in detail Si₃N₄microresonators with small or intermediate dimensions and an SiO₂microresonator with large dimensions, corresponding to prior experimental work. We also discuss the impact of thermal effects on the stable regions for the cnoidal waves. Their principal effect is to increase the detuning for all the stable regions, but they also skew the stable regions, since higher pump power corresponds to higher power and hence increased temperature and detuning. The change in the detuning is smaller for single solitons than it is for soliton crystals. Without temperature effects, the stable regions for single solitons and soliton crystals almost completely overlap. When thermal effects are included, the stable region for single solitons separates from the stable regions for the soliton crystals, explaining in part the effectiveness of backwards-detuning to obtaining single solitons.

 

Pumped Kerr microresonators have recently emerged as a promising source of optical frequency combs. The production of octave-spanning spectrum by dispersive waves and consequent demonstration of carrier-envelope phase locking has paved the way toward a wide field of comb applications. Nevertheless, there remain some obstacles before the goal of a simple off-the-shelf comb source is achieved. Current microcomb implementations rely on cavity solitons, and several of the present limitations of microcombs are tied to those of soliton waveforms. Cavity solitons exist only in a small red-detuned region of the pump parameters, where waveforms suffer from thermal instabilities. Furthermore, solitons are always obtained in the multistable regime, and therefore cannot be continuously connected to cw, so that elaborate, often non-deterministic, access protocols are needed to produce them. Another issue is that because solitons are accompanied by a strong pedestal, their comb power efficiency is low. 

We show that nonlinear frequency pulling shifts the stability region of periodic waveforms in strongly driven Kerr microresonators to shorter periods. Consequently, optimized narrow-band combs are obtained by judiciously adjusting the period.