Microresonator soliton crystal pattern-fitting algorithm

Soliton crystal combs are a common type of frequency comb generated in optical microresonators, which in the time domain consist of an often complex repeating pattern of identical solitons, and in the frequency domain have intricate spectra caused by interference between the solitons. Calculating the spectrum from the soliton pattern is simply a matter of taking the Fourier transform. However, determining the pattern from the comb line amplitudes without knowing their phases is, in general, extremely difficult computationally, bearing strong similarities to the calculations in x-ray crystallography. Here, we present an algorithm to fit the soliton crystal pattern to experimental microcomb spectra. The probabilistic algorithm, which is written in Python and runs in less than 20 s on a standard laptop for almost all the tested combs, determines the number of solitons, their amplitude and duration, and their relative positions, providing very good agreement with the experimental comb line amplitudes and correctly predicting their measured phases. In all the fitted patterns, the soliton spacings fall within tight bands in a manner that is consistent with the established mechanism for soliton crystal locking via an extended background wave.