Role of Eckhaus instability and pattern cracking in ultraslow dynamics of Kerr combs

Abstract

The Eckhaus instability is a secondary instability of nonlinear spatiotemporal patterns in which high-wave-number periodic solutions become unstable against small-wave-number perturbations. Here we show that this instability can take place in Kerr combs corresponding to subcritical Turing patterns upon changes in the laser detuning. The development of the Eckhaus instability leads to the cracking of patterns and a long-lived transient where the peaks of the pattern rearrange in space due to spatial interactions. In the spectral domain, this results in a metastable Kerr comb dynamics with timescales that can be larger than 1 min. This time is, at least, seven orders of magnitude larger than the intracavity photon lifetime and is in sharp contrast with all the transient behaviors reported so far in cavity nonlinear optics that are typically only a few photon lifetimes long (i.e., in the picosecond to the microsecond range). This phenomenology, studied theoretically in the Lugiato-Lefever model and the observed dynamics is compatible with experimental observations in Kerr combs generated in ultra-high-Q whispering-gallery mode resonators.