Observation of the Eckhaus Instability in Whispering-Gallery Mode Resonators

TL;DR

This paper demonstrates the observation of the Eckhaus instability in Kerr combs generated by ultra-high Q whispering-gallery mode resonators, revealing ultra-slow metastable dynamics explained by the Lugiato-Lefever model.

Contribution

It provides the first experimental evidence of Eckhaus instability in Kerr combs and links it to ultra-slow metastable behaviors in whispering-gallery resonators.

Findings

Eckhaus instability causes long-lived transient patterns in Kerr combs.

Metastable Kerr comb dynamics can last over a minute, much longer than photon lifetimes.

Theoretical analysis with the Lugiato-Lefever model matches experimental results.

Abstract

The Eckhaus instability is a secondary instability of nonlinear spatiotemporal patterns in which high-wavenumber periodic solutions become unstable against small-wavenumber perturbations. We show in this letter that this instability can take place in Kerr combs generated with ultra-high $Q$ whispering-gallery mode resonators. In our experiment, sub-critical Turing patterns (rolls) undergo Eckhaus instabilities upon changes in the laser detuning leading to cracking patterns with long-lived transients. In the spectral domain, this results in a metastable Kerr comb dynamics with a timescale that can be larger than one minute. This ultra-slow timescale 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 few photon lifetimes long (i.e., in the ps range). We show that this phenomenology is well explained by the Lugiato-Lefever model, as the result of an Eckhaus instability. Our theoretical analysis is found to be in excellent agreement with the experimental measurements.