Ladder of Eckhaus instabilities and parametric conversion in chi(2) microresonators

TL;DR

This paper reveals that the stepwise frequency conversion in chi(2) microresonators is caused by Eckhaus instabilities, providing a new theoretical understanding of their ladder-like frequency tuning behavior.

Contribution

It introduces the concept that Eckhaus instabilities explain the stepwise frequency changes in chi(2) microresonators, linking fluid dynamics phenomena to nonlinear optics.

Findings

Eckhaus instabilities cause stepwise frequency conversion.

The ladder-like frequency tuning curves are explained by these instabilities.

The theory bridges fluid dynamics and nonlinear optical microresonator behavior.

Abstract

Low loss microresonators have revolutionised nonlinear and quantum optics over the past decade. In particular, microresonators with the second order, chi(2), nonlinearity have the advantages of broad spectral tunability and low power frequency conversion. Recent observations have highlighted that the parametric frequency conversion in chi(2) microresonators is accompanied by stepwise changes in the signal and idler frequencies. Therefore, a better understanding of the mechanisms and development of the theory underpinning this behaviour is timely. Here, we report that the stepwise frequency conversion originates from the discrete sequence of the so-called Eckhaus instabilities. After discovering these instabilities in fluid dynamics in the 1960s, they have become a broadly spread interdisciplinary concept. Now, we demonstrate that the Eckhaus mechanism also underpins the ladder-like structure of the frequency tuning curves in chi(2) microresonators.