Parametric patterns in optical fiber ring nonlinear resonators

TL;DR

This paper explores the emergence of Faraday patterns in nonlinear fiber resonators with periodically varying Kerr nonlinearity, analyzing their formation through Floquet theory and numerical simulations, revealing an inverted modulation scenario.

Contribution

It introduces the concept of spatial modulation inducing temporal patterns in fiber resonators, expanding understanding of parametric pattern formation in nonlinear optics.

Findings

Parametric instability analyzed via Floquet theory.

Numerical simulations confirm pattern formation.

Inverted modulation scenario demonstrated.

Abstract

We propose that parametrically excited patterns, also known as Faraday patterns, can be observed in nonlinear fiber resonators, where the coefficient of Kerr nonlinearity is periodically varying along the fiber in resonator. We study the parametric instability analytically on the basis of the Floquet theory, also numerically, by direct integration of the system. Instead of classical Faraday wave excitation scenario, where modulation in time causes formation of patterns in space, here we propose an inverted scenario, where the modulation in space excites the patterns in time.