Switching fronts, plateaus and Kerr oscillations of counterpropagating light in ring resonators

TL;DR

This paper investigates the formation and stability of stationary fronts, dark solitons, and complex oscillatory states in counterpropagating light within ring resonators, revealing new multi-stable and oscillatory phenomena influenced by nonlocal coupling.

Contribution

It introduces a detailed analysis of stationary fronts and dark solitons in nonlocally coupled ring resonators, linking solutions to the Lugiato-Lefever equation at the Maxwell point, and explores multi-stability and oscillations.

Findings

Stable plateau and front solutions are identified in counterpropagating fields.

Solutions are linked to the Lugiato-Lefever equation at the Maxwell point.

Multi-stable states and oscillations coexist with stable fronts.

Abstract

We characterise stationary fronts and dark solitons for counterpropagating waves in micro-ring and fibre resonators with two input fields, normal dispersion and nonlocal coupling. These features are different from those in systems with local coupling in that their existence and stability are due to a careful balance of the areas of offset from homogeneous solutions. When scanning one of the two cavity detunings, stable solutions formed plateaus separated by two fronts are present in one of the counter-propagating fields with the power of the other field being homogeneous. Two front plateau solutions have a one-to-one correspondence to solutions of a Lugiato-Lefever equation at the unique Maxwell point. By defining effective detunings and for fixed values of the input powers where the fronts are found, we determine expressions for both the Maxwell point and the distance of the stable fronts as functions of detunings and input powers of both fields in good agreement with numerical simulations. For certain values of the detunings we find multi-stable states of plateaus with fronts, oscillating homogeneous states and non-oscillating homogeneous states of the counter-propagating fields. Robustness and parameter ranges of these unusual dynamical states coexisting with stable non-homogeneous front solutions are provided.