Modulational instability windows in the nonlinear Schr\"odinger equation involving higher-order Kerr responses

TL;DR

This paper provides a comprehensive analytical and numerical analysis of modulational instability in nonlinear Schrödinger equations with higher-order Kerr effects, revealing new stability regimes and instability landscapes.

Contribution

It introduces simple analytical criteria for stability analysis and uncovers a novel parametric regime with multiple stability and instability windows.

Findings

Identification of multiple stability and instability regimes

Discovery of a new parametric regime with alternating stability windows

Analytical criteria applicable to higher-order Kerr nonlinearities

Abstract

We introduce a complete analytical and numerical study of the modulational instability process in a system governed by a canonical nonlinear Schr\"odinger equation involving local, arbitrary nonlinear responses to the applied field. In particular, our theory accounts for the recently proposed higher-order Kerr nonlinearities, providing very simple analytical criteria for the identification of multiple regimes of stability and instability of plane-wave solutions in such systems. Moreover, we discuss a new parametric regime in the higher-order Kerr response which allows for the observation of several, alternating stability-instability windows defining a yet unexplored instability landscape.