Modulation instability in dispersive parity-broken systems

TL;DR

This paper investigates how parity-breaking influences modulation instability in two different systems, revealing that parity breaking can stabilize envelope dynamics and lead to chiral-dependent behaviors in both hydrodynamic and optical models.

Contribution

It introduces a novel analysis of parity-breaking effects on modulation instability in hydrodynamic and optical systems, deriving NLSEs with distinct stability properties.

Findings

Parity breaking causes chirality-dependent stability in gravity wave NLSEs.

A window of stable wave numbers exists due to odd viscosity effects.

Parity breaking stabilizes envelope dynamics in PT-symmetric optical models.

Abstract

This work explores the interplay between dispersive parity breaking and non-linearity in two contrasting continuous dynamical systems that exhibit Modulation Instability (MI). We begin by examining deep water odd surface gravity waves and derive the non-linear Schr\"odinger equation (NLSE) for the modulated envelope dynamics using the method of multiple scales. The parity breaking in the odd gravity waves results in distinct NLSEs for the right and the left mover, leading to chirality-dependent stability properties for the envelope dynamics. Moreover, the resonant interaction of gravity waves and odd viscosity-induced capillary dynamics creates a window of wave numbers in one of the chiral sectors where the envelope propagation remains stable. Following the odd gravity results, we design a one-dimensional non-reciprocal PT-symmetric dielectric model that exhibits parity-breaking effects that are analogous to the odd viscosity term in 2D hydrodynamics. With cubic non-linearity in the polarization dynamics, we derive the corresponding NLSE. Once again, we observe that parity breaking stabilizes the modulated envelope dynamics in the lower polariton bands. We then compare the similarities and differences between this case and that of odd gravity waves.