Modulational instability in nonlocal Kerr media with sine-oscillatory response

TL;DR

This paper investigates modulational instability in nonlocal Kerr media with sine-oscillatory response, revealing unique properties such as MI occurrence in both focusing and defocusing regimes and a gain unaffected by wave intensity.

Contribution

It introduces a novel physical mechanism for MI based on four-wave mixing, explaining MI conditions in nonlocal Kerr media with sine-oscillatory response.

Findings

MI exists for both positive and negative Kerr coefficients

Maximum MI gain is independent of wave intensity

MI occurs when phase mismatch is sufficiently small

Abstract

We discuss the modulational instability (MI) of plane waves in nonlocal Kerr media with the sine-oscillation response function, which can model the nematic liquid crystal with negative dielectric anisotropy. The results in the framework of the nonlocal nonlinear Schr\"{o}dinger equation show that the MI in this system has two extraordinary properties. First, MI exists in both cases of negative Kerr coefficient $(n_{2}<0)$ and positive Kerr coefficient $(n_{2}>0)$. Second, the maximum gain of MI is not affected by the intensity of the plane wave, and the wave number %spatial frequency of the maximum gain depends on the oscillation period of the response function. We also explore, for the first time to the best of our knowledge, the physical mechanism of MI in the framework of the four-wave mixing (FWM). %FWM interaction. By introducing a phase mismatch term $\triangle k$ and a (nonlinear) growth factor $\gamma$ (both of them have clear physical meanings), we find that the necessary and sufficient condition for the MI appearance is that the phase mismatching during the FWM process should be small enough such that $|\triangle k|<2|\gamma|$. Basing on the discover, we present a new scenario to uniformly and consistently explain why the MI can happen for the focusing local Kerr media and cannot for the defocusing local Kerr media, as well as the MI phenomena in the nonlocal cases.