Modulation instability in nonlinear complex parity-time (PT) symmetric periodic structures

TL;DR

This paper analyzes modulation instability in nonlinear complex PT-symmetric periodic structures across different regimes, revealing conditions under which MI occurs or is suppressed, and suggesting the potential for soliton formation.

Contribution

It provides a comprehensive MI analysis in PT-symmetric structures, including the behavior at and beyond the PT-symmetry breaking point, which was not fully understood before.

Findings

MI exists beyond the PT-symmetry threshold, indicating possible soliton existence.

MI does not occur at the PT-symmetry breaking point in normal dispersion below a nonlinear threshold.

In anomalous dispersion, MI persists even at the PT-symmetry breaking point.

Abstract

We carry out a modulation instability (MI) analysis in nonlinear complex parity-time (PT) symmetric periodic structures. All the three regimes defined by the PT-symmetry breaking point or threshold, namely, below threshold, at threshold and above threshold are discussed. It is found that MI exists even beyond the PT-symmetry threshold indicating the possible existence of solitons or solitary waves, in conformity with some recent reports. We find that MI does not exist at the PT-symmetry breaking point in the case of normal dispersion below a certain nonlinear threshold. However, in the case of anomalous dispersion regime, MI does exist even at the PT-symmetry breaking point.