Modulational instability in $\mathcal{PT}$-symmetric Bragg grating structures with four-wave mixing

TL;DR

This paper explores how $ ext{PT}$-symmetric fiber Bragg gratings with four-wave mixing exhibit unique modulational instability patterns and dispersion features, revealing new phenomena due to gain-loss interplay.

Contribution

It introduces the analysis of modulational instability in $ ext{PT}$-symmetric gratings with four-wave mixing, uncovering novel dispersion structures and MI behaviors not seen in conventional systems.

Findings

Unusual double-loop dispersion structure in $ ext{PT}$-symmetric gratings.

Unique tilted two-conical MI pattern observed.

Impact of system parameters on MI in normal and anomalous regimes.

Abstract

We investigate the dynamics of modulational instability (MI) in $\cal PT$-symmetric fiber Bragg gratings with a phenomenon of intermodulation known as four-wave mixing (FWM). Although the impact of FWM has already been analyzed in the conventional systems, the inclusion of gain and loss, which induces the notion of $\cal PT$- symmetry, gives rise to many noteworthy outcomes. These include the manifestation of an unusual double-loop structure in the dispersion curve, which was unprecedented in the context of conventional periodic structures. When it comes to the study of MI, which is usually obtained in the system by imposing a small amount of perturbations on the continuous wave by executing linear stability analysis, different regimes which range from conventional to broken $\cal PT$- symmetry tend to create quite a few types of MI spectra. Among them, we observe a unique MI pattern that mimics a tilted two-conical structure facing opposite to each other. In addition, we also address the impact of other non-trivial system parameters, such as input power, gain and loss and self-phase modulation in two important broad domains, including normal and anomalous dispersion regimes under the three types of $\cal PT$- symmetric conditions in detail.