Modulational instability in PT-symmetric Bragg grating structures with four-wave mixing

Abstract

We explore the dynamics of modulational instability (MI) in $\mathrm{PT}$-symmetric fiber Bragg gratings, focusing on the intermodulation phenomenon known as four-wave mixing (FWM). While the role of FWM has been already studied in conventional systems, introducing equal amount of gain and loss, which are the key elements of $\mathrm{PT}$-symmetric notion, leads to intriguing new outcomes. Notably, it results in an unprecedented double-loop structure in the dispersion curve, a feature which is not observed in any conventional periodic Bragg system. In our investigation of MI which is achieved by applying small perturbations to the continuous wave and performing a linear stability analysis, we identify many peculiar MI spectra in a range of regimes spanning conventional to broken $\mathrm{PT}$-symmetry. Among these, we uncover a remarkable MI pattern resembling two oppositely tilted conical structures. Furthermore, we examine the influence of key system parameters such as pump power, gain and loss, and self-phase modulation across two critical domains including normal and anomalous dispersion regimes. Particularly, we find that the impact of pump power enhances the MI spectra in all the regimes irrespective of the stand-alone effect of system parameters.