Spatiotemporal instabilities in non-Kerr nonlinear complex parity-time symmetric structures

Spatiotemporal modulation instability (MI) in a fiber Bragg grating with cubic-quintic nonlinearities and parity-time symmetry is studied. A linear stability analysis is used to derive the dispersion relation equation of the spatiotemporal MI. In particular, we investigate the impact of quintic nonlinearity and gain/loss coefficient on the occurrence of the spatiotemporal MI. The investigations are performed both in normal and anomalous dispersion regime and on each regime defined by the parity-time (PT)-symmetry threshold, below threshold and above. In the anomalous dispersion regime, it is observed that temporal and spatial instabilities develop simultaneously at the top of photonic bandgap in favor of the gain/loss coefficient, both for the case of low and high values of the quintic nonlinearity. In the normal dispersion regime with low value of the quintic nonlinearity, it is found that below and at the PT-symmetry threshold, the maximum MI gain occurs for a zero value of the transverse perturbation, which means that the spatial instability dominates on the temporal ones. However, above the PT-symmetry, spatial and temporal instabilities can develop simultaneously. In the case where the value of the quintic nonlinearity is high, spatial and temporal instability can coexist in the three regime of the PT-symmetry.

Automated summary

The spatiotemporal modulation instability (MI) in a fiber Bragg grating with cubic-quintic nonlinearities and parity-time symmetry is investigated. The dispersion relation equation of the spatiotemporal MI is derived using a linear stability analysis. The impact of quintic nonlinearity and gain/loss coefficient on the occurrence of the spatiotemporal MI is studied in both normal and anomalous dispersion regimes.