Spatiotemporal instabilities in [formula omitted]-symmetric periodic structures with non-Kerr fiber Bragg gratings

Abstract

The influence of cubic–quintic (CQ) nonlinearity on the modulation instability (MI) in fiber Bragg grating structures in the conventional and three PT-symmetry types such as unbroken, singularity and broken are investigated. The MI gain was obtained through standard linear stability analysis. The effect of cubic nonlinearity combined with focusing and defocusing quintic nonlinearity on MI for both anomalous and normal GVD regimes, as well as the top and bottom edges of the photonic bandgap. We find that the MI gain varies dramatically because of the consequences of cubic–quintic nonlinearity. Finally, we show that even in the presence of PT-symmetry, effective control of the MI can be brought to light by adjusting the spatial instability parameter, cubic nonlinearity, focusing and defocusing quintic nonlinearity. The investigation yields a variety of spectrum types, including symmetry, asymmetry, monotonically increasing gain, sideband spectrum, broad spectrum, and so on. For the few physical variables, we observe an unusual spectrum that is more discrete in nature rather than continuous. After introducing the PT-symmetry, the emergence of solitons as in nonlinear periodic structure is also explored.