Abstract
In this paper, we study Modulation Instability (MI) and its correlated gain spectrum with Parity-Time ([Formula: see text])-symmetry. The cubic-quintic nonlinearities in the Bragg grating structure produce ultrashort pulses. The MI evaluation started with a linear stability approach, and we investigated the effects of various system functions regarding the instability gain spectra at the top and bottom sides of the Photonic BandGap (PBG), in addition to the anomalous and normal dispersion domains. The interaction of cubic and quintic (focusing and de-focusing) nonlinearity is highlighted, resulting in a new type of MI band. Due to the consequences of quintic nonlinearity, an additional MI band appears for the three dynamics associated with the gain/loss function for the edges of the bottom PBG. After enforcing the [Formula: see text]-symmetry for the anomalous dispersion system, the dent transformed into a split under the influence of the power in the de-focusing quintic effect. Overall, MI gain and bandwidths across the entire MI gain spectrum are usually increasing. As an outcome, we are confident that these studies will aid in the generation of gap solitons in [Formula: see text]-symmetry regimes.
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