Modulational instability in PT-symmetric Bragg grating structures with saturable nonlinearity

We investigate the nontrivial characteristics of modulational instability (MI) in a system of Bragg gratings with saturable nonlinearity. We also introduce an equal amount of gain and loss into the existing system, which gives rise to an additional degree of freedom, due to the concept of PT symmetry. We obtain the nonlinear dispersion relation of the saturable model and discover that such dispersion relations for both the conventional and PT-symmetric cases contradict the conventional Kerr and saturable systems by not displaying the typical signature of loop formation in either the upper branch or lower branch of the curve drawn against the wave number and detuning parameter. We employ a standard linear stability analysis to study the MI dynamics of the continuous waves perturbed by an infinitesimal perturbation. The main objective of this paper is twofold: We investigate the dynamics of the MI gain spectrum at the top and bottom of the photonic band gap followed by a comprehensive analysis carried out in the anomalous and normal dispersion regimes. As a result, this perturbed system driven by the saturable nonlinearity and gain or loss yields a variety of instability spectra, which include the conventional sidebands, monotonically increasing gain, the emergence of a single spectrum in either of the Stokes wave-number regions, and so on. In particular, we observe a remarkably peculiar spectrum, which is caused predominantly by the system parameter, though the perturbation wave number boosts the former. We also address the impact of all the physical parameters considered in the proposed model, which include the coupling coefficient, dispersion parameter, and saturable nonlinearity on the phenomenon of MI for different PT-symmetric regimes ranging from the unbroken one to the broken one in greater detail.

Automated summary

In this article, we investigate the nontrivial characteristics of modulational instability in a system of Bragg gratings with saturable nonlinearity. By introducing an equal amount of gain and loss, we explore the additional degree of freedom due to the concept of PT symmetry. Our findings reveal that the dispersion relations for both the conventional and PT-symmetric cases contradict the typical signature of loop formation displayed by conventional Kerr and saturable systems. Through comprehensive analyses, we observe a variety of instability spectra and address the impact of physical parameters on the phenomenon of modulational instability in different PT-symmetric regimes.