Multifaceted dynamics and gap solitons in $\mathcal{PT}$-symmetric periodic structures

Abstract: We report the role of $\mathcal{PT}$-symmetry in switching characteristics of a highly nonlinear fiber Bragg grating (FBG) with cubic-quintic-septic nonlinearities. We demonstrate that the device shows novel bi-(multi-) stable states in the broken regime as a direct consequence of the shift in the photonic band gap influenced by both $\mathcal{PT}$-symmetry and higher-order nonlinearities. We also numerically depict that such FBGs provide a productive test bed where the broken $\mathcal{PT}$-symmetric regime can be exploited to set up all-optical applications such as binary switches, multi-level signal processing and optical computing. Unlike optical bistability (OB) in the traditional and unbroken $\mathcal{PT}$-symmetric FBG, it exhibits many peculiar features such as flat-top stable states and ramp like input-output characteristics before the onset of OB phenomenon in the broken regime. The gain/loss parameter plays a dual role in controlling the switching intensities between the stable states which is facilitated by reversing the direction of light incidence. We also find that the gain/loss parameter tailors the formation of gap solitons pertaining to transmission resonances which clearly indicates that it can be employed to set up optical storage devices. Moreover, the interplay between gain/loss and higher order nonlinearities brings notable changes in the nonlinear reflection spectra of the system under constant pump powers. The influence of each control parameters on the switching operation is also presented in a nutshell to validate that FBG offers more degrees of freedom in controlling light with light.