Title: Unique multistable states in periodic structures with saturable nonlinearity. II. Broken $\mathcal{PT}$-symmetric regime

Abstract: In this work, we observe that the $\mathcal{PT}$-symmetric fiber Bragg gratings (PTFBGs) with saturable nonlinearity (SNL) exhibit ramp-like, mixed, optical multistability (OM) in the broken regime. The interplay between nonlinearity and detuning parameter plays a central role in transforming the characteristics of the hysteresis curves and facilitates the realization of different OM curves. Also, it plays a crucial role in reducing the switch-up and down intensities of various stable branches of an OM curve. In a mixed OM curve, either the ramp-like hysteresis curves or S-like hysteresis curves can appear predominantly depending on the magnitude of the detuning parameter. An increase in the device length or nonlinearity increases the number of stable states for fixed values of input intensity. Under a reversal in the direction of light incidence, the ramp-like OM and mixed OM curves assume an unusual vortex-like envelope at lower intensities. Numerical simulations reveal that the switch-up and down intensities of different stable branches of a ramp-like OM and mixed OM curves drift towards the higher and lower intensity sides, respectively (opposite direction). The drift is severe to the extent that an intermediate hysteresis curve features switch-down action at near-zero switching intensities. Also, the input intensities required to realize ramp-like, and mixed OM curves reduce dramatically under a reversal in the direction of light incidence.