Unique multistable states in periodic structures with saturable nonlinearity. I. Conventional case and unbroken $\mathcal{PT}$-symmetric regime

TL;DR

This paper predicts novel ramp-like optical bistability and multistability in periodic structures with saturable nonlinearity, highlighting conditions for hysteresis revival and nonreciprocal switching influenced by system parameters.

Contribution

It introduces the existence of ramp-like OB and OM curves in saturable nonlinear periodic structures and explores conditions for hysteresis and nonreciprocal switching.

Findings

Ramp-like OB and OM curves are observed without gain and loss.

Increasing nonlinearity or gain-loss parameters affects switching intensities.

Detuning and system parameters influence the type and stability of multistable states.

Abstract

In this work, we predict that periodic structures without gain and loss do not exhibit an S-shaped hysteresis curve in the presence of saturable nonlinearity (SNL). Instead, the input-output characteristics of the system admit ramp-like optical bistability (OB) and multistability (OM) curves that are unprecedented in the context of conventional periodic structures in the literature. An increase in the nonlinearity (NL) or the gain-loss parameter increases the switch-up and down intensities of different stable branches in a ramp-like OM curve. Revival of the typical S-shaped hysteresis curve requires the device to work under the combined influence of frequency detuning and $\mathcal{PT}$-symmetry. An increase in the detuning, NL and gain-loss parameters reduces the switching intensities of the S-shaped OB (OM) curves. During the process, mixed OM curves that feature a fusion between ramp-like and S-shaped OM curves emanate at low values of the detuning parameter in the input-output characteristics. The detuning parameter values for which ramp-like, S-shaped, and mixed OM appear varies with the NL coefficient. For a given range of input intensities, the number of stable states admitted by the system increases with the device length or NL. When the laser light enters the device from the opposite end of the grating, nonreciprocal switching occurs at ultra-low intensities via an interplay between NL, detuning, and gain-loss parameters.