Perturbative Dynamics of Stationary States in Nonlinear Parity-Time Symmetric Coupler

TL;DR

This paper explores the nonlinear dynamics of PT-symmetric optical couplers, revealing phase transitions, stability changes, and chaotic behavior influenced by gain/loss parameters, with implications for controlling optical power evolution.

Contribution

It provides a detailed dynamical analysis of nonlinear PT-symmetric couplers, highlighting stability phase transitions and chaotic attractors not previously characterized.

Findings

Stability of the ground state changes at the PT threshold.

Instabilities can cause aperiodic oscillations and exponential growth/decay.

Chaotic attractors can be controlled through waveguide parameters.

Abstract

We investigate the nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. As opposed to linear PT-coupler where the PT threshold dictates the evolutionary characteristics of optical power in the two waveguides, in a nonlinear coupler, the PT threshold governs the existence of stationary points. We have found that the stability of the ground state undergoes a phase transition when the gain/loss coefficient is increased from zero to beyond the PT threshold. Moreover, we found that instabilities in initial conditions can lead to aperiodic oscillations as well as exponential growth and decay of optical power. At the PT threshold, we observed the existence of a stable attractor under the influence of fluctuating gain/loss coefficient. Phase plane analysis has shown us the presence of a toroidal chaotic attractor. The chaotic dynamics can be controlled by a judicious choice of the waveguide parameters.