Chaotic Dynamics and Optical Power Saturation in Parity-Time (PT) Symmetric Double Ring Resonator

TL;DR

This paper investigates the complex dynamics of a parity-time symmetric double ring resonator, revealing power saturation, chaos, and divergence phenomena influenced by nonlinearity and PT symmetry properties.

Contribution

It introduces a discrete-time Ikeda Map model for the system and uncovers new chaotic and saturation behaviors related to PT symmetry and Kerr nonlinearity.

Findings

Power saturation occurs below PT threshold due to stable states.

Chaotic spiking emerges with Kerr nonlinearity.

Largest Lyapunov exponent indicates chaos and divergence.

Abstract

We report emergence of saturation and chaotic spiking of optical power in a double ring resonator with balanced loss and gain, obeying the so-called parity-time symmetry. We have modeled the system using a discrete-time iterative equation known as the Ikeda Map. In the linear regime, evolution of optical power in the system shows power saturation behavior below the PT threshold and exponential blow-up above the PT threshold. We found that in the unbroken PT regime, optical power saturation occurs owing to the existence of stable stationary states, which lies on the surface of 4-dimensional hypersphere. Inclusion of Kerr nonlinearity into our model leads to the emergence of a stable, chaotic and divergent region in the parameter basin for period-1 cycle. A closer inspection into the system shows us that the largest Lyapunov exponent blows up in the divergent region. It is found that the existence of high non-negative largest Lyapunov exponent causes chaotic spiking of optical power in the resonators.