Minimal universal model for chaos in laser with feedback

TL;DR

This paper introduces a minimal three-variable nonlinear model for laser feedback systems that captures chaos through specific nonlinearities, with analytical and experimental validation across different time scales.

Contribution

It presents a simplified yet comprehensive model of laser chaos emphasizing the essential nonlinearities and demonstrates its validity through analytical and electronic experiments.

Findings

The model exhibits chaos via homoclinic bifurcations.

Analytical proof of chaos-inducing nonlinearities.

Experimental electronic implementation confirms model predictions.

Abstract

We revisit the model of the laser with feedback and the minimal nonlinearity leading to chaos. Although the model has its origin in laser physics, with peculiarities related to the CO2 laser, it belongs to the class of the three dimensional paradigmatic nonlinear oscillator models giving chaos. The proposed model contains three key nonlinearities, two of which are of the type xy, where x and y are the fast and slow variables. The third one is of the type xz^2, where z is an intermediate feedback variable. We analytically demonstrate that it is essential for producing chaos via local or global homoclinic bifurcations. Its electronic implementation in the range of kilo Hertz region confirms its potential in describing phenomena evolving on different time scales.