Lyapunov Potential Description for Laser Dynamics

TL;DR

This paper introduces a Lyapunov potential framework to analyze the dynamics of class A and class B lasers, providing new insights into their deterministic and stochastic behaviors, relaxation oscillations, and the effects of gain saturation.

Contribution

It develops a Lyapunov potential approach for laser dynamics, including stochastic effects for class A lasers and a new expression relating relaxation oscillation periods to the potential for class B lasers.

Findings

Phase of electric field drifts in stochastic class A lasers.

Derived a relation between relaxation oscillation period and potential.

Semi-empirical formula for oscillation period far from steady state.

Abstract

We describe the dynamical behavior of both class A and class B lasers in terms of a Lyapunov potential. For class A lasers we use the potential to analyze both deterministic and stochastic dynamics. In the stochastic case it is found that the phase of the electric field drifts with time in the steady state. For class B lasers, the potential obtained is valid in the absence of noise. In this case, a general expression relating the period of the relaxation oscillations to the potential is found. We have included in this expression the terms corresponding to the gain saturation and the mean value of the spontaneously emitted power, which were not considered previously. The validity of this expression is also discussed and a semi-empirical relation giving the period of the relaxation oscillations far from the stationary state is proposed and checked against numerical simulations.