The Yamada model for a self-pulsing laser: bifurcation structure for non-identical decay times of gain and absorber

TL;DR

This paper analyzes the bifurcation structure of a self-pulsing laser model with different gain and absorber decay times, revealing ten distinct bifurcation scenarios and detailed phase space organization.

Contribution

It provides a comprehensive bifurcation analysis of the Yamada laser model with non-identical decay times, highlighting ten qualitatively different bifurcation diagrams and phase space structures.

Findings

Ten distinct bifurcation diagram cases identified

Detailed phase space organization for each case

Insights into multi-stability and excitability in lasers

Abstract

We consider self-pulsing in lasers with a gain section and an absorber section via a mechanism known as Q-switching, as described mathematically by the Yamada ordinary differential equation model for the gain, the absorber and the laser intensity. More specifically, we are interested in the case that gain and absorber decay on different time scales. We present the overall bifurcation structure by showing how the two-parameter bifurcation diagram in the plane of pump strength versus decay rate of the gain changes with the ratio between the two decay rates. In total, there are ten cases BI to BX of qualitatively different two-parameter bifurcation diagrams, which we present with an explanation of the transitions between them. Moroever, we show for each of the associated eleven cases of structurally stable phase portraits (in open regions of the parameter space) a three-dimensional representation of the organisation of phase space by the two-dimensional manifolds of saddle equilibria and saddle periodic orbits. The overall bifurcation structure constitutes a comprehensive picture of the exact nature of the observable dynamics, including multi-stability and excitability, which we expect to be of relevance for experimental work on Q-switching lasers with different kinds of saturable absorbers.