Influence of time-delayed feedback on the dynamics of temporal localized structures in passively mode-locked semiconductor lasers

TL;DR

This study investigates how time-delayed optical feedback influences the behavior and stability of temporal localized structures in passively mode-locked semiconductor lasers, revealing complex bifurcation phenomena and noise effects.

Contribution

It introduces a detailed analysis of feedback-induced dynamics in mode-locked lasers using delay differential equations, highlighting new bifurcation mechanisms and stability conditions.

Findings

Feedback creates pulse echos whose position and size depend on feedback parameters.

Long-cavity regime shows echos can replace main pulses, defining their lifetime.

Resonances increase stability of multi-pulse solutions and connect solution branches via period doubling bifurcations.

Abstract

In this paper, we analyze the effect of optical feedback on the dynamics of a passively mode-locked ring laser operating in the regime of temporal localized structures. This laser system is modeled by a system of delay differential equations, which include delay terms associated with the laser cavity and the feedback loop. Using a combination of direct numerical simulations and path-continuation techniques, we show that the feedback loop creates echos of the main pulse whose position and size strongly depend on the feedback parameters. We demonstrate that in the long-cavity regime, these echos can successively replace the main pulses, which defines their lifetime. This pulse instability mechanism originates from a global bifurcation of the saddle-node infinite-period type. In addition, we show that, under the influence of noise, the stable pulses exhibit forms of behavior characteristic of excitable systems. Furthermore, for the harmonic solutions consisting of multiple equispaced pulses per round-trip we show that if the location of the pulses coincide with the echo of another, the range of stability of these solutions is increased. Finally, it is shown that around these resonances, branches of different solutions are connected by period doubling bifurcations.