# Bifurcation structure of cavity soliton dynamics in a VCSEL with saturable absorber and time-delayed feedback

## TL;DR

This paper analyzes how time-delayed feedback influences the bifurcation structure and complex dynamics of cavity solitons in a VCSEL with a saturable absorber, revealing routes to chaos and multistability.

## Contribution

It provides a detailed bifurcation analysis of cavity soliton dynamics in a VCSEL with saturable absorber under time-delayed feedback, highlighting complex behaviors.

## Key findings

- Time-delayed feedback induces complex spatiotemporal dynamics.
- Identification of bifurcations leading to chaos and multistability.
- Mapping of bifurcation scenarios in feedback parameter space.

## Abstract

We consider a wide-aperture surface-emitting laser with a saturable absorber section subjected to time-delayed feedback. We adopt the mean-field approach assuming a single longitudinal mode operation of the solitary VCSEL. We investigate cavity soliton dynamics under the effect of time- delayed feedback in a self-imaging configuration where diffraction in the external cavity is negligible. Using bifurcation analysis, direct numerical simulations and numerical path continuation methods, we identify the possible bifurcations and map them in a plane of feedback parameters. We show that for both the homogeneous and localized stationary lasing solutions in one spatial dimension the time-delayed feedback induces complex spatiotemporal dynamics, in particular a period doubling route to chaos, quasiperiodic oscillations and multistability of the stationary solutions.