Influence of Time-Delayed Feedback on the Dynamics of Temporal Localized Structures in Passively Mode-Locked Semiconductor Lasers

We analyze both theoretically and experimentally the impact of optical feedback on the dynamics of external-cavity mode-locked semiconductor lasers (VECSELs) operated in the long cavity regime [1]. In particular, by choosing certain ratios between the cavity round-trip time and the feedback delay, we show that feedback acts as a solution discriminator that either reinforces or hinders the appearance of one of the multiple harmonic arrangements of temporal localized structures. For the theoretical modeling, the delayed differential equation model [2] is extended by a term describing the optical feedback. Denoting by A the amplitude of the optical field,
$G$
the gain, and
$Q$
the saturable losses, the model reads