Phase-Incoherent Photonic Molecules in V-Shaped Mode-Locked Vertical-External-Cavity Surface-Emitting Semiconductor Lasers

Passively mode-locked vertical external-cavity surface-emitting semiconductor lasers (VECSELs) composed of a gain chip and a semiconductor saturable absorber have been drawing much attention due to their excellent performance figures. In this work we investigate how localized structures and incoherent, nonlocally bound, pulse molecules emerge in a long cavity VECSEL using a $\mathsf{V}$-shaped cavity geometry. We show that these states are bistable with the laser off state and that they are individually addressable. Using a model based upon delay differential equations, we demonstrate that pulse clusters result from the cavity geometry and from the nonlocal coupling with the gain medium; in the long cavity regime this leads to locally independent, yet globally bound, phase incoherent photonic molecules. Using a multiple timescale analysis, we derive an amplitude equation for the field that allows us to predict analytically the distance between the elements of a cluster.