Nonlinear Dynamics in Semiconductor Lasers - Abstract
We analyze the impact of time-delayed optical feedback (OF) on the spatiotemporal dynamics of the Lugiato-Lefever and cavity-soliton laser models. First, we carry out linear stability analysis and reveal the role of the OF strength and phase on the shape of the bistable curve as well as on Turing, Andronov-Hopf, and traveling-wave instability regions. Further, we demonstrate how the OF impacts the spatial dynamics by shifting the regions with different spatial eigenvalue spectra. In addition, we reveal a clustering behaviour of cavity solitons as a function of the OF strength at a fixed OF phase. Depending on the feedback parameters, OF can also induce a drift bifurcation of a stationary cavity soliton, as well as an Andronov-Hopf bifurcation of a drifting soliton. We present an analytical expression for the threshold of the drift bifurcation and show that above a certain value of the OF strength the system enters a region of spatiotemporal chaos. For the case of vertical-cavity surface-emitting laser with saturable absorption (cavity-soliton model) we show that the inclusion of OF leads to a period doubling route to chaos of spatially localized light structures. Finally, in both systems the delayed feedback can induce a spontaneous formation of rogue waves while the stationary spatial pulses are stationary in absence of feedback. The rogue waves are exited and controlled by the delay feedback. We characterize their formation by computing the probability distribution of the pulse height. The long-tailed statistical contribution which is often considered as a signature of the presence of rogue waves appears for sufficiently strong feedback.