Delayed feedback control of self-mobile cavity solitons

Abstract

Control of the motion of cavity solitons is one the central problems in nonlinear optical pattern formation. We report on the impact of the phase of the time-delayed optical feedback and carrier lifetime on the self-mobility of localized structures of light in broad-area semiconductor cavities. We show both analytically and numerically that the feedback phase strongly affects the drift instability threshold as well as the velocity of cavity soliton motion above this threshold. In addition we demonstrate that the noninstantaneous carrier response of the semiconductor medium is responsible for the increase of the critical feedback rate corresponding to the drift instability.

Bifurcation structure of cavity soliton dynamics in a vertical-cavity surface-emitting laser with a saturable absorber and time-delayed feedback

“…In addition, we assume that the laser operates in a single-longitudinal mode. The system of model equations reads [29][30][31]40]…”

“…Optical feedback impacts the VCSEL's modal properties and dynamics in quite the same way as those of traditional edge-emitting semiconductor lasers [34,35] with the additional peculiarity of introducing polarization switching and two-polarization mode dynamics [36][37][38]. Recently, first studies of CS behavior in optically injected broad-area VCSELs subjected to time-delayed optical feedback have appeared [29][30][31]39]. These studies elucidated the role of the strength and the phase of the time-delayed feedback for the creation of a drift bifurcation that causes the CSs to spontaneously move.…”

“…The impact of time-delayed feedback on CS dynamics has been theoretically investigated for the cases of a driven nonlinear optical resonator [27,28] and broad-area VCSELs [29][30][31]. Delayed optical feedback is known to strongly modify the dynamical behavior of semiconductor lasers leading to external cavity mode hopping, periodic or aperiodic dynamics and even coherence collapse [32,33].…”

Localized Structures in Broad Area VCSELs: Experiments and Delay-Induced Motion

“…At the pitchfork bifurcation the stationary LS loses stability and a branch of moving LSs with the velocity v = |v| bifurcates from the stationary LS branch of solutions. The bifurcation point can be obtained from the first order expansion of the uniformly moving LS in power series of the small velocity v. Close to the bifurcation point, the uniformly moving LS can be expanded in power series in the small velocity v and through the solvability condition, we obtain the drift instability threshold [98,99] …”

“…8 (1-dimensional setting, (Eq.5)) and 11(2-dimensional setting, Eqs (1) and (2)). Redrawn from [98].…”