Delayed feedback control of self-mobile cavity solitons in a wide-aperture laser with a saturable absorber

Abstract

We investigate the spatiotemporal dynamics of cavity solitons in a broad area vertical-cavity surface-emitting laser with saturable absorption subjected to time-delayed optical feedback. Using a combination of analytical, numerical, and path continuation methods, we analyze the bifurcation structure of stationary and moving cavity solitons and identify two different types of traveling localized solutions, corresponding to slow and fast motion. We show that the delay impacts both stationary and moving solutions either causing drifting and wiggling dynamics of initially stationary cavity solitons or leading to stabilization of intrinsically moving solutions. Finally, we demonstrate that the fast cavity solitons can be associated with a lateral mode-locking regime in a broad-area laser with a single longitudinal mode.

Stationary localized structures and the effect of the delayed feedback in the Brusselator model

“…The delayed feedback may also induce a drift bifurcation of the localized structure in the Brusselator model, similar to that reported in the case of Swift-Hohenberg [48], equations and the semiconductor laser model [49,[60][61][62]. Such a feedback-induced drift of a localized structure is illustrated in the one-dimensional case in figure 8a for the case of The localized structure is launched at t = 0 and starts moving after a certain timespan, which decreases as the feedback strength is increased (see also [49]).…”

“…Furthermore, it was shown that delayed feedback can induce motion and breathing localized structures in chemical reaction-diffusion systems [52,59]. In advanced photonic devices, the effect of the phase on the self-mobility of dissipative localized structures has been theoretically investigated in [60][61][62]. In driven Kerr cavities described by the Lugiato-Lefever equation, timedelayed feedback induces a drift of localized structures, and the route to spatiotemporal chaos has been discussed in [ Recently, time-delayed feedback control has attracted a lot of interest in various fields of nonlinear science such as nonlinear optics, fibre optics, biology, ecology, fluid mechanics, granular matter, plant ecology (see recent overview [67]), and the excellent book by Erneux [54].…”

Delayed feedback control of active particles: a controlled journey towards the destination

“…It should be noted that, due to the usage of the position at an earlier time, our control method falls into the class of delayed feedback control strategies, which are well established in the area of chaos control [26,27], e.g. in laser systems [28,29] and in chemical reaction networks [30][31][32]. On a theoretical level, time delay considerably complicates the mathematical treatment since the underlying stochastic equations become non-Markovian in character.…”