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

Abstract

We consider a wide-aperture surface-emitting laser with a saturable absorber section subjected to time-delayed feedback. We adopt the mean-field approach assuming a single longitudinal mode operation of the solitary VCSEL. We investigate cavity soliton dynamics under the effect of timedelayed feedback in a self-imaging configuration where diffraction in the external cavity is negligible. Using bifurcation analysis, direct numerical simulations and numerical path continuation methods, we identify the possible bifurcations and map them in a plane of feedback parameters. We show that for both the homogeneous and localized stationary lasing solutions in one spatial dimension the time-delayed feedback induces complex spatiotemporal dynamics, in particular a period doubling route to chaos, quasiperiodic oscillations and multistability of the stationary solutions.

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].…”

Localized chaos of elliptically polarized cavity solitons in broad-area VCSEL with a saturable absorber

“…In this Letter, we introduce a spin-flip model for a broad-area VCSEL with a saturable absorber and demon- * Electronic address: kpanajot@b-phot.org strate a period doubling route to spatially localized chaos of elliptically polarized CSs. CS, which become chaotic by period doubling have been predicted for a driven damped nonlinear Shrödinger equation [34,35], for a Josephson junction ladder, for forced and damped van der Pol model [36] and for semiconductor laser with saturable absorber subject to optical feedback [37,38]. Oscillatory dynamics of localized structures has been experimentally observed in optically pumped VCSEL with saturable absorber [39].…”