Drifting instabilities of cavity solitons in vertical-cavity surface-emitting lasers with frequency-selective feedback

Paulau, P.V.; Gomila, D.; Colet, P.; Matías, M.A.; Loiko, N.A.; Firth, W.J.
Physical Review A 80, 023808 (1-8) (2009)

vertical-cavity surface-emitting lasers (VCSELs)subjected to external frequency-selective feedback and build their bifurcation diagram for the case where carrier dynamics is eliminated. For low pump currents, we find
that they emerge from the modulational instability point of the trivial solution, where traveling waves with a critical wave number are formed. For large currents, the branch of self-propelled solitons merges with the branch of resting solitons via a pitchfork bifurcation. We also show that a feedback phase variation of $\\\\\\\\pm 2\\\\\\\\pi$ can transform a CS (whether resting or moving) into a different one associated to an adjacent longitudinal external cavity mode. Finally, we investigate the influence of the carrier dynamics, relevant for VCSELs. We find and analyze qualitative changes in the stability properties of resting CSs when increasing the carrier relaxation
time. In addition to a drifting instability of resting CSs, a distinctive kind of instability appears for certain ranges of carrier lifetime, leading to a swinging motion of the CS center position. Furthermore, for carrier relaxation times typical of VCSELs the system can display multistability of CSs.

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