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We analyze the emergence of wiggling temporal localized states in a passivelymode-locked Vertical External- Cavity Surface-Emitting Laser composed by a gainchip and a resonant saturable absorber mirror. We show that the wigglinginstability stems from the interplay between the third-order dispersion inducedby the micro-cavities and their frequency mismatch. The latter is identified asan experimentally crucial parameter defining the range of existence of stableemission. We reveal the homoclinic scenario underlying the wiggling phenomenonand we show how it allows to control the oscillation.

Wiggling Instabilities of Temporal Localized States in Passively Mode-Locked Vertical External-Cavity Surface-Emitting Lasers