Time-Localized Fourier Patterns

Spatial and temporal localized structures in optical cavities, also called Dissipative Solitons, have attracted a great deal of attention in the last two decades [1] , [2] . Beyond their fundamental interest, these structures can be used to code and process information bits in optical resonators. In general, two conditions appear to be necessary for a system to exhibit LSs: i) to have a large aspect-ratio and ii) to feature a multistable response. We have recently shown that an optically pumped passively mode-locked Vertical External Cavity Surface Emitting Laser (VECSEL) can be operated in a regime where mode-locked pulses becomes localized, i.e. they are individually addressable [3] , [4] . This regime requires long external cavity, i.e. cavity roundtrip time be significantly larger than gain recovery time, τ c >> τ g . Both the gain section and the saturable absorber mirrors needs to be properly engineered to provide multistability between different PML solutions with different number of pulses per roundtrip. Moreover, VECSEL geometry is very interesting because the external cavity can be designed in a self-imaging configuration which allow for reaching high-Fresnel number, hence paving the way also to spatial LSs [5] .