Spatio-temporal extreme events in a laser with a saturable absorber

We study extreme events occurring in the transverse $(x,y)$ section of the field emitted by a broad-area semiconductor laser with a saturable absorber. The spatio-temporal events on which we perform the statistical analysis are identified as maxima of the field intensity in the 3D space $(x,y,t)$. We identify regions in the parameter space where extreme events are more likely to occur and we study the connection of those extreme events with the cavity solitons that are known to exist in the same system, both stationary and self-pulsing.