  Statistics and dynamics of 2D rogue waves in a broad-area semiconductor laser
with an intracavity saturable absorber are numerically investigated under the
effect of transverse carrier diffusion. We show that lateral diffusion of
carriers alters the statistics of rogue waves by enhancing their formation in
smaller ratios of carrier lifetimes in the active and passive materials while
suppressing them when the ratio is larger. Temporal dynamics of the emitted
rogue waves is also studied and shown that finite nonzero transverse carrier
diffusion coefficient gives them a longer duration. To further approach the
realistic experimental situation, we also investigated statistics and dynamics
of rogue waves by simulating a circular disk-shape pump which replaces the flat
pump profile typically used in numerical simulations of broad-area lasers. We
show that finite pump shape reduces the number emitted rogue waves per unit
area for large carrier lifetime ratios and increases that for smaller values of
the ratio in both below and above laser threshold. Temporal width of the
emitted rogue waves is also shown to reduce as a consequence of removing the
nonphysical effects of infinite flat pump on carrier dynamics.
