Filamentation of a laser beam interacting with an underdense plasma and its coupling to stimulated Brillouin scattering

The nonlinear behavior of a single laser beam with power above critical is investigated in three spatial dimensions without the paraxial approximation. In the case where stimulated Brillouin scattering (SBS) is suppressed by strong damping, it is found numerically that the hot spot contracts spatially in all directions, leading to transverse dimensions smaller than the laser wavelength, even when the ion response is nonlinearly saturated. This contraction leads to the three dimensional collapse of the transverse wave in the absence of nonlinear saturation of the ion response. When the saturation of the ion response is properly retained, a narrow filament forms initially, This filament then appears to be unstable and exhibits violent modulations of the laser wave intensity along the direction of its propagation, leading to a complicated dynamical behavior. In the case of moderate SBS damping, one still observes the initial spatial contraction in all directions and the formation of a narrow channel. SBS then occurs in violent bursts, and does not stop the complex dynamical behavior of the filament.