Cross-focusing of two laser beams in a plasma

Cross-focusing of two copropagating laser beams in a plasma is investigated using paraxial ray theory. If the lasers have a frequency difference equal to the electron plasma frequency, they can drive a large amplitude plasma wave. The ponderomotive force due to the plasma wave forces the plasma electrons outwards thereby generating a parabolic density profile giving rise to cross-focusing. The results show a decrease in threshold for focusing by two orders of magnitude as compared to focusing due to the ponderomotive force of the laser beams.