Propagation and cross-focusing of hollow Gaussian laser beams in plasma

This paper presents the cross focusing of two high power Hollow Gaussian laser beams (HGLB) by considering ponderomotive nonlinearity in a collisionless plasma. On account of the nonlinearity present in the plasma the two laser beams affect the dynamics of each other and cross-focusing takes place. The expressions for the laser beam intensities by using the eikonal method have been derived and the beam width parameter is calculated in the case when only ponderomotive nonlinearity is operative. The numerical appreciation of the cross focusing has been presented graphically by plotting beam-width parameter vs. dimensionless distance of propagation. Theself focusing of one laser beam is affected due to the optical inhomogeneities introduced by another copropagatingHGLBin the plasma. It is observed thatthe presence of one HGLBalso affects the self focusing of different order's (n) of the other HGLB.