The effect of the initial phase distortion of the laser on near-field transmission characteristics in free space is investigated both numerically and theoretically. It is demonstrated and proposed that the near-field modulation and fluence contrast of the output laser beam are changing with the increase of both spatial low- and high-frequency wavefront distortion. The simulation results show that in order to ensure the beam quality in propagation, the Fresnel number should be controlled not <50 generally and the wavefront distortion should also be minimized by controlling both low- and high-frequency phase coefficient not larger than 0.6.

Propagation of an intense laser pulse in plasma with a periodically modulated density is considered using envelope equations. The laser induces modifications of the plasma refractive index via relativistic and ponderomotive nonlinearities. In the region of high plasma density, the self focusing effect of nonlinearity suppresses the diffraction divergence, and the laser converges. As the beam enters into the low density region, the diffraction tends to diverge it offsetting the convergence due to the curvature it has acquired. For a given set of plasma parameters, there is a critical power of the laser above which it propagates in a periodically focused manner. Below this power the laser undergoes overall divergence. At substantially higher powers, the laser beam continues to converge until the saturation effect of nonlinearity suppresses the self focusing and diffraction predominates. The effect of density ripple is to cause overall increase in the self focusing length. The minimum spot size decreases with the wave number of the ripple.