Influence of random initial amplitude perturbations on the lilamentation ot prefocused femtosecond laser pulses is numerically studied. Simulations are performed for the filamentation of laser pulses with different modulation degrees and initial geometric focusings. The transverse waist of the laser beam is 5 mm. The behavior of the filament is strongly affected by the initial non-uniformity of the laser pulse envelope for a short initial focal length （f = 1 m）. In this case, the filament and plasma channel can survive for a longer distance with a small initial amplitude perturbation. For a laser pulse focused by a lens with a long focal length （f = 4 m）, decrease in the initial perturbation does not contribute to the length of the filament and the plasma channel.
Two interacting light filaments with different initial phases propagating in air are investigated numerically by using a ray tracing method. The evolution of the rays of a filament is governed by a potential field. During propagation, the two potential wells of the two filaments can merge into one or repel each other, depending on the initial phase difference between the two filaments. The study provides a simple description of the interacting filaments.
The propagation of picosecond deep ultraviolet laser pulse at wavelength of 193 nm in air is numerically investigated. Long plasma channel can be formed due to the competition between Kerr self-focusing and ionization induced defocusing. The plasma channel with electron density of above 10^13/cm^3 can be formed over 70 m by 50-ps, 20-mJ laser pulses. The fluctuation of laser intensity and electron density inside ultraviolet （UV） plasma channel is significantly lower UV laser by air is considered in the simulation and it the limit of the length of plasma channel. than that of infrared pulse. The linear absorption of is shown that the linear absorption is important for the limit of the length of plasma channel.
