The nonlinear propagation over long distances of moderate intensity laser pulses in tenuous gases is studied. The dynamics of these pulses will be affected by nonlinear focusing and dispersion due to the background gas, and by plasma induced refraction and dispersion. Laser propagation is studied numerically using the simulation code WAKE. Different phenomena are found for different regimes of peak input power. For powers near the critical power, temporal pulse narrowing and splitting due to phase modulation and group velocity dispersion is seen. For slightly higher powers, plasma generation and the formation of a trailing pulse, which is guided off axis by plasma refraction and nonlinear gas focusing, is observed. For even higher powers, the laser pulse is partially trapped by the plasma and then exhibits a form of self-interference.

The processes affecting the spectrum of the pulse is also studied. Among these are self-phase modulation, nonlinear self-focusing, plasma generation, and group velocity dispersion. The combination of these factors leads to an asymmetric spectrum. If group velocity dispersion cannot arrest nonlinear self-focusing, self-phase modulation, coupled with nonlinear self-focusing, gives rise to a red shifted spectrum. In case plasma is generated, large blue shifted components are observed. The maximum blue shift is determined by both the maximum value of the electron density, and the distance over which the plasma extends.

Finally, the injection of laser pulses into hydrodynamically preformed plasma channels is investigated. The injection of laser pulses into hydrodynamically preformed plasma channels can be hindered by the conditions at the entrance of the channel. In particular, neutral gas and narrowing of the channel prevent efficient coupling of laser pulse entering into the channel. To solve this problem, a funnel shaped plasma lens can be grafted onto the channel using an auxiliary formation pulse. Simulations of channel formation show that such a funnel can be made in the density ramp of a gas jet. Simulations of laser pulse propagation show that such a funnel efficiently couples pulse energy into the channel. For a backfill target with a funnel, the coupling efficiency is lower and required funnel parameters are more restrictive than for the gas jet case.