Modifications to the lidar equation due to nonlinear propagation in air

We study how the well-known lidar equation is affected by the use of ultra-short, high-power laser pulses. Because of the self-focusing and self-guiding, the overlap function ξ, representing the reduction fraction of the signal resulting from geometrical effects inside the experimental system, needs to be reconsidered. The losses due to multi-photon ionisation in the filament entail a heavy weakening of the return signal. We also investigate the contribution of the white-light components generated by self-phase modulation. Received: 2 January 2001 / Revised version: 8 June 2001 / Published online: 18 July 2001