Numerical Simulation of Ultra-Short Laser Pulses

This chapter contains the numerical models used to describe ultra-short pulse propagation while taking a brief look on their derivation from the Maxwell equations. The main models described here are the unidirectional pulse propagation equation (UPPE) and the modified Kadomtsev-Petviashvili equation (MKP), while a brief look is taken at the main envelope counterpart, the nonlinear envelope equation (NEE) model. The chapter concludes with the presentation of various applications of the UPPE and the MKP in the study of carrier wave shocks in various realistically model media, and a special case of the propagation properties of the two-dimensional XY Airy beam and its radial symmetric version, the ring-Airy beam, in the linear and nonlinear regimes.