Accurate description of ultra-short tightly focused Gaussian laser pulses and vacuum laser acceleration

Abstract

High-order correction terms to the expression of the field of ultra-short tightly focused Gaussian laser pulses are derived. Terms up to seventh order in the small dimensionless spatial parameter s=1/(k0w00) and first order in the small dimensionless temporal parameter e=1/(ω0t0) are explicitly presented (ω0=ck0 the central oscillatory frequency, 2t0 the pulse duration, w00 the beam waist radius at the central frequency ω0). To evaluate the correction efficacy, both the corrected and the paraxial field equations are used in detailed simulation studies of laser/electron interaction dynamics. Special attention is given to the vacuum laser acceleration scheme. The influence on the electron dynamics due to the diffraction edge field of a tightly focused laser beam is also investigated.