Three-dimensional relativistic electron scattering in an ultrahigh-intensity laser focus

The relativistic dynamics of an electron submitted to the three-dimensional field of a focused ultrahigh-intensity laser pulse are studied numerically. The diffracting field in vacuum is modeled by the paraxial propagator and exactly satisfies the Lorentz gauge condition everywhere.:In rectangular coordinates, the electromagnetic field is Fourier transformed into transverse and longitudinal wave packets, and diffraction is described through the different phase shifts accumulated by the various Fourier components, as constrained by the dispersion relation. In cylindrical geometry, the radial dependence of the focusing wave is described as a continuous spectrum of Bessel functions and can be obtained by using Hankel's integral theorem. To define the boundary conditions for this problem, the beam profile is matched to a Gaussian-Hermite distribution at focus, where the wave front is planar. Plane-wave dynamics are verified for large f numbers, including canonical momentum invariance, while high-energy scattering is predicted for smaller values of f at relativistic laser intensities. [S1063-651X(98)08210-5].