Field description and electron acceleration of focused flattened Gaussian laser beams

By using the superposition of N suitably weighted Laguerre-Gaussian beams, the analytical expressions of all six electromagnetic field components of focused Flattened Gaussian Beams (FGBs) are obtained in the Lorentz gauge. The phase velocity distributions of the field near the focus of FGBs propagating in vacuum are investigated. There exists a subluminous wave phase velocity region surrounding the laser beam axis. We further apply this focused FGB to vacuum laser acceleration. As with the focused Standard Gaussian Beam (SGB), electrons injected into the focused FGB can be captured in the acceleration phase and then violently accelerated.