Electron Acceleration by a Focused Gaussian Laser Pulse in Vacuum

By numerically solving the relativistic equations of motion of a single electron in laser fields modeled by a Gaussian laser beam, we get the trajectory and energy of the electron. When the drifting distance is comparable to or even longer than the corresponding Rayleigh length, the evolution of the beam waist cannot be neglected. The asymmetry of intensity in acceleration and deceleration leads to the conclusion that the electron can be accelerated effectively and extracted by the longitudinal ponderomotive force. For intensities above, an electron's energy gain about MeV can be realized, and the energetic electron is parallel with the propagation axis.