Optimal injection scheme for electron acceleration by a tightly focused laser beam

Electron dynamics and energy gain in a tightly focused laser beam in vacuum are investigated by numerical simulations. There exist two acceleration mechanisms, i.e. acceleration by the longitudinal field or by the transverse field, which corresponds to two different trajectories. The relationship between the energy gain and the injection parameters of electrons, including the injection angle and momentum, is shown. For given laser parameters, the optimum injection parameters can be obtained.