Acceleration of electrons by tightly focused femtosecond laser pulses

The problem of the acceleration of a test electron in the field of a tightly focused relativistic laser pulse is solved in the case when the focal spot size is of the order of the radiation wavelength and the exact solution of Maxwell's equations for the electromagnetic field should be used. The electron acceleration is studied depending on the initial position of the electron in the focal plane and is compared with the results corresponding to the paraxial approximation for the laser field. The maximum energy acquired by the electron in the laser focus is found. The dependences of the ejection angle of the electron on its initial position near the focus are analysed.