Subluminous phase velocity of a focused laser beam and vacuum laser acceleration

It has been found that for a focused laser beam propagating in free space, there exists, surrounding the laser beam axis, a subluminous wave phase velocity region. Relativistic electrons injected into this region can be trapped in the acceleration phase and remain in phase with the laser field for sufficiently long times, thereby receiving considerable energy from the field. Optics placed near the laser focus are not necessary, thus allowing high intensities and large energy gains. Important features of this process are examined via test particle simulations. The resulting energy gains are in agreement with theoretical estimates based on acceleration by the axial laser field.