Vacuum propagation of a shaped laser beam and direct vacuum acceleration

The vacuum propagation of a laser beam is strictly solved on the basis of (1) the wave equation, (2) Gauss’s law, (3) finite power, and (4) a group velocity equal to c. The direct vacuum acceleration of the classic charge is then studied based on the strictly solved vacuum laser field. Different vacuum states of the laser beam are chosen by the physical nature of the interface between the vacuum and the solid optical material.