Laser focusing of cold atoms: Analytical solution of the problem

The motion of paraxial atomic beams in a laser radiation field is studied within the framework of a parabolic equation. Exact analytical solutions of the parabolic equation are found for a variety of potentials featuring a nonuniformity in the propagation direction. Special attention is paid to the propagation of cold atomic beams in the gradient field of the TEM01* laser radiation mode. Explicit analytical expressions are found for the position of the focal points, focal spot radius, and spatial intensity distribution.