LASER FOCUSING OF ATOMIC-BEAMS

The focusing of an atomic beam using near-resonant laser light is considered. Path-integral techniques are employed to transform the problem into a standard diffraction integral. This approach is general and allows us to deal with thick laser lenses. Starting from the basic form of the potential energy for an atom in a laser beam, we derive the propagation kernel for the atomic wave function for the particular case of a TEM01*, or doughnut, mode laser beam. Both the full three-dimensional propagation kernel and its paraxial approximation are discussed. We show that the paraxial case can be obtained from the three-dimensional case by a stationary-phase approximation of the propagation equation. Numerical results for the focusing of a Gaussian atomic beam are presented. These results show that spot diameters on the order of 20 angstrom are obtainable for many reasonable choices of laser and atomic beam parameters and that for most of these cases the thin-lens approximation is not valid. The effects of the lowest-order aberrations are also briefly discussed. Spherical aberration is found to contribute significantly to the focal spot diameter, at least for the doughnut mode laser beam considered here.