De Broglie-wave lens

Abstract

A simple focusing device is proposed for de Broglie matter waves—a diffractive lens, based on the optical effect of diffractive multifocal focusing of radiation. This matter-wave lens consists of two coaxial circular apertures in which the second aperture of smaller diameter is located where the Fresnel number of the first aperture is unity. It is shown that diffraction of a de Broglie matter wave by a system of two pinholes on an optical axis exhibits the multifocal focusing effect of matter waves in the near-field (Fresnel) zone, which creates a very intense, spatially localized beam of atoms. Theoretical predictions for the focusing efficiency of a neutral atomic beam by the diffractive lens are as follows. The spot diameter is ~0.1 µm, the ratio of focal and incident intensities is ~15, the focal length of the diffractive lens is in the range ~0.13 to 6 cm, the focusing depth is in the range ~15 to 30 cm, and the energy transmitting efficiency is ~30 %. For the relatively large diameters of the pinholes, 5.0 µm, the proposed configuration acts as a matter-wave lens with a large focal length and a long focusing depth.