Wide optical lenses for atomic beams.

The field of atom-optics offers considerable potential in fundamental and applied physics, both for imaging atoms and their deposition (to create nano-structures). Here we work in the paraxial approximation throughout and can therefore assume that the scalar modes represent (e. g., linearly polarized) electro-magnetic laser-field modes. For atomic lens design, based on the optical dipole force, it is necessary to coherently superpose suitable laser modes in order to create wide thin parabolic lenses with large numerical apertures. Only in this manner can the tiny diffraction limits promised by the extraordinary smallness of the de Broglie wavelengths of atomic beams be realized.