Hollow beams of simple polarization for trapping and storing atoms

We propose a scheme for producing and magnifying a hollow beam, as might be desired for purposes of storing and guiding cold atoms, through the use of a simple spherically aberrating lens and a projection lens. The field is a superposition of J0 Bessel fields, so that simple (linear, circular) polarizations can be utilized. analyze some of the beam properties through analytical approximations. Some examples of field zeros along the optical axis are given, together with some of their characteristics. Numerical calculations largely confirm the validity of the analytical expressions. For the most important zero nearly all of the beam power is contained within the first two Bessel spacings, with a resulting highly efficient trapping. Isophotes are calculated and displayed for the region surrounding this null point. They have regular shapes, for which we give an approximate expression.