Normalized formalism for the analysis of diffractionless beams

Recently there has been much interest in a whole class of field solutions which have the property of being either diffractionless or nearly diffractionless. These beams propagate in free space with their energy confined around the axis of propagation with little or no beam divergence. In this paper the authors investigate the generation and normalization aspects of the zeroth order Bessel function (J_o) which was the first of the class of diffractionless fields. An annular aperture with obscuration ratio close to unity produces in the far field an approximation to the J_o distribution. Through scale normalization they show that the solution of the integral equations depend on a myriad of physical parameters in a very compact fashion. Specifically, the solution is expressed in terms of the obscuration ratio of the annulus, a normalized on-axis propagation distance and a truncation parameter