Calculation of hyper-geometric modes

An algorithm for calculating hyper-geometric modes of light field, which are the solution of a paraxial Schroedinger-type wave equation, is developed. Propagation of the hyper-geometric modes containing a phase spiral singularity (vortex) is computer simulated. Comparison is made between the rigorous analytical solution and an approximate solution derived using the integral Kirchhoff operator of propagation. Unlike the familiar paraxial (Gaussian and Bessel) modes, the major radius of the hypergeometric modes increases with distance as a square root, with the distance between adjacent diffraction maxima (minima) being in inverse proportion to the radial coordinate.