Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate.

We derive what we believe to be new analytical relations to describe the Fraunhofer diffraction of the finite-radius plane wave by a helical axicon (HA) and a spiral phase plate (SPP). The solutions are deduced in the form of a series of the Bessel functions for the HA and a finite sum of the Bessel functions for the SPP. The solution for the HA changes to that for the SPP if the axicon parameter is set equal to zero.