Simple optical vortices formed by a spiral phase plate

This paper discusses paraxial diffraction at a spiral phase plate of a limited light field whose phase is constant (a plane wave) while its amplitude varies as a power function with integer exponent n (positive or negative). It is shown that the Fraunhofer diffraction in this case is described by a Bessel function of the first kind of (n+1)st or (n−1)st order. Light fields that form diffraction patterns described by Bessel functions in the far zone are called simple optical vortices. Expressions are obtained for the amplitude of the Fraunhofer diffraction pattern of pure optical vortices and hypergeometric modes. The experimental part of the paper describes the formation of a vortex beam with an intensity distribution in the form of a double ring of arbitrary radius. Diffraction optical elements were created in this case by three methods: by electron lithography, by photolithography, and by means of a liquid-crystal display. Experiments are presented on the rotation of microparticles in a double ring.