Remarkable laser beams formed by computer-generated optical elements: properties and applications

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) with an arbitrary-order phase singularity and an analytical expression for far-field diffraction of the Gaussian beam by a SSP with n-th order. The SPP was implemented as a 32-level "helical" microrelief on a low-contrast resist using an electron beam. Experiments of diffraction of the Gaussian beam by SPPs with the second-order singularity and of trapping polystyrene beads using computer-generated optical elements are discussed.