Generation of multi-contour plane curves using vortex beams

Abstract

We propose a simple method for the generation of multi-contour plane curves based on vortex beam illumination of an optical element calculated using the Whittaker integral and parametric curve definition. The effect of splitting the contour of the curve into several lines is based on the optical fulfillment of the differentiation. Spiral phase plates can be used to perform the radial Hilbert transformation as an analog of the differentiation operation independent of the direction. In this paper, we use the invariance property of the vortex phase singularity of a laser beam both during propagation in free space and when passing through lens systems. Thus, when a vortex beam illuminates an optical element designed to form a focal curve, two operations are simultaneously performed: splitting the contour of the light curve and introducing a phase gradient along this curve. The splitting of the contour is applied in optical capture and manipulation of opaque particles. A split contour of the light curve can serve as light barriers for opaque particles, as well as for capturing several transparent microparticles simultaneously. Phase gradient generation is also in demand in various applications, since a transverse energy flow is generated in a certain direction.