Strongly focused vortex beams by using flat Fresnel-spiral lenses

Abstract

We report geometrically-optimal diffraction gratings for sharp vortex beam focusing using Fresnel-spiral curves. The lenses are built based on the Fresnel-spiral, a spiral curve that combine the focusing properties of Fresnel zone plates and the phase dislocations produced by spiral gratings. On the one hand, the constructive and destructive interferences between open and opaque zones in the grating, in analogy to the Fresnel zone plate, allow sharp beam focusing. On the other hand, the spiral shape of the grating retains the helicity, rotating the phase of the diffracted waves and creating a phase dislocation along the axis. This allows the generation of geometrically optimal focused vortex beams, enhancing the field intensity at the focus up to 170 times. In particular, this system offers a tunable topological charge of the vortex beam by using different arms in the Fresnel-spiral diffraction grating, being the topological charge equal to the number of arms. Two different Fresnel-spiral diffraction gratings with topological charge of 1 and 5 are experimentally tested showing excellent agreement with theory and simulations. These diffraction gratings will allow the design of effective wave-matter interaction systems, with direct applications in industry and biomedical engineering.We report geometrically-optimal diffraction gratings for sharp vortex beam focusing using Fresnel-spiral curves. The lenses are built based on the Fresnel-spiral, a spiral curve that combine the focusing properties of Fresnel zone plates and the phase dislocations produced by spiral gratings. On the one hand, the constructive and destructive interferences between open and opaque zones in the grating, in analogy to the Fresnel zone plate, allow sharp beam focusing. On the other hand, the spiral shape of the grating retains the helicity, rotating the phase of the diffracted waves and creating a phase dislocation along the axis. This allows the generation of geometrically optimal focused vortex beams, enhancing the field intensity at the focus up to 170 times. In particular, this system offers a tunable topological charge of the vortex beam by using different arms in the Fresnel-spiral diffraction grating, being the topological charge equal to the number of arms. Two different Fresnel-spiral diffraction grat...