Study on the hollow extinction ratio of Gaussian vortex light

Optical vortices are beams with spiral phase wave fronts capable of carrying different topological charges. This paper presents the expression for Gaussian vortex light and simulates vortices with topological charges of 0, 1, and 2, revealing a “hollow” extinction phenomenon. We derive the relationship between the radius of Gaussian vortex beams and their topological charges, express the extinction ratio of hollow vortices, and calculate the beam radius. The study demonstrates a linear relationship between the extinction ratio and topological charge (from 1 to 20). The fitting accuracy between the simulated hollow radius and the Gaussian vortex approximated radius reaches 85.93%, with an error margin of 17%. In laboratory experiments using a liquid crystal spatial light modulator, we constructed a vortex light system employing a 532.0 nm laser to generate 10 interference fringes of hollow vortex light with topological charges ranging from 10 to 100 on a CCD detector. Pixel measurements were taken for both inner and outer radii corresponding to these charge patterns, enabling precise calculation of extinction ratio. The experimental results show a similar trend to the theoretical predictions, demonstrating that hollow vortex light with extinction properties holds potential applications in signal encryption.