Optical Vortex Braiding in Composite Bessels

We theoretically propose and experimentally demonstrate the braiding of optical vortices in a laser beam with more than 2π rotation by superposing Bessel modes with a plane wave. Laser beams containing a single, centered vortex with integer-valued orbital angular momentum (OAM) have been extensively studied and engineered, but beams with two or more optical vortices have received less attention. Optical vortex braiding refers to the periodic rotation of two or more vortices around the central axis of propagation in a laser beam. Braiding is a topological feature in knot theory, but no physically-realizable scheme for optical vortex braiding beyond a ¼ - rotation has been identified, much less experimentally demonstrated. In this work, we present a theoretical proposition for braiding optical vortices in Bessel beams, along with analytical expressions for the braiding trajectories and braiding period. We accompany this work with the experimental realization of vortex braiding in physical laser beams, using Bessel-Gaussian beams. We show two vortices braiding completely three times, the most observed to our knowledge.