2024/07/28 by Benjamin Bode, Bode, Benjamin
Engineering · Physics and Astronomy · #Advanced Fiber Laser Technologies #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Optics (physics.optics) #Orbital Angular Momentum in Optics #Photonic Crystal and Fiber Optics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2407.19443
openalex publication_date 2024/07/28 · openalex created_date 2024/08/01 · openalex updated_date 2026/07/28
The curves of zero intensity of a complex optical field can form knots and links: optical vortex knots. Both theoretical constructions and experiments have so far been restricted to the very small families of torus knots or lemniscate knots. Here we describe a mathematical construction that presumably allows us to generate optical vortices in the shape of any given knot or link. We support this claim by producing for every knot K in the knot table up to 8 crossings a complex field Ψ:ℝ3→ℂ that satisfies the paraxial wave equation and whose zeros have a connected component in the shape of K. These fields thus describe optical beams in the paraxial regime with knotted optical vortices that go far beyond previously known examples.