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Bibliographic Details
Main Author: Bode, Benjamin
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2407.19443
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author Bode, Benjamin
author_facet Bode, Benjamin
contents 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 $Ψ:\mathbb{R}^3\to\mathbb{C}$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_19443
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Complex optical vortex knots
Bode, Benjamin
Geometric Topology
Optics
Quantum Physics
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 $Ψ:\mathbb{R}^3\to\mathbb{C}$ 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.
title Complex optical vortex knots
topic Geometric Topology
Optics
Quantum Physics
url https://arxiv.org/abs/2407.19443