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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.19443 |
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| _version_ | 1866909272183406592 |
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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 |