{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/knotting-fractional-order-knots-with-the","title":"Knotting fractional-order knots with the polarization state of light","arxiv_id":"1808.05193","date":"2018-08-15","proceeding":null,"authors":["Emilio Pisanty","Gerard J. Machado","Verónica Vicuña-Hernández","Antonio Picón","Alessio Celi","Juan P. Torres","Maciej Lewenstein"],"abstract":"The fundamental polarization singularities of monochromatic light are normally associated with invariance under coordinated rotations: symmetry operations that rotate the spatial dependence of an electromagnetic field by an angle $\\theta$ and its polarization by a multiple $\\gamma\\theta$ of that angle. These symmetries are generated by mixed angular momenta of the form $J_\\gamma = L + \\gamma S$ and they generally induce M\\\"obius-strip topologies, with the coordination parameter $\\gamma$ restricted to integer and half-integer values. In this work we construct beams of light that are invariant under coordinated rotations for arbitrary $\\gamma$, by exploiting the higher internal symmetry of 'bicircular' superpositions of counter-rotating circularly polarized beams at different frequencies. We show that these beams have the topology of a torus knot, which reflects the subgroup generated by the torus-knot angular momentum $J_\\gamma$, and we characterize the resulting optical polarization singularity using third-and higher-order field moment tensors, which we experimentally observe using nonlinear polarization tomography.","url_abs":"http://arxiv.org/abs/1808.05193v1","url_pdf":"http://arxiv.org/pdf/1808.05193v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"knotting-fractional-order-knots-with-the","repo_url":"https://github.com/episanty/LIRE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"knotting-fractional-order-knots-with-the","repo_url":"https://github.com/episanty/LISSAFIRE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}