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The author would like to thank Mark Dennis for helpful discussions and advice and Danica Sugic for advice on the computational aspects of the project.

Analysis of institutional authors

Bode, BenjaminCorresponding Author

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February 16, 2025
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Complex optical vortex knots

Publicated to:Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences. 481 (2306): 20240605- - 2025-01-31 481(2306), DOI: 10.1098/rspa.2024.0605

Authors: Bode, Benjamin

Affiliations

CSIC, Inst Ciencias Matemat ICMAT, Campus Cantoblanco UAM,C-Nicolas Cabrera 13-15, Madrid 28049, Spain - Author
Univ Politecn Madrid, Dept Matemat Aplicada & Ingn Ind, ETSIDI, Rda Valencia 3, Madrid 28012, Spain - Author

Abstract

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 Psi : R 3 -> 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.

Keywords

BraidLinksOptical vortex knotParaxial light beamPhase singularitiesPolynomiaSurface

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2025, it was in position 32/134, thus managing to position itself as a Q1 (Primer Cuartil), in the category Multidisciplinary Sciences.

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-04:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 1 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 1.

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (BODE, BENJAMIN) and Last Author (BODE, BENJAMIN).

the author responsible for correspondence tasks has been BODE, BENJAMIN.