Reconstructing the topology of optical polarization knots

Hugo Larocque, Danica Sugic, Dominic Mortimer, Alexander Taylor, Robert Fickler, Robert W Boyd, Mark Dennis, Ebrahim Karimi

Research output: Contribution to journalArticle (Academic Journal)peer-review

39 Citations (Scopus)
296 Downloads (Pure)

Abstract

Knots are topological structures describing how a looped thread can be arranged in space. Although most familiar as knotted material filaments, it is also possible to create knots in singular structures within three-dimensional physical fields such as fluid vortices and the nulls of optical fields. Here we produce, in the transverse polarization profile of optical beams, knotted lines of circular transverse polarization. We generate and observe both simple torus knots and links as well as the topologically more complicated figure-eight knot. The presence of these knotted polarization singularities endows a nontrivial topological structure on the entire three-dimensional propagating wavefield. In particular, the contours of constant polarization azimuth form Seifert surfaces of high genus, which we are able to resolve experimentally in a process we call seifertometry. This analysis reveals a level of topological complexity, present in all experimentally generated polarization fields, that goes beyond the conventional reconstruction of polarization singularity lines.
Original languageEnglish
Number of pages5
JournalNature Physics
Early online date30 Jul 2018
DOIs
Publication statusE-pub ahead of print - 30 Jul 2018

Structured keywords

  • SPOCK

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