Knotting fractional-order knots with the polarization state of light
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 ¿ and its polarization by a multiple ¿¿ of that angle. These symmetrie...
| Authors: | , , , , , , |
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| Format: | article |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/171868 |
| Online Access: | https://hdl.handle.net/2117/171868 https://dx.doi.org/10.1038/s41566-019-0450-2 |
| Access Level: | Open access |
| Keyword: | Photonics Nonlinear optics Optical physics Optical techniques Other photonics Fotònica Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Telecomunicació òptica::Fotònica |
| Summary: | 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 ¿ and its polarization by a multiple ¿¿ of that angle. These symmetries are generated by mixed angular momenta of the form J¿¿=¿L¿+¿¿S, and they generally induce Möbius-strip topologies, with the coordination parameter ¿ restricted to integer and half-integer values. In this work we construct beams of light that are invariant under coordinated rotations for arbitrary rational ¿, 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¿, and we characterize the resulting optical polarization singularity using third- and higher-order field moment tensors, which we experimentally observe using nonlinear polarization tomography. |
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