Journal
NATURE PHOTONICS
Volume 13, Issue 8, Pages 569-+Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/s41566-019-0450-2
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Funding
- Cellex-ICFO-MPQ
- Spanish Ministry MINECO [FIS2016-79508-P, SEV-2015-0522]
- European Social Fund
- Fundacio Cellex
- Generalitat de Catalunya (AGAUR) [2017 SGR 1341]
- ERC AdG OSYRIS
- EU FETPRO QUIC
- National Science Centre, Poland-Symfonia grant [2016/20/W/ST4/00314]
- Secretaria de Ciencia, Tecnologia e Innovacion de la Ciudad de Mexico
- Generalitat de Catalunya (Program ICREA Academia)
- Secretaria d'Universitats i Recerca del Departament d'Economia i Coneixement de la Generalitat de Catalunya
- European Social Fund-FEDER
- Comunidad de Madrid through TALENTO [2017-T1/IND-5432]
- ERC Synergy Grant UQUAM
- UAB Talent Research programme
- Spanish Ministry of Economy and Competitiveness [FIS2017-86530-P]
- SFB FoQuS (FWF project) [F4016-N23]
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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 Mobius-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 rational 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.
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