2018/08/31 by Emilio Pisanty, Gerard J. Machado, Verónica Vicuña-Hernández +4 · 1 citation
Physics and Astronomy · #physics.optics
paper · pdf · doi:10.1038/s41566-019-0450-2
published as Nature Photonics 13 no. 8, 569 (2019) · Submitted Manuscript, including a subset of the figures from the published Supplementary Information
arxiv created 2019/06/10 · arxiv updated 2019/08/15
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 θ and its polarization by a multiple γθ of that angle. These symmetries are generated by mixed angular momenta of the form Jγ= L + γS and they generally induce Möbius-strip topologies, with the coordination parameter γ restricted to integer and half-integer values. In this work we construct beams of light that are invariant under coordinated rotations for arbitrary γ, 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 Jγ, and we characterize the resulting optical polarization singularity using third-and higher-order field moment tensors, which we experimentally observe using nonlinear polarization tomography.