Knotting fractional-order knots with the polarization state of light

• DOI: 10.1038/s41566-019-0450-2
• Publication Date: 2019-06-10T16:02:43Z
• Authors: Emilio Pisanty; Gerard J. Machado; Verónica Vicuña-H...; Antonio Picón; Alessio Celi; Juan P. Torres; Maciej Lewenstein
• Keywords: Complex Optics; polarization; Nonlinear optics; :Física [Àrees temàtiques de la UPC]; Àrees temàtiques de la UPC::Física; Topologies; Fotònica; Polarització (Llum); FOS: Physical sciences; Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Telecomunicació òptica::Fotònica; 01 natural sciences; Photonics; Optical physics; 0103 physical sciences; Other photonics; :Enginyeria de la telecomunicació::Telecomunicació òptica::Fotònica [Àrees temàtiques de la UPC]; Optical techniques; Polarization (Light); Physics - Optics; Optics (physics.optics)

Submitted Manuscript, including a subset of the figures from the published Supplementary Information<br/>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 M��bius-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 $��$, 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.<br/>