Papers › Knotting fractional-order knots with the polarization state of light
Knotting fractional-order knots with the polarization state of light
Emilio Pisanty, Gerard J. Machado, Verónica Vicuña-Hernández, Antonio Picón, Alessio Celi, Juan P. Torres, Maciej Lewenstein
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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 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 M\"obius-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.
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