Fine characteristics of polarization singularities in a three-dimensional electromagnetic field and their properties in the near field of a metallic nanospheroid

K. S. Grigoriev, N. Yu. Kuznetsov, Yu. V. Vladimirova, and V. A. Makarov

Isotropy parameters of truly linear (LT) and truly circular (CT) polarization singularities in a three-dimensional monochromatic electromagnetic field are defined. It is demonstrated that these parameters characterize the distribution of polarization ellipses near the singular points in a more detailed way than a topological index. A numerical algorithm which tracks CT and LT lines and visualizes the changes of isotropy parameters along the lines is proposed. The algorithm is applied to visualize the polarization singularity lines and their properties in the vicinity of a metallic nanospheroid that is irradiated by a plane elliptically polarized wave. It is shown that both CT and LT lines appear close to the surface of the nanoparticle and they are three-dimensional closed loops or arcs that start and end at the surface of the nanospheroid. In most cases the singular lines of different types are topologically linked.