Polarization Singularities in Light Scattering by Small Particles

TL;DR

This study investigates polarization singularities in light scattering by small particles using simulations and analytical methods, revealing how particle shape and incident light influence singularity behavior in near and far fields.

Contribution

It provides new insights into the topological properties and trajectories of polarization singularities in light scattering, highlighting shape-dependent near-field effects and the role of multipole interference.

Findings

Four singularities identified in the far-field with a topological index sum of two.

Near-field singularities depend on particle shape and incident polarization.

Sign flipping of polarization indices can occur from near to far field.

Abstract

Using full-wave numerical simulations and analytical multipole expansions we investigated the properties of real-space polarization singularities that emerge in light scattering by subwavelength particles. We considered spherical and torus particles made of dielectric or perfect-electric-conductor material. We determined the topological indices and the trajectories of electric-field polarization singularities in both the near-field and far-field regions. In the far-field region, a total of four singularities are identified and the sum of their polarization topological indices is two, independent of the particle's geometric shape. In the near-field region, the polarization singularities strongly depend on the particle's shape and the polarization of incident light, and their index sum is not governed by the Poincar\'e-Hopf theorem anymore due to the non-transverse nature of the fields. From near field to far field, a flipping of sign can happen to the polarization topological indices of the C lines. The far-field properties of the singularities can be well explained by the interference of the excited multipoles, but their near-field properties can be strongly affected by the evanescent fields that are not captured by the multipole expansions. Our work uncovers the important relationship between particles' geometric properties and the polarization singularities of their scattering field. The results can be applied to manipulate polarization singularities in nanophotonic systems and could generate novel applications in optical sensing.