Optical Polarization Möbius Strips on All-Dielectric Optical Scatterers
In this article, we study the emergence of polarization singularities in the scattering of optical resonators excited by linearly polarized light. First, we prove analytically that spherical all-dielectric nanoparticles described by combinations of electric and magnetic isotropic polarizabilities can sustain L surfaces and C lines that propagate from the near-field to the far field. Based on these analytical results, we are able to derive anomalous scattering Kerker conditions using singular optics arguments. Next, through full-field calculations, we demonstrate that high refractive index spherical resonators present such topologically protected features. We calculate the polarization structure of light around the generated C lines, unveiling a Mobius strip structure in the main axis of the polarization ellipse when calculated on a closed path around the C line. These results prove that high-index nanoparticles are excellent candidates for the generation of polarization singularities and that they may lea...