Singularities and Poincaré Indexes of Electromagnetic Multipoles

Abstract

Electromagnetic multipoles have been broadly adopted as a fundamental language throughout photonics, of which general features such as radiation patterns and polarization distributions are generically known, while their singularities and topological properties have mostly slipped into oblivion. Here we map all the singularities of multipolar radiations of different orders, identify their indexes, and show explicitly the index sum over the entire momentum sphere is always $2$, consistent with the Poincaré-Hopf theorem. Upon those revealed properties, we can attribute the formation of bound states in the continuum to overlapping of multipolar singularities with open radiation channels. This insight unveils a subtle connection between indexes of multipolar singularities and topological charges of those bound states, revealing that essentially they are the same. Our work has fused two fundamental and sweeping concepts of multipoles and topologies, which can potentially bring unforeseen opportunities for many multipole related fields within and beyond photonics.

Supplemental material incorporated, without changes to the main article

References in corpus (8)

• Topological Photonics
• Topological Acoustics
• Topological nature of bound states in the radiation continuum
• Electromagnetic multipole theory for optical nanomaterials
• Multipolar nonlinear nanophotonics
• Ultra-directional forward scattering by individual core-shell nanoparticles
• Generalized magnetic mirrors
• Beam steering with dielectric metalattices

Cited by in corpus (5)

• Generation and Annihilation of Topologically-Protected Bound States in the Continuum and Circularly-Polarized States by Symmetry Breaking
• Topological Polarization Singularities in Metaphotonics
• Polarization Singularities in Light Scattering by Small Particles
• Arbitrary Polarization-Independent Backscattering or Reflection by Rotationally-Symmetric Reciprocal Structures
• Topological charge engineering in lasing bound states in continuum