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  • Letter
  • Open Access

Electromagnetic vectoriality beyond polarization

Chunchao Wen, Jianfa Zhang*, Chaofan Zhang†, Shiqiao Qin, Zhihong Zhu, and Wei Liu‡

  • *Contact author: jfzhang85@nudt.edu.cn
  • †Contact author: c.zhang@nudt.edu.cn
  • ‡Contact author: wei.liu.pku@gmail.com
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Phys. Rev. Research 7, L032050 – Published 8 September, 2025

DOI: https://doi.org/10.1103/5bnh-4xls

Abstract

For arbitrary charge-current distributions, is it possible that along all directions their radiations are nonzero and are all circularly polarized? Our current descriptions of vectorial electromagnetic waves based on polarizations and the associated polarization ellipses fail to give an answer. In this study, we introduce the concept of instantaneous optical singularities, which together with the fundamental mathematical theorem of Poincaré-Hopf immediately rules out the above possibility of nonzero and all circularly polarized radiations. Based on both the conventional polarization singularities and the instantaneous singularities, we have established a general framework to capture the singular nature of vectorial electromagnetic waves, revealing that radiation patterns without dark directions (zero radiations) must have both points of circular polarizations and lines of linear polarizations, or equivalently, patterns without circular polarizations or linear polarizations must have dark directions. The framework established is further applied to the classical problem of scattering by electromagnetic dual particles, revealing the existence of scattering dark directions that have been hidden from all other theoretical explorations. We have essentially proved that polarizations are insufficient for descriptions of vectorial electromagnetic waves and revealed the complementarity (instantaneous and steady fields and their singularities) that can provide broader and deeper insights into not only electromagnetism, but also other branches of wave physics where singularities are generic and ubiquitous. Our work can potentially fully reshape singular photonics and chiral optics.

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Phys. Rev. Research 7, L032050– Published 8 September, 2025
  • Received 11 June 2024
  • Accepted 12 August 2025
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