Singular Electromagnetics: From Phase Singularities to Optical Skyrmions and Beyond

Abstract

Singular electromagnetics, also known as singular optics in the visible spectrum, is a branch of modern electromagnetics/optics that studies the solutions with nontrivial topological features to Maxwell's equations under different boundary conditions. These nontrivial topological features are called optical singularities, which can be viewed as topological defects of electromagnetic (EM) fields, including phase singularities in complex scalar fields, polarization singularities in complex vector fields, 3D topological defects (such as optical skyrmions, merons, hopfions, knots, links, and Möbius strips), and even higher‐dimensional optical singularities. In this manuscript, the definitions, the topological invariants, and the geometric representations of these optical singularities are reviewed. Along the way of the discussion, it is emphasized that how symmetries can impact optical singularities (for phase, polarization and spatiotemporal singularities). Very importantly, it is demonstrated that how a very complex optical singularity (e.g., a skyrmion) can be constructed based on simpler “building block” singularities (e.g., phase and polarization singularities), so that a hierarchical picture on the many diverse topics in singular electromagnetics is built up. This review can be considered a tutorial‐cum‐review article, which can provide a clear and concise physical picture for constantly emergent topics in singular electromagnetics.