Analysis of the Topology of a Plasmonic Target-Skyrmion Texture

Abstract Topological concepts are frequently used to describe structured optical fields, including plasmonic near fields. Topological descriptions in terms of skyrmion numbers implicitly assume the compactness of the underlying manifold. While this concept works for constrained fields due to inherent integration boundaries, compactness is usually not fulfilled in extended optical fields. Here, we use time-resolved polarimetric photoemission microscopy to determine the electric field vectors of a surface plasmon polariton nanofocus on Au(111) with deep sub-wavelength spatial and sub-fs temporal resolution. The surface plasmon polaritons were excited with circularly polarized light at an Archimedean spiral that was milled into the Au surface by a focused ion beam. The full vectorial field information provided by polarimetric PEEM allows for a spatiotemporal analysis of the skyrmion number of the field texture. At a fixed time, the skyrmion number oscillates as a function of the radius. Furthermore, the skyrmion number oscillates in time. The experimental findings are compared to analytical calculations that lead to the same conclusion: a global skyrmion number cannot be assigned in such non-compact fields. Our results reveal the limitations of the skyrmion number for optical fields and motivate the search for new topological invariants suited for optical fields.