Perspective: Topological photonics in nanoscaled systems with far-field radiation and polarization singularities

Topology is a powerful framework for controlling and manipulating light, minimizing detrimental perturbations on the photonic properties. Combining nanophotonics with topological concepts presents opportunities for both fundamental physics and technological applications. Although most topological photonic realizations have been inspired by condensed-matter analogue models, new topological ideas have just begun to be realized at the nanoscale. Nanophotonics is characterized by subtle phenomena that are not usually considered in other topological models' realizations, such as nonlocality, strong field confinement, and light radiating to the far-field continuum. In this perspective, we will discuss how standard topological band theory for photonic crystals needs to be extended by a more comprehensive approach that properly treats such nanophotonic intrinsic effects and, in particular, the interplay of polarization and far-field radiation. We highlight the emerging role that polarization singularities might play in defining the topological invariants in the far field, which are not fully captured by bulk observables alone. We conclude by outlining a set of open questions and promising directions for exploring novel concepts in topological nanophotonics and shaping next-generation photonic devices.