Non-radiating sources: fundamental and higher-order anapole states in all-dielectric nanostructures

Non-radiating sources are radiationless electromagnetic states characterized by vanishing scattering in the far-field and robust energy localization in the near field. Initially developed in quantum mechanics and astrophysics to model elementary particles noninteracting with the electromagnetic field, non-radiating states have gained a prominent role in nanophotonics following the experimental demonstration of anapole states. This chapter provides an overview of the theoretical foundations and critical milestones in investigating optical anapole states and their application in subwavelength dielectric nanostructures, discussing past results and present challenges.