Symmetry-Imposed Selection Rules for Excitations of Nontrivial Plasmonic Topologies.

Nontrivial nearfield topologies in nano-optics refer to nearfield configurations embedded within singularities or topological defects, providing an ideal platform to explore integrated optoelectronics and higher-dimensional topological physics. Exciting such field topologies relies on selection rules related to various conserved quantities. Unfortunately, existing algebraic rules focus primarily on scalar singularities in nano-optical (e.g., plasmonic) systems and largely neglect the vectorial nature of the fields. More critically, these rules remain phenomenological. Given the intrinsic link between conserved quantities and symmetries, here we establish a unified selection rule using group theory that govern the excitations of nontrivial field topologies across three photonic spin states in generic nanophotonic systems. This rule can act as building blocks for constructing selection rules for exciting and engineering higher-dimensional field topologies (embedded within vectorial singularities and quasiparticles). These rules are derived purely from symmetry arguments and are therefore rooted in first principles. The proposed rules further predict two novel physical effects in plasmonic systems: spin-orbit splitting of vortices and multidimensional nested vortices. Phase-resolved in-situ measurements of nested multidimensional plasmonic topologies well demonstrate our findings. Our group-theory-based approach can serve as a versatile framework for engineering symmetry- and singularity-related phenomena-like circular meron lattices and plasmonic quasicrystals-in diverse wave systems.