Geometric Phases and Holonomy in Structured Optical Fields

Geometric phases are widely used in modern optics, yet their meaning and underlying geometry depend on the actual physical settings, which can substantially differ from one another. This tutorial article introduces geometric phases in nanophotonic systems, focusing on the interaction of structured light with nanostructures or metaatoms. We compare the present setting with conventional geometric phases of structured-light optics and show that similar phase laws may correspond to genuinely different underlying geometries. Our aim is to provide a pedagogical bridge between the mathematical language of geometric phases and experimentally relevant examples from nanophotonics.