Hidden Symmetry Protection and Topology in Surface Maxwell Waves

Since the latter half of the 20th century, the use of metal in optics has become a promising plasmonics field for controlling light at a deep subwavelength scale. Surface plasmon polaritons localized on metal surfaces are crucial in plasmonics. However, despite the long history of plasmonics, the underlying mechanism producing the surface waves is not fully understood. This study unveils the hidden symmetry protection that ensures the existence of degenerated electric zero modes. These zero modes are identified as physical origins of surface plasmon polaritons, and similar zero modes can be directly excited at a temporal boundary. In real space, the zero modes possess vector-field rotation related to surface impedance. Focusing on the surface impedance, we prove the bulk-edge correspondence, which guarantees the existence of surface plasmon polaritons even with nonuniformity. Lastly, we extract the underlying physics in the topological transition between metal and dielectric material using a minimal circuit model with duality. The transition is considered the crossover between electric and magnetic zero modes.