Topology of Bloch impedance: traveling waves, dispersive media, and electromagnetic energy

Abstract The bulk-boundary correspondence (b-bc) principle, which relates interface modes between two periodic structures to topological invariants of the respective Bloch bands, is widely accepted in electrodynamics. However, this acceptance stems largely from condensed matter (CM) theories. It is desirable to establish direct connections between the topological principles and Maxwell electrodynamics, rather than relying on CM results. Such connections have in recent years been found in the case of standing evanescent waves in periodic dielectric media. This paper extends these analyses to waves propagating along an interface between two periodic structures, possibly with frequency-dependent dielectric permittivities. The paper shows that the b-bc principle continues to hold for any physically realizable structures, in which the density of electromagnetic energy must be positive. The paper rigorously proves that in this physically valid case impedance of traveling interface modes within any given bandgap decreases monotonically as a function of frequency.