Topological bands and triply-degenerate points in non-Hermitian hyperbolic metamaterials

Hyperbolic metamaterials (HMMs) can host topological edge modes, but earlier approaches that focus on equal-frequency surfaces may not correctly describe the topology of full photonic bands. The authors formulate a topological band description for continuous HMMs using a non-Hermitian Hamiltonian derived from Maxwell’s equations. They identify two kinds of three-dimensional non-Hermitian triply-degenerate points with complex linear dispersions and topological charges of +2 and 0, attributed to chiral and gyromagnetic effects. Because these are photonic systems, the vacuum band is emphasized as important for topological edge states and bulk-edge correspondence in HMMs. The resulting topological band picture is numerically confirmed by direct simulation of Maxwell’s equations, and the work is positioned as a general framework for exploring topological phases in photonic continua and for device implementations of topological HMMs.