Photonic surface Dirac cones in reciprocal magnetoelectric metamaterials

Abstract

We investigate photonic surface Dirac cones in reciprocal magnetoelectric metamaterials characterized by purely imaginary antisymmetric off-diagonal chirality parameters. The underlying medium is considered a photonic analog of topological insulators that support topologically protected edge states. As the spin-degenerate condition is satisfied, bulk modes are featured by Dirac cones with linear dispersion. In the presence of chirality parameter, a bandgap is opened between the bulk modes, within which surface modes appear at the boundary between two media with opposite chirality. In particular, the surface modes also feature with Dirac cones, indicating the existence of ideal topologically protected edge states. Both the bulk and surface modes are analytically formulated by algebraic equations based on Maxwell’s equations for the underlying medium and boundary conditions at the interface. Specifically, the topological property of the system is analyzed by spin–orbit Hamiltonians of spin 1 constructed from Maxwell’s equations for two pseudospin states formed by the linear combination of electric and magnetic field components. The topological property is further characterized by the topological invariants of the Hamiltonians and illustrated with the robust transport of surface waves at an irregular boundary.