Photonic topological semimetals in bigyrotropic metamaterials.

We investigate the photonic topological phases in bigyrotropic metamaterials characterized by the gyroelectric and gyromagnetic parameters. The underlying medium is considered a photonic analogue of the topological semimetal featured with a pair of Weyl cones separated by a distance in the frequency-wave vector space. As the 'spin'-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between two bigyrotropic metamaterials with opposite sign of the gyrotropic parameters exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, two types of surface modes are tangent to or wrapping around the Weyl cones, which form a bent and two twisted surface sheets. At the Weyl frequency, the surface modes contain a typical and two open Fermi arc-like states that concatenate to yield an infinite straight line. Topological features of the bigyrotropic metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

Photonic topological insulators in bianisotropic metamaterials.

We analyze the photonic topological phases in bianisotropic metamaterials characterized by a lossless and reciprocal magnetoelectric tensor. The underlying medium is considered a topological insulator that supports a pair of counterpropagating helical edge states. By introducing the pseudospin basis, the photonic system can be described by the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between two bianisotropic media with opposite chirality exist in their common band gap, which are represented by elliptic or hyperbolic equations. In particular, two branches of hyperbolic surfaces are degenerate at the frequency where the chiral nihility occurs, which depict the helical nature of edge states between two distinct topological phases. Topological features of the bianisotropic metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

Photonic topological semimetals in bianisotropic metamaterials.

We analyze the photonic topological phases in bianisotropic metamaterials characterized by a chirality tensor with zero trace. We found that the strength of chirality component determines the topological character of the metamaterial. The underlying medium can be considered as a topological semimetal with the nontrivial band gap in the momentum space. The topological properties are described by the spin-orbit Hamiltonians with spin 1 and characterized by the nonzero topological invariants. In particular, photonic quantum Hall states exist when the longitudinal chirality component exceeds the permittivity, whereas photonic quantum spin Hall states are present when the chiral nihility occurs. Considering the dispersion in the frequency domain, the bianisotropic metamaterial is regarded as a photonic Weyl system that supports the Weyl points and Fermi arcs. The topological features are further illustrated with the robust transport of edge states at an irregular boundary of the metamaterial.

Photonic topological phases in dispersive metamaterials.

We analyze the photonic topological phases in dispersive metamaterials which satisfy the degenerate condition at a reference frequency. The electromagnetic duality allows for the hybrid modes to be decoupled and described by the spin-orbit Hamiltonians with pseudospin 1, which result in nonzero spin Chern numbers that characterize the topological phases. In particular, the combined Hamiltonian of the hybrid modes complies with a fermionic-like pseudo time-reversal symmetry that ensures the Kramers degeneracy, leading to the topological protection of helical edge states. The transverse spin generated by the evanescent surface waves is perpendicular to the wave vector, which exhibits the spin-momentum locking as in the surface states for three-dimensional topological insulators. The topological properties of the helical edge states are further illustrated with the robust transport of a pair of counterpropagating surface waves with opposite polarization handedness at an irregular boundary of the metamaterial.

Chiral surface waves on hyperbolic-gyromagnetic metamaterials.

The existence of surface waves at the boundary of a hyperbolic-gyromagnetic metamaterial is studied. The surface waves, which are analytically formulated in terms of the eigenfields, appear in the spatial gap between two elliptically polarized bulk modes of the metamaterial. The surface waves are chiral in the sense that they propagate unidirectionally along the edge and reverse the propagation direction upon changing sign of the gyrotropic parameter. The topological feature of the chiral surface waves can be characterized by the Berry phases of the bulk modes, showing the bulk-edge correspondence for the underlying medium. The unidirectionality of the chiral surface waves and their immunity to disorder are further demonstrated by the propagation of electromagnetic waves around sharp corners.