Unidirectional weak visibility in bandgap and singular scattering in conduction band of one-dimensional -symmetry photonic crystal

Abstract

We explore the scattering properties of one-dimensional -symmetric photonic crystal on the basis of band structure and eigenmodes of the scattering matrix. Two criteria for differentiating -exact phase and -broken phase are applied to analyze the scattering properties. In the first criterion, which originates from eigen-equation of effective Hamiltonian and is revealed through complex band structure, the scattering properties are analyzed. Near exceptional points, singular scattering is found and explained, where transmittance and reflectances from both sides reach very large values simultaneously and tend to infinity. In the bandgap, a phenomenon we call unidirectional weak visibility is disclosed and analyzed, where transmittance is zero, the reflectance from one side is very large, while the reflectance from the other side is very small. In the second criterion originating from eigen-equation of scattering matrix, the corresponding distributions of -exact phase and -broken phase are studied. Moreover, the singular scattering, which arises at the poles and zeros of the scattering matrix, and unidirectional weak visibility, which corresponds to the scattering of the eigenstates, are explained thoroughly. After serious analysis and comparison, the first criterion is preferable because it is consistent with the universally accepted definition.