Radiative topological states in one-dimensional resonant photonic crystals

We present a theory of topological edge states in one-dimensional resonant photonic crystals with compoundunit cell.We demonstrate how the structure, despite being one-dimensional, can be characterized by topologicalindices.Contrary to conventional electronic topological states the modes under consideration are radiative,i.e., they decay in time due to the light escape through the structure boundaries. We demonstrate that theedge states survive despite radiative decay and can be detected both in time- and frequency-dependent lightreflection.