Radiative topological states in one-dimensional resonant photonic crystals

We present a theory of topological edge states in onedimensional resonant photonic crystals with compound unit cell. We demonstrate how the structure, despite being onedimensional, can be characterized by topological indices. 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 the edge states survive despite radiative decay and can be detected both in timeand frequency-dependent light reflection.