Finite-size effects on topological interface states in one-dimensional scattering systems

Abstract : Topological edge modes in one-dimensional photonic systems are usually studied considering the interface between two different semi-infinite periodic crystals (PCs) with inverted band structure around the Dirac point. Here we consider the case where the two PCs are finite, constituting an open scattering system, and we study the influence of the size of this finite structure on the interface mode by inspecting the complex resonances. First we show the complex resonance distribution corresponding to the band inversion around the Dirac point. Perturbations from the Dirac point display the emergence of the localized interface mode. We also report on a remarkable robustness of the interface mode as the system size varies, which persists even for the smallest possible size.