We study the Floquet edge states in arrays of periodically curved optical waveguides described by the modulated Su-Schrieffer-Heeger model. Beyond the bulk-edge correspondence, our study explores the interplay between band topology and periodic modulations. By analyzing the quasienergy spectra and Zak phase, we reveal that, although topological and nontopological edge states can exist for the same parameters, they cannot appear in the same spectral gap. In the high-frequency limit, we find analytically all boundaries between the different phases and study the coexistence of topological and nontopological edge states. In contrast to unmodulated systems, the edge states appear due to either band topology or modulation-induced defects. This means that periodic modulations may not only tune the parametric regions with nontrivial topology, but may also support novel edge states.

• Received 11 April 2018

DOI:https://doi.org/10.1103/PhysRevA.98.013855