Edge states in dynamical superlattices

We address edge states and rich localization regimes available in one-dimensional dynamically modulated superlattices, both theoretically and numerically. In contrast to conventional lattices with straight waveguides, not only is the quasi-energy band of an infinite modulated superlattice periodic in the transverse Bloch momentum, but it also changes periodically with an increase in the coupling strength between waveguides. Due to the collapse of quasi-energy bands, dynamical superlattices admit a known dynamical localization effect. If, however, such a lattice is truncated, periodic longitudinal modulation leads to the appearance of specific edge states that exist within certain periodically spaced intervals of coupling constants. We discuss unusual transport properties of such truncated superlattices and illustrate different excitation regimes and enhanced robustness of edge states in them that are associated with the topology of the quasi-energy band.