Floquet engineering with spatially non-uniform driving fields

Abstract: In Floquet engineering, we apply a time-periodic modulation to change the effective behavior of a wave system. In this work, we generalize Floquet engineering to exploit spatial degrees of freedom, expanding the scope of effective behaviors we can access. We develop a perturbative procedure to engineer space-time dependent driving forces that effectively transform broad classes of tight-binding systems into one another. We demonstrate several applications, including removing disorder, undoing Anderson localization, and enhancing localization to an extreme in spatially modulated waveguides. This procedure straightforwardly extends to other types of physical systems and different Floquet driving field implementations.