Topological Transitions and Surface Umklapp Scattering in Weakly Modulated Periodic Metasurfaces.

Controlling and manipulating surface waves is highly beneficial for imaging applications, nanophotonic device design, and light-matter interactions. While deep-subwavelength structuring of the metal-dielectric interface can influence surface waves by forming strong effective anisotropy, it disregards important structural degrees of freedom such as the interplay between corrugation periodicity and depth and its effect on the beam transport. Here, we unlock these degrees of freedom, introducing weakly modulated metasurfaces, structured metal-dielectric surfaces beyond effective medium. We utilize groove-structuring with varying depths and periodicities to demonstrate control over the transport of surface waves, dominated by the depth-period interplay. We show unique backward focusing of surface waves driven by an umklapp process-momentum relaxation empowered by the periodic nature of the structure and discover a yet unexplored, dual-stage topological transition. Our findings can be applied to any type of guided wave, introducing a simple and versatile approach for controlling wave propagation in artificial media.