Shaping the Profile and Dispersion of Waves Guided Between Spatiotemporally Dispersive, Electrically and Magnetically Conductive Metasurface Boundaries

Metasurfaces have been utilized pervasively to manipulate the wavefront of structured beams propagating in free space. However, they also enable us to create nontrivial waveguide boundaries which offer novel opportunities for the manipulation of the mode profile and propagation constant of electromagnetic waves confined in the space enclosed by them. Here, we study a waveguide that is formed by a general class of metasurfaces which are both electrically and magnetically polarizable, support multiple resonances, and exhibit temporal and spatial dispersion. We investigate the opportunities offered by tailoring the temporal dispersion of the surface conductivities and study three different cases of spatial dispersion, namely, no dispersion, an ideal case of very specific dispersion of the form σ _se ∝ k_t and σ _sm ∝ 1/ k_t , and the realistic dispersion of an actual physical implementation based on a metal-backed cut-wire unit cell. Both analytical derivations and full wave numerical simulations are performed for addressing the different scenarios and verifying the results. We show that the proposed metasurface waveguides can enable (i) the ability to shape the mode profile from concave, to flat, to convex and (ii) the possibility of both superluminal and subluminal propagation, as well as both normal and anomalous group velocity dispersion. An example application of controlling the mode profile along propagation is showcased, highlighting the potential of metasurfaces as waveguide boundaries.