Surface waves supported by metasurfaces with self-complementary geometries

This paper investigates the fundamental dispersion properties of surface waves (SWs) supported by a class of metasurfaces (MTSs) that consists of a planar layer made of metal patches and apertures with self-complementary geometries. When the MTS is suspended in free space, the supported SW is TM or TE depending on whether the vertexes of the metallic parts are interconnected or not, whereas the phase velocity is equal in the two cases. A simple analytical model, that depends only on the geometry, is derived to predict the dispersion curves for a quite general class of geometries. The proposed model is also extended to cases in which the MTSs are printed on a grounded or ungrounded dielectric slab, by using an equivalent dielectric constant. Comparisons with dispersion curves obtained through full-wave simulations confirm the accuracy of the model all over the Brillouin region. Finally, it is shown that connecting or disconnecting the metal patches along a given path allows for a confinement of the SWs on such a path. An experimental validation of this concept is also presented. This feature provides the possibility of controlling the wave's direction of propagation by changing the vertexes status by means of miniaturized switches or optical control.