Transformation of a metasurface on the substrate interface into the same metasurface in a homogenized substrate based on two kinds of modified Babinet’s principles

Previously, the metasurface was usually manufactured on a dielectric substrate using the printed circuit boards (PCB) technology. However, due to the existence of the substrate interface, the electromagnetic radiation and coupling of the sub-wavelength metasurface becomes more complex for theoretical analysis. To this end, an indirect method is developed to transform the problem of a metasurface in a dielectric half-space into a simpler problem of the same metasurface in a homogenized dielectric space. Specifically, two different theoretical models of complementary metasurfaces in a dielectric half-space are first given. A specific yet unknown relative permittivity is included in one model to realize the above transformation. By comparing these two theoretical models in terms of the surface impedance matrix, the specific yet unknown relative permittivity is analytically derived as ϵr,unk=ϵr,1/2+ϵr,2/2 . Finally, two arbitrary metasurfaces are given to verify the proposed theory for arbitrary incidence wave in dielectric half-space. The theory can greatly simplify the analysis and design of the metasurface in a dielectric halfspace, because only the metasurface in a homogenized dielectric space like vacuum needs to be theoretically solved after completing the above transformation.