Topology-induced, strongly diamagnetic response of hollow structured metals at broadband microwave frequencies

Fractal is a type of exotic geometrical shape. By employing the H-fractal and the effective medium view, we show a broadband, strongly diamagnetic response, μ r eff ~0, arising from the structured metallic plate with hollow fractal apertures and without loading high-permittivity dielectrics. In particular, such ~0 permeability is induced by the inherent topology of the fractal aperture and is hardly achieved among other metallodielectric structures with low volumetric ratio of metal. As a demonstration, we present a design of structured metal of 64 % hollowness, which gives rise to a close-to-zero effective permeability with relative bandwidth 175 %.