Homogenization analysis of complementary waveguide metamaterials

We analyze the properties of complementary metamaterials as effective inclusions patterned into the conducting walls of metal waveguide structures. We show that guided wave metamaterials can be homogenized using the same retrieval techniques used for volumetric metamaterials, leading to a description in which a given complementary element is conceptually replaced by a block of material within the waveguide whose effective permittivity and permeability result in equivalent scattering characteristics. The use of effective constitutive parameters for waveguide materials provides an alternative point-of-view for the design of waveguide and microstrip based components, including planar lenses and filters, as well as devices with derived from a bulk material response. In addition to imparting effective constitutive properties to the waveguide, complementary metamaterials also couple energy from waveguide modes into radiation. Thus, complementary waveguide metamaterials can be used to modify and optimize a variety of antenna structures.