Sum rules for metamaterials in parallel plate waveguides

An optical theorem and forward scattering approach for a bounded object confined between the plates of a parallel plate waveguide is investigated. A forward scattering sum rule together with the properties of positive real functions is used to show that the total absorption and scattering of an object is bounded by its static polarizability. A parallel plate waveguide and a parallel plate capacitor are used to estimate the dynamic and static properties, respectively. The results verify that the total cross section of an object integrated over the entire spectrum is proportional to the static polarizability.