Sum Rules for Parallel Plate Waveguides: Experimental Results and Theory

An experimental approach to verify the forward scattering sum rule for periodic structures is presented. This approach allows an upper bound on the total cross section integrated over a bandwidth from a simple static problem to be found. Based on energy conservation, the optical theorem is used to construct a relation between the total cross section and the forward scattering
of periodic structures as well as single scatterers inside a parallel plate waveguide. Dynamic measurements are performed using a parallel plate waveguide and a parallel plate capacitor is utilized to �find the static polarizability. Convex optimization is introduced to identify the total scattering in the dynamic
measurements. The results show that the all spectrum interaction between the electromagnetic �field and an object are proportional to the static polarizability of the object.