On the Relation Between Optimal Wideband Matching and Scattering of Spherical Waves

Using an exact circuit analogy for the scattering of vector spherical waves, it is shown how the problem of determining the optimal scattering bounds for a homogeneous sphere in its high-contrast limit is identical to the closely related, and yet very different problem of finding the broadband tuning limits of the spherical waves. Using integral relations similar to Fano's broadband matching bounds, the optimal scattering limitations are determined by the static response as well as the high-frequency asymptotics of the reflection coefficient. The scattering view of the matching problem yields explicitly the necessary low-frequency asymptotics of the reflection coefficient that is used with Fano's broadband matching bounds for spherical waves, something that appears to be non-trivial to derive from the classical network point of view.