Physical limitations on the scattering of electromagnetic vector spherical waves

Understanding the interaction between electromagnetic waves and matter
is vital in applications ranging from classical optics to antenna theory. This paper
derives physical limitations on the scattering of electromagnetic vector spherical waves.
The assumptions made are that the heterogeneous scatterer is passive, and has
constitutive relations which are on convolution form in the time domain and anisotropic
in the static limit. The resulting bounds limit the reflection coefficient of the modes
over a frequency interval, and can thus be interpreted as limitations on the absorption
of power from a single mode. They can be used within a wide range of applications,
and are particularly useful for electrically small scatterers. The derivation follows a
general approach to derive sum rules and physical limitations on passive systems on
convolution form. The time domain versions of the vector spherical waves are used
to describe the passivity of the scatterer, and a set of integral identities for Herglotz
functions are applied to derive sum rules from which the physical limitations follow.