Generalized Clausius-Mossotti homogenization for the permittivity of an electric quadrupolar medium

An approximate effective macroscopic permittivity of a 3D cubic array of point electric quadrupoles is derived using a generalized Clausius-Mossotti (C-M) derivation. At low frequencies the C-M permittivity is shown to closely approximate the permittivity of the fundamental Floquet mode of the array. This generalized C-M derivation appears to be the first application of the C-M method to media with multipoles of higher order than dipoles.