Exact Derivation of the Radiation Law of Antennas Embedded into Generic Nonlocal Metamaterials: A Momentum-Space Approach

We solve the problem of how antennas radiate into generic nonlocal metamaterials by using a momentum-space formalism to rigorously derive the general radiation formula. The energy per Hertz by unit solid angle is computed by first deriving the dyadic Green's function of nonlocal media in the momentum space. We show that due to causality only the antihermitian part of the dyad will contribute to the radiation field. We avoid any spectral integration or using the Poynting vector (the latter known to be already inadequate in nonlocal media) by working directly with momentum space formulation and derive analytically the exact expression. The final result depends only on the modal analysis of the metamaterial.