Generalized Lorentz-Lorenz formulas for microstructured materials

In this work the homogenization approach recently proposed in [M. Silveirinha, Phys. Rev. B 75, 115104 (2007)] is applied to derive the analog of the classical Lorentz-Lorenz formula in a generic dielectric crystal, considering the effects of frequency and spatial dispersion. In particular, we obtain a rigorous formula for the interaction constants that relate the local fields with the macroscopic fields and the induced dipole moments, when the response of the particles is described by only the dipole-type terms. To illustrate the application of the results, we homogenize a material formed by plasmonic spheres, demonstrating that the spatial dispersion effects are of crucial importance near the plasmonic resonance.