Local-field effects in magnetodielectric media: Negative refraction and absorption reduction

Abstract

We give a microscopic derivation of the Clausius-Mossotti relations for a homogeneous and isotropic magnetodielectric medium consisting of radiatively broadened atomic oscillators. To this end the diagram series of electromagnetic propagators is calculated exactly for an infinite bicubic lattice of dielectric and magnetic dipoles for a small lattice constant compared to the resonance wavelength $\ensuremath{\lambda}$. Modifications of transition frequencies and linewidth of the elementary oscillators are taken into account in a self-consistent way by a proper incorporation of the singular self-interaction terms. We show that in radiatively broadened media sufficiently close to the free-space resonance the real part of the index of refraction approaches the value $\ensuremath{-}2$ in the limit of $\ensuremath{\rho}{\ensuremath{\lambda}}^{3}⪢1$, where $\ensuremath{\rho}$ is the number density of scatterers. Since at the same time the imaginary part vanishes as $1∕\ensuremath{\rho}$, local field effects can have important consequences for realizing low-loss negative index materials.