# Local-field effects in radiatively broadened magneto-dielectric media: negative refraction and absorption reduction

## TL;DR

This paper derives microscopic relations for magneto-dielectric media, showing that near resonance, the index of refraction can approach -2 with minimal absorption, enabling low-loss negative refraction.

## Contribution

It provides a microscopic derivation of the Clausius-Mossotti relations for radiatively broadened media, incorporating local field effects and self-interactions.

## Key findings

- Refractive index approaches -2 near resonance at high densities
- Imaginary part of index diminishes as 1/ρ, reducing absorption
- Potential for low-loss negative index materials

## Abstract

We give a microscopic derivation of the Clausius-Mossotti relations for a homogeneous and isotropic magneto-dielectric medium consisting of radiatively broadened atomic oscillators. To this end the diagram series of electromagnetic propagators is calculated exactly for an infinite bi-cubic lattice of dielectric and magnetic dipoles for a lattice constant small compared to the resonance wavelength $\lambda$. Modifications of transition frequencies and linewidth of the elementary oscillators are taken into account in a selfconsistent 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 -2 in the limit of $\rho \lambda^3 \gg 1$, where $\rho$ is the number density of scatterers. Since at the same time the imaginary part vanishes as $1/\rho$ local field effects can have important consequences for realizing low-loss negative index materials.