Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies

A negative effective permeability is shown to exist at infrared frequencies in a three-dimensional collection of polaritonic spheres. This is demonstrated by an effective medium theory which relates the Mie resonances of the constituent spheres to the bulk response of the composite. The derived permittivity and permeability are shown to be isotropic. The results are verified by a comparison with multiple-scattering photonic band calculations. The existence of an anomalous dispersion region with a negative group velocity and the appropriate signs associated with the imaginary parts of the permittivity and permeability are also discussed.