Physics of composite media with a periodic microstructure

A composite medium with a periodic microstructure can have some amazing physical properties. We will discuss some of those, including two which have only recently been discovered. We review the phenomenon of sharp resonances which are predicted to occur when a periodic array of identical, small (compared to the wavelength and skin depth) metallic inclusions is imbedded in a dielectric host. We show that if either the dielectric host or the metallic inclusions have nonlinear electrical properties, then by exciting the system near to one of those resonances it should be possible to achieve bistable optical behavior even when the nonlinearity is weak everywhere. Under the influence of a strong magnetic field H, the magnetoresistance of a composite conductor with a periodic microstructure is shown, by calculations, to exhibit a strong dependence on the direction of H. This is surprisingly similar, both qualitatively and quantitatively, to the behavior of the magnetoresistance of a uniform metallic crystal, where it is thought to be due to the open structure of the Fermi surface. In the case of a composite medium there is of course no Fermi surface in the theory, and this behavior can be understood, at least qualitatively, from simple geometric considerations on the microstructure and the local current distribution.