Propagation in random media: Calculation of the effective dispersive permittivity by use of the replica method

Abstract

In this paper we use the replica method together with a variational method in order to study the propagation of a wave traveling in a disordered composite. We compute the effective permittivity tensor, which takes into account the effects of spatial dispersion. Our calculation is not perturbative in the frequency, and we obtain a self-consistent formula for the longitudinal and transverse parts of the permittivity tensor applicable to the whole range of frequency. Our result appears as a self-consistent version of the usual weak-disorder expansion and thus recovers all weak-disorder results. We have checked that the solution to the self-consistent equations is correct in the limits of high and low spatial frequency.