  We generalize the Bergman-Milton spectral representation, originally derived
for a two-component composite, to extract the spectral density function for the
effective dielectric constant of a graded composite. This work has been
motivated by a recent study of the optical absorption spectrum of a graded
metallic film [Applied Physics Letters, 85, 94 (2004)] in which a broad
surface-plasmon absorption band has been shown to be responsible for enhanced
nonlinear optical response as well as an attractive figure of merit. It turns
out that, unlike in the case of homogeneous constituent components, the
characteristic function of a graded composite is a continuous function because
of the continuous variation of the dielectric function within the constituent
components. Analytic generalization to three dimensional graded composites is
discussed, and numerical calculations of multilayered composites are given as a
simple application.
