  All metamaterial applications are based upon the idea that extreme material
properties can be achieved through appropriate dynamic homogenization of
composites. This homogenization is almost always done for infinite domains and
the results are then applied to finite samples. This process ignores the
evanescent waves which appear at the boundaries of such finite samples. In this
paper we first clarify the emergence and purpose of these evanescent waves in a
model problem consisting of an interface between a layered composite and a
homogeneous medium. We show that these evanescent waves form boundary layers on
either side of the interface beyond which the composite can be represented by
appropriate infinite domain homogenized relations. We show that if one ignores
the boundary layers then the displacement and stress fields are discontinuous
across the interface. Therefore, the scattering coefficients at such an
interface cannot be determined through the conventional continuity conditions
involving only propagating modes. Here we propose an approximate variational
approach for sidestepping these boundary layers. The aim is to determine the
scattering coefficients without the knowledge of evanescent modes. Through
various numerical examples we show that our technique gives very good estimates
of the actual scattering coefficients beyond the long wavelength limit.
