  We study the optical properties of crystals with spatial dispersion and show
that the usual Fresnel approach becomes invalid near frequencies where the
group velocity of the wave packets inside the crystal vanishes. Near these
special frequencies the reflectivity depends on the atomic structure of the
crystal provided that disorder and dissipation are very low. This is
demonstrated explicitly by a detailed study of layered superconductors with
identical or two different alternating junctions in the frequency range near
the Josephson plasma resonance. Accounting for both inductive and charge
coupling of the intrinsic junctions, we show that multiple modes are excited
inside the crystal by the incident light, determine their relative amplitude by
the microscopic calculation of the additional boundary conditions and finally
obtain the reflectivity.
  Spatial dispersion also provides a novel method to stop light pulses, which
has possible applications for quantum information processing and the artificial
creation of event horizons in a solid.
