  Effective medium theory is used to model a one dimensional lossy dielectric
quaternary photonic crystal as a homogeneous slab. The unit cell of the
original crystal is inversion symmetric with layer sequence ACBCA. The behavior
of the branch frequency singularities in the effective refractive index is
investigated as parameters in the layered structure change. A heterostructure
composed of multiple photonic crystals is also modeled with effective medium
theory. It is shown that the effective refractive index of such a structure
possesses regions of normal dispersion that correspond to localized interface
states within the overall regions of anomalous dispersion representing the
photonic band gap.
