  We investigate the propagation of electromagnetic waves in stratified
anisotropic dielectric-magnetic materials using the integral equation method
(IEM). Based on the superposition principle, we use Hertz vector formulations
of radiated fields to study the interaction of wave with matter. We derive in a
new way the dispersion relation, Snell's law and reflection/transmission
coefficients by self-consistent analyses. Moreover, we find two new forms of
the generalized extinction theorem. Applying the IEM, we investigate the wave
propagation through a slab and disclose the underlying physics which are
further verified by numerical simulations. The results lead to a unified
framework of the IEM for the propagation of wave incident either from a medium
or vacuum in stratified dielectric-magnetic materials.
