  We generalize the invariant imbedding theory of the wave propagation and
derive new invariant imbedding equations for the propagation of arbitrary
number of coupled waves of any kind in arbitrarily-inhomogeneous stratified
media, where the wave equations are effectively one-dimensional. By doing this,
we transform the original boundary value problem of coupled second-order
differential equations to an initial value problem of coupled first-order
differential equations, which makes the numerical solution of the coupled wave
equations much easier. Using the invariant imbedding equations, we are able to
calculate the matrix reflection and transmission coefficients and the wave
amplitudes inside the inhomogeneous media exactly and efficiently. We establish
the validity and the usefulness of our results by applying them to the
propagation of circularly-polarized electromagnetic waves in one-dimensional
photonic crystals made of isotropic chiral media. We find that there are three
kinds of bandgaps in these structures and clarify the nature of these bandgaps
by exact calculations.

Optics;Other Condensed Matter;Plasma Physics