We present a theory that includes birefringence in the description of one-d
imensional photonic band-gap materials with a Kerr nonlinearity. The Bloch
functions in the absence of nonlinearity completely characterize the linear
problem, for deep as well as shallow gratings, and the method of multiple
scales is used to include the effects of nonlinearity and finite optical pu
lse length. We derive two sets of equations appropriate in different freque
ncy regimes, a set of coupled mode equations and a set of coupled nonlinear
Schrodinger equations; we investigate thc connections between these equati
ons and when their regimes of validity overlap. Finally, we use our results
to describe energy exchange between polarization modes in a birefringent m
edium.