Light propagation through birefringent, nonlinear media with deep gratings

We present a theory that includes birefringence in the description of one-dimensional 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 pulse length. We derive two sets of equations appropriate in different frequency regimes, a set of coupled mode equations and a set of coupled nonlinear Schrodinger equations; we investigate the connections between these equations and where their regimes of validity overlap. Finally, we use our results to describe energy exchange between polarization modes in a birefringent medium.