Vector k small middle dotp approach for photonic band structures

We point out that k small middle dotp treatments of photonic band gap materials based on the usual master equation must employ not only the physical photonic band solutions of that equation, but also unphysical solutions, in order to form a complete set. Nonetheless, it is possible to construct correct k small middle dotp expressions for the group velocity and its dispersion in terms of matrix elements involving only the photonic band solutions.

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.