Semi-analytical formulations for the surface modes of photonic woodpiles

We describe semi-analytical methods for modeling the optical surface modes of finite and semi-infinite photonic woodpiles, and find that the behavior of the surface modes depends greatly on the whether the number of layers is even or odd. We also demonstrate analytically that coupling between the top and bottom surfaces can occur even when the top layer is orthogonal to the bottom layer. The coupling strength exhibits a strong dependence on the direction of propagation; for certain directions, decoupling occurs even when the number of layers is small. The dispersion curves of two different coupled modes can anticross or be interwoven. We also describe the conditions under which coupled surface modes will exist when two woodpiles are used to create a Fabry-Pérot cavity.