Generation of Wannier functions for photonic crystals

We present an approach for the efficient generation of Wannier functions for Photonic Crystal computations that is based on a combination of group-theoretical analysis and efficient minimization strategies. In particular, we describe the symmetry properties that allow for exponential localization of Wannier functions and how they are related to the underlying Bloch mode symmetries of the photonic band structure and we show that no exponentially localized Wannier functions can be created from the physical modes of a three-dimensional crystal. Moreover, we comment on the use of conjugate gradient and randomized minimization algorithms that-together with the group theoretical considerations-facilitate the efficient numerical determination of maximally localized Wannier functions for many bands. This is a requirement for the accurate computation of Photonic Crystal functional elements and devices.