Generalized Wannier Function Method For Photonic Crystals

The concept of generalized Wannier functions, adopted from the electronic theory of solids, is used to build a localized representation of electromagnetic waves in dielectric materials. For two-dimensional photonic crystals, we demonstrate the existence of such a localized state basis, and we establish an efficient computational method, allowing a tight-binding-like parameter free modelization of any dielectric structure deviating from periodicity. Numerical simulations of a T-shaped photonic crystal waveguide prove its ability to deal with large-scale systems and complex structures.