Photonic crystal modelling using a tight-binding Wannier function method

Using the concept of generalized Wannier functions, adapted from the electronic theory of solids, we demonstrate for two-dimensional photonic crystals the existence of 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. Examples of numerical simulations using this formalism, including modal analysis of microcavities and waveguides are presented to prove the ability of this approach to deal accurately with large scale systems and complex structures. A tight-binding version of the transfer matrix method is proposed to describe the transmission and reflection properties of finite samples of photonic crystals.