Wannier-Function based Scattering-Matrix Formalism for Photonic Crystal Circuitry

In this dissertation, I develop and investigate in detail a scattering-matrix approach for the efficient treatment of Photonic Crystal circuits and demonstrate its applicability to large-scale 2D circuits. The approach relies on the efficient calculation of the scattering matrices of basic functional elements using an expansion of fields into photonic Wannier functions, which represent a basis ideally suited to describe localized fields within defect structures in Photonic Crystals.