Defect computations in photonic crystals: a solid state theoretical approach

We describe two different approaches to efficiently analyse the optical properties of defect structures embedded in photonic crystals (PCs). The first one is based on an expansion of the electromagnetic field into optimally localized photonic Wannier functions and thus efficiently utilizes the information of the underlying PCs. The second is based on the recently developed multipole method and is specially suited to deal with finite-size structures. We demonstrate the efficiency of these approaches by considering several defect structures for TM-polarized radiation in two-dimensional PCs.