Light propagation through two-dimensional photonic crystal slab waveguide bends solved by three-dimensional plane-wave transfer-matrix method

Abstract

We propose a technique, based on three-dimensional (3D) plane-wave transfer-matrix method, to analyze light propagation through two-dimensional (2D) photonic crystal (PC) slab waveguide bend structures. By means of the supercell technique, the waveguide bend is modeled by two semi-infinite 3D periodic arrays of 2D PC slab waveguides face to face or separated by a sandwiched slab of bend region from which the intrinsic transmission, reflection, and radiation loss coefficients of waveguide modes can be calculated. The proposed approach is efficient, accurate, and numerically friendly for understanding and designing waveguide bends in different 2D PC slab and 3D PC structures with complex geometries. The 3D method can also help to evaluate the accuracy of the simplified 2D model under an effective refractive index approximation, which has been extensively adopted in simulations and designs of 2D PC slab structures.