Statistical theory of multiple scattering of waves applied to three-dimensional layered photonic crystals

Abstract

On the basis of the statistical theory of multiple scattering of waves, we offer a numerical approach to calculate coherent transmission and reflection for the three-dimensional (3-D) photonic crystals that consist of partially disordered dielectric spheres. With the proposed scheme, which we call the transfer-matrix (TM) method with quasi-crystalline approximation (QCA), we consider a quasi-regular 3-D assembly of particles as a stack of close-packed monolayers with a short-range ordering. Single-scattering characteristics are determined by Mie theory. Lateral electrodynamic coupling between the particles of a monolayer is treated in the QCA. Multibeam interference between monolayers is described in a manner analogous to the TM technique. We apply the TM-QCA calculation technique to study two revealed effects: (1) short-wavelength attenuation due to particles of finite sizes and (2) nonmonotonic dependence of the pseudogap depth on the particle size, refractive-index contrast, and intermonolayer distances.