ABSTRACT
Photonic crystals are periodic dielectric or metallic structures in which any electromagnetic wave propagation is forbidden within a fairly large frequency range. This chapter examines the cylindrical harmonic expansion method and bring it to a simple and tractable formulation for modeling the electromagnetic scattering and guidance by photonic crystals consisting of layered parallel or crossed arrays of cylindrical objects standing in free space or embedded in a dielectric slab. The results are used to analyze the reflection and transmission by a single layer of periodic array of circular cylinders. The derivation of the generalized reflection and transmission matrices for the multilayered parallel arrays is described in detail. The extension of the formulation to the three-dimensional scattering by multilayered crossed-arrays is discussed. The chapter analyses using the T-matrix, the two-dimensional or three-dimensional scattering of a plane wave by an infinitely long circular cylinder isolated in free space.
