Calculation of Transmittance of Light for an Array of Dielectric Rods Using Vector Cylindrical Waves: Complex Unit Cells

Abstract

Formulation of the transmission and reflection of light in terms of vector cylindrical waves is given for two-dimensional photonic crystals having complex unit cells which contain two or more rods in a unit cell. Some examples of the numerical calculations using the supercell method are given for arrays of cylinders which have impurities or defects. It is shown that the computed transmittance for a multilayer with periodic impurities agrees very closely with the band-structure calculation of the impurity band. We also examined the waveguide effect of the line defect in a photonic band gap, and demonstrated the possibility of using this method in the design of defect waveguides.