Analytical and Numerical Treatment of the Spectral Properties of a Photonic Crystal Coupled Resonator Optical Waveguide

Coupled resonator optical waveguide (CROW) may play an important role in future integrated optical devices. In this paper, a closed form formula for the calculation of the transfer function of a photonic crystal (PC) CROW coupled to an input and an output PC waveguide is derived. Coupled mode theory (CMT) is initially used for the derivation of a semi-analytical transfer function model. This model requires the computation of the inverse of a matrix containing the coupling coefficients of the device. The model is compared to the results obtained by the finite-difference time domain (FDTD) and good agreement is obtained. Using the tight-binding approximation, the semi-analytical model is used to derive an analytical solution for the transfer function of the structure directly from the coupling coefficients of the device. Based on this analytical model, the resonant frequencies of the structure are determined.