Coupled-mode formulation of two-parallel photonic-crystal waveguides.

A self-contained coupled-mode formulation for coupled two-dimensional photonic-crystal waveguides (PCWs) is discussed. Using a perturbation theory, the first-order coupled-mode equations are systematically derived, which govern the evolution of the modal amplitude of individual PCWs in isolation. The coupled-mode equations are used to analyze the coupled symmetric PCWs consisting of a square lattice of circular dielectric rods or air holes. It is shown that the results are in good agreement with those obtained by the rigorous direct analysis of the coupled waveguide system.