Tight-binding theory for coupled photonic crystal waveguides

The point-defect coupling under the tight-binding approximation is introduced to describe the behavior of dispersion relations of the guided modes in a single photonic crystal waveguide (PCW) and two coupled identical PCWs. The cross-coupling coefficient beta of a point defect in one PCW to the nearest-neighboring (NN) defect in the other PCW causes the split of the dispersion curves, whereas the cross-coupling coefficient gamma to the next-NN defects causes a sinusoidal modulation to the dispersion curves. Furthermore, the sign of beta determines the parities of the fundamental guided modes, which can be either even or odd, and the inequality parallel to beta parallel to <parallel to 2 gamma parallel to is the criterion for the crossing of split dispersion curves. The model developed in this work allows for deriving the coupled-mode equations and the coupling length.