Tight-binding theory for coupled photonic crystal waveguides

摘要

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 β 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 γ to the next-NN defects causes a sinusoidal modulation to the dispersion curves. Furthermore, the sign of β determines the parities of the fundamental guided modes, which can be either even or odd, and the inequality |β| < |2γ| 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.