We demonstrate that the fundamental mode of the two coupled photonic crystal waveguides (PCWs) can be odd parity in a triangular photonic crystal and their dispersion curves do intersect. Thus, the PCWs are decoupled at the crossing point. By employing the decoupling at the crossing-point frequency and ultra short coupling length for another frequency, we designed a dual-wavelength demultiplexer with a coupling length of only two wavelengths and output power ratio as high as 15 dB. A loop-shape PCW is adapted to eliminate the backward energy flow.

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 ͑PCW͒ and two coupled identical PCWs. The cross-coupling coefficient ␤ of a point defect in one PCW to the nearest-neighboring ͑NN͒ defect in the other PCW causes the split of the dispersion curves, whereas the cross-coupling coefficient ␥ to the next-NN defects causes a sinusoidal modulation to the dispersion curves. Furthermore, the sign of ␤ determines the parities of the fundamental guided modes, which can be either even or odd, and the inequality ͉␤ ͉ Ͻ ͉2␥͉ 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.

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