By considering the next nearest neighboring defects between two photonic crystal waveguides (PCWs) and analytic formulae derived from the tight binding theory, we will explain the physical properties of an asymmetric directional coupler made from two coupled PCWS: (1) The dispersion curves of a photonic crystal coupler will decouple into the dispersion curves of a single line defect, and the electric field will only be localized in one waveguide of the coupler at a particular point, which we name a decoupling point. (2) The parities of the eigenmodes switch at the decoupling point, even though the dispersion curves are not crossing. (3) The eigenfield at a higher (lower) dispersion curve is always mainly localized in the waveguides that have higher (lower) eigenfrequencies of single line defects, even though the eigenmodes are switched. As a given frequency is incident into the coupler, the energy transfer between two waveguides and the coupling length can be expressed analytically. Due to there being no dispersion curve crossing, the coupling length is no longer infinite at the decoupling point in asymmetric PCWs, but it still has the minimal energy transfer between two waveguides when the frequency of the incident wave is close to the decoupling point.
