The decoupling point is a crossing in the dispersion curves of a photonic-crystal coupler. At this point, the energy in one waveguide cannot be transferred into the other one. Controlling the decoupling point can modify the properties of the coupler. From the extended tight-binding theory (TBT), which includes coupling of the guiding mode field up to the next nearest-neighboring defects, we found there is a blueshift in the frequency of the decoupling point in the square lattice and a redshift in the triangular lattice by translating the defect rods along the axis of the coupler. By moving the defects of the coupler close to each other transversely, not only the eigenfrequencies of the coupler but also separations of dispersion curves increase due to the stronger coupling between the defect rods. From the simulation results of the plane wave expansion and the finite difference time domain methods, the theoretical analyses of TBT agree with the numerical ones. Therefore, we successfully derive the design rules using the TBT for tuning the coupling length and decoupling frequency of a directional coupler.
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