Resonant frequency shift in coupled photonic crystal defects described by the tight-binding method

The resonant frequency splitting caused by photonic crystal (PC) defect coupling can be well described by the tight-binding (TB) approximation in which only two coupling parameters are used. However, the description of the resonant frequency shift that represents the difference between the center resonant frequency of the coupled structure containing odd number of defects and the resonant frequency of a single defect, requires the employment of the rigorous TB that involves three coupling parameters. By using the relation between the coupling parameters and the resonant frequencies, we extract the values of the three coupling parameters from the simulation of a three-coupled-defect structure and use them to predict the resonant frequency shift and splitting of the coupled structures consisting of arbitrary number of PC defects. They are in good agreement with the simulation results based on the finite-difference time-domain method.