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通常采用含两个耦合参数的紧束缚近似,就能很好地描述光子晶体缺陷因耦合而导致的共振频率分裂.然而,缺陷耦合造成的共振频率移动,即包含奇数个缺陷的耦合系统的中央共振频率位置与原来单缺陷时的共振频率位置存在差异,则只有采用含三个耦合参数的严格紧束缚方法才能正确描述.根据耦合参数与共振频率的关系,利用三缺陷耦合系统的模拟计算结果确定了三个耦合参数的具体值,从而在理论上能够预言由任意个缺陷构成的耦合系统的共振频率的移动和分裂.理论预言与基于有限时域差分法的数值计算完全相符.
The tight bond approximation with two coupling parameters is usually used to describe the resonance frequency splitting caused by the coupling of the photonic crystal defects well.However, the resonance frequency caused by the defect coupling moves, that is, the center of the coupling system containing an odd number of defects According to the relationship between the coupling parameters and the resonance frequency, the simulation results of the three-defect coupled system are used to describe the resonance frequency location and the resonance frequency location of the original single defect. The specific values of the three coupling parameters are determined, which theoretically predict the movement and splitting of the resonant frequency of a coupled system composed of any number of defects.The theoretical predictions are in good agreement with the numerical calculations based on the finite-difference time-domain method.