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为计算有耗色散光子晶体的带隙结构,提出了新的本征值分析方法.该方法借助于量子输运问题中的思想,在本征值方程的推导过程中进行了巧妙的变换,将复杂的非线性本征值问题转化为线性本征值问题:并利用频域有限差分(FDFD)方法直接求解线性本征值方程,最终得到有耗色散光子晶体结构的相关物理参数.与其他方法相比,该方法的最大特点为概念清晰、计算简便,最终节省了计算时间及所需内存量.利用该方法,对介质光子晶体结构进行模拟,结果与传统FDFD方法符合较好,从而验证了方法的有效性.此外,利用所提方法计算了有耗色散光子晶体结构的色散曲线,得到了表面等离子波激发的区域,进一步讨论了损耗对其色散曲线及本征模场的影响.相关结果对色散有耗光子晶体的研究具有一定的理论指导意义.
In order to calculate the bandgap structure of dissipative photonic crystal, a new eigenvalue analysis method is proposed. By means of the idea of quantum transport problem, this method makes clever changes in the derivation of eigenvalue equations. The complex nonlinear eigenvalue problem is transformed into a linear eigenvalue problem: the FDED method is used to directly solve the linear eigenvalue equation, and finally the related physical parameters of the dissipative photonic crystal structure are obtained. Compared with other methods Compared with the traditional FDFD method, the photon crystal structure of the medium is simulated by the proposed method, which has clear concept and simple calculation, and finally saves the calculation time and the required amount of memory. The dispersion curve of the dissipative photonic crystal structure was calculated by the proposed method and the area excited by the surface plasmon wave was obtained and the influence of loss on the dispersion curve and the eigenmode field was further discussed.Results The study of dispersion dissipative photonic crystal has some theoretical significance.