CAJ | 학술논문

将精细积分方法与谱单元法结合，对含有各向异性介质的波导介质层光子带隙（PBG）结构的传输特性进行了研究。从矢量波动方程相对应的单变量变分形式出发，对含有各向异性介质波导横截面采用谱单元进行离散，引入对偶变量，将单变量变分原理导入到哈密顿体系，利用精细积分法求出出口刚度矩阵。数值算例将半解析谱元法与常规有限元法、半解析有限元法进行了比较，表明本文方法具有高精度、高效率的特点，而且计算精度随着谱单元阶数的增加呈指数增长。
장정세적분방법여보단원법결합，대함유각향이성개질적파도개질층광자대극（PBG）결구적전수특성진행료연구。종시량파동방정상대응적단변량변분형식출발，대함유각향이성개질파도횡절면채용보단원진행리산，인입대우변량，장단변량변분원리도입도합밀돈체계，이용정세적분법구출출구강도구진。수치산례장반해석보원법여상규유한원법、반해석유한원법진행료비교，표명본문방법구유고정도、고효솔적특점，이차계산정도수착보단원계수적증가정지수증장。
Precise integration method combined with the spectral element is used to simulate and analyze the stop-band char-acteristic of anisotropic dielectric layer photonic band-gap (PBG)structures in waveguide.From the variational principle based on single variable corresponding to the vector wave equation,2-D spectral elements are employed to discretize the cross section of the layered structure,which contains anisotropic dielectric.Introducing the dual-variables,the variational principle is cast into the Hamil-tonian system,and then the high precision integration method is utilized to perform the stiff matrices.Compared with conventional fi-nite element method and semianalytical finite element method,numerical results demonstrate that the semianalytical spectral element method is more accurate and efficient for anisotropic PBG structures analysis,and it can achieve spectral accuracy with the increase of interpolation degrees of basis functions.