A Fast Computation Method of Bands and Band Field Solutions of 3D Periodic Structures Using Broadband Green's Function-multiple Scattering Theory

L. Tsang, T. Liao, Shurun Tan
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引用次数: 3

Abstract

|We extended the previous 2D method of BBGF-MST (Broadband Green’s function-Multiple Scattering Theory) approach to 3D problems in periodic structures. Band Structures and Band Field Solutions are calculated. A feature of BBGF is that the lattice Green’s functions are broadband so that the coefficients of the spherical wave expansions are calculated rapidly for many frequencies. These are then used for speedy calculations of the matrix elements of the KKR (Korringa-Kohn-Rostoker) eigenvalue equation. Using BBGF-MST, a low order matrix eigenvalue equation for the bands is derived. For the (cid:12)rst two bands, the dimension of the KKR matrix equation is only 4 by 4. With the use of BBGF, the CPU requirement for the BBGF-MST technique is 0.27 seconds on a standard laptop for solving the KKR eigenvalue equation. Numerical results of the band diagrams are illustrated. Higher order spherical waves are next used to calculate the normalized band (cid:12)eld solutions for the entire cell.
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基于宽带格林函数-多重散射理论的三维周期结构能带和带场解快速计算方法
我们将BBGF-MST(宽带格林函数-多重散射理论)方法扩展到周期结构的三维问题。计算了带结构和带场解。BBGF的一个特点是晶格格林函数是宽带的,因此可以在许多频率下快速计算球面波展开的系数。然后将这些用于KKR (Korringa-Kohn-Rostoker)特征值方程的矩阵元素的快速计算。利用BBGF-MST,导出了低阶矩阵特征值方程。对于(cid:12)前两个波段,KKR矩阵方程的维数仅为4 × 4。通过使用BBGF, BBGF- mst技术在标准笔记本电脑上求解KKR特征值方程所需的CPU时间为0.27秒。给出了带图的数值结果。高阶球面波随后用于计算整个细胞的归一化带(cid:12)场解。
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