Fast Calculations of Vector Electromagnetics in 3D Periodic Structures Based on Multiple Scattering Theory and Broadband Green's Function

We have developed a fast method of using Multiple Scattering Theory-Broadband Green's Function (BBGF-MST) for band field calculations. In this paper, we successfully extended the method to the vector electromagnetic case of 3D periodic structures. In the MST-BBGF approach, the broadband transformation to vector spherical waves for 3D is derived using the Broadband Green's function. The band eigenvalue problem is expressed in terms of the single scatterer T' matrix which is independent of the periodic lattice nor the Bloch vector. For the first five bands, the dimension of the KKR eigen equation is merely 6, as 6 vector spherical waves are utilized for the scattered waves. We make extensive comparisons of the results with the commercial software COMSOL in both accuracy and computation efficiency. The CPU requirement on a standard laptop for the MST-BBGF method is merely 0.309 seconds for the first 5 bands. The MST-BBGF method is accurate and is at least two orders of magnitude faster than commercial software COMSOL. In the band field calculations, we employ the approach of extended coefficient to use the low order eigenvector of 6 to extend to 240 vector spherical wave coefficients without the need of recalculating the eigenvalue nor the eigenvector of the KKR equation. The extended coefficients approach gives accurate band field solutions for the entire (0, 0, 0) cell.