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

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 first 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 secondson 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 field solutions for the entire cell.