Computing Floquet–Bloch modes in biperiodic slabs with boundary elements

摘要

A new variational formulation for the boundary element computation of Floquet–Bloch solutions to the Helmholtz equation is derived. The method is applicable to geometries that are layered in the vertical and biperiodic in two horizontal directions. The discretization leads to a nonlinear Hermitian eigenvalue problem which is solved using a homotopy approach. Numerical examples demonstrate that with the boundary element approach a high accuracy can be achieved with a small number of degrees of freedom in the discretization.