Spectral element boundary integral method with periodic layered medium dyadic Green's function for multiscale nano-optical scattering analysis.

In this work, we propose a numerical solver combining the spectral element - boundary integral (SEBI) method with the periodic layered medium dyadic Green's function. The periodic layered medium dyadic Green's function is formulated under matrix representation. The surface integral equations (SIEs) are then implemented as the radiation boundary condition to truncate the top and bottom computation domain. After describing the interior computation domain with the vector wave equations, and treating the lateral boundaries with Bloch periodic boundary conditions, the whole computation domains are discretized with mixed-order Gauss- Lobatto-Legendre basis functions in the SEBI method. This method avoids the discretization of the top and bottom layered media, so it can be much more efficient than conventional methods. Numerical results validate the proposed solver with fast convergence throughout the whole computation domain and good performance for typical multiscale nano-optical applications.