Spectral element boundary integral method for rapid and accurate simulations of inhomogeneous objects in layered media in nanophotonics

Abstract

We recently developed an efficient numerical solver, the spectral element boundary integral (SEBI) method with the periodic layered medium dyadic Green's functions, to perform rapid and accurate simulations in nanophotonic applications. The problem is Bloch (Floquet) periodic in the lateral directions but has a multilayer background medium in the vertical direction, and arbitrary objects are embedded in the layered medium. We employ the periodic layered medium dyadic Green's function, and the surface integral equations as the radiation boundary condition to truncate the top and bottom computation boundaries of the interior domain that is simulated by the spectral element method. Therefore, all multiple scatterings within the top and bottom layered media have been analytically accounted for in the radiation boundary condition, and the computational domain is only limited to the inhomogeneous objects embedded in the layered medium. Consequently, this SEBI solver can be much more efficient than conventional methods. We demonstrate the accuracy and efficiency of this solver for several typical nanophotonic applications.