A fast 3D full-wave solver for nanophotonics

Abstract

Conventional fast integral equation solvers seem to be ideal approaches for simulating 3-D nanophotonic devices, as these devices are considered to be open structures, generating fields in both an interior channel and in the infinite exterior domain. However, many devices of interest, such as optical ring resonator filters or waveguides, have channels that can not be terminated without generating numerical reflections. Therefore, designing absorbers for these channels is a new problem for integral equation methods, as integral equation methods were initially developed for problems with finite surfaces. In this thesis we present a technique to eliminate reflections, making the channel volume conductive outside the domain of interest. The surface integral equation (SIE) method is employed to take advantage of the piecewise homogeneous medium. The Poggio-Miller-Chang-Harrington-Wu (PM-CHW) formulation is formed and the boundary element method is employed to construct and solve a linear system. Moreover, the block Toeplitz matrix property and using FFT helps reduce memory requirement, and accelerate the circulant matrix vector product. Numerical experiments are presented to demonstrate that this method can effectively reduce reflections to 1%, and is easily incorporated in an fast integral equation solver.