A novel boundary element method using surface conductive absorbers for full-wave analysis of 3-D nanophotonics

Abstract

Fast surface integral equation (SIE) solvers seem to be ideal approaches for simulating 3-D nanophotonic devices, as these devices generate fields both in an interior channel and in the infinite exterior domain. However, many devices of interest, such as optical couplers, have channels that can not be terminated without generating reflections. Generating absorbers for these channels is a new problem for SIE methods, as the methods were initially developed for problems with finite surfaces. In this paper we show that the obvious approach for eliminating reflections, making the channel mildly conductive outside the domain of interest, is inaccurate. We describe a new method, in which the absorber has a gradually increasing surface conductivity; such an absorber can be easily incorporated in fast integral equation solvers. Numerical experiments from a surface-conductivity modified FFT-accelerated PMCHW-based solver are correlated with analytic results, demonstrating that this new method is orders of magnitude more effective than a volume absorber, and that the smoothness of the surface conductivity function determines the performance of the absorber. In particular, we show that the magnitude of the transition reflection is proportional to 1/L^(2d+2), where L is the absorber length and d is the order of the differentiability of the surface conductivity function.