三维纳米光子学全波分析的表面导电吸收体边界元法
A novel boundary element method using surface conductive absorbers for full-wave analysis of 3-D nanophotonics
摘要：
快速表面积分方程（SIE）求解器似乎是模拟3-D纳米光子器件的理想方法，因为这些器件在内部通道和无限外部域中都产生场。然而，许多感兴趣的器件，例如光耦合器，具有不能在不产生反射的情况下终止的通道。为这些通道生成吸收体是SIE方法的一个新问题，因为这些方法最初是为有限表面问题开发的。在本文中，我们表明，明显的方法，消除反射，使通道温和的导电域以外的利益，是不准确的。我们描述了一种新的方法，其中吸收体具有逐渐增加的表面电导率，这样的吸收体可以很容易地纳入快速积分方程求解器。从表面电导率修改的FFT加速PMCHW为基础的求解器的数值实验与分析结果相关，表明这种新方法是数量级更有效的比体积吸收体，和表面电导率函数的平滑度决定的吸收体的性能。特别地，我们证明了过渡反射的大小与1/L^（2d+2）成比例，其中L是吸收体长度，d是表面电导率函数的可微性的阶数。
英文摘要：
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.
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