用体积积分方程法模拟光子学中的绝热吸收体
Adiabatic absorbers in photonics simulations with the volume integral equation method
摘要：
本文描述了一种用于模拟截断纳米光子学结构的FFT加速体积积分方程（VIE）方法中绝热吸收层的实现和性能。在截断的网站，我们放置的吸收区，电导率逐渐增加，以尽量减少反射。在连续设置中，这种绝热吸收器已经通过耦合模理论示出，以产生以与吸收轮廓函数的平滑度相关的速率减小的反射。我们采用的VIE公式依赖于均匀离散的几何形状，在连续变化的字段和材料属性表示的分段常数函数。这种离散化使得能够通过FFT加速该方法，并且此外，可以以直接的方式执行变化吸收的引入，而不会损害这种加速。我们证明，尽管粗糙的离散近似光滑的吸收轮廓，我们的方法恢复理论预测的绝热吸收体的反射行为。因此，我们表明，FFT加速的VIE方法是一种有效的和快速的模拟工具，纳米光子学模拟。
英文摘要：
This paper describes the implementation and performance of adiabatic absorbing layers in an FFT-accelerated volume integral equation (VIE) method for simulating truncated nanophotonics structures. At the truncation sites, we place absorbing regions in which the conductivity is increased gradually in order to minimize reflections. In the continuous setting, such adiabatic absorbers have been shown via coupled-mode theory to produce reflections that diminish at a rate related to the smoothness of the absorption profile function. The VIE formulation we employ relies on uniform discretizations of the geometry over which the continuously varying fields and material properties are represented by piecewise constant functions. Such a discretization enables the acceleration of the method via the FFT and, furthermore, the introduction of varying absorption can be performed in a straightforward manner without compromising this speedup. We demonstrate that, in spite of the crude discrete approximation to the smooth absorption profiles, our approach recovers the theoretically predicted reflection behavior of adiabatic absorbers. We thereby show that the FFT-accelerated VIE method is an effective and fast simulation tool for nanophotonics simulations.
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