论文标题
可区分散射矩阵以优化光子结构
Differentiable Scattering Matrix for Optimization of Photonic Structures
论文作者
论文摘要
量化光子结构的光学反射和传输的散射矩阵对于理解结构的性能至关重要。在许多光子设计任务中，还希望知道结构的光学性能如何相对于设计参数，即散射矩阵的衍生物（或梯度）。在这里，我们解决了这一需求。我们提出了一种用于准确，稳健地计算散射矩阵衍生物的新算法。特别是，我们专注于半分析方法中的计算（例如严格的耦合波分析）。为了计算结构的散射矩阵，这些方法必须解决特征分类问题。但是，在计算散射矩阵衍生物时，区分特征分解会带来重大的数值困难。我们表明，特征分类问题的分化可以完全避开，从而提出了一种强大的算法。为了证明其功效，我们使用算法来优化跨表面结构并实现各种光学设计目标。
The scattering matrix, which quantifies the optical reflection and transmission of a photonic structure, is pivotal for understanding the performance of the structure. In many photonic design tasks, it is also desired to know how the structure's optical performance changes with respect to design parameters, that is, the scattering matrix's derivatives (or gradient). Here we address this need. We present a new algorithm for computing scattering matrix derivatives accurately and robustly. In particular, we focus on the computation in semi-analytical methods (such as rigorous coupled-wave analysis). To compute the scattering matrix of a structure, these methods must solve an eigen-decomposition problem. However, when it comes to computing scattering matrix derivatives, differentiating the eigen-decomposition poses significant numerical difficulties. We show that the differentiation of the eigen-decomposition problem can be completely sidestepped, and thereby propose a robust algorithm. To demonstrate its efficacy, we use our algorithm to optimize metasurface structures and reach various optical design goals.
