论文标题
高晶体优化：光子逆设计的平滑歧管上的近似基于梯度的二进制优化
Hypersphere Optimization: Approximated Gradient-Based Binary Optimization on Smooth Manifold for Photonic Inverse Design
论文作者
论文摘要
光子逆设计通常寻求通过二进制阵列参数化的设计，其中每个元素的值对应于空间中特定点的材料的存在或不存在。基于梯度的光子逆设计方法通常包括非二进制优化阵列的阈值；当阈值足够锋利时，将获得二进制设计。但是，由于尖锐阈值的梯度消失，可能会出现困难，这导致优化失速。在这里，我们提出了超晶体优化，这是一种在高维歧管上执行二元化光子优化的新方法。我们从数值上表明，在歧管上，来自目标函数的上游梯度可以将设计从一个几乎二进制阵列平滑地转移到另一个近二元阵列，并使用最小的像素翻转。我们的方法是一种基于梯度的近似二进制阵列的优化方法，可以应用于各种光子逆设计问题及其他地区。
Photonic inverse design typically seeks designs parameterized by binary arrays, where the values of each element correspond to the presence or absence of material at a particular point in space. Gradient-based approaches to photonic inverse design often include thresholding of non-binary optimization arrays; when the thresholding is sufficiently sharp, binary designs are obtained. However, difficulty can arise due to vanishing gradients for sharp thresholds, which cause optimization to stall. Here, we present hypersphere optimization, a new method of carrying out binarized photonic optimization on a high dimensional manifold. We numerically show that, on the manifold, upstream gradients from the objective function can smoothly transition a design from one nearly-binary array to another with minimal pixel flips. Our method is an approximate gradient-based optimization method for binary arrays that can be applied to various photonic inverse design problems and beyond.
