We present a topology optimization method for a 1D dielectric metasurface, based on a new concept: fluctuation and trend analysis for initial random conditions. The key point of the proposed optimization method is that the procedure initially generates a couple of device distributions termed fluctuation/mother and trend/father, with specific spectra that efficiently sample not the local minimum of the objective function but basins of optimal solutions in the design space. Studying a 1D dielectric metagrating deflecting a normal polarized incident wave onto a range of angles, we show that a suitable choice of a specific power density spectrum for this initial couple highly increases the probability of reaching a basin of high-performance devices. We guess initial geometries holding the physical properties of the desired final device, allowing accurate targeting of these high-performance device basins in the design space. To include desired physical properties in the initial geometry model, we introduce a formalism allowing generation of a random process with a particular power density or correlation function. By means of a suitable definition of the trend function, we identify an ultimate power density bandlimited spectrum for the fluctuation functions allowing a very high probability and leading to a rapid descent to favorable basins of optimal solutions, consequently reaching high-performance final structure in the design space.

中文翻译：

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光子学设备的拓扑优化：波动趋势分析概念；高斯和Durden-Vesecky功率密度带限谱的随机初始条件

我们基于一种新概念，提出了一种针对一维介电超表面的拓扑优化方法：针对初始随机条件的波动和趋势分析。所提出的优化方法的关键在于，该过程最初会生成一对设备分布，称为波动/母亲和趋势/父亲，其特定的光谱可以有效地采样目标函数的局部最小值而不是设计中的最优解。空间。研究一种1D电介质metagrating偏转正常偏振波入射到一个角度范围内，我们表明，对于该初始耦合特定功率谱密度的适当选择高度增加达到高性能器件盆的概率。我们猜测初始几何形状具有所需最终设备的物理特性，可以在设计空间中精确定位这些高性能设备池。为了在初始几何模型中包括所需的物理特性，我们引入形式主义，以允许生成具有特定功率密度或相关函数的随机过程。通过对趋势函数的适当定义，我们确定了波动函数的极限功率密度带限谱，从而允许很高的概率，并导致快速下降到最优解的有利盆地，从而在模型中达到高性能的最终结构。设计空间。我们引入形式主义，以允许生成具有特定功率密度或相关函数的随机过程。通过对趋势函数的适当定义，我们确定了波动函数的极限功率密度带限谱，从而允许很高的概率，并导致快速下降到最优解的有利盆地，从而在模型中达到高性能的最终结构。设计空间。我们引入形式主义，以允许生成具有特定功率密度或相关函数的随机过程。通过对趋势函数的适当定义，我们确定了波动函数的极限功率密度带限谱，从而允许很高的概率，并导致快速下降到最优解的有利盆地，从而在模型中达到高性能的最终结构。设计空间。