We present a topology optimization method for a 1D dielectric metasurface, coupling the classical fluctuations-trend analysis (FTA) and diamond-square algorithm (DSA). In classical FTA, a couple of device distributions termed fluctuation or mother and trends or father, with specific spectra, is initially generated. The spectral properties of the trend function allow one to efficiently target the basin of optimal solutions. For optimizing a 1D metasurface to deflect a normally incident plane wave into a given deflecting angle, a cosine-like function has been identified to be an optimal father profile, allowing one to efficiently target a basin of local minima. However, there is no efficient method to predict the father profile number of oscillations that effectively allows one to avoid undesirable local optima. It would be natural to suggest a randomization of the variable that controls the number of oscillations of the father function. However, one of the main drawbacks of the randomness searching process is that, combined with a gradient method, the algorithm can target undesirable local minima. The method proposed in this paper improves the possibility of classical FTA to avoid the trapping of undesirable local optimal solutions. This is accomplished by extending the initial candidate family to higher-quality offspring that are generated due to the DSA. Doing so ensures that the main features of the best trends are stored in the genes of all offspring structures.

中文翻译：

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通过拓扑优化对一维介电超表面进行逆设计：菱形平方算法辅助的波动趋势分析

我们提出了一种一维介电超表面的拓扑优化方法，结合了经典的波动趋势分析（FTA）和菱形平方算法（DSA）。在经典FTA中，最初会生成具有特定频谱的称为波动或母体趋势或父体的几个设备分布。趋势函数的频谱特性使人们可以有效地针对最优解的盆地。为了优化一维超颖表面以将垂直入射的平面波偏转到给定的偏转角度，已将余弦函数确定为最佳父轮廓，从而可以有效地瞄准局部极小盆。然而，没有一种有效的方法来预测振荡的父分布图数量，该方法有效地避免了不希望的局部最优。建议将控制父函数振荡次数的变量随机化是很自然的。但是，随机性搜索过程的主要缺点之一是，与梯度方法结合使用时，该算法可以针对不需要的局部最小值。本文提出的方法提高了经典FTA避免陷入不良的局部最优解的可能性。这是通过将最初的候选家族扩展到DSA产生的更高品质的后代来实现的。这样可以确保最佳趋势的主要特征存储在所有后代结构的基因中。结合梯度法，该算法可以针对不良的局部最小值。本文提出的方法提高了经典FTA避免陷入不良的局部最优解的可能性。这是通过将最初的候选家族扩展到DSA产生的更高品质的后代来实现的。这样可以确保最佳趋势的主要特征存储在所有后代结构的基因中。结合梯度法，该算法可以针对不良的局部最小值。本文提出的方法提高了经典FTA避免陷入不良的局部最优解的可能性。这是通过将最初的候选家族扩展到DSA产生的更高品质的后代来实现的。这样可以确保最佳趋势的主要特征存储在所有后代结构的基因中。