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.
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