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We present a topology optimization (TO) method for a 1D dielectricmetasurface, coupling the classical trend-fluctuations analysis (FTA) and thediamond-square-algorithm (DSA). In the classical FTA, a couple of devicedistributions termed Fluctuation or mother and Trends or father, with specificspectra is initially generated. The spectral properties of the trend function,allow to target efficiently the basin of optimal solutions. For optimizing a 1Dmetasurface to deflect a normally incident plane wave into a given deflectingangle, a cosine-like function has been identified to be an optimal fatherprofile allowing to efficiently target a basin of local minima. However thereis no efficient method to predict the father profile number of oscillationsthat effectively allows to avoid undesirable local optima. It would be naturalto suggest a randomization of the variable which controls the number ofoscillations of the father function. However, one of the main drawbacks of therandomness searching process is that, combined with a gradient method, thealgorithm can target, undesirable local minima. The method proposed in thispaper improves the possibility of the classical FTA to avoid the trapping ofundesirable local optimal solutions. This is accomplished by extending theinitial candidate family to higher quality offspring that are generated thanksto a diamond-square-algorithm (DSA). Doing so, ensures that the main featuresof the best trends are stored in the genes of all Offspring structures.

Inverse design of a 1D dielectric metasurface by topology optimization: fluctuations-trend analysis assisted by a diamond-square algorithm