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

We present a topology optimization (TO) method for a 1D dielectric metasurface, coupling the classical trend-fluctuations analysis (FTA) and the diamond-square-algorithm (DSA). In the 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 to target efficiently 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 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 to avoid undesirable local optima. It would be natural to suggest a randomization of the variable which 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 the 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 thanks to a diamond-square-algorithm (DSA). Doing so, ensures that the main features of the best trends are stored in the genes of all Offspring structures.