  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.
