Slime mold algorithm for topology optimization: metagratings inverse design

In this paper we discuss the use of a metaheuristic (MH) gradient-free optimization method, specifically the slime mold algorithm (SMA), combined with the topology optimization (TO) method to design metasurfaces using a spectral modal method. The motivation behind using a MH approach comes from the drawbacks associated with traditional gradient-based methods. Normally, gradient-based methods require the calculation of the electromagnetic (EM) field at certain nodes within the computation domain. However, in spectral modal methods, this is unnecessary since these methods can compute the EM response without the need for field component values. Second, optimizing metagratings often involves a multimodal objective function with multiple local minimums and gradient-based methods might struggle with finding the global optimum. So to overcome these drawbacks, we propose using a MH approach, specifically the slime mold algorithm (SMA). We apply SMA to a metasurface design, especially in the context of TO and spectral methods, which is relatively unexplored. By coupling both TO with SMA, we successfully design metagratings capable of deflecting incident waves into a desired transmission angle.