2D freeform topology optimization in the real and spectral domains using the slime mold algorithm

The photonics community has shown increasing interest in the inverse design of photonic components and devices using gradient-based methods. This is due to its efficient gradient computation and suitability for large parameter and continuous design spaces when it is combined with the adjoint method. Despite their strong potential and ability to escape local minima, metaheuristic methods remain underutilized, particularly in photonics for topology optimization. The slime mold algorithm (SMA) is an advanced metaheuristic method that has proven its effectiveness in designing 1D structures. In this paper, we extend its application to the inverse design of 2D freeform structures. Two strategies are proposed and compared in this work: the first strategy involves using the values in the real domain of the permittivity tensor components as design variables. The second, more innovative strategy, involves optimizing the design through the Fourier coefficients of the components of the permittivity tensor. This latter method, which aligns better with the Fourier modal method (FMM) and spectral methods in general, reduces the dimensionality of the optimization problem.