Design of arbitrary energy distribution beam splitters base on multilayer metagratings by a hybrid evolutionary particle swarm optimization.

Multilayer metagratings have strong wavefront manipulation capabilities and find important applications in beam splitters. Traditional methods rely on the phase gradient design of generalized Snell's law, which can achieve highly efficient beam splitters with uniform energy distribution. However, designing arbitrary energy distributions in different channels under two orthogonal polarizations remains a challenge because it requires more complex structures to modulate the energy flow. In this work, we employed a hybrid evolutionary particle swarm optimization (HEPSO) from the combination of particle swarm optimization (PSO) and genetic algorithm (GA) which has a strong ability to find the optimal structures that satisfy the specific energy flow distributions. We used the crossover and mutation operators of GA to improve the global search capabilities, and the velocity updating formula of PSO to replace the selection operator of GA to avoid local optimization. Using this approach, we successfully designed a uniform beam splitter with an efficiency of over 90% and two beam splitters with arbitrary energy distributions, achieving an average error of about 0.5%. The optimal and average efficiencies obtained from running 10 optimizations are 2.2% and 4% higher than those obtained using PSO alone with 30 populations and 75 iterations. We envision that the proposed method can also provide an idea for other photonics design problems.