Inverse design of sub-wavelength convergent grating based on the “stepped particle swarm algorithm”

In this Letter, a novel "stepped particle swarm optimization" (SPSO) based on field intensity adjustment is proposed. After that, we used this algorithm to design a sub-wavelength converging grating that could be integrated with the detector on the back. Firstly, the advantages of reverse design in the process of two-dimensional or multi-element grating pattern design were summarized by comparing the theory of forward and reverse design. Then, the common "particle swarm optimization" (PSO) and our proposal were compared in the reverse design process; we found that the field strength at the focal point obtained by the improved algorithm was approximately twice of the conventional PSO, and the SPSO had higher computational efficiency and better global convergence. The value of the SPSO had been steadily enlarged, which significantly improved the performance of the sub-wavelength convergent grating. Finally, the property of the sub-wavelength converging grating was simulated, and we found that the grating could achieve good convergence in the focal length range of 100-150 µm, and had a strong ability to compensate for the position deviation of the incident light. In actual optical communications, this sub-wavelength converging grating will play an important role in alleviating the bandwidth and quantum efficiency, improving the performance of the detectors.