An improved Fourier modal method for design of metasurface diffractive optical elements

An improved Fourier modal method (FMM) is developed for the design of metasurface diffractive optical elements (DOEs), which combines the iterative Fourier transform algorithm (IFTA) with FMM. In which, the IFTA is executed for a coarse solution; then, FMM is for a precise solution. We take a 5 × 5 metasurface DOE with nanorods as an example to explore the improved FMM (IFTA + FMM). By varying the diameter of the nanorods on the metasurface DOE, a 5 × 5 spot array DOE has been created with a diffraction angle of 48°× 48° in the far field. The analysis results show that the improved FMM (IFTA + FMM) requires fewer iterations, about 17 times, while direct FMM requires about 70 times. The DOE designed with an improved FMM achieves a diffraction efficiency of 79.6% with a uniformity of 24.2%, while the DOE designed with a direct FMM shows a diffraction efficiency of 76.9% with a uniformity of 27.7%. The improved FMM (IFTA + FMM) shows a similar accuracy, but is more timesaving, simple, and intuitive.