Topology-optimized freeform broadband optical metagrating for high-efficiency large-angle deflection

A metagrating made of periodic arrays of subwavelength inclusions has great capability for efficient manipulation of the impinging wavefront at subwavelength scale. However, it suffers from a significant practical issue in that the diffraction efficiency declines rapidly along with the increase of deflection angle, especially for broadband application scenarios. Here, we comprehensively investigated different topology optimization approaches to design the broadband optical metagrating for high-efficiency large-angle deflection, including single-wavelength optimization (SO), max-min optimization (MO), and average optimization (AO). It is demonstrated that the AO approach is more appropriate to optimize the broadband high-efficiency metagrating. Specifically, a freeform metagrating of up to about a 70° deflection angle at a central wavelength of 10.6 µm with diffraction efficiency exceeding 80% over a broad bandwidth of 4.36 µm in the infrared range is demonstrated based on the AO approach. It is also shown that, for all three optimization approaches, the quasi-catenary metagrating optimized from initial catenary structures has the evident advantage on bandwidth compared to that optimized from initial discrete structures. Our results provide insights into the inverse design of metagratings and may find potential applications in broadband achromatic metalenses and other broadband meta-devices.