Nano-cylindrical hole metamaterials for high-efficiency ultra-bandwidth two-dimensional diffraction

Two-dimensional (2D) grating as the core component of the 2D grating displacement measurement system has a more demanding performance in recent years. In this paper, a 2D metal grating with an array of nano-cylindrical holes is proposed, which can achieve a high diffraction efficiency (DE) output of 2 × 2 at a wavelength of 780 nm, where the DEs of (0, ±1) and (±1, 0) orders are over 23% with a nonuniformity of 0.23%. Meanwhile, the results of the finite-difference time-domain method are in good agreement with those of the finite element method. Notably, the proposed grating has a wavelength bandwidth of 44 nm and a large angular bandwidth of 12° when the DE of all main diffraction orders is chosen to be above 20% as the target condition. This angular bandwidth is a significant improvement relative to previous reports. Moreover, the results show that the proposed grating has good manufacturing tolerances while ensuring high performance, demonstrating its feasibility in practical manufacturing. Therefore, this grating has significant potential in the field of 2D grating displacement measurement due to its simplicity, high efficiency, good uniformity, wide bandwidth and good process tolerance. •The two-dimensional metal grating is studied based on nano-cylindrical hole metamaterials.•The grating presents outstanding wavelength and angular bandwidths for 2 × 2 splitting diffraction.•Efficiencies of 2 × 2 output in (0, ±1) and (±1, 0) orders are over 23% with a nonuniformity of 0.23%.•The grating exhibits two-dimensional high efficiency, good uniformity and excellent tolerance for fabrication.