Abstract <p>Rigorous calculations of the absolute diffraction efficiency η performed earlier using two commercial computer solvers based on electromagnetic methods have shown that the maximum η of neutron gratings with sinusoidal and lamellar groove profiles can exceed known analytical limits. Thus, for a sinusoidal grating with a period of <i>d</i> = 50 μm and a groove depth of <i>h</i> = 53.4 nm at an incidence angle of θ = 89.72° (θ_c&#xa0;= 89.53°), η(–1) = 46.8% was obtained at a wavelength of λ = 1 nm, which is 38.5% higher than the maximum scalar efficiency. For a similar lamellar grating, η(–1) = 46.05% was determined, which is 13.7% higher than the scalar one. In this work, gratings with sinusoidal and lamellar groove profiles were investigated for copper, one of the most promising materials for cold neutron optics. The most efficient gratings with a triangular profile (“with a blaze”) were also considered. For a grating with <i>d</i> = 50 µm and <i>h</i> = 41.1 nm, η(–1) = 79.2% was achieved for θ = 89.37° and λ = 1 nm. The data calculated using both software with an accuracy of ~0.1% for the main diffraction orders of gratings of all groove profiles converge well and correspond to the estimates obtained using the phenomenological approach.</p>