“…By introducing certain symmetry into the scattering potential, significant higher-order scattering takes place and leads to asymmetric diffraction according to the second condition of Friedel's law. In our previous work [37], we employed a pure phase grating with an odd symmetric (antisymmetric) distribution of refractive index in space (n = n + δn, δn(−x) = −δn(x)) to achieve higher order scattering, resulting in one-dimensional asymmetric diffraction and enabling specific functions, including directional elimination, group elimination, and directional diffraction, whose considerable robustness against disorders in offset refractive indices is nearly up to 30%. Moreover, many researchers have successfully synthesized media with tunable refractive indices through various materials and methods [38,39], thereby allowing for the feasible fabrication of such gratings in experiments.…”