Inverse Grating Problem: Efficient Design of Anomalous Flexural Wave Reflectors and Refractors

To obtain a desired profile of transmitted wave modes, what must a diffraction grating look like? This work presents a generalized, systematic method to design devices for control of the flow of wave energy. This control is achieved by engineering the diffraction properties of gratings, and simplified configurations are found, compared to similar gradient-metasurface devices. Although focused on flexural waves in thin elastic plates, this approach can be easily applied to other domains, such as optics, electronics, or fluid acoustics, as the diffraction principles are the same in all of these contexts.