Metaclusters for the Full Control of Mechanical Waves

We present a method for the control of waves based on inverse multiple scattering theory. Conceived as a generalization of the concept of metagrating, we call metaclusters to a finite set of scatterers whose position and properties are obtained by inverse design once we have defined their response to some external incident field. The particular focus is on designing passive metaclusters that do not require an external source of energy. The method is applied to the propagation of flexural waves in thin plates, and to the design of far-field patterns, although its generalization to acoustic or electromagnetic waves is straightforward. Numerical examples are presented to the design of uni- and bidirectional ``anomalous scatterers,'' which will bend the scattering energy along a specific direction, ``odd pole'' scatterers, whose radiation pattern presents an odd number of poles, and to the generation of vortical patterns. Finally, some considerations about the optimal design of these metaclusters are discussed.