The ability to design the electromagnetic properties of materials to achieve any given wave scattering effect is key to many technologies, from communications to cloaking and biological imaging. Currently, common design methods either neglect degrees of freedom or are difficult to interpret. Here, we derive a simple and efficient method for designing wave–shaping materials composed of dipole scatterers, taking into account multiple scattering effects and both magnetic and electric polarizabilities. As an application of our theory, we design aperiodic metasurfaces that re-structure the radiation from a dipole emitter: (i) modifying of the near-field to provide a 4-fold enhancement in power emission; (ii) re-shaping the far-field radiation pattern to exhibit chosen directivity; and (iii) the design of a discrete Luneburg–like lens. Additionally, we develop a clear physical interpretation of the optimised structure, by extracting eigen-polarizabilities of the system, finding that a large eigen-polarizability corresponds to a large collective response of the scatterers.

设计材料的电磁特性以实现任何给定的波散射效应的能力是许多技术的关键，从通信到隐形和生物成像。目前，常见的设计方法要么忽略自由度，要么难以解释。在这里，我们推导出一种简单有效的方法来设计由偶极子散射体组成的造波材料，同时考虑到多重散射效应以及磁极化和电极化。作为我们理论的应用，我们设计了重新构建偶极子发射器辐射的非周期性超表面：（i）修改近场以提供功率发射的 4 倍增强；(ii) 重新塑造远场辐射方向图以展示选定的方向性；(iii) 离散 Luneburg 式透镜的设计。此外，