Multifunctional elastic metasurface design with topology optimization

Abstract Metasurfaces have emerged as promising materials for wave manipulation due to their compact form. While various innovative designs have been proposed and impressive wave-shaping capabilities have been demonstrated, the practical applications of these materials require additional features and functionalities such as high-energy transmission and robust manipulation, which are difficult to realize based on physics-driven design approaches. In this work, we propose a systematic design method based on topology optimization for the design of elastic metasurfaces with multiple objectives/requirements. Theoretical analyses were conducted to identify the conditions for achieving high transmission and robust manipulation. Based on the analyses, a topology optimization formulation is proposed for achieving specific phase delays and high transmission within a given frequency band. Genetic algorithm is adopted to solve the optimization problem, with special treatments on the structural connectivity. Both locally resonant and non-resonant structures can be obtained from this method, and there is no need to pre-determine the type of structures to be designed. Depending on the design emphasis and the working frequency range, the proposed design method can automatically determine the best type of structures that meet the design requirements. With this method, metasurfaces for anomalous refraction of longitudinal waves were designed. Nearly full transmission with robust performance has been confirmed by numerical simulations. To demonstrate the generality of the proposed method, a multi-functional metasurface for simultaneously control of longitudinal and shear waves has also been designed, which is the first realization of such functionality.