Simultaneous manipulation of longitudinal and transverse elastic waves with a sharp focusing effect and customizable energy splitting ratios

Mode coupling and conversion between longitudinal and transverse modes are ubiquitous and universal in elastic waves, presenting a challenge in realistic applications such as nondestructive evaluation and geological exploration, where independent and separate manipulation of each mode is demanded. In this article, we propose a design of elastic metalens that can realize a high-efficiency focusing for the longitudinal wave and a V-shaped converging pattern for the transverse wave at the same time. The metalens is constructed from a metagrating, where each meta-atom has a simple configuration and renders high diffraction efficiency even for large steering angles, enabled by concurrent utilization of grating diffraction theory and advanced optimization algorithms. Interestingly, an arbitrary energy splitting ratio between the reflected longitudinal and transverse waves can be obtained by precisely controlling the coupling strength and conversion efficiency between them, providing improved flexibility and adaptability to various application environments. Two illustrative examples with a sharp focusing effect and tailored conversion efficiency are explicitly demonstrated, with a 50/50 energy splitting ratio between the longitudinal and transverse waves in the first case, and a 70/30 ratio in the second one.