The sub-wavelength focusing of flexural waves achieved by splitting one plane lens into two halves with a controllable angle

The flexural wave focusing in plates and shells is of great importance for energy harvesting and vibration control. Traditional plane lens based on gradient index and metasurface usually exhibits normal focusing, i.e., the focusing spot size is larger than half wavelength. In order to improve its working performance, increase energy at the focal point, reduce the focusing spot size and further achieve subwavelength focusing, a novel design scheme is proposed, i.e., splitting one traditional plane lens into two halves with a controllable inner angle. Firstly, the transmission and phase are calculated by using the Timoshenko beam theory, utilizing which the lens design is finalized via changing beam thickness perpendicular to wave propagation. After that, the working performance of two sub -lenses is compared with that of one single lens via numerical simulations, including the focal position, energy distribution, and spot size, which are further validated through experimental measurements. It is demonstrated that the flexural wave can exhibit subwavelength focusing after traveling across two adjacent halves, with the focusing spot size smaller than half wavelength. Specifically, the subwavelength focusing is broadband, and still occurs in a frequency region centered at the designed frequency. The proposed design scheme is expected to provide an innovative approach for the lens design in acoustics and optics.