A novel method for sub-wavelength focusing of flexural waves

A novel method for achieving sub-wavelength focusing of reflected flexural waves in a single-phase plate is proposed in this paper. The original plane lens is divided into two adjacent lenses, and modulating the internal angle between them, more reflected wave components from broader directions can arrive at the focusing posi-tion, which leads to the sub-wavelength focusing phenomenon with the focusing size smaller than half wave-length. Firstly, Mindlin plate theory is adopted to solve the reflected wave, and lenses with different width values are designed based on phase modulation for wave focusing. After that, the sub-wavelength focusing is exem-plified numerically and experimentally, with the reason explained systematically. Remarkably, the focusing size perpendicular to wave propagation direction locates (0.4 lambda, 0.5 lambda), which is controlled by the internal angle. It is demonstrated that the subwavelength focusing is general because it is still suitable when the lenses are designed via the thickness variation or other phase distribution. Additionally, the lenses exhibit broadband property, which can work in a certain frequency region centered the designed frequency. Not limited by flexural wave in plates, the design methodology in this paper can also lay the foundation for wave control in electromagnetics and acoustics.