Broadband achromatic flexural wave Mikaelian lens for high resolution focusing

Conformal transformation method (CTM) has been extensively applied to control propagation of electromagnetic waves and acoustics waves due to the form-invariant property of Maxwell equations and acoustic equations. However, CTM's application in elastic waves is rarely reported due to the governing equation of elastic waves do not have form invariant property. In this paper, through igniting evanescent waves at the interface of conformally mapped Mikaelian lens with hyperbolic secant refractive index profile, CTM is successfully used to achieve highly efficient (above 75%) broadband (30-80 kHz) achromatic high-resolution flexural wave focusing in thin plate with full width at half maximum (FWHM) around 0.2λ. The proposed Mikaelian lens is designed by linking refractive index with the thickness in plates. Simulated results agree well with theoretical prediction. This high performance for flexural wave focusing could be used for energy harvesting and medical imaging.