Conformal Mikaelian lens for flexural wave self-focusing, bending, non-diffraction Talbot effects, vibration reduction and energy harvesting

In this study, we employ conformal transformation methodology to design an arc-shaped flexural Mikaelian lens — hereafter termed the Conformal Mikaelian Lens (CML). The lens’s graded refractive index profile is engineered through coordinate transformation of conventional Mikaelian lens parameters into polar space. Beyond geometric transformation, we interpret the CML as an effective Riemannian space and analyze wave propagation along geodesic trajectories, which enables broadband conformal self-focusing and controllable wavefront bending. Numerical simulations and experimental results consistently demonstrate that the lens supports broadband flexural wave self-focusing and stable wavefront bending. Within this framework, we discover a conformal Talbot effect, in which periodic wavefronts exhibit shifted and non-uniformly scaled self-images due to curvature-induced metric distortion. Furthermore, leveraging the lens’s intrinsic self-focusing effect, the CML enables broadband vibration suppression and efficient energy harvesting, as confirmed by experimental results. This work establishes a theoretical and experimental foundation for multifunctional applications such as wave steering, sensing, energy conversion, and vibration control in curved flexural systems.