Tunneling of Elastic Waves in a Tapered Waveguide

Abstract: Understanding how evanescent modes mediate energy transfer in tapered elastic waveguides is of paramount interest, as it unlocks new strategies for wave control and manipulation. Evanescent modes play a crucial role in energy localization and in the emergence of thickness resonances. We report the first unambiguous experimental evidence of Lamb mode tunneling near turning points, revealing how energy can traverse an evanescent barrier and recover its propagative nature after a finite transit time. Focusing on waveguides with linearly varying thickness, we show that the $S_2$ mode becomes evanescent over a narrow frequency band, enabling a tunnelinglike phenomenon. Our study demonstrates that the barrier width is governed by the elastic properties of the material, particularly the Poisson's ratio, within a confined range bordering the Dirac cone. Numerical results exhibit excellent agreement with predictions from the Wentzel-Kramers-Brillouin approximation. These findings provide compelling evidence that, for a specific barrier width, evanescent modes mediate energy transfer across regions classically forbidden to propagating waves, revealing the mechanisms governing transmission, localization, and mode conversion in structured or corrugated elastic waveguides.