Perfect transmission of elastic waves obliquely incident at solid–solid interfaces

Abstract

Perfect wave transmission across dissimilar media is critical in wave devices. However, the existing impedance matching theory allows perfect wave transmission only in special cases dealing with electromagnetic waves or acoustic waves in fluids. For the cases where elastic waves are incident at an arbitrary angle from one solid to another, even elaborately designed layers satisfying the conventional theory cannot realize perfect wave transmission. Elastic waves in isotropic solids always carry waves of both longitudinal and transverse modes and this multimodality generally couples the two wave modes at solid–solid interfaces, making the conventional impedance matching theory inapplicable for elastic waves. Here, we establish a novel theory for the perfect transmission through solid–solid interfaces and propose a unique nonresonant anisotropic single-phase metamaterial realizing the theory. The theory dictates intriguing interferences among longitudinal–shear coupled waves existing inside a metamaterial. The theory is shown to be valid for any form of wave transmissions, either mode-preserving or mode-converting. Experiments using highly impedance-mismatched elastic plates were conducted to verify the validity of the proposed theory. A further analysis confirmed transmittance enhancement over a wide range of frequencies and incidence angles. Our findings will be useful in developing new types of powerful wave devices.