Modeling Elastic Wave Mode Conversion within Zero-Phase-Difference Ultrathin Anisotropic Medium

Xinyue Bi^1*Yucheng Gao²

• ¹China University of Geosciences School of Mathematics and Physics, Wuhan, China
• ²University of New South Wales, Sydney, Australia

We investigate a novel mechanism for elastic wave mode conversion in structured media composed of periodic resonant scatterers. Traditional models typically rely on phase accumulation between longitudinal and transverse wave components as they propagate through an anisotropic layer. This limits their effectiveness in the low-frequency or thin-layer regime. In contrast, we propose a new model based on oblique resonance within a homogenized anisotropic block, which generates oblique displacements and introduces tangential motion at the interface. it is carried out under the limiting condition where the scatterer thickness approaches zero . Previous studies, such as Ref. [25], did not consider this zero-thickness limit. If one directly substitutes d=0 into their formulations, the result becomes a trivial solution.This fundamentally differs from existing literature that derive methods for finite-thickness structures. We derive the boundary conditions and establish a coupled system of equations to describe the transmission and reflection behavior. Effective parameters, including mass density and impedance, are extracted from field quantities within the computational region and are shown to be angle-dependent. The conversion rates predicted by our model show excellent agreement with simulations, confirming both the physical assumptions and the analytical formulation. The proposed approach provides a new pathway for low-frequency, compact, and efficient control of elastic wave modes.