Scattering of surface waves by inhomogeneities in crystalline structures

TL;DR

This paper investigates how inhomogeneities in crystalline structures affect surface wave propagation, providing an exact transmittance formula and analyzing energy leakage in a scalar wave model on a square lattice.

Contribution

It introduces an exact solution for surface wave transmittance considering inhomogeneities, extending previous models with explicit energy leakage expressions.

Findings

Derived an explicit formula for surface wave transmittance.

Quantified energy leakage into bulk waves.

Provided graphical analysis for various surface parameters.

Abstract

In current scientific and technological scenario, studies of transmittance of surface waves across structured interfaces have gained some wind amidst applications to metasurfaces, electronic edge-waves, crystal grain boundaries, etc. The results presented in the present article shed a light on the influence of material inhomogeneities on propagation of surface waves. Within the framework of classical mechanics, an analog of Gurtin-Murdoch model is employed where elastic properties on surface are assumed to be distinct from bulk. Restricting to scalar waves on prototype square lattice half-plane, particles on considered structured surface have piecewise-constant mass and surface force-constants across an interfacial point. Particles in bulk lattice interact with nearest neighbours in a way that involves unequal force-constants parallel to surface versus normal to it. A surface wave band exists for such lattice structure wherein the waveform decays exponentially inside half-plane. A formula for surface wave transmittance is given based on an exact solution on half-plane, and, thus, previous work of Sharma & Eremeyev 2019 Int. J. Eng. Sci. 143, 33-38 is extended. An explicit expression for fraction of energy influx leaked via bulk waves is a highlight. Included are graphical results for several illustrative values of surface structure parameters.