Scattering of surface waves by inhomogeneities in crystalline structures

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-03-20 DOI:10.1098/rspa.2023.0683
Basant Lal Sharma
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Abstract

In current scientific and technological scenarios, 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 analogue of the 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 the half-plane. A formula for surface wave transmittance is given based on an exact solution on half-plane, and, thus, previous work (Sharma & Eremeyev 2019 Int. J. Eng. Sci. 143, 33–38 (doi:10.1016/j.ijengsci.2019.06.007)) 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.

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晶体结构中的不均匀性对表面波的散射
在当前的科学和技术领域,表面波在结构化界面上的透射率研究在超表面、电子边波、晶体晶界等方面的应用中获得了一些进展。本文介绍的结果揭示了材料不均匀性对表面波传播的影响。在经典力学框架内,采用了类似于古尔廷-默多克模型的方法,假定表面的弹性特性与主体不同。限于原型方格半平面上的标量波,被考虑的结构表面上的粒子具有片断恒定质量和跨界面点的表面力常数。体格中的粒子与近邻粒子相互作用时,平行于表面的力常数与法向力常数不相等。这种晶格结构存在一个表面波带,波形在半平面内呈指数衰减。根据半平面上的精确解法给出了表面波透射率公式,因此,之前的工作(Sharma & Eremeyev 2019 Int.J. Eng.Sci. 143, 33-38 (doi:10.1016/j.ijengsci.2019.06.007) )进行了扩展。通过体波泄露的能量流入部分的明确表达是一大亮点。文中还包含了几个表面结构参数值的图解结果。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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