横向周期超晶格中的表面声波

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS Wave Motion Pub Date : 2024-05-07 DOI:10.1016/j.wavemoti.2024.103331
A.L. Shuvalov
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引用次数: 0

摘要

研究了横向周期性超晶格中表面声波(SAW)的存在,这种超晶格被模拟为各向异性的弹性半空间,其材料特性沿平行于表面的分层方向(称作 X)存在任意周期性变化。与均质半空间不同,这种结构允许产生不止一个(色散)声表面波。具体来说,研究表明,任何具有一般周期性轮廓形状的超晶格最多可容纳三个声表面波色散分支 ω(Kx),即在任何固定布洛赫文波数 Kx 下,最多可容纳三个不同的声表面波频率。此外,在一对超晶格中,固定 Kx 处的声表面波总数也不能超过三个,这对超晶格的周期性剖面是通过轴 X 的反转而相互获得的。在这两个超晶格中,必须至少有一个声表面波分支存在,除非体波阈值是所谓的特殊波(即承认表面掠过波)。在超晶格对反转 X→-X 不变的特殊情况下,声表面波分支是唯一的。弱调制超晶格的扰动理论推导说明了上述一般结果。对于每个相互 "反转 "的超晶格中由瑞利波演化而来的准瑞利波分支,以及其中一个超晶格中由特殊体波阈值演化而来的准体波分支,都得到了明确的前导阶公式。
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Surface acoustic waves in laterally periodic superlattices

The existence of surface acoustic waves (SAWs) is studied in laterally periodic superlattices, modelled as an anisotropic elastic half-space with an arbitrary periodic variation of its material properties along the stratification direction (call it X) parallel to the surface. Unlike a homogeneous half-space, such a structure allows for more than one (dispersive) SAW. Specifically, it is shown that any superlattice with a generic shape of periodicity profile admits at most three SAW dispersion branches ω(Kx), i.e., at most three different SAW frequencies at any fixed Bloch wavenumber Kx. Moreover, the total number of SAWs at fixed Kx in a pair of superlattices with periodicity profiles obtained from one another by the inversion of the axis X cannot exceed three either. At least one SAW branch must exist in one of these two superlattices unless the bulk-wave threshold is the so-called exceptional (i.e., admits surface skimming wave). The SAW branch is unique in the particular case of a superlattice invariant to the inversion XX. The above general results are illustrated by the perturbation theory derivations for the weakly modulated superlattices. Explicit leading-order formulas are obtained for the quasi-Rayleigh wave branch evolving from the Rayleigh wave in each of the mutually ”inverse” superlattices and for the quasibulk wave branch evolving from the exceptional bulk-wave threshold in one of the superlattices.

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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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