声晶格共振和广义瑞利-布洛赫波

G. J. Chaplain, S. C. Hawkins, M. A. Peter, L. G. Bennetts, T. A. Starkey
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引用次数: 0

摘要

数十年来,周期性晶格和光栅上的波的奥秘一直引起物理学家和数学家的共鸣。我们对看似最简单的阵列系统进行了深入分析:由嵌入无色散介质中的二维散射体组成的一维周期性晶格,该介质受亥姆霍兹方程控制。我们对这种系统进行了研究,并通过实验证实了一类新的广义雷利-布洛赫波的存在。在这里,我们通过实验观测到了第一截点以上的第一种广义雷利-布洛赫波,即辐射波。我们考虑了沿衍射光栅的辐射声晶格共振,并通过考虑嵌入空气中的非共振二维圆柱形 Neumannscatterers 短阵列和长阵列,将它们与广义瑞利-布洛赫波联系起来。在短阵列上,我们观察到连续波激励下的有限晶格共振,而在长阵列上,我们观察到脉冲激励下的传播瑞利-布洛赫波。我们通过考虑多波散射理论来解释这种现象,并在此过程中统一了用于描述无限周期阵列和无限阵列上的波的不同术语及其色散特性的解释。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Acoustic Lattice Resonances and Generalised Rayleigh--Bloch Waves
The intrigue of waves on periodic lattices and gratings has resonated with physicists and mathematicians alike for decades. In-depth analysis has been devoted to the seemingly simplest array system: a one-dimensionally periodic lattice of two-dimensional scatterers embedded in a dispersionless medium governed by the Helmholtz equation. We investigate such a system and experimentally confirm the existence of a new class of generalised Rayleigh--Bloch waves that have been recently theorised to exist in classical wave regimes, without the need for resonant scatterers. Airborne acoustics serves as such a regime and here we experimentally observe the first generalised Rayleigh--Bloch waves above the first cut-off, i.e., in the radiative regime. We consider radiative acoustic lattice resonances along a diffraction grating and connect them to generalised Rayleigh--Bloch waves by considering both short and long arrays of non-resonant 2D cylindrical Neumann scatterers embedded in air. On short arrays, we observe finite lattice resonances under continuous wave excitation, and on long arrays, we observe propagating Rayleigh--Bloch waves under pulsed excitation. We interpret their existence by considering multiple wave scattering theory and, in doing so, unify differing nomenclatures used to describe waves on infinite periodic and finite arrays and the interpretation of their dispersive properties.
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