声学晶格共振与广义Rayleigh--Bloch波
Acoustic Lattice Resonances and Generalised Rayleigh--Bloch Waves
AI总结：
本研究针对一维周期声学晶格系统，通过空气声学实验首次观测到辐射区内无需共振散射体的广义Rayleigh--Bloch波，结合多波散射理论统一了有限与无限周期阵列波动的命名及色散解释。
摘要：
数十年来，周期晶格与光栅上的波动现象一直吸引着物理学家与数学家的研究兴趣。学界已对看似最简单的阵列系统开展了深入分析：嵌入在无色散介质中、满足Helmholtz方程的二维散射体构成的一维周期晶格。我们对该系统展开研究，通过实验证实了一类新型广义Rayleigh--Bloch波的存在，这类波近期被理论预测存在于经典波体系中，且无需共振散射体即可存在。空气声学正是这样的体系，我们在此通过实验首次观测到第一截止频率以上（即辐射区）的广义Rayleigh--Bloch波。我们研究了沿衍射光栅的辐射声学晶格共振，并通过研究嵌入空气中的非共振二维圆柱形Neumann散射体的短阵列与长阵列，将这类共振与广义Rayleigh--Bloch波关联起来。在短阵列上，我们观测到连续波激发下的有限晶格共振；在长阵列上，我们观测到脉冲激发下的传播型Rayleigh--Bloch波。我们借助多波散射理论解释其存在机制，借此统一了描述无限周期阵列与有限阵列上波动的不同命名体系，以及对其色散特性的解释。
英文摘要：
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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