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摘要

以变截面含可穿透散射体波导为模型, 理论研究声波在非均匀波导中的最大透射问题. 通过耦合简正波理论构建模态域内透射矩阵和水平波数矩阵, 推导透射波能流的具体表达式, 分析任意入射波的能流透射率随频率的变化, 进而讨论任意给定频率下能够产生最大能流透射率的最佳入射波, 并给出数组全透射声场算例. 最佳入射波仅由可传播模态决定, 与衰逝模态无关. 利用衰逝模态不携带能流的特性, 讨论衰逝模态对产生能流最大透射声场的影响, 并分析最大能流透射的鲁棒性. 在频率满足一定条件时, 全透射声场可能表现出完美鲁棒性. 文中所述方法可延伸至多种非均匀波导以分析其中的能流最大透射问题.

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Abstract

Inhomogeneity in a medium will cause wave scattering, influencing the transfer of energy or information. However, it is possible to prepare a prescribed wavefront which propagates through an inhomogeneous medium with unity flux-transmittance. This phenomenon is first predicted in the context of mesoscopic electron transport. Another remarkable phenomenon is the bimodal distribution of the transmission singular values, which implies that in a lossless medium the full solution space in the scattering region can be spanned only by open channels, which are completely transmitted, and closed channels, which are completely reflected. In mesoscopic physics, random-matrix theory is usually utilized to deal with the statistical properties of matrices with randomly distributed entries since the medium is assumed to be randomly fluctuating. In this paper, we propose a method of systematically studying the maximal flux transmission through an inhomogeneous acoustic waveguide. The model is chosen to be a waveguide with varying cross-sections and a penetrable scatterer, and the method is based on the coupled mode theory. This method can be used to analyze the frequency of nearly complete transmission for an arbitrary incident wave, and to analyze the incident wave that is able to generate the maximal flux-transmittance for any given frequency. We construct the transmission matrix and the horizontal wavenumber matrix by using orthonormal basis functions, and give the expression of flux-transmittance. Then the optimal incident wave which brings the maximal transmittance through the scattering region is derived based on singular value decomposition. The optimal incident waves are independent of the evanescent modes since evanescent modes do not transfer any energy. But the evanescent modes can give rise to the multivaluedness of wave solutions with complete flux transmission. Considering the fact that acoustic waveguides can naturally resist the influence of highly oscillating perturbations since most of them correspond to evanescent modes), the maximal flux transmission in waveguide is thus found to be highly robust. Especially at a specific frequency, the complete wave transmission has perfect robustness. This proposed method can be generalized to any other frequency, to other types of scatterers, or to other kinds of boundary conditions, and can provide guidance in designing acoustic metamaterials and in highly efficient communication.

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作者及机构信息

郭威³,
杨德森^1,2,3

1.
2.
3.

通信作者:杨德森,dshyang@hrbeu.edu.cn

Authors and contacts

Guo Wei³,
Yang De-Sen^1,2,3

1.
2.
3.

Corresponding author:Yang De-Sen,dshyang@hrbeu.edu.cn

文章全文: translate this paragraph

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施引文献

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

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