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This article was submitted to Physical Acoustics and Ultrasonics, a section of the journal Frontiers in Physics

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There are many achievements associated with using metamaterials and metasurfaces, particularly due to their extraordinary capabilities and subwavelength dimensions. Recently new discoveries in metasurfaces, including anisotropy, nonlocal effects, integer parity property, and exceptional points in a non-Hermitian system [

We propose here for the first time a locally resonant metasurface for low-frequency transmissive underwater acoustic waves. The target frequency is as low as 300 Hz. Full phase shift can be covered by changing a single design parameter of one unit and the transmission ratio is always higher than 60%. Asymmetric transmission, self-bending, and source illusion are chosen as three applications to demonstrate the strong ability of the metasurface. This work offers a new means of designing underwater transmissive metasurface and contributes to underwater acoustic devices.

One unit of the metasurface considered is illustrated in

One metasurface unit:

The process of exposing the metasurface to waves is simulated using the commercial finite element software Comsol Multiphysics. Previous study has shown that underwater fluid-solid interaction can cause strong nonlocal influence between the metasurface units, leading to phenomena hard to predict analytically [^{3}, and the associated Poisson’s ratios are .28 and .4, respectively. Using the proposed finite element model, the phase shift and transmission ratio as functions of the ratio

The first application considered for the proposed design is asymmetric transmission. When the unit width of the metasurface is far less than the target wavelength, the principle of a wave passing through the metasurface interface can be described by Generalized Snell’s Law

Asymmetric transmission:

The second application is a self-bending beam, which is useful to bypass obstacles for underwater communication. By tracing individual caustic rays [

Normalized self-bending beam pressure distribution under an upward incident wave. The design target is the white half circle with a radius equal to 5λ. The inset shows the

Another application of the metasurface is source illusion. For instance, a point source can be transformed to a prescribed wavefront. Here we surround the point source by the proposed metasurface in a circular pattern. To give an additional integer angular momentum to the point source, the phase shift introduced by the metasurface should be

Source illusion: Normalized pressure field of a point source reconstructed to a spiral wave front with different angular momentums:

Although the metasurface is designed for 300 Hz, it can work in a relatively wide range. For instance, the self-bending beam function of the metasurface working under 260, 280, 320, and 350 Hz is shown in

Normalized pressure field of the proposed self-bending beam metasurface structure working under different frequencies (

A locally resonant metasurface for manipulating low-frequency underwater waves is devised. In this design, the phase of the transmitted wave can be tailored by adjusting the height ratio of the steel resonating plate and the connecting rubber support in each metasurface unit. Asymmetric transmission, self-bending, and source illusion are chosen as demonstrations of applications of the design. Simulated results agree well with theoretical predictions. Three applications are demonstrated. Asymmetric transmission empowers an object to receive information from outside without sending out wave signals. Self-bending beams can help waves surpass obstacles to establish communication. The source illusion effect can be used for submarines to create misleading signals when there is a passive sonar being used to receive waves to detect them. Besides, here we design the dimensions of the metasurface unit by trial and error. Next, we plan to adopt optimization method by choosing efficiency as the objective function, design parameters as variables to find an optimal design. Similarly, we can adopt a multi-objective optimization method to further expand working bandwidth. The target wave pattern under different frequencies can be chosen as objective functions. This design has broad potential applications in areas of low-frequency underwater wave manipulation after further improvement.

The original contributions presented in the study are included in the article/

ZC and MN contributed to conception and design of the study. SG and ZG organized the database. QX performed the statistical analysis. ZC wrote the first draft of the manuscript. ZL provided funding. All authors contributed to manuscript revision, read, and approved the submitted version.

This work was supported by National Natural Science Foundation of China (Grant Nos 12172008 and 11991033).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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