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  • Review Article
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Controlling water waves with artificial structures

Nature Reviews Physics volume 6, pages 231–245 (2024)Cite this article

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Abstract

Because of analogies between the 2D Maxwell equations and water wave equations, methods for manipulating electromagnetic waves based on photonic crystals and metamaterials can be extended to manipulate water waves. Doing so provides new opportunities to investigate the interaction of water waves with structures. In this Review, we introduce the research progress of controlling water waves with water wave crystals and metamaterials and summarize the basic theory and calculation methods for water waves. The working principles and design methods for water wave crystals and metamaterials are described, and their properties and applications are presented. We also discuss the current challenges in this field and future directions.

Key points

  • Artificial water wave structures, including water wave crystals and water wave metamaterials, provide an efficient way to control water waves by extending the methods for controlling electromagnetic waves with photonic crystals and electromagnetic metamaterials.

  • By engineering the band structures of water wave crystals, interesting phenomenon such as Bloch states, superlensing effect, self-collimating phenomenon and Anderson localization can be observed directly in water waves.

  • The band structures of water wave crystals can be calculated by different methods, such as plane-wave expansion method, multiple scattering method, transfer matrix method and finite element method.

  • Equivalent material parameters need to be pre-calculated before designing water wave metamaterials with special functionality, and effective medium theory can be used because the water wavelength is much larger than the period of water wave metamaterials.

  • Water wave metamaterials have potential applications such as anisotropy of water waves, water wave cloaks, concentration of water waves, isolation and unidirectional propagation of water waves.

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Fig. 1: Structures for manipulating water waves.
Fig. 2: A typical periodic structure in water with corresponding band structures and transmittance results.
Fig. 3: Phenomena based on band structures in water waves.
Fig. 4: Equivalent parameters of metamaterials in water waves.
Fig. 5: Water wave metamaterials with anisotropic water depth.
Fig. 6: Water wave cloaks and superscatters.
Fig. 7: Water wave lens and concentrators.
Fig. 8: Isolation and unidirectional propagation of water waves.

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Acknowledgements

The authors acknowledge the National Natural Science Foundation of China (Grant No. 12374410), National Key Research and Development Program of China (Grant Nos 2023YFA1406901 and 2023YFA1407100) and Fundamental Research Funds for the Central Universities (Grant No. 20720220033).

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  1. These authors contributed equally: Shan Zhu, Xinyu Zhao, Linkang Han.

Authors and Affiliations

  1. Department of Physics, Xiamen University, Xiamen, China

    Shan Zhu, Linkang Han & Huanyang Chen

  2. Department of Materials Science and Key Laboratory of Micro- and Nano-Photonic Structures (Ministry of Education), Fudan University, Shanghai, China

    Xinyu Zhao & Xinhua Hu

  3. Department of Physics and Key Laboratory of Surface Physics, Fudan University, Shanghai, China

    Jian Zi

  4. Department of Physics, Xiamen University Malaysia, Sepang, Malaysia

    Huanyang Chen

  5. Key Laboratory of Underwater Acoustic Communication and Marine Information Technology, Xiamen University, Xiamen, China

    Huanyang Chen

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Contributions

S.Z., X.Z. and L.H. researched data for the article. S.Z., X.Z., L.H., X.H. and H.C. contributed substantially to discussion of the content. S.Z., X.Z. and L.H. wrote the article. X.H. and H.C. conceived and supervised the whole project. All authors reviewed and/or edited the manuscript before submission.

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Correspondence to Xinhua Hu or Huanyang Chen.

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Zhu, S., Zhao, X., Han, L. et al. Controlling water waves with artificial structures. Nat Rev Phys 6, 231–245 (2024). https://doi.org/10.1038/s42254-024-00701-8

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