Abstract
We demonstrate the localization of water surface waves and its evolution by introducing a defect into a trough with periodic sidewalls. Taking the advantage of water wave visualization, we observed a defect mode arising in the forbidden band and its formation process, that the water waves gradually accumulate at the defect, and accordingly, the energy gets smaller in the incidence part but larger in the exit part. After a certain time, when the accumulated energy gets large enough to produce a defect mode, we can obtain a steady state and an extraordinary transmission. It was also found that the transmission frequency linearly depends on the defect length with the negative slope and the localizations in different defects were also observed and analyzed. Due to the ubiquity of wave phenomena, the observation of water wave localization not only present a visual picture for the fundamental resonance concept, but also find applications in various fields, such as underwater acoustics, ultrasonics, electromagnetic waves, and optics.
Highlights
The study of waves in periodic media has a long research history, which can be traced back to Lord Rayleigh in late 1880s
We have demonstrated the localization of water surface waves and its frequency sifting characteristics by introducing a defect into the trough with periodic sidewalls
The distribution of energy along the symmetry axial of the trough has been measured at different moments when the water surface wave was generated at the frequency of the extraordinary transmission
Summary
The study of waves in periodic media has a long research history, which can be traced back to Lord Rayleigh in late 1880s. Due to the existence of a periodic structure, there will be a lot of interesting phenomena during the wave propagation, such as negative refractive index,[2] slow light,[3] etc It has great application prospects in photonic crystals,[4,5] phononic crystals,[6,7,8,9] and bio-inspired periodic composites.[10,11] When defects are introduced in a perfect periodic structure, the waves are always localized around the defect.[12] In this way, the additional passbands and band gaps are created in the original energy band structure. Compared with the undulating bottom, the two-dimensional periodic sidewalls can provide richer physical contents and can excite Bragg and even non-Bragg resonances.[25] the defect induced localization of water surface waves have not been transiently analyzed and the localization characteristics have not been observed by naked eyes until now. We introduce the defects into a periodic sidewall trough and observe the localization and its characteristics of water surface waves. The major results and conclusions are summarized in the concluding section
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