Abstract
Topological concepts have been introduced into electronic, photonic, and phononic systems, but have not been studied in surface-water-wave systems. Here we study a one-dimensional periodic resonant surface-water-wave system and demonstrate its topological transition. By selecting three different water depths, we can construct different types of water waves - shallow, intermediate and deep water waves. The periodic surface-water-wave system consists of an array of cylindrical water tanks connected with narrow water channels. As the width of connecting channel varies, the band diagram undergoes a topological transition which can be further characterized by Zak phase. This topological transition holds true for shallow, intermediate and deep water waves. However, the interface state at the boundary separating two topologically distinct arrays of water tanks can exhibit different bands for shallow, intermediate and deep water waves. Our work studies for the first time topological properties of water wave systems, and paves the way to potential management of water waves.
Highlights
Topological concepts have been introduced into electronic, photonic, and phononic systems, but have not been studied in surface-water-wave systems
The periodic surface-water-wave system consists of an array of cylindrical water tanks connected with narrow water channels
As the width of connecting channel varies, the band diagram undergoes a topological transition which can be further characterized by Zak phase
Summary
Topological concepts have been introduced into electronic, photonic, and phononic systems, but have not been studied in surface-water-wave systems. As the width of connecting channel varies, the band diagram undergoes a topological transition which can be further characterized by Zak phase This topological transition holds true for shallow, intermediate and deep water waves. Water waves propagating through periodic structures can exhibit many interesting phenomena, such as band gaps in periodic lattice[1,2,3], super-lensing effect[4], refraction[5], cloaking[6], and others[7,8], most of which are inspired by rapid progress in photonic systems[9,10,11] in the last three decades These phenomena of water waves are still isolated from topological concepts of recent topological physics[12,13,14,15]. The interface state at the boundary separating two topologically distinct arrays of water tanks can exhibit different bands for shallow, intermediate and deep water waves
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