Chain reaction of wave splitting based on roton-like dispersion in graded nonlocal periodic structures

Abstract Although rotons are fundamental to quantum fluid dynamics, their classical analogues in engineered systems remain underexploited for wave control applications. This study explores wave manipulation mechanisms of one-dimensional nonlocal periodic structures with roton-like dispersion characteristics. A nonlocal model with long-range interactions is established. It can produce roton-like dispersion relations. Theoretical analysis is conducted to explore the influence of nonlocal effects on the dispersion characteristics. The multiple wavevector regions where positive and negative slopes coexist are obtained. Numerical simulations demonstrate that wave propagation within these regions induces energy decoupling and subsequent wave splitting. To amplify this effect, a gradient-stitched design strategy that establishes chain reaction of wave splitting processes enabling multi-channel energy distribution. These findings enhance the fundamental understanding of wave manipulation in artificial structures and simultaneously provide a design strategy for multifunctional wave control devices.