Research on non-reciprocal propagation of waves is of great significance in the field of photonic and phononic crystals for realizing flexible one-way propagation devices with potential engineering applications. Here, non-reciprocal Rayleigh waves are investigated in a continuous two-dimensional (2D) semi-infinite medium bound with an array of space–time modulated spring–mass oscillators. The involved modulation is a wave-like perturbation of the surface of the continuous medium that breaks time-reversal symmetry and reciprocity. To characterize the propagation of Rayleigh waves in such a complex 2D medium with continuous and discrete interface, an analytical study is performed to obtain dispersion-engineered bandgaps by adopting the asymptotic method and coupled mode theory, which is also validated by numerical simulation. Specifically, the non-reciprocal transmission of Rayleigh waves with one-way mode conversion is illustrated, and various relevant physical quantities, including conversion length and band gap size, are quantitatively estimated. This work sheds light on versatile control of Rayleigh wave propagation ranging from sensing and evaluation of engineering structures to guided wave-based damage detection techniques.

波的单向传播研究对于光子和声子晶体领域具有潜在的工程应用意义，对于实现灵活的单向传播装置具有重要意义。在这里，不可逆瑞利波是在连续二维（2D）半无限介质中进行研究的，该介质以时空调制弹簧-质量振荡器阵列为边界。涉及的调制是连续介质表面的波状扰动，破坏了时间反转的对称性和互易性。为了表征瑞利波在具有连续和离散界面的复杂2D介质中的传播，通过采用渐近方法和耦合模式理论进行了分析研究，以获得色散工程的带隙，并通过数值模拟对其进行了验证。特别，说明了单向模式转换的瑞利波的不可逆传输，并定量估计了各种相关物理量，包括转换长度和带隙大小。这项工作为瑞利波传播的通用控制提供了启示，从控制和评估工程结构到基于导波的损伤检测技术。