In recent years, topological valley physics with valley pseudospin degrees of freedom have attracted significant attention. The topological valley boundary states in phononic crystals have important application prospects in efficient guidance and sensing for acoustic and elastic wave due to their unique transmission characteristics with backscattering immunity. However, the coupling effect of the valley edge states in multi-layer topological heterostructure was still a challenge in the elastic system due to the complicated multi-mode polarization of elastic waves. This article constructed a valley topological phononic crystal plate with multi-layer heterostructure to explore the multi-mode interference characteristics of the valley edge states based on the analogy of elastic wave quantum valley Hall effect. The coupling behavior of valley edge states for the out-of-plane polarized elastic wave in multi-layer topological heterostructure was systematically studied. By adjusting the layer numbers of the topological heterostructure, the formation mechanism and regulation law of coupled valley edge states for elastic wave in finite size multi-layer heterogeneous structures were revealed. Furthermore, through topological transmission calculations, the multi-mode interference effect of coupled valley edge states for elastic wave was achieved and its transmission robustness was well verified. Finally, as an application example, an elastic topological wavelength demultiplexing device was designed based on the multi-mode interference effect of valley edge state. By utilizing the difference in coupling wavelengths of elastic valley edge states at different coupling frequencies, directional separation of incident elastic waves in defect resistant channels was achieved, which could be as a prototype model for the novel application of elastic wavelength demultiplex device. This study provides a new paradigm for the manipulation of elastic wave topological transport, which is also expected to promote the practical design of new multifunctional elastic wave coupling and sensing devices.
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