Topological birefraction of elastic waves in phononic crystals

The refraction of waves at the interface between two different media is one of the most common phenomena in nature, which is always accompanied by reflection. Topological phononic crystals (PCs) offer unprecedented opportunities to manipulate the refraction of acoustic waves without generating reflected waves. Here, we propose and demonstrate the topological birefraction of elastic waves in PC by simulation. Starting from the perforated elastic plate with a honeycomb-like structure, we designed a circular trajectory based on structural parameters and revealed that two points on the trajectory with a π phase difference correspond to distinct topological phases. By engineering a non-uniform PC along the circular trajectory, we demonstrate the one-way valley switches and topological birefraction of elastic edge states. Specifically, we design the topological heterostructure by expanding the parameter trajectory to a 2D circular region; the edge states extend to the bulk states; therefore, the topological birefraction of elastic bulk states is demonstrated. Our results may have significance in elastic beam splitters, switches, and filters and are also applicable to on-chip elastic surface waves with higher frequencies, which are of significance in information processing and sensing.