Abnormal topological refraction into free medium at subwavelength scale in valley phononic crystal plates

In this work we propose a topological valley phononic crystal plate and extensively investigate the refraction of modes into surrounding homogeneous medium. This includes two sublattices resonators (A B) modeled by mass-spring systems. We show that edge states confined at AB/BA BA/AB type domain walls exhibit different symmetries in physical space energy peaks Fourier space. As result, distinct behaviors, especially through an armchair cut edge, are observed. On other hand, decay depth these localized modes, which is found to be solely determined relative resonant strength between scatterers, significantly affects patterns. More interestingly, outgoing traveling wave zigzag interface becomes evanescent when operating deep subwavelength scale. realized tuning average strength. only exist along particular outlet they can couple with both states. also present near-ideal monopole dipole emitter based on our structure.