No abstract

Reflection and refraction of waves occur at the interface between two different media. These two fundamental interfacial wave phenomena form the basis of fabricating various wave components, such as optical lenses. Classical refraction-now referred to as positive refraction-causes the transmitted wave to appear on the opposite side of the interface normal compared to the incident wave. By contrast, negative refraction results in the transmitted wave emerging on the same side of the interface normal. It has been observed in artificial materials, following its theoretical prediction, and has stimulated many applications including super-resolution imaging. In general, reflection is inevitable during the refraction process, but this is often undesirable in designing wave functional devices. Here we report negative refraction of topological surface waves hosted by a Weyl phononic crystal-an acoustic analogue of the recently discovered Weyl semimetals. The interfaces at which this topological negative refraction occurs are one-dimensional edges separating different facets of the crystal. By tailoring the surface terminations of the Weyl phononic crystal, constant-frequency contours of surface acoustic waves can be designed to produce negative refraction at certain interfaces, while positive refraction is realized at different interfaces within the same sample. In contrast to the more familiar behaviour of waves at interfaces, unwanted reflection can be prevented in our crystal, owing to the open nature of the constant-frequency contours, which is a hallmark of the topologically protected  surface states in Weyl crystals.

SignificanceWavefront shaping with spatial light modulators has recently motivated many studies in the field of light manipulation in diffusive media. Here, we extend this concept to acoustic waves by designing and building a binary phase-modulating spatial sound modulator (SSM). The SSM is an acoustic metasurface consisting of unit cells with two states, switchable through programmed electronics. We demonstrate in audible frequencies, and in a reverberating environment, the capability of controlling and reshaping any complex sound field. Our work will not only open avenues to study wave propagation in complex and chaotic media but also inspire applications in acoustic engineering.

Recently, intense efforts have been devoted to realizing classical analogues of various topological phases of matter. In this Letter, we explore the intriguing Weyl physics by a simple one-dimensional sonic crystal, in which two extra structural parameters are combined to construct a synthetic three-dimensional space.Based on our underwater ultrasonic experiments, we have not only observed the synthetic Weyl points directly, but also probed the novel reflection phase singularity that connects inherently with the topological robustness of Weyl points. As a smoking gun evidence of the topological states of matter, the presence of nontrivial interface modes has been demonstrated further. All experimental data agree well with our full-wave simulations. As the first realization of topological acoustics in synthetic space, our study exhibits great potential of probing high-dimensional topological phenomena by such easily-fabricated and -detected low-dimension acoustic systems.