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 materials1,2,3,4,5, following its theoretical prediction6, and has stimulated many applications including super-resolution imaging7. 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 semimetals8,9,10,11,12. 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 crystals8,9,10,11,12.
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We thank M. Xiao for discussions. This work is supported by the National Basic Research Program of China (grant number 2015CB755500), the National Natural Science Foundation of China (grant numbers 11774275, 11674250, 11534013 and 11747310) and the Natural Science Foundation of Hubei Province (grant number 2017CFA042). F.Z. was supported by UT Dallas research enhancement funds.
Nature thanks A. Grushin, B. Zhang and the other anonymous reviewer(s) for their contribution to the peer review of this work.
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Communications Physics (2018)