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Published September 2020 | public
Journal Article

Nonreciprocity in acoustic and elastic materials


The law of reciprocity in acoustics and elastodynamics codifies a relation of symmetry between action and reaction in fluids and solids. In its simplest form, it states that the frequency-response functions between any two material points remain the same after swapping source and receiver, regardless of the presence of inhomogeneities and losses. As such, reciprocity has enabled numerous applications that make use of acoustic and elastic wave propagation. A recent change in paradigm has prompted us to see reciprocity under a new light: as an obstruction to the realization of wave-bearing media in which the source and receiver are not interchangeable. Such materials may enable the creation of devices such as acoustic one-way mirrors, isolators and topological insulators. Here, we review how reciprocity breaks down in materials with momentum bias, structured space-dependent and time-dependent constitutive properties, and constitutive nonlinearity, and report on recent advances in the modelling and fabrication of these materials, as well as on experiments demonstrating nonreciprocal acoustic and elastic wave propagation therein. The success of these efforts holds promise to enable robust, unidirectional acoustic and elastic wave-steering capabilities that exceed what is currently possible in conventional materials, metamaterials or phononic crystals.

Additional Information

© 2020 Springer Nature Limited. Accepted 01 May 2020. Published 06 July 2020. A.N.N., G.H. and M.R.H. acknowledge support from NSF EFRI award no. 1641078. M.R.H. acknowledges support from ONR YIP award no. N00014-18-1-2335. C.D. acknowledges support from NSF EFRI award no. 1741565. A.A. acknowledges support from NSF EFRI award no. 1641069, the DARPA Nascent program and AFOSR MURI award no. FA9550-18-1-0379. R.F. acknowledges support from the Swiss National Science Foundation under SNSF grant no. 172487 and the SNSF Eccellenza award no. 181232. Author Contributions: H.N., B.Y., M.R. and R.F. provided initial drafts of portions of the manuscript. All authors subsequently integrated, reviewed and revised the full manuscript. M.R.H. and G.H. coordinated manuscript writing and organization. The authors declare no competing interests.

Additional details

August 22, 2023
October 20, 2023