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Nonreciprocity in acoustic and elastic materials

Nature Reviews Materials volume 5, pages 667–685 (2020)Cite this article

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Abstract

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.

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Fig. 1: Acoustic reciprocity from fluid motion.
Fig. 2: Examples of activated media.
Fig. 3: Experimental demonstrations of nonreciprocity in dynamic media.
Fig. 4: Topological effects in dynamic media.
Fig. 5: Quantum Hall effect analogues in mechanics and acoustics.
Fig. 6: Overview of nonreciprocity in nonlinear media.

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Acknowledgements

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.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO, USA

    Hussein Nassar & Guoliang Huang

  2. Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, QC, Canada

    Behrooz Yousefzadeh

  3. Laboratory of Wave Engineering, Swiss Federal Institute of Technology in Lausanne (EPFL), Lausanne, Switzerland

    Romain Fleury

  4. Department of Mechanical Engineering, University of Colorado Boulder, Boulder, CO, USA

    Massimo Ruzzene

  5. Advanced Science Research Center, City University of New York, New York, NY, USA

    Andrea Alù

  6. Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA, USA

    Chiara Daraio

  7. Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ, USA

    Andrew N. Norris

  8. Walker Department of Mechanical Engineering and Applied Research Laboratories, The University of Texas at Austin, Austin, TX, USA

    Michael R. Haberman

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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.

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Nassar, H., Yousefzadeh, B., Fleury, R. et al. Nonreciprocity in acoustic and elastic materials. Nat Rev Mater 5, 667–685 (2020). https://doi.org/10.1038/s41578-020-0206-0

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