When waves impinge on a disordered material they are back-scattered and form a highly complex interference pattern. Suppressing any such distortions of a wave’s free propagation is a challenging task with many applications in a number of different disciplines. In a recent theoretical proposal, it was pointed out that both perfect transmission through disorder as well as a complete suppression of any variation in a wave’s intensity can be achieved by adding a continuous gain–loss distribution to the disorder. Here we propose a practical discretized version of this abstract concept and implement it in a realistic acoustic system. Our prototype consists of an acoustic waveguide containing several inclusions that scatter the incoming wave in a passive configuration and provide the gain or loss when being actively controlled. Our measurements on this non-Hermitian acoustic metamaterial demonstrate the creation of a reflectionless scattering wave state that features a unique form of discrete constant-amplitude pressure waves. In addition to demonstrating that gain–loss additions can turn localized systems into transparent ones, we expect our proof-of-principle demonstration to trigger interesting new developments, not only in sound engineering, but also in other related fields such as in non-Hermitian photonics.

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The authors would like to thank M. Paolone and the Distributed Electrical Systems Laboratory at Ecole Polytechnique Fédérale de Lausanne (EPFL) for lending us the National Instrument CompactRIO-9068 platform for the experiment.

Author information


  1. Signal Processing Laboratory 2, EPFL, Lausanne, Switzerland

    • Etienne Rivet
    •  & Hervé Lissek
  2. Institute for Theoretical Physics, Vienna University of Technology (TU Wien), Vienna, Austria

    • Andre Brandstötter
    •  & Stefan Rotter
  3. Department of Physics, University of Crete, Heraklion, Greece

    • Konstantinos G. Makris
  4. Laboratory of Wave Engineering, EPFL, Lausanne, Switzerland

    • Romain Fleury


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A.B., K.G.M. and S.R. developed the concept and theory of continuous constant amplitude waves. E.R. and R.F. developed the discrete theory of constant-amplitude waves and performed the numerical simulations. E.R. formulated the acoustic impedance control theory, developed the control technology used in the experiment, and performed the experiment. H.L. supervised the experimental work. S.R. and R.F. initiated and supervised the project. All authors discussed the results and contributed to writing the manuscript.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Romain Fleury.

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