Abstract
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.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Tourin, A., Fink, M. & Derode, A. Multiple scattering of sound. Waves Random Media 10, R31–R60 (2000).
Akkermans, É. & Montambaux, G. Mesoscopic Physics of Electrons and Photons (Cambridge Univ. Press, Cambridge, 2007).
Sheng, P. Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Springer, 2006).
Mudry, K. M., Plonsey, R. & Bronzino, J. D. Biomedical Imaging (CRC Press, Boca Raton, FL, 2003).
Pendry, J. B., Schurig, D. & Smith, D. R. Controlling Electromagnetic Fields. Science 312, 1780–1782 (2006).
Iniewski, K. Wireless Technologies: Circuits, Systems, and Devices (CRC Press, Boca Raton, FL, 2007).
Florescu, M., Torquato, S. & Steinhardt, P. J. Designer disordered materials with large, complete photonic band gaps. Proc. Natl Acad. Sci. USA 106, 20658–20663 (2009).
Tyson, R. Principles of Adaptive Optics (CRC Press, Boca Raton, FL, 2010).
Mosk, A. P., Lagendijk, A., Lerosey, G. & Fink, M. Controlling waves in space and time for imaging and focusing in complex media. Nat. Photon. 6, 283–292 (2012).
Rotter, S. & Gigan, S. Light fields in complex media: Mesoscopic scattering meets wave control. Rev. Mod. Phys. 89, 015005 (2017).
Leseur, O., Pierrat, R. & Carminati, R. High-density hyperuniform materials can be transparent. Optica 3, 763–767 (2016).
Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological states in photonic systems. Nat. Phys. 12, 626–629 (2016).
Bender, C. M. & Boettcher, S. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998).
El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).
Makris, K. G., El-Ganainy, R., Christodoulides, D. N. & Musslimani, Z. H. Beam dynamics in PT symmetric optical lattices. Phys. Rev. Lett. 100, 103904 (2008).
Guo, A. et al. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009).
Rüter, C. E. et al. Observation of parity–time symmetry in optics. Nat. Phys. 6, 192–195 (2010).
Regensburger, A. et al. Parity–time synthetic photonic lattices. Nature 488, 167–171 (2012).
Feng, L. et al. Experimental demonstration of a unidirectional reflectionless parity–time metamaterial at optical frequencies. Nat. Mater. 12, 108–113 (2013).
Assawaworrarit, S., Yu, X. & Fan, S. Robust wireless power transfer using a nonlinear parity–time-symmetric circuit. Nature 546, 387–390 (2017).
Fleury, R., Sounas, D. & Alù, A. An invisible acoustic sensor based on parity–time symmetry. Nat. Commun. 6, 5905 (2015).
Shi, C. et al. Accessing the exceptional points of parity–time symmetric acoustics. Nat. Commun. 7, 11110 (2016).
Aurégan, Y. & Pagneux, V. PT-symmetric scattering in flow-duct acoustics. Phys. Rev. Lett. 118, 174301 (2017).
Konotop, V. V. & Zezyulin, D. A. Families of stationary modes in complex potentials. Opt. Lett. 39, 5535–5538 (2014).
Peng, B. et al. Loss-induced suppression and revival of lasing. Science 346, 328–332 (2014).
Doppler, J. et al. Dynamically encircling an exceptional point for asymmetric mode switching. Nature 537, 76–79 (2016).
Xu, H., Mason, D., Jiang, L. & Harris, J. G. E. Topological energy transfer in an optomechanical system with exceptional points. Nature 537, 80–83 (2016).
Makris, K. G., Musslimani, Z. H., Christodoulides, D. N. & Rotter, S. Constant intensity waves and their modulation instabilities in non-Hermitian potentials. Nat. Commun. 6, 7257 (2015).
Makris, K. G., Brandstötter, A., Ambichl, P., Musslimani, Z. H. & Rotter, S. Wave propagation through disordered media without backscattering and intensity variations. Light Sci. Appl. 6, e17035 (2017).
Fleury, R. & Alù, A. Extraordinary sound transmission through density-near-zero ultranarrow channels. Phys. Rev. Lett. 111, 055501 (2013).
Pozar D. M. in Microwave Engineering 206–210 (Wiley, New York, NY, 2011).
Rivet, E., Karkar, S. & Lissek, H. Broadband low-frequency electroacoustic absorbers through hybrid sensor-/shunt-based impedance control. IEEE Trans. Control Syst. Technol. 25, 63–72 (2017).
Prandoni P. & Vetterli M. in Signal Processing for Communications 348–349 (Collection le savoir Suisse, Lausanne, 2008).
Lissek, H., Boulandet, R. & Fleury, R. Electroacoustic absorbers: bridging the gap between shunt loudspeakers and active sound absorption. J. Acoust. Soc. Am. 129, 2968–2978 (2011).
Acknowledgements
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
Authors and Affiliations
Contributions
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.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary material
Supplementary figures 1 and 2
Rights and permissions
About this article
Cite this article
Rivet, E., Brandstötter, A., Makris, K.G. et al. Constant-pressure sound waves in non-Hermitian disordered media. Nature Phys 14, 942–947 (2018). https://doi.org/10.1038/s41567-018-0188-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41567-018-0188-7
This article is cited by
-
Ultrabroadband sound control with deep-subwavelength plasmacoustic metalayers
Nature Communications (2023)
-
Total acoustic transmission in a honeycomb network empowered by compact acoustic isolator
Scientific Reports (2023)
-
Observation of non-reciprocal harmonic conversion in real sounds
Communications Physics (2023)
-
Manipulation of invisible cloaking in \(\mathcal{PT}\)-symmetric thermoacoustic dimer
Science China Physics, Mechanics & Astronomy (2023)
-
Exceptional points in lossy media lead to deep polynomial wave penetration with spatially uniform power loss
Nature Nanotechnology (2022)