Non-reciprocal and highly nonlinear active acoustic metamaterials

ARTICLE Received 11 Nov 2013 | Accepted 6 Feb 2014 | Published 27 Feb 2014 DOI: 10.1038/ncomms4398 Non-reciprocal and highly nonlinear active acoustic metamaterials Bogdan-Ioan Popa1 & Steven A. Cummer1 Unidirectional devices that pass acoustic energy in only one direction have numerous applications and, consequently, have recently received significant attention. However, for most practical applications that require unidirectionality at audio and low frequencies, subwavelength implementations capable of the necessary time-reversal symmetry breaking remain elusive. Here we describe a design approach based on metamaterial techniques that provides highly subwavelength and strongly non-reciprocal devices. We demonstrate this approach by designing and experimentally characterizing a non-reciprocal active acoustic metamaterial unit cell composed of a single piezoelectric membrane augmented by a nonlinear electronic circuit, and sandwiched between Helmholtz cavities tuned to different frequencies. The design is thinner than a tenth of a wavelength, yet it has an isolation factor of 410 dB. The design method generates relatively broadband unidirectional devices and is a good candidate for numerous acoustic applications. 1 Department of Electrical and Computer Engineering, Duke University, PO Box 90291, Durham, North Carolina 27708, USA. Correspondence and requests for materials should be addressed to S.A.C. (email: ). NATURE COMMUNICATIONS | 5:3398 | DOI: 10.1038/ncomms4398 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. 1 ARTICLE T NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4398 he development of acoustic metamaterials has brought with it a strong drive towards bringing electromagnetic concepts to acoustics. Thus, the extended range of material parameters provided by metamaterials has lead to the implementation of devices such as acoustic lenses1–6, or even exotic structures designed using coordinate transformation methods7,8. Recently, significant attention has been given to unidirectional devices that pass acoustic energy in only one direction9–15 and therefore mimic the general behaviour of diodes in the microwave regime, and Faraday rotator media in the optical domain. The unidirectional acoustic devices are the focus of this article. These devices have received many names, such as acoustic diodes, rectifiers, isolators and non-reciprocal media. There is an ongoing debate on what constitutes proper terminology. In this article, we take the more conservative approach of Maznev et al.16 and only consider non-reciprocal media capable of breaking the transmission symmetry property, that is, they transmit acoustic energy in only one direction regardless of the spatial spectrum of the incident acoustic excitation. In other words, we eliminate passive devices9–13 that exhibit time-reversal symmetry. The non-reciprocal devices fitting the above description reported so far14,15 achieve non-reciprocity in nonlinear macroscopic structures that contain, among other elements, at least one phononic crystal filter. The idea behind this type of approach was adapted first in theory17 from a thermal diode design18–20 in which the heat transport due to phonons was controlled in a nonlinear, asymmetric structure (see Li et al.21 for more details). The effectiveness of the acoustic non-reciprocal device strongly depends on the phononic filter selectivity, and, consequently, depends on the thickness of the phononic crystal, which necessarily needs to be much larger than the wavelength of the incoming acoustic wave. For example, Liang et al.14 used a thickness of E30 l, and Boechler et al.15 employed a thickness of E10 l, which makes these devices inadequate for audio and lowfrequency applications. Instead, compact and subwavelength implementations are desirable in most practical applications. Metamaterial concepts have been shown to provide the right platform for the design of non-reciprocal electromagnetic media22. In this article, we nontrivially extend this methodology to acoustics, and describe a design approach that results in structures highly subwavelength, but strongly non-reciprocal for their size. We demonstrate this approach by designing a non-reciprocal device l/10 thick and having an isolation factor of 410 dB. We use two highly subwavelength Helmholtz cavities tuned on different frequencies to create the asymmetry needed for the non-reciprocal behaviour. These cavities share a common wall consisting of a piezoelectric membrane (PZM) augmented by a nonlinear electronic circuit that sets the behaviour of the membrane. Similar to conventional acoustic media that absorb the incident sound field and then reradiate it, the role of the membrane is to sense the ambient acoustic field and, at the same time, generate an acoustic response controlled by the electronic circuit. The Helmholtz cavities play the secondary role of matching the PZM impedance with that of the air background, thus increasing the intensity of the PZM acoustic response. Note that this approach complements the linear and reciprocal active architecture of Popa et al.23, which employed separate sensing and driven elements connected by linear circuits. Unlike previous designs that relied on very selective, therefore, bulky filters, the highly subwavelength Helmholtz cavities have a rather wide half-amplitude bandwidth of E40%. Instead, their key property is their improved directivity as sound sensors and generators, because they mostly couple to sound coming from the semiplane to which the cavity opening points. This design approach results in 2 acoustically thin non-reciprocal structures having high isolation factors. The structures have relatively large bandwidths and are designed to be very robust given that the nonlinear behaviour is generated by the electronics and not by the physical structure of the material. Results Non-reciprocal metamaterial cell design. Figure 1a shows the non-reciprocal metamaterial cell representation (front and back) and behaviour. Central to the design is the PZM produced by Murata (part number 7BB-35-3CL0) and illustrated in the top-left inset. As with most commercial PZMs, a thin layer of piezoelectric ceramic is deposited on a brass disk. Two conducting electrodes are then deposited on top of the ceramic to create a two-capacitor, three-terminal membrane. This design, together with the property of the piezoelectric material to convert back and forth between electric and acoustic energy, allows us to use the membrane as an acoustic sensor of the background acoustic field and, at the same time, a sound-producing element able to change the acoustic properties of the incoming sound wave (spatial and temporal spectra) in the same way a conventional acoustic material functions. The small terminal forms the sensing terminal, while the big electrode covering most of the piezoelectric ceramic is called the main terminal. These terminals are conne (...truncated)