Page 16 - Summer 2015

Nonreciprocal Acoustics
New nonreciprocal acoustic devices put sound on a one-way street.
Introduction
In conventional propagation media, wave motion obeys a fundamental property, reciprocity, that describes the symmetry in wave transmission between two points in space. Reciprocity guarantees that wave propagation always occurs in a sym- metrical fashion. If waves can make their way from a source to an observer, the opposite propagation path, from the observer to the source, is equally possible and the transmission is symmetric. Reciprocity is a concept so natural that we implic- itly assume its validity in our everyday lives. When we hear our neighbors through a common wall, we also know that they can hear us.
It is well known in the field of theoretical acoustics that reciprocity may not hold in specific situations, for instance, in the presence of fluid in motion (Morse and In- gard, 1968; Godin, 1997). Furthermore, recent work has shown engineered devices with strongly nonreciprocal responses (Liang et al., 2009, 2010; Boechler et al., 2011; Fleury et al., 2014, 2015; Popa and Cummer, 2014). These devices force the acoustic energy to flow only in one direction and thereby create a "one-way street" for sound. How can such extreme behavior, somewhat contrary to common sense, be achieved? What are the technological implications and potential applications of strongly nonreciprocal acoustic devices? In this article, we provide an overview of the relevant physical concepts and discuss the recent progress in the emerging field of nonreciprocal acoustics. This review highlights the challenges associated with breaking reciprocity and provides our vision on the future of this research area. We discuss promising applications of these devices and their potential to funda- mentally alter the existing wave propagation paradigm in acoustics, offering un- precedented control over sound transmission. We envision that devices exploiting nonreciprocal wave phenomena may lead to new solutions to existing problems in a variety of acoustics-related fields, including energy concentration and harvest- ing, communications and imaging systems, signal processing, and even thermal management.
Rayleigh Reciprocity Theorem
Postal:
Department of Electrical and Computer Engineering The University of Texas at Austin 1616 Guadalupe Street UTA 7.215 Austin, Texas 78712 USA
Email:
alu@mail.utexas.edu
Romain Fleury
Postal:
Department of Electrical and Computer Engineering The University of Texas at Austin 1616 Guadalupe Street UTA 7.215 Austin, Texas 78712 USA
Email:
romain.fleury@utexas.edu
Dimitrios Sounas
Postal:
Department of Electrical and Computer Engineering The University of Texas at Austin 1616 Guadalupe Street UTA 7.215 Austin, Texas 78712 USA
Email:
dimitrios.sounas@utexas.edu
Michael R. Haberman
Postal:
Applied Research Laboratories The University of Texas at Austin P.O. Box 8029 Austin, Texas 78713-8029 USA
Email:
haberman@arlut.utexas.edu
Andrea Alù
To our knowledge, the first reciprocity relationship written specifically for acous- tic waves appears in a work by Helmholtz (1860) on the theory of airborne noise in pipes with open ends. Although Lamb (1888) provided additional insight into acoustic reciprocity for more general scenarios, it was the work of Rayleigh (1873) that formulated the general reciprocity theorem for sound. Consider an acoustic medium at rest, as represented in Figure 1a (possibly inhomogeneous, as repre- sented by the darker purple region). At any point A, acoustic waves may be excited. According to Rayleigh, “the resulting velocity potential at a second point B is the same both in magnitude and in phase, as it would have been at A, had B been the source of sound” (Figure 1b). This statement about the exact equality of the velocity potentials in both situations may be at first surprising because it holds
14 | Acoustics Today | Summer 2015 , volume 11, issue 3 ©2015 Acoustical Society of America. All rights reserved.