Page 18 - Summer 2015

Nonreciprocal Acoustics
and unique wave manipulation features of these devices, we briefly review basic examples of nonreciprocal electromag- netic devices, namely, isolators and circulators, which have long been used in the microwave and photonics industry (Pozar, 2005). Isolators are two-port devices that allow sig- nal transmission in only one direction (Figure 2a). They are used to protect sources from unwanted reflections or to con- nect different circuits together in a modular way such that interference with reflected signals is minimized. Circulators combine three isolators into a three-port network that al- lows signal transmission in a unirotational fashion. Figure 2b shows a circulator that allows signal transmission in the right-handed direction: signals from ports 1, 2, and 3 can only be transmitted to ports 2, 3, and 1, respectively. Circu- lators allow a receiver and a transmitter to be connected to the same antenna. As such, they are essential parts of radar systems, and they are becoming crucial components to en- able full duplex operation in the next generation of commu- nication devices (Figure 2c).
Figure 2. Nonreciprocal devices. (a) Isolator, allowing transmission from port 1 to port 2 but not in the opposite direction. (b) Circulator, allowing transmission between ports in a unirotational fashion from port 1 to port 2, from port 2 to port 3, and from port 3 to port 1 but not in the opposite direction. (c) Operation of a circulator for full duplex operation, connecting a transmitter (Tx) and a receiver (Rx) to the same antenna. The circulator allows the signal from the Tx to reach the antenna and be routed to free space while a received signal can be received at the same time and on the same frequency channel and be routed to the Rx. The signal from the Tx, typically at a much larger intensity than the received one, is prevented from leaking into the Rx.
Nonreciprocal Acoustic
Devices Based on Nonlinearity
The functionality of isolators and circulators has been re- cently extended to acoustic waves. Given that magneto- acoustic effects are much weaker than their electromagnetic counterparts, alternative ways to break reciprocity than conventional magnetic bias have been explored. The first works that reported large nonreciprocal acoustic effects in compact devices all relied on nonlinear effects, breaking one 16 | Acoustics Today | Summer 2015
of the fundamental assumptions behind Rayleigh reciproc- ity. Liang et al. (2009) showed that nonreciprocal isolation could be achieved by pairing a nonlinear acoustic medium and a frequency selective mirror, as represented in Figure 3, left. The frequency-selective acoustic mirror is created using a sonic crystal with a bandgap between the frequencies ƒ1 and ƒ2 . Due to its structure, the mirror reflects any harmonic signal of frequency ƒ0 in the range ƒ1 < ƒ0 < ƒ2 . The nonlin- ear medium is placed to the right of the frequency-selective mirror. When an acoustic wave with fundamental frequency ƒ0 is incident from the left (Figure 3, right, red), it is strongly reflected by the mirror and no signal is transmitted from left to right, i.e., tL→R ≈ 0. However, when the same signal comes from the right (Figure 3, right, green), it enters the nonlin- ear medium first, which converts some of the incident en- ergy from ƒ0 to 2ƒ0 through second-harmonic generation (SHG). If the bandgap is designed such that 2ƒ0 is not in the bandgap, some of the acoustic energy is transmitted through the mirror to the other side: tR→L ≠ 0, breaking reciprocity. A relevant metric of the performance of these types of devices is the isolation, IS = 20 log(|tR→L /tL→R|) which quantifies the transmission contrast. For nonlinear devices like those in- troduced by Liang et al. (2009), the IS is extremely large due to the excellent reflection properties of sonic crystals oper- ated in their bandgap. The large IS implies that reciprocity is strongly broken by this method. The insertion loss in trans- mit mode, however, is relatively large. It depends on the ef- ficiency of the SHG in the nonlinear medium and the loss in both the medium and the frequency-selective mirror. The method was later experimentally tested (Liang et al., 2010) using layers of water and glass to realize a sonic crystal and an ultrasound contrast agent microbubble solution as the nonlinear medium. The experiment demonstrated isolation levels up to 80 dB obtained for incident acoustic waves of 5 kPa or larger. The same principle was used in a subsequent experimental work (Boechler et al., 2011) to obtain similar isolation levels by using bifurcation and chaos as the source of nonlinear frequency conversion in a granular sonic crys- tal. Later, Popa and Cummer (2014) proposed a different ap- proach based on an electroacoustic transducer loaded with a nonlinear electronic circuit placed between two Fabry-Perot cavities tuned to different frequencies. They measured up to 10 dB of isolation in a system whose main advantage over the previous nonlinear methods was its subwavelength size, enabled by the use of active elements.
It should be mentioned that these nonlinear solutions to nonreciprocal acoustics do not break the Rayleigh theorem at the fundamental frequency. In these approaches, trans-