Page 15 - Fall2021

bias (Khanikaev et al., 2015) or rotating spatiotempo- ral modulation patterns (Figure 1a) (Fleury et al., 2016; Darabi et al., 2020), provide a stronger form of topological robustness because the corresponding boundary waves are truly unidirectional. The absence of such backward modes and of bulk modes ensures truly robust one-way boundary sound propagation, irrespective of the form of disorder and imperfections.
Figure 2a shows measurements on a practical example of this type of topological insulator for elastic waves, real- ized by electrically controlling a two-dimensional array of piezoelectric patches, similar to the design in Figure 1a, with electrical modulation signals suitably varying in space and time to impart a form of synthetic rotation that induces the desired pseudospin and breaks reciproc- ity (Darabi et al., 2020). Figure 2a shows the measured displacement extracted with a laser vibrometer, dem- onstrating that signals travel unidirectionally along the array boundaries.
Nonlinearities combined with geometrical asymmetries can also support pseudospins supporting nontrivial topological sound (Hadad et al., 2018). Although these systems are passive and obey time-reversal symmetry (as long as the nonlinearity is instantaneous), the com- bination of nonlinearities and geometrical asymmetries breaks reciprocity and enables unidirectional sound trans- port along the boundaries. An extreme example, seen in Figure 2b, shows a mechanical metamaterial made from
a three-dimensional printed polymer, which supports a topological response at zero frequency. Mechanical non- linearities are amplified at the small hinges connecting the diamond-shaped regions in Figure 2b, and the tilted ele- ments introduce carefully tuned asymmetries that enable nonreciprocal transport of mechanical displacement when a force is applied to the structure from opposite sides. Interestingly, it can be shown that maximum nonreci- procity is achieved at the transition when the metamaterial changes the topological state, as controlled by the underly- ing geometrical asymmetries (Coulais et al., 2017). This metamaterial supports an unusual mechanical response; it strongly transmits displacement in one direction, but it dampens it in the opposite one.
Radio-Frequency Technology Based on Topological Sound
The pseudospins discussed previously can robustly break
reciprocity, enabling fundamental functionalities for sev- eral electronics and electromagnetics technologies. For example, nonreciprocity can be used to isolate transmit- ter and receiver modules in our cell phones, an important functionality in modern communication systems to avoid interference between the strong transmitted signals and the stream of weak signals received from the cell phone tower (Kord et al., 2020). Acoustic signals offer several opportuni- ties in this context because of their small wavelengths and lower rate of energy loss compared with electromagnetic components. These properties have been harvested, for example, in surface acoustic wave (SAW) or bulk acoustic wave (BAW) filters used to process the radio-frequency (RF) signal received by antennas in portable communication devices. However, current solutions rely on linear, passive, single-frequency devices that are unsuitable for the next generation of RF systems because they have a limited range of functionalities and require integration with ever more complex electronic components. More desirable features, ideal for agile communication systems with enhanced data rates and serving many users, target narrowband, low-loss filters, with a small size and a tunable center frequency.
Topological acoustics provides fertile ground to advance these technologies and address current technological challenges. For example, topological acoustics reduces scattering and enables devices approaching the theo- retical limits of the intrinsic material losses. The natural robustness to defects associated with topological prop- erties can decrease manufacturing costs, reducing the
Figure 2. a: Elastic displacement measured with a laser vibrometer over a spatiotemporally modulated array of piezoelectric patches, demonstrating the emergence of a one- way topological boundary propagation of sound (Darabi et al., 2020). b: A topological mechanical metamaterial made of a three-dimensional printed elastic polymer based on asymmetric nonlinearities (Coulais et al., 2017).
Fall 2021 • Acoustics Today 15