Page 14 - Fall2021

TOPOLOGICAL ACOUSTICS
Figure 1. Exotic acoustic phenomena enabled by topological concepts. a: Pressure field (p) distribution in a phononic topological insulator formed by an array of subwavelength resonators whose properties are modulated in space and time to impart a pseudospin in the form of angular momentum. The result is a one-way, edge-bound propagation of acoustic pressure (Fleury et al., 2016). b: Topological features around an exceptional point (EP) in the space formed by changing two independent parameters in an acoustic system, for example, a pair of coupled resonators whose resonant features can be controlled by changing two geometrical parameters (Miri and Alù, 2019). c: Pressure distribution (yellow, larger pressure fields) forming an orbital angular momentum sound beam. See text for detailed explanations.
as parameters controlling the system are changed. This may correspond to two coupled acoustic cavities, which we can independently tune through geometric changes. Through proper design, the coupled cavity system can support an exceptional point (EP) in the space spanned tuning the two geometric parameters. At the EP, the eigenvalues of the system and the corresponding eigen- modes coalesce and become degenerate. As a result of this degeneracy, the system effectively loses one dimen- sion. This singularity is associated with highly nontrivial topological properties (Xu et al., 2016) that can again provide unusual robustness of the response and at the same time offer opportunities for sensing (Shi et al., 2016; Miri and Alù, 2019).
Finally, topological features can also emerge in real space. Figure 1c shows an example of sound propagation with a nonzero orbital angular momentum (OAM) and the pressure distribution of an OAM sound wave traveling in free space. A carefully controlled array of sound emitters can emit such a vortex sound beam whose acoustic phase fronts are characterized by a nonzero topological charge, which can be leveraged to enhance the channel capacity in multiplexing applications and for robust sound propa- gation (Wang et al., 2018). In this article, we dive deeper into a few applications afforded by topological sound that may be of interest to the acoustics community at large.
Applications
Topological Sound Transport Based on Pseudospin Bias
Acoustic waveguides are inherently prone to disorder and imperfections that impact the quality and efficiency of sound transport.Undesiredbackreflectionsandscatteringcancause interference and distortions that impact several applications. Topological sound has been opening new opportunities for robust information transfer, multiplexing and processing, and data storage and manipulation. The simplest form of pseu- dospin to enable topological sound relies on geometrical asymmetries, for example, an acoustic array of subwave- length resonators with carefully tailored asymmetries act like a spin on sound waves (Ni et al., 2018). The resulting devices are passive and support topological boundary sound waves somewhat robust to disorder. Their main limitation stems from the fact that these acoustic topological insulators obey time-reversal symmetry, requiring that for any given wave supported in a certain direction and characterized by one pseudospin, the structure also supports an oppositely propagating wave with a reversed pseudospin. In the ideal case, the two modes are orthogonal to each other, but when disorder and imperfections are considered, their asymmetry may couple the two, limiting the overall robustness.
In contrast, topological sound enabled by pseudospins that break time-reversal symmetry, such as angular-momentum
14 Acoustics Today • Fall 2021