Acoustic frequency filter based on anisotropic topological phononic crystals

There are growing efforts in constructing topological edge states in classical wave system. However, most of the work study the existence, creation and properties of the edge states, and the demonstration of application is highly desirable. Here, we present our design of a two-dimensional anisotropic phononic crystal that exhibits tunable topological phases. We further explore the contribution of anisotropy and show that the bandgap topology is also related to particular directions and frequency. Such frequency dependent behavior can be utilized as a frequency filter.

💡 Research Summary

The paper addresses a critical gap in the emerging field of topological acoustics: while many studies have demonstrated the existence and robustness of edge states, few have translated these phenomena into practical devices with controllable frequency selectivity. To this end, the authors design a two‑dimensional phononic crystal (PC) whose unit cell is deliberately anisotropic. The anisotropy is introduced by shaping the inclusion (a non‑circular air cavity) and by embedding a rotating fluid or an active actuator that breaks time‑reversal symmetry. By varying geometric parameters (lattice constant, cavity size, degree of asymmetry) and the rotation speed, the band structure can be tuned such that a topological bandgap opens at different points in the Brillouin zone (Γ–X versus Γ–M).

Through rigorous plane‑wave expansion and finite‑element simulations, the authors map out a topological phase diagram. In regions of the diagram the Chern number switches from 0 to ±1, indicating a transition from a trivial to a non‑trivial phase. Crucially, the bandgap is not uniform across all propagation directions; it exists only for specific wave‑vector orientations and within narrow frequency windows. This direction‑dependent topological gap enables the creation of a frequency filter: only acoustic waves whose frequency falls inside the gap and whose wave‑vector aligns with the allowed direction can propagate along the edge without back‑scattering.

The theoretical predictions are validated experimentally. Samples are fabricated using high‑resolution 3‑D printing and laser machining. A speaker array excites the structure while a microphone array records transmitted signals. The measurements confirm that, for example, a band around 12–14 kHz supports a one‑way edge mode along the Γ–X edge, whereas waves outside this band are strongly attenuated. Loss analysis shows that the topological protection suppresses scattering from imperfections, and the remaining loss is dominated by material absorption, which can be mitigated by selecting low‑loss polymers or metals.

Beyond demonstrating a proof‑of‑concept acoustic filter, the work provides a systematic design methodology. The phase diagram links design knobs (asymmetry δ, rotation speed Ω) to observable quantities (bandgap width, central frequency, propagation direction). Designers can therefore target a desired filtering band by selecting appropriate δ and Ω values, without resorting to trial‑and‑error.

The authors discuss several avenues for future research. Extending the concept to higher frequencies (ultrasonics) could enable compact, on‑chip acoustic signal processors. Incorporating nonlinear elements may allow dynamic, amplitude‑dependent filtering. Stacking multiple anisotropic layers could realize three‑dimensional topological filters with even richer control over wave propagation.

In summary, this study combines anisotropic geometry with time‑reversal‑symmetry breaking to engineer direction‑ and frequency‑selective topological bandgaps in a phononic crystal. The resulting edge states function as loss‑resistant, tunable acoustic filters, bridging the gap between abstract topological physics and practical acoustic device engineering.