Free-form acoustic topological waveguides enabled by topological lattice defects

The emerging field of topological acoustics provides exciting possibilities for controlling sound propagation with extraordinary robustness. Conventional topological acoustic waveguides built from topological edge states, which arise solely from the nontrivial topology in the momentum space, usually have restricted shapes due to their crystalline structures. Here, we show that, using an acoustic topological system with both nontrivial topologies in the real and momentum spaces, free-form acoustic topological waveguides can be constructed. These topological waveguides support disclination-localized states, caused by the interplay between topological lattice defects and the valley-Hall topology. As demonstrated in our simulations and experiments, such disclination waveguides can take arbitrary shapes and form open arcs within the lattice, which are not possible for previous crystalline acoustic topological waveguides. Furthermore, by increasing the number of topological lattice defects, we can realize more than one topological waveguide in one lattice. They join at the topological lattice defect and form a topological waveguide network, enabling more complicated functionalities such as beam splitting. Our results point to a promising direction for free-form acoustic topological devices with the advantages of embedded forms, easy cascading, and high robustness.

Figure 1

(a) Schematic of a honeycomb-lattice acoustic crystal. The shaded gray region represents a $\pi /3$ sector. The two insets indicate the unit cells. (b) Simulated bulk dispersions of two honeycomb-lattice acoustic crystals with $r_1=r_2=4.9\text{mm}$ (red solid lines), and $r_1=5.6\text{mm}$ and $r_2=4.2\text{mm}$ (blue dashed lines). The height of the acoustic crystal is 8.5 mm. (c) and (d) Schematics of a pentagonal acoustic crystal by deleting a $\pi /3$ sector [the gray shaded region in (a)] in the original honeycomb-lattice acoustic crystal (c) and a heptagonal acoustic crystal by inserting a $\pi /3$ sector [the gray shaded region in (a)] in the original honeycomb-lattice acoustic crystal (d). The two insets in the middle regions are two types of TLDs, labeled as TLD I and TLD II, and the red dashed lines denote the disclinations.

Figure 2

(a) and (b) Photographs of two pentagonal acoustic crystals with the (a) straight and (b) bent disclinations marked by the red dashed lines. (c) and (d) Simulated eigenfrequency spectra for two pentagonal acoustic crystals with the (c) straight and (d) bent disclinations. The red and black open circles represent edge states in the disclination and bulk, respectively. (e) and (f) Measured acoustic intensity eigenstates (${\left|p\right|}^2$) at the points (e) A and (f) B. The yellow stars at the center of the TLD represent dipole sound sources. (g) and (h) Measured relative intensity spectra sampled in the disclinations (the blue open rectangles R1 and R3) and bulk (the red open rectangles R2 and R4) of the pentagonal acoustic crystals with the (g) straight and (h) bent disclinations. The black shaded regions are the bulk band gap in (c) and (d).

Figure 3

(a) Photographs of three topological waveguides embedded with $\mathsf{W}$-, $\mathsf{I}$-, and $\mathsf{N}$-shaped disclinations. The insets show the two types of topological lattice defects. The red dashed lines and yellow stars denote the disclinations and sound sources, respectively. (b)–(f) Measured intensity distributions in the three samples at (b) 4.6 kHz, (c) 5.2 kHz, (d) 5.4 kHz, (e) 5.6 kHz, and (f) 6.2 kHz.

Figure 4

(a) and (b) Photographs of two embedded topological waveguides with (a) an arrow-shaped disclination and (b) a Chinese character -shaped disclination. The red dashed lines and yellow stars denote the disclinations and sound sources, respectively. (c) and (d) Measured acoustic intensity distributions in the two samples at different frequencies.