Valley Topological Phases in Bilayer Sonic Crystals

Recently, the topological physics in artificial crystals for classical waves has become an emerging research area. In this Letter, we propose a unique bilayer design of sonic crystals that are constructed by two layers of coupled hexagonal array of triangular scatterers. Assisted by the additional layer degree of freedom, a rich topological phase diagram is achieved by simply rotating scatterers in both layers. Under a unified theoretical framework, two kinds of valley-projected topological acoustic insulators are distinguished analytically, i.e., the layer-mixed and layer-polarized topological valley Hall phases, respectively. The theory is evidently confirmed by our numerical and experimental observations of the nontrivial edge states that propagate along the interfaces separating different topological phases. Various applications such as sound communications in integrated devices can be anticipated by the intriguing acoustic edge states enriched by the layer information.

Figure 1

(a) Schematic of the coupled BSC of hexagonal lattice. Air is filled inside the structured channels with hard boundaries. (b) Side (left) and top (right) views of the unit cell. Specifically, the angles $\alpha$ and $\beta$ together characterize the orientations of the triangular scatterers in both layers. (c) Numerical dispersion for the BSC with zero angles. Inset: the first Brillouin zone. (d)–(g) Local views of the band structures for the four BSCs with specified rod orientations.

Figure 2

(a) Band edge frequencies of the 2nd and 3rd bands, varied along the angular path depicted in the inset. (b) Reduced phase diagram parametrized by the angles $(\alpha ,\beta )$, distinguished by the quantized topological invariants $C_V^K$ and $C_L^K$. The numerical phase boundaries (solid lines) correspond to the closure of the omnidirectional band gap, consistent with the model predictions (dots).

Figure 3

Projected dispersions along an interface separating two topologically distinct AVH BSCs (a), and two topologically distinct ALH BSCs (b). Rod orientations are labeled for the BSCs located at the left ($L$) and right ($R$) sides. Red and blue curves correspond to the edge modes projected by the $K$ and $K^{\prime }$ valleys, respectively. The insets exemplify two eigenstates projected to the $K$ valley. (c) The amplitude field simulated for a finite-size sample with an AVH interface, excited by a point source (red star) positioned at the left entrance of the upper layer. A side view of the interface is zoomed-in to show the sound distribution in both layers. (d) The same as (c), but for the ALH case.

Figure 4

Experimental evidences for the edge modes involved in Fig. 3. (a1) Experimental setup for the AVH case, where the red dashed line indicates the crystal interface. Inset: local view of the sample. The cover plate is removed for displaying more sample details. (b1) Experimental pressure amplitudes along the crystal interface, measured for both layers at 15.3 kHz. (c1) Experimental edge dispersions (bright color) achieved by Fourier transforming the pressure fields scanned inside the upper and lower layers, where the green curves label the simulated edge modes with positive group velocities. (a2)–(c2): The same as (a1)–(c1), but for the ALH case.

Figure 5

A layer-polarization converter constructed by four BSCs with rod orientations $(\pm 10°,3°)$ and $(0,\pm 20°)$, belonging to ALH and AVH acoustic insulators, respectively. (a) Full-wave simulation at 15.3 kHz, which shows sound concentration varying from the upper layer to the lower layer. (b) Pressure amplitudes measured for the upper and lower interfaces along the $x$ direction, where the shadow region indicates clearly the interlayer conversion.