Robust Acoustic Pulling Using Chiral Surface Waves

We show that long-range and robust acoustic pulling can be achieved by using a pair of one-way chiral surface waves supported on the interface between two phononic crystals composed of spinning cylinders with equal but opposite spinning velocities embedded in water. When the chiral surface mode with a relatively small Bloch wave vector is excited, the particle located in the interface waveguide will scatter the excited surface mode to another chiral surface mode with a greater Bloch wave vector, resulting in an acoustic pulling force, irrespective of the size and material of the particle. Thanks to the backscattering immunity of the chiral surface waves against local disorders, the particle can be pulled, following a flexible trajectory, as determined by the shape of the interface. As such, this acoustic pulling scheme overcomes some of the limitations of the traditional acoustic pulling using structured beams, such as short pulling distances, straight-line type pulling, and a strong dependence on the scattering properties of the particle. Our work may also inspire the application of topological acoustics to acoustic manipulations.

Figure 1

Band structures of phononic crystals composed of (a) static cylinders and (b) spinning cylinders arranged into a square lattice embedded in water. Parameters of water and static cylinder are ${\rho }_0={10}^3\mathrm{kg/}{\mathrm{m}}^3,c_0=1489\mathrm{m/s},\rho =1.3\times {10}^3\mathrm{kg/}{\mathrm{m}}^3,c=400\mathrm{m/s}$, the radius of the cylinder is $r_c=0.16a$, and the spinning circular frequency is $\mathrm{\Omega }=1.678a/c_0$.

Figure 2

(a) Bulk (black) and surface (red and blue) state dispersion relations calculated using multiple scattering method in conjunction with a supercell calculation. (b) Pressure field patterns for four surface modes. (c) Full-wave simulations for the one-way surface wave being scattered by a cylindrical particle. Spinning cylinders are shown by the black disks in (b),(c). In (c), scatter is represented by the white disk, and the two line sources (red and blue dots) $p_0{H}_0^{(1)}(k_0{r}_1)$ and $-p_0{H}_0^{(1)}(k_0{r}_2)$ are located at ${\mathbf{r}}_1=(-10,0.2)$ and ${\mathbf{r}}_2=(-10,-0.2)$, respectively.

Figure 3

(a) Acoustic forces acting on the particle as a function of the location $(x_s,y_s)$ of the particle within a rectangular region, as marked in Fig. 2. Parameters of the cylinder are $r_s=0.35a,{\rho }_s=7800\mathrm{kg/}{\mathrm{m}}^3,c_s=6010\mathrm{m/s}$. (b) Spatially averaged longitudinal acoustic force ${\overline{F}}_x$ as functions of $y_s$ for different particles. For the red and black symbol lines, the mass density and sound speed of the particle are ${\rho }_s=7800\mathrm{kg/}{\mathrm{m}}^3$ and $c_s=6010\mathrm{m/s}$, while for the blue symbol lines, the mass density and sound speed of the particle are ${\rho }_s^{\mathrm{\prime }}=1.3\mathrm{kg/}{\mathrm{m}}^3$ and $c_s^{\mathrm{\prime }}=340\mathrm{m/s}$.

Figure 4

(a) $|g(k_{B,n},y)|$ and (b)$|g(k_{D,n},y)|$ as functions of vertical coordinate y. Insets show $|g(k,y)|$ as functions of plane-wave vector k at $y=0.5a$.

Figure 5

(a),(b) Intensities $I_B,I_D$, and relative phases ${\varphi }_B,{\varphi }_D$ of modes B and D of zero order in the scattered wave, which are normalized by the intensity of the incident wave as functions of the particle location $x_s$. Vertical coordinate of the particle is $y_s=0.3a$. Inset in (a) shows the intensity distributions of eigenmodes B and D. (c),(d) Longitudinal acoustic forces $F_x$ acting on the particle as functions of particle location $x_s$_, which are calculated using the Lorenz-Mie formula, Eq. (5) (red lines), and response theory, Eq. (8) (blue circles). Vertical coordinates of the particle in (c),(d) are $y_s=0.3a$ and $y_s=0.1a$_, respectively. Parameters of the particle are $r_s=0.25a$, ${\rho }_s=7800\mathrm{kg/}{\mathrm{m}}^3,$ and $c_s=6010\mathrm{m/s}$.

Figure 6

(a) Magnitude of the velocity field along the x direction, $|v_x|$_, inside the channel. Velocity is normalized by $p_0/({\rho }_0{c}_0)$. (b) $U=-(3/4\omega )|v_x|(d|v_x|/dx)$ inside the channel. U is normalized by $p_0^2/({\rho }_0^2{c}_0^3)$.