Generation of multiband spoof surface acoustic waves via high-order modes

Through theoretical analysis and numerical calculation, it is found that the textured surface of a perfect rigid body whose groove height is sufficiently large can support multiple modes of propagating spoof surface acoustic waves (SSAWs). Dispersion curves and group velocities/refractive index versus height and width of the groove are depicted for infinitely thick perfect rigid body to make a thoroughly inquiry into the multiband transmission of SSAWs. We also give the dispersion relations of samples with finite thickness which are more practical to realize, and the corresponding experimental results are in accordance with simulated results. Theoretical, simulated, and measured acoustic pressure field distributions are given to further illustrate the characteristics of different modes. Our work could have implications for applications such as acoustic filter design and energy harvesting.

Figure 1

(a) An acoustic plane wave incident on the one-dimensional PRB with periodic grooves induces the propagating SSAWs with wave number ${\beta }_x$. The corresponding geometry parameters are marked by $d, h$, and $a$, respectively. Dispersion curves with different (b) height, $h$, and (c) width, $a$, are plotted. The cavity modes of fundamental mode and second-order mode are denoted by horizontal red dotted lines in (c).

Figure 2

(a) Group velocity $v_g$ and (b) group refractive index $n_g$ of the one-dimensional structure along the propagation direction when the groove has different width $a$ and different height $h$, respectively. The cases where $v_g/c_0=0, v_g/c_0=1$, and $n_g=1$ are depicted by black dashed lines in (a) and (b).

Figure 3

(a) Band structure of the propagating modes along $x$ direction for the one-dimensional structure. The geometric parameters are set as $a=0.8d,h=2d$. (b) The corresponding normalized acoustic pressure distribution as the function of the wave number ${\beta }_0$ (in unit of $\pi /d$) and relative height h/d, in the grooves. Zero values are marked by the white dotted line. The wave numbers ${\beta }_1=0.220\pi /d, {\beta }_2=0.582\pi /d$, and ${\beta }_3=0.651\pi /d$ are marked by blue dashed lines.

Figure 4

(a) Simulation setup for the eigenmode analysis of the unit structure. The blue lines stand for periodic boundary condition, and the pressure field is calculated in air at different wave numbers: (b) ${\beta }_1=0.220\pi /d$, (c) ${\beta }_2=0.582\pi /d$, and (d) ${\beta }_3=0.651\pi /d$. The white lines in (c) and (d) are the positions with pressure being zero.

Figure 5

(a) Dispersion curves of the structure with different finite thicknesses ($t$). Other parameters are $h=4d$ and $a=0.8d$. The simulated dispersion curves with $t=3d$ and $t=\infty$ (2D case) and 2D theoretical ones are encircled by the black ellipses to highlight their first and second modes. (b) The structure unit cell with finite thickness. (c–f) The pressure field distributions on the xoz plane with $y=0$ at ${\beta }_0=0.351\pi /d$ marked in (a) when the thickness takes different values: (c) $t=0.1d$, (d) $t=d$, (e) $t=3d$, and (f) $t=\infty$ (2D case).

Figure 6

Simulated pressure-field distribution at 8.52 kHz on the xoz plane with (a) $y=0$ mm and (b) $y=1.5$ mm, respectively. The unit cells are delimited by the black dashed lines in (a). (d) The corresponding measured result for $y=1.5$ mm. 1D Fourier transformation spectrum of the pressure for $z=h$ is shown in (e). The experimental setup is shown in (c) and the results are shown in (f). The experimental dispersion curves (black circle) agree well with the simulated results (solid line). The air line (dash line) is also plotted.

Figure 7

Simulated near- and far-field wave field (normalized pressure magnitude square) at (a) ${\beta }_1=0.215\pi /d$, (b) ${\beta }_2=0.303\pi /d$, (c) ${\beta }_3=0.397\pi /d$, and (d) ${\beta }_4=0.429\pi /d$. The corresponding experimental results are shown in (e), (f), (g), and (h), respectively.