Angle-Dependent Ultrasonic Transmission through Plates with Subwavelength Hole Arrays

We study the angle and frequency dependence of sound transmission through water-immersed perforated aluminum plates. Three types of resonances are found to govern the acoustic properties of the plates: lattice resonances in periodic arrays, Fabry-Perot modes of the hole cavities, and elastic Lamb modes. The last two of them are still present in random arrays and have no parallel in optical transmission through holes. These modes are identified by comparing experiment with various levels of theoretical analysis, including full solution of the elasto-acoustic wave equations. We observe strong mixture of different transmission mechanisms, giving rise to unique acoustic behavior and opening new perspectives for exotic wave phenomena.

Figure 1

Angle dependence of sound transmission through aluminum plates immersed in water and perforated by holes of fixed diameter $d=3\mathrm{mm}$, arranged in a square array of period $a=5\mathrm{mm}$. (a) Schematic representation of a drilled plate, the incident sound wave vector $\mathbf{k}$, and its component parallel to the film ${\mathbf{k}}_{\parallel }$. (b)–(d) Measured sound transmission as a function of $k_{\parallel }$ and frequency $\omega$ for three different film thicknesses $t$, as indicated by text insets. (e)–(g) Theoretical counterpart of (b)–(d), obtained by solving the full elasto-acoustic wave equations. The transmission is represented in linear gray scale.

Figure 2

Measured transmission and full-theory calculation compared with hard-solid and homogeneous-plate models for thickness $t=2\mathrm{mm}$. (a) Dependence of the measured transmission intensity on parallel wave vector $k_{\parallel }$ and frequency $\omega$ for a water-immersed perforated aluminum film of period $a=5\mathrm{mm}$ and hole diameter $d=3\mathrm{mm}$. (b) Calculated transmission in a hard-solid model [11]. (c) Calculated transmission for a homogeneous aluminum plate of the same thickness [12]. (d) Numerical solution of the full elasto-acoustic wave equations for the actual perforated aluminum plate. The transmission is represented in dB gray scale.

Figure 3

Transmission through disordered hole arrays compared to ordered arrays. (a) Dependence of the measured transmission intensity on parallel wave vector $k_{\parallel }$ and frequency $\omega$ for a water-immersed perforated aluminum film of thickness $t=5\mathrm{mm}$, period $a=5\mathrm{mm}$, and hole diameter $d=3\mathrm{mm}$. (b) Measured transmission for an array of randomly distributed holes of the same thickness and diameter and with the same filling fraction of the holes in the plate. (c),(d) 2D Fourier transforms (contour plots in log scale) of the film openings for the (c) periodic and (d) random arrays.