Far-field imaging of acoustic waves by a two-dimensional sonic crystal

The negative refraction behavior and imaging effect for acoustic waves in two-dimensional sonic crystals consisting of hexagonal arrays of steel cylinders in air are studied in this paper. The negative refraction and left-handed behaviors are demonstrated by the simulation of a Gaussian beam through a slab of the sonic crystal. Imaging effects by the sonic crystal slab with effective refraction index $n\ne -1$ and $n=-1$ are investigated, respectively. Far-field images by two-dimensional sonic-crystal-based superlens for both cases are obtained by exact numerical simulations, which is in agreement with the physical analysis based on the wave-beam negative refraction law. Thus, extensive applications of such a phenomenon to acoustic devices are anticipated.

Figure 1

(a) Band structure for the sonic crystal consisting of steel cylinders in air background arranged in a hexagonal lattice, with a filling ratio 0.47. The straight line beginning at point $\Gamma$ represents the dispersion relation of air, i.e., $\omega =ck$, and the horizontal line marks the frequency 0.65. (b) EFCs for some frequencies at the second band, moving inwards with increasing frequencies.

Figure 2

Pressure field patterns generated by an incident Gaussian beam on a nine-layer sample. Light and dark regions denote positive and negative pressures, respectively, and the vertical black lines mark the sample surfaces. The propagation directions of the Gaussian beam are marked by arrows, with $\alpha$ and $\beta$ denoting the incident and refractive angles. The scale is in unit of $a$, the lattice constant.

Figure 3

A “ray-trace” schematic picture governed by wave-beam refraction law.

Figure 4

The intensity distributions of pressure field of a point source and its image across a nine-layer sample, with $D_1=6a$. Lightness and darkness denote strong and weak intensity distributions of pressure field, respectively. The vertical lines mark the sample surfaces.

Figure 5

The intensity distributions of pressure field of a point source and its image across a 15-layer sample, with (a) $D_1=6a$ and (b) $D_1=11a$, respectively. Lightness and darkness denote strong and weak intensity distributions of pressure field, respectively. The vertical lines mark the sample surfaces.

Figure 6

(a) Band structure for the sonic crystal consisting of steel cylinders in air background arranged in a hexagonal lattice, with a filling ratio 0.906. The straight line beginning at point $\Gamma$ represents dispersion relation of air $\omega =ck$, and the horizontal line denotes frequency 0.365. (b) EFCs for some frequencies at the second band, moving inwards with increasing frequencies.

Figure 7

The isotropic negative ERI $n$ vs frequency.

Figure 8

Pressure patterns of a point source and its image across (a) six-layer, (b) seven-layer, and (c) nine-layer samples, respectively, with $D_1=3.5a$ kept fixed. Light and dark regions denote positive and negative pressure fields, respectively.

Figure 9

Pressure patterns of a point source and its image across a 6-layer sample, with (a) $D_1=0.5a$, (b) $D_1=2.5a$ and (c) $D_1=4.5a$, respectively. Light and dark regions denote positive and negative pressure fields, respectively.