After exactly half a century of Anderson localization, the subject is more alive than ever. Direct observation of Anderson localization of electrons was always hampered by interactions and finite temperatures. Yet, many theoretical breakthroughs were made, highlighted by finite-size scaling, the self-consistent theory and the numerical solution of the Anderson tight-binding model. Theoretical understanding is based on simplified models or approximations and comparison with experiment is crucial. Despite a wealth of new experimental data, with microwaves, light, ultrasound and cold atoms, many questions remain, especially for three dimensions. Here we report the first observation of sound localization in a random three-dimensional elastic network. We study the time-dependent transmission below the mobility edge, and report ``transverse localization'' in three dimensions, which has never been observed previously with any wave. The data are well described by the self-consistent theory of localization. The transmission reveals non-Gaussian statistics, consistent with theoretical predictions.Comment: Final published version, 5 pages, 4 figure

We present a combined experimental and theoretical study of phonon focusing phenomena in a pass band above the complete band gap in a 3D phononic crystal. Wave propagation was found to depend dramatically on both frequency and incident direction. This propagation anisotropy leads to very large negative refraction, which can be used to focus a diverging ultrasonic beam into a narrow focal spot with a large focal depth. The experimental field patterns are well explained using a Fourier imaging technique, based on the 3D equifrequency surfaces calculated from multiple scattering theory. DOI: 10.1103/PhysRevLett.93.024301 PACS numbers: 43.35.+d, 63.20.-e The past decade has witnessed a rapid growth in the study of phononic crystals [1][2][3][4][5][6][7][8][9][10][11][12], which are periodic composite materials that are the elastic and acoustic analogues of photonic crystals [13][14][15][16][17][18][19][20][21]. This growing interest is fueled not only by potential applications as novel acoustic devices [7,8,10 -12], but also by the rich physics governing elastic and acoustic wave propagation in periodic media [1][2][3][4][5][6][7][8][9][10][11][12]. In addition, ultrasonic and acoustic techniques, coupled with powerful theoretical approaches, provide some unique advantages for directly investigating wave phenomena in these systems. Most of the studies until now have focused on the existence and properties of phononic band gaps [1-7,9], which occur due to Bragg scattering when the wavelength is comparable with the lattice constants, leading to frequency bands where wave propagation is forbidden. The result has been considerable progress in understanding how to achieve large complete band gaps in physically realizable materials, and in elucidating the mechanism of wave transport at gap frequencies, which has been shown to occur by tunneling [9].However, relatively little attention has been paid to investigating how periodicity affects wave propagation over a wide range of frequencies outside the band gaps, where novel refractive, diffractive, and focusing effects may all be possible. At low frequencies, an effective medium or continuum approximation can be adopted to study the wave properties and accurately predict the wave speeds. In this frequency range, there is much in common with the properties of low frequency phonons in atomic crystals, where phonon focusing phenomena have been systematically studied [22]. Recently, low frequency 2D sonic crystal refractive acoustic devices for airborne sound have been demonstrated [10] and theoretically analyzed [11] at wavelengths well below the first acoustic band gap. Also, a theory for tailoring sonic devices with dimensions on the order of several wavelengths has been investigated, where image formation was shown to occur predominantly through a diffraction mechanism rather than by refraction [12]. By contrast, much less is known about the behavior at higher frequencies in pass bands where the wavelengths can be much less than the lattice constant. In this Letter, we ...

We extend the multiple-scattering theory for elastic waves by taking into account the full vector character. The formalism for both the band structure calculation and the reflection and transmission calculations for finite slabs is presented. The latter is based on a double-layer scheme which obtains the reflection and transmission matrix elements for the multilayer slab from those of a single layer. As a demonstration of applications of the formalism, we calculate the band structures of elastic waves propagating in a three-dimensional periodic arrangement of spherical particles and voids, as well as the transmission coefficients through finite slabs. In contrast with the plane-wave method, the multiple-scattering approach exhibits advantages in handling specialized geometries ͑spherical geometry in the present case͒. We also present a comparison between theory and ultrasound experiment for a hexagonal-close-packed array of steel balls immersed in water. Excellent agreement is obtained.

We show experimentally and theoretically that super resolution can be achieved while imaging with a flat lens consisting of a phononic crystal exhibiting negative refraction. This phenomenon is related to the coupling between the incident evanescent waves and a bound slab mode of the phononic crystal lens, leading to amplification of evanescent waves by the slab mode. Super resolution is only observed when the source is located very near to the lens, and is very sensitive to the location of the source parallel to the lens surface as well as to site disorder in the phononic crystal lattice.

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