Delay time of waves performing Lévy walks in 1D random media.

The time that waves spend inside 1D random media with the possibility of performing Lévy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered systems via the delay time. We show that a wide class of disorder-Lévy disorder-leads to strong random fluctuations of the delay time; nevertheless, some statistical properties such as the tail of the distribution and the average of the delay time are insensitive to Lévy walks. Our results reveal a universal character of wave propagation that goes beyond standard Brownian wave-diffusion.

Experimental Evidence of Rainbow Trapping and Bloch Oscillations of Torsional Waves in Chirped Metallic Beams.

The Bloch oscillations (BO) and the rainbow trapping (RT) are two apparently unrelated phenomena, the former arising in solid state physics and the latter in metamaterials. A Bloch oscillation, on the one hand, is a counter-intuitive effect in which electrons start to oscillate in a crystalline structure when a static electric field is applied. This effect has been observed not only in solid state physics but also in optical and acoustical structured systems since a static electric field can be mimicked by a chirped structure. The RT, on the other hand, is a phenomenon in which the speed of a wave packet is slowed down in a dielectric structure; different colors then arrive to different depths within the structure thus separating the colors also in time. Here we show experimentally the emergence of both phenomena studying the propagation of torsional waves in chirped metallic beams. Experiments are performed in three aluminum beams in which different structures were machined: one periodic and two chirped. For the smaller value of the chirping parameter the wave packets, with different central frequencies, are back-scattered at different positions inside the corrugated beam; the packets with higher central frequencies being the ones with larger penetration depths. This behavior represents the mechanical analogue of the rainbow trapping effect. This phenomenon is the precursor of the mechanical Bloch oscillations, which are here demonstrated for a larger value of the chirping parameter. It is observed that the oscillatory behavior observed at small values of the chirp parameter is rectified according to the penetration length of the wave packet.

Beyond Anderson localization in 1D: anomalous localization of microwaves in random waveguides.

Experimental evidence demonstrating that anomalous localization of waves can be induced in a controllable manner is reported. A microwave waveguide with dielectric slabs randomly placed is used to confirm the presence of anomalous localization. If the random spacing between slabs follows a distribution with a power-law tail (Lévy-type distribution), unconventional properties in the microwave-transmission fluctuations take place revealing the presence of anomalous localization. We study both theoretically and experimentally the complete distribution of the transmission through random waveguides characterized by α=1/2 ("Lévy waveguides") and α=3/4, α being the exponent of the power-law tail of the Lévy-type distribution. As we show, the transmission distributions are determined by only two parameters, both of them experimentally accessible. Effects of anomalous localization on the transmission are compared with those from the standard Anderson localization.

Analogue transformations in physics and their application to acoustics.

Transformation optics has shaped up a revolutionary electromagnetic design paradigm, enabling scientists to build astonishing devices such as invisibility cloaks. Unfortunately, the application of transformation techniques to other branches of physics is often constrained by the structure of the field equations. We develop here a complete transformation method using the idea of analogue spacetimes. The method is general and could be considered as a new paradigm for controlling waves in different branches of physics, from acoustics in quantum fluids to graphene electronics. As an application, we derive an "analogue transformation acoustics" formalism that naturally allows the use of transformations mixing space and time or involving moving fluids, both of which were impossible with the standard approach. To demonstrate the power of our method, we give explicit designs of a dynamic compressor, a spacetime cloak for acoustic waves and a carpet cloak for a moving aircraft.

Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere.

This Letter presents the design, fabrication, and experimental characterization of a directional three-dimensional acoustic cloak for airborne sound. The cloak consists of 60 concentric acoustically rigid tori surrounding the cloaked object, a sphere of radius 4 cm. The major radii and positions of the tori along the symmetry axis are determined using the condition of complete cancellation of the acoustic field scattered from the sphere. They are obtained through an optimization technique that combines genetic algorithm and simulated annealing. The scattering cross section of the sphere with the cloak, which is the magnitude that is minimized, is calculated using the method of fundamental solutions. The low-loss fabricated cloak shows a reduction of the 90% of the sphere scattering cross section at the frequency of 8.55 kHz.

Radial Photonic Crystal for detection of frequency and position of radiation sources.

Based on the concepts of artificially microstructured materials, i.e. metamaterials, we present here the first practical realization of a radial wave crystal. This type of device was introduced as a theoretical proposal in the field of acoustics, and can be briefly defined as a structured medium with radial symmetry, where the constitutive parameters are invariant under radial geometrical translations. Our practical demonstration is realized in the electromagnetic microwave spectrum, because of the equivalence between the wave problems in both fields. A device has been designed, fabricated and experimentally characterized. It is able to perform beam shaping of punctual wave sources, and also to sense position and frequency of external radiators. Owing to the flexibility offered by the design concept, other possible applications are discussed.

Comment on "Theory of tailoring sonic devices: diffraction dominates over refraction".

Recently, Garcia et al. [Phys. Rev. E 67, 046606 (2003)] studied theoretically several acoustic devices with dimensions on the order of several wavelengths. Those authors also discussed experimental results previously reported by several of us [Phys. Rev. Lett. 88, 023902 (2002)]] and concluded that it is diffraction rather than refraction that is the dominating mechanism explaining the focusing effects observed in those experiments. In this Comment we reexamined their calculations and discussed why some of their interpretations of our results are misleading.

Evidence of fano-like interference phenomena in locally resonant materials.

Sonic crystals consisting of three-dimensional arrays of units which exhibit localized resonances have been discovered recently. Here, it is shown that their two-dimensional counterparts behave in a similar manner. Particularly, it is observed that the transmittance spectra show very asymmetric peaks which are explained as a Fano-like interference phenomenon. A finite difference time domain method is employed to perform a comprehensive study of the resonance line shape as a function of the mass density of the structural units. Also, a simple analytical model is introduced to give an intuitive account of the origin of the interference phenomenon.

Refractive acoustic devices for airborne sound.

We show that a sonic crystal made of periodic distributions of rigid cylinders in air acts as a new material which allows the construction of refractive acoustic devices for airborne sound. It is demonstrated that, in the long-wave regime, the crystal has low impedance and the sound is transmitted at subsonic velocities. Here, the fabrication and characterization of a convergent lens are presented. Also, an example of a Fabry-Perot interferometer based on this crystal is analyzed. It is concluded that refractive devices based on sonic crystals behave in a manner similar to that of optical systems.

Reflectance properties of two-dimensional sonic band-gap crystals.

An analysis of the reflectance of sonic band-gap crystals consisting of square arrays of rigid cylinders in air is presented. The standing wave formed in front of the structures is studied both experimentally and theoretically. Experiments have been performed with a mobile robotized microphone that obtains pressure maps on the plane perpendicular to the axes of the cylinders. Enhancements of the standing wave ratio (SWR) are observed in frequency regions where attenuation bands appear in zero-order transmission experiments. Also, the SWR presents oscillations that can be related to the finite dimension of the structure (Fabry-Perot effect). Both features are well described by calculations based on a double-scattering approach.

Large two-dimensional sonic band gaps.

We show that absolute sonic band gaps produced by two-dimensional square and triangular lattices of rigid cylinders in air can be increased by reducing the structure symmetry. In the case of square lattices, symmetry reduction is achieved by a smaller diameter cylinder placed at the center of each unit cell. For triangular lattices the reduction is achieved by decreasing the diameter of the cylinder at the center of the hexagons in the lattice. Theoretical predictions are also demonstrated experimentally: starting from a honeycomb lattice (using cylinders of 4 cm of diameter size and 6.35 cm nearest-neighbor distance) we have studied the transition to a triangular symmetry by putting rods with increasing diameter (in the range 0.6-4 cm) at the center. The greatest enhancement of the attenuation strength observed in transmission experiments has been obtained in the high frequency region for diameter ratios in the range 0.1-0.3.