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 ¼ 1=2 ("Lévy waveguides") and α ¼ 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.

No abstract

The unusual viscoelastic properties of silica aerogel plates are efficiently used to design subwavelength perfect sound absorbers. We theoretically, numerically and experimentally report a perfect absorbing metamaterial panel made of periodically arranged resonant building blocks consisting of a slit loaded by a clamped aerogel plate backed by a closed cavity. The impedance matching condition is analyzed using the Argand diagram of the reflection coefficient, i.e., the trajectory of the reflection coefficient as a function of frequency in the complex plane. The lack or excess of losses in the system can be identified via this Argand diagram in order to achieve the impedance matching condition. The universality of this tool can be further exploited to design more complex metasurfaces for perfect sound absorption, thus allowing the rapid design of novel and efficient absorbing metamaterials.

We study the electromagnetic transmission T through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed distribution -Lévy-type distribution. Based on recent predictions made for 1D coherent transport with Lévy-type disorder, we show numerically that for a system of length L (i) the average − ln T ∝ L α for 0 < α < 1, while − ln T ∝ L for 1 ≤ α < 2, α being the exponent of the power-law decay of the layer-thickness probability distribution; and (ii) the transmission distribution P (T ) is independent of the angle of incidence and frequency of the electromagnetic wave, but it is fully determined by the values of α and ln T . Additionally we have found and numerically verified that T ∝ L −α with 0 < α < 1. Random processes characterized by density probabilities with a long tail (Lévy-type processes) have been found and studied in very different phenomena and fields such as biology, economy, and physics. One of the main features of a Lévy-type density distribution p(l) is the slow decay of its tail. More precisely, for large l,with 0 < α < 2. Note that the second moment diverges for all α and if 0 < α < 1 also the first moment diverge. This kind of distributions are also known as α-stable distributions [1]. A window on new optical materials which allow for the experimental study of Lévy flights in an outstanding controllable way was recently opened with the construction of the so-called Lévy glass [2]: titanium dioxide particles are suspended in a matrix made of glass microspheres. The distribution of the microsphere diameters is properly chosen in order that light can travel performing Lévy flights within the microspheres. The diameter distribution is characterized by the exponent α of the power-law decay of its tail; it was found [2] that when 0 < α < 1 the transport is supperdiffusive, while for α = 2 the normal diffusive transport is recovered. This experimental investigation has motivated several theoretical works on the effects of the presence of Lévy-type processes on different transport quantities in one dimension, as well as in higher dimensional systems [3][4][5][6]8].On the other hand, coherent electron transport through one-dimensional (1D) quantum wires with Lévy-type disorder was studied in Ref. [6]. It was found that for the dimensionless conductance, or transmission, T :(i) the average (over different disorder realizations) of the logarithm of the transmission behaves asand (ii) the distribution of transmission P (T ) is fully determined by the exponent α and the ensemble average ln T .We point out that although for 1 ≤ α < 2, the average ln T depends linearly on L, as in the standard Anderson localization problem, it is interesting to remark that the statistical properties of T are not those predicted by the standard scaling approach to localization, in particular by the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation [7]. That is, for 1 ≤ α < 2 the transmission fluctuations are larger than those considered in the DMPK equation. Thus, the standard statist...