Wireless communications with diffuse waves

Diffuse, multiple-scattered waves can be very efficient for information transfer through disordered media, provided that antenna arrays are used for both transmission and reception of signals. Information capacity C of a communication channel between two identical linear arrays of n equally-spaced antennas, placed in a disordered medium with diffuse scattering, grows linearly with n and can attain considerable values, if antenna spacing a > lambda/2, where lambda is the wavelength. Decrease of a below lambda/2 makes the signals received by different antennas partially correlated, thus introducing redundancy and reducing capacity of the communication system. When the size of antenna arrays is well below lambda/2, the scaling of C with n becomes logarithmic and capacity is low.Comment: RevTEX 4, 3 pages, 2 figure

Finite-size scaling analysis of localization transition for scalar waves in a 3D ensemble of resonant point scatterers

We use the random Green's matrix model to study the scaling properties of the localization transition for scalar waves in a three-dimensional (3D) ensemble of resonant point scatterers. We show that the probability density $p(g)$ of normalized decay rates of quasi-modes $g$ is very broad at the transition and in the localized regime and that it does not obey a single-parameter scaling law for finite system sizes that we can access. The single-parameter scaling law holds, however, for the small-$g$ part of $p(g)$ which we exploit to estimate the critical exponent $\nu$ of the localization transition. Finite-size scaling analysis of small-$q$ percentiles $g_q$ of $p(g)$ yields an estimate $\nu \simeq 1.55 \pm 0.07$. This value is consistent with previous results for Anderson transition in the 3D orthogonal universality class and suggests that the localization transition under study belongs to the same class.Comment: 11 pages, 10 figures, revised manuscrip

Spatio-temporal speckle correlations for imaging in turbid media

We discuss the far-field spatio-temporal cross-correlations of waves multiple-scattered in a turbid medium in which is embedded a hidden heterogeneous region (inclusion) characterized by a distinct scatterer dynamics (as compared to the rest of the medium). We show that the spatio-temporal correlation is affected by the inclusion which suggests a new method of imaging in turbid media. Our results allow qualitative interpretation in terms of diffraction theory: the cross-correlation of scattered waves behaves similarly to the intensity of a wave diffracted by an aperture.Comment: RevTeX, 4 pages, a modified version is published in "Waves and Imaging Through Complex Media", ed. by P. Sebbah (Kluwer Academic Publishers, Dordrecht, 2001

Localization transition for light scattering by cold atoms in an external magnetic field

We establish a localization phase diagram for light in a random three-dimensional (3D) ensemble of motionless two-level atoms with a three-fold degenerate upper level, in a strong static magnetic field. Localized modes appear in a narrow spectral band when the number density of atoms $\rho$ exceeds a critical value $\rho_c \simeq 0.1 k_0^3$, where $k_0$ is the wave number of light in the free space. A critical exponent of the localization transition taking place upon varying the frequency of light at a constant $\rho > \rho_c$ is estimated to be $\nu = 1.57 \pm 0.07$. This classifies the transition as an Anderson localization transition of 3D orthogonal universality class.Comment: 5 pages, 3 figures + supplemental materia

Eigenvalue distributions of large Euclidean random matrices for waves in random media

We study probability distributions of eigenvalues of Hermitian and non-Hermitian Euclidean random matrices that are typically encountered in the problems of wave propagation in random media.Comment: 29 pages, 10 figure

Long-range correlations of density in a Bose-Einstein condensate expanding in a random potential

We study correlations of atomic density in a weakly interacting Bose-Einstein condensate, expanding diffusively in a random potential. We show that these correlations are long-range and that they are strongly enhanced at long times. Density at distant points exhibits negative correlations.Comment: 4 pages, 5 figure

Photon noise in a random laser amplifier with fluctuating properties

We study fluctuations of the number of photocounts measured by an ideal photodetector illuminated by light scattered in an amplifying disordered medium, below the threshold for random lasing. We show that the variance of fluctuations and their correlation function carry information about fluctuating properties of the medium. A direct link is established between the fluctuations of the number of photocounts due to the amplified spontaneous emission (ASE) and the dimensionless conductance g of the medium. Our results suggest a possibility of probing amplifying disordered media by analyzing statistics of their ASE, without illuminating them from outside by a probe beam.Comment: 14 pages, 9 figure

Ioffe-Regel criterion of Anderson localization in the model of resonant point scatterers

We establish a phase diagram of a model in which scalar waves are scattered by resonant point scatterers pinned at random positions in the free three-dimensional (3D) space. A transition to Anderson localization takes place in a narrow frequency band near the resonance frequency provided that the number density of scatterers $\rho$ exceeds a critical value $\rho_c \simeq 0.08 k_0^{3}$, where $k_0$ is the wave number in the free space. The localization condition $\rho > \rho_c$ can be rewritten as $k_0 \ell_0 < 1$, where $\ell_0$ is the on-resonance mean free path in the independent-scattering approximation. At mobility edges, the decay of the average amplitude of a monochromatic plane wave is not purely exponential and the growth of its phase is nonlinear with the propagation distance. This makes it impossible to define the mean free path $\ell$ and the effective wave number $k$ in a usual way. If the latter are defined as an effective decay length of the intensity and an effective growth rate of the phase of the average wave field, the Ioffe-Regel parameter $(k\ell)_c$ at the mobility edges can be calculated and takes values from 0.3 to 1.2 depending on $\rho$. Thus, the Ioffe-Regel criterion of localization $k\ell < (k\ell)_c = \mathrm{const} \sim 1$ is valid only qualitatively and cannot be used as a quantitative condition of Anderson localization in 3D.Comment: Revised and extended version. 9 pages, 6 figure

Finite-time scaling at the Anderson transition for vibrations in solids

A model in which a three-dimensional elastic medium is represented by a network of identical masses connected by springs of random strengths and allowed to vibrate only along a selected axis of the reference frame, exhibits an Anderson localization transition. To study this transition, we assume that the dynamical matrix of the network is given by a product of a sparse random matrix with real, independent, Gaussian-distributed non-zero entries and its transpose. A finite-time scaling analysis of system's response to an initial excitation allows us to estimate the critical parameters of the localization transition. The critical exponent is found to be $\nu = 1.57 \pm 0.02$ in agreement with previous studies of Anderson transition belonging to the three-dimensional orthogonal universality class.Comment: Revised manuscript. 8 pages, 5 figure