B. A. van Tiggelen

Resonant multiple scattering of light

Abstract This educational work presents a new approach towards resonant interaction between classical light and matter. The interaction between light and matter is considered from three different points of view: the light picture (where the material degrees of freedom have been integrated out, and leaving one with scattering theory), the matter picture (where the radiative degrees of freedom have been eliminated and providing one essentially with atomic physics). In addition the polariton approach is discussed, in which the degrees of freedom of light and matter are treated on the same footing. Although the first approach will by far be given most of the attention, we will frequently emphasize the equivalence of the three methods. Much of the presented material is selfcontained. We demonstrate that in the dynamical properties of multiple scattering of light the “matter” properties play a dominant role. Several “paradigms of atomic physics” will be discussed from the view point of light scattering theory. We shall introduce the far-reaching analogy between the dielectric “Mie” sphere in classical optics, and the two-level atom in semi-classical atomic physics. This mapping turns out to be much more faithful than the widely used analogy between scattering theory for De Broglie waves and classical waves. In scattering theory the semi-classical two-level atom is equivalent to a point scatterer.

Localization of ultrasound in a three-dimensional elastic network

A systematic study of the propagation of ultrasound through a random network of aluminium beads provides the first demonstration of the Anderson localization of classical waves in a 3D system.

Green function retrieval and time reversal in a disordered world.

We apply the theory of multiple wave scattering to two contemporary, related topics: imaging with diffuse correlations and stability of the time reversal of diffuse waves, using equipartition, coherent backscattering, and frequency speckles as fundamental concepts.

Energy partition of seismic coda waves in layered media: Theory and application to Pinyon Flats Observatory

SUMMARY We have studied the partition of shear, compressional and kinetic energies in the coda of 10 earthquakes recorded on a dense array, located at Pinyon Flats Observatory (PFO), California. Deformation energies are estimated by measuring finite differences of the wavefield components. We have thoroughly studied the validity and stability of this technique for the PFO data and obtained reliable measurements in the 5–7 Hz frequency band. We observe a clear stabilization of the ratio between shear and compressional energies (W S /W P ) in the coda, with similar values for all 10 earthquakes under study. We interpret this observation as a signature of equipartition. The average W S /W P ratio is about 2.8, which is smaller by a factor 2.5 than the expected value, around 7.2, for equipartitioned elastic waves at the surface of a homogeneous Poisson half-space. The ratio between the vertical and horizontal kinetic energies (V 2 /H 2 ) also exhibits stabilization in the coda and can be measured from 5 to 25 Hz. The V 2 /H 2 ratio shows an abrupt transition from 0.1 in the 5–10 Hz band, to about 0.8 in the 15–25 Hz band. These measured values are again in sharp contrast with the theoretical prediction, around 0.56, for equipartitioned elastic waves at the surface of a Poisson half-space. To explain these observations, we have developed a theory of equipartition in a layered elastic half-space. Using a rigorous spectral decomposition of the elastic wave equation, we define equipartition as a white noise distributed over the complete set of eigenfunctions. This definition is shown to agree with the standard physical concepts in canonical cases. The theory predicts that close to the resonance frequency of a low-velocity layer, the ratio between the shear and compressional energies strongly decreases. Using a detailed model of the subsurface at PFO, this counter-intuitive result is found to be in good qualitative and quantitative agreement with the observations. Near the resonance frequency of the low-velocity structure, the drop of the energy ratios W S /W P and V 2 /H 2 is controlled by the change of ellipticity of the Rayleigh wave and the large contribution of the fundamental Love mode. At higher frequencies, the interplay between Rayleigh and Love modes trapped in shallow low-velocity layers is responsible for the abrupt increase of the kinetic energy ratio V 2 /H 2 . Our study demonstrates that the partition

Dynamics of anderson localization in open 3D media

We develop a self-consistent theoretical approach to the dynamics of Anderson localization in open three-dimensional (3D) disordered media. The approach allows us to study time-dependent transmission and reflection, and the distribution of decay rates of quasimodes of 3D disordered slabs near the Anderson mobility edge.

Anderson Localization of a Bose-Einstein Condensate in a 3D Random Potential

We study the effect of Anderson localization on the expansion of a Bose-Einstein condensate, released from a harmonic trap, in a 3D random potential. We use scaling arguments and the self-consistent theory of localization to show that the long-time behavior of the condensate density is controlled by a single parameter equal to the ratio of the mobility edge and the chemical potential of the condensate. We find that the two critical exponents of the localization transition determine the evolution of the condensate density in time and space.

Dynamics of weakly localized waves.

We develop a transport theory to describe the dynamics of (weakly) localized waves in a quasi-1D tube geometry both in reflection and in transmission. We compare our results to recent experiments with microwaves and to other theories, such as random matrix theory and supersymmetric theory.

Localization of Waves

Writing a short and critical review about localization of waves is an ambiguous project, doomed to be incomplete, and doomed to be unfair to the many good papers that have been written on this fascinating subject. At least every subject raised in this modest contribution merits, I think, an entire review and, fortunately, some exist already. By no means is this review going to be a replacement for the excellent works by Thouless [1], Ramakrishnan [2], Mott [3], Souillard [4], John [5, 6], and Vollhardt and Wolfle [7]. Answering the question whether or not reported experiments reveal wave localization is not the aim of this review either. The emphasis in this review will be on definitions, features and consequences.

Numerical and experimental study of disordered multilayers for broadband x-ray reflection

The effect of layer thickness disorder in periodic multilayers on x-ray reflectivity is investigated numerically and experimentally. We present ensemble calculations, taking into account absorption and interfacial roughness. It is demonstrated that layer thickness disorder yields band broadening and increased integrated reflectivity For applications we concentrate on extrema of the ensembles, giving the highest integrated reflectivity We develop global optimization methods that can also be used to generate specified reflection band structures. In a few examples, applications of the optimization methods are discussed. To illustrate the practical applicability of the methods, we compare experimental realizations to the calculation. In one case we achieve a 42% increase in integrated reflectivity in the 130 Å < λ < 190 Å spectral range with respect to a periodic multilayer with its first-order Bragg peak in the center of that range. Accurate control of layer thicknesses is our main experimental obstacle.

Optics of a Faraday-active Mie sphere

We present an exact calculation for the scattering of light from a single sphere made of a Faraday-active material into first order of the external magnetic field. When the size of the sphere is small compared with the wavelength, the known T matrix for a magneto-active Rayleigh scatterer is found. We address the issue of whether there is a so-called photonic Hall effect—a magneto-transverse anisotropy in light scattering—for one Mie scatterer. In the limit of geometrical optics, we compare our results with the Faraday effect in a Fabry–Perot etalon.