We study the statistical properties of wave scattering in a disordered waveguide. The statistical properties of a "building block" of length δL are derived from a potential model and used to find the evolution with length of the expectation value of physical quantities. In the potential model the scattering units consist of thin potential slices, idealized as delta slices, perpendicular to the longitudinal direction of the waveguide; the variation of the potential in the transverse direction may be arbitrary. The sets of parameters defining a given slice are taken to be statistically independent from those of any other slice and identically distributed. In the dense-weak-scattering limit, in which the potential slices are very weak and their linear density is very large, so that the resulting mean free paths are fixed, the corresponding statistical properties of the full waveguide depend only on the mean free paths and on no other property of the slice distribution. The universality that arises demonstrates the existence of a generalized central-limit theorem.Our final result is a diffusion equation in the space of transfer matrices of our system, which describes the evolution with the length L of the disordered waveguide of the transport properties of interest. In contrast to earlier publications, in the present analysis the energy of the incident particle is fully taken into account.For one propagating mode, N = 1, we have been able to solve the diffusion equation for a number of particular observables, and the solution is in excellent agreement with the results of microscopic calculations. In general, we have not succeeded in finding a solution of the diffusion equation.We have thus developed a numerical simulation, to be called "random walk in the transfer matrix space", in which the universal statistical properties of a "building block" are first implemented numerically, and then the various building blocks are combined to find the statistical properties of the full waveguide. The reported results thus obtained (in which use was made of a "shortwavelength approximation") are in very good agreement with those arising from truly microscopic calculations, for both bulk and surface disorder.

Lossless dielectric nanospheres (made of nonmagnetic materials) with relatively low refraction index may present strong electric and magnetic dipolar resonances. We establish a relationship between the optical force from a plane wave on small electric and magnetic dipolar particles, the transport cross section, and the scattering asymmetry parameter g. In this way we predict negative g (that minimize the transport mean free path below values of the scattering mean free path) for a dilute suspension of both perfectly reflecting spheres as well as of lossless dielectric nanospheres made of moderate permittivity materials, e.g., silicon or germanium nanospheres in the infrared region. Lossless dielectric Mie spheres of relatively low refraction index (as low as 2.2) are shown to present negative g in specific spectral ranges. [5] to mention a few. Our current understanding of the diffusive transport through nonabsorbing media is based on the knowledge of two key quantities: the transport and scattering mean free paths (MFPs). The scatter density and cross section define the scattering MFP s . The relevant scattering length for diffusive light power transport is the transport MFP * . Both quantities are connected by the scattering asymmetry parameter g defined [6,7] as the average of the cosine of the scattering angle g ≡ cos θ with * = s 1−g , where * is usually equal to or larger than s , i.e., g is positive. For instance, the isotropic Rayleigh scattering of small particles leads to g ∼ 0 while Mie particles (or human tissue) [7] scatter strongly in the forward direction (small scattering angles) and hence g ∼ 1. Negative values of g were reported [8] for magnetic particles having electric permittivity > 1 and large values of the magnetic permeability μ 1. Nevertheless, no concrete example of such particles that might present g < 0 in the visible or infrared regions has been proposed yet. However, recently it has been shown that subwavelength spheres made of nonabsorbing dielectric material with relatively low refractive index produce anisotropic angular distributions of scattered intensity [9][10][11][12]. As we will show here, these particles can present negative-g values in specific wavelength regions, i.e., a random dispersion of such particles will show the unusual characteristic of having * < s , even in the absence of positional correlations. * mnieto@icmm.csic.es † juanjo.saenz@uam.esThe transport mean free path can be strongly modified by the presence of short-range structural order in the system [13,14]. Positional correlations usually lead to positive-g values, i.e., to * values significantly larger than s , which are responsible, for example, for the relatively large conductivity of disordered liquid metals [15] or the transparency of the cornea to visible light [16]. However, short-range order can also lead to negative values of the asymmetry parameter as it has been recently shown in experiments in colloidal liquids [17] and amorphous photonic materials [18]. These negative values, observed at spec...

The single-parameter scaling hypothesis relating the average and variance of the logarithm of the conductance is a pillar of the theory of electronic transport. We use a maximum-entropy ansatz to explore the logarithm of the energy density, ln W(x), at a depth x into a random one-dimensional system. Single-parameter scaling would be the special case in which x = L (the system length). We find the result, confirmed in microwave measurements and computer simulations, that the average of ln W(x) is independent of L and equal to −x/ℓ, with ℓ the mean free path. At the beginning of the sample, var[ln W(x)] rises linearly with x and is also independent of L, with a sublinear increase near the sample output. At x = L we find a correction to the value of var[ln T ] predicted by single-parameter scaling.

We consider a wave propagating through a thin disordered slab inside a wire or waveguide of finite width. In the dense weak scattering limit, the statistics for the complex reflection and transmission coefficients (the coherent field) is found to depend dramatically on the contribution of evanescent modes or closed channels, leading to an effective refractive index whose real part is quite sensitive to the closed channels inclusion. In contrast, evanescent modes play no role in the statistical average of transmittances and reflectances. The theoretical predictions, based on the perturbative Born series expansion, are in excellent agreement with numerical simulations in disordered wires. CONTENTS

We study the problem of wave transport in a one-dimensional disordered system, where the scatterers of the chain are n barriers and wells with statistically independent intensities and with a spatial extension l c which may contain an arbitrary number δ/2π of wavelengths, where δ = kl c .We analyze the average Landauer resistance and transmission coefficient of the chain as a function of n and the phase parameter δ. For weak scatterers, we find: i) a regime, to be called I, associated with an exponential behavior of the resistance with n, ii) a regime, to be called II, for δ in the vicinity of π, where the system is almost transparent and less localized, and iii) right in the middle of regime II, for δ very close to π, the formation of a band gap, which becomes ever more conspicuous as n increases. In regime II, both the average Landauer resistance and the transmission coefficient show an oscillatory behavior with n and δ. These characteristics of the system are found analytically, some of them exactly and some others approximately. The agreement between theory and simulations is excellent, which suggests a strong motivation for the experimental study of these systems. We also present a qualitative discussion of the results.