The infrared properties of granular metals and superconductors are qualitatively in accord with effective medium ideas, with insulating behavior below a percolation transition and metallic response above. An exception is the far-infrared absorption at low metallic concentrations, which is much stronger than theoretical predictions. Measurements of superconductors and of normal metals in different hosts suggest that this absorption is predominately electric dipole rather than the magnetic dipole (eddy current) absorption which is expected to be the dominant low-frequency loss in highly conducting particles. Measurements of clustered and non-clustered samples suggest that the strong far-infrared absorption does not arise from the clustering together of the individual metallic particles, although clustering does lead to about a tenfold increase in absorption.

A semiclassical model based on the measured properties of the free carriers in bulk bismuth successfully accounts for far infrared (ῶ ≤ 60 cm−1) magnetic field dependent resonances observed in free-standing powders of ∼0.5 μm diameter Bi particles prepared by inert gas evaporation. In earlier work, we found that particles with each of the three principal axes aligned parallel to the applied field were required to explain the data. The conclusion that these particles are bulk-like in nature remains valid when an ensemble of randomly oriented particles is treated using a Monte Carlo method.

Measurements of the refractive index of discontinuous metallic films, consisting of gold clusters embedded in a dielectric matrix prepared in a capacitively coupled coplanar diode radio frequency discharged system, are reported.

These composite films were analyzed to determine the metal volume fraction, the thickness and the cluster size.

Optical characterizations in the visible and near infrared regions of the electromagnetic spectrum, particularly, in the near-IR region (Nd/YAG laser wavelength 1.0642 μm), where the absorption coefficient of these materials is very low (k < 0.001) were performed. Optical guided modes analysis allowed careful measurement of the effective medium refractive index.

In situ measurements of optical absorption and x-ray diffraction for small supported silver particles were performed under defined atmospheres at temperatures below 723 K. We found, for the first time, reversible changes both in optical absorption spectrum and lattice parameter of silver particles against the cyclic exchange of ambient gases between 5% H2/He and 1% 02/He. The present data indicate that the adsorption of oxygen results in a reduction in surface stress of silver particles, leading to a change in the shape of particles.

I discuss coatings for energy efficient windows of several different kinds with a view to the possibility of modelling their optical properties by effective medium theory. Special attention is given to spectrally selective noble-metal-based coatings with induced transmission due to voids, angular selective metal coatings with oblique columnar microstructure, and tentative theoretical descriptions of chromogenic materials having dynamic radiative properties.

This review covers most of new physical aspects opened by the recent interest in the optical properties of heterogeneous media close to the percolation transition: relevant parameters and lengths, caracteristic optical behaviour (transmittance, reflectance and absorptance), theoretical models, dimensionali ty effects, discrimination between optical, electrical and morphological percolation transitions. Morphological aspects are emphasized as the key of optical properties at percolation.

We present a calculation of the optical properties of thin semi-continuous metal films near the percolative metal-insulator transition. The model is based on scaling assumptions, reflecting the fractal nature of these films. The film is divided into small squares of linear size L and the local complex conductivity of each square is calculated, using finite size scaling arguments and taking into account both ohmic resistance within the metallic clusters and intercluster capacitance. The size L, over which the finite size scaling is done, is related to the optical frequency by the anomalous diffusion relation, i.e. L(ω) α ωl/(2+θ). In this calculation two types of conductivities are found : good ones for the ‘metallic’ squares, showing that large clusters are present within these squares, and poor conductivities for ‘dielectric’ squares, where only small clusters are present. Moreover, the ‘metallic’ and ‘dielectric’ squares are not identical, thus a certain distribution of each type has to be considered. The width of the distribution is quite large close to the percolation threshold and decreases to zero when the film becomes homogeneous. The optical properties of the whole sample are obtained by summing the contribution from all squares, using a wide bimodal distribution function. Comparison with recent experimental results shows good agreement between this model and the experimental data.

In order to take into account the actual morphology of the inhomogeneous media, we have developed, effective medium models based on a 2D and 3D position space renormalization /1,2/. These models predict the dipolar resonance and the percolation transition with critical exponents in good agreement with theoretical values and fairly reproduce most of the experimental results, whatever the concentration is. Further more, this allows a valuable comparison of the predictions of our models when applied on different lattices like real digitized TEM of cermet films or randomly occupied lattices.

We analyze the optical properties of a metal-insulator composite thin film close to the percolation transition pc. Using a mean field approximation, it is possible to predict the existence of an optical threshold at a concentration p* slightly larger than pc. At that concentration defined by the vanishing of the real part of the dielectric constant and which depends of the relaxation time and therefore of the microgeometry, the composite optical absorption is frequency independent up to the near infrared frequencies. This property has been observed in a number of granular and cermet films.

We show that this property is quite general and can be obtained by generalizing the percolation scaling laws to a mixture of resistors, inductors and capacitors. The quality factor is shown to be a relevant physical quantity.

We report and discuss the results of simulations on real analogic LCR circuits and on computer which confirm and explicit these conclusions.

We present a brief summary of our recent work on classical and nonclassical optical diffusion in disorder metal oxides. Results on the optical transmission through a slab of titania spheres is presented and discussed in some detail illustrating the experimental method for obtaining the optical diffusion coefficient and photon absorption time from the transmission data. We conclude that the optical field-field correlation function with frequency is the Fourier transform of the time of flight distribution.

We use Brillouin scattering to measure the dispersion of the propagating acoustic modes in a suspension of hard sphere colloids. We find two distinct longitudinal modes when the sound wavelength becomes comparable to the sphere diameter. The higher frequency mode has a velocity intermediate between those of the pure solid and the pure liquid phases, and its velocity increases with increasing volume fraction, ø. The lower frequency mode has a velocity less than the velocities in either the pure fluid or pure solid phases, and its velocity decreases with increasing ø. We interpret the higher frequency mode as a compressional wave which propagates through both the solid and the fluid, as expected for a composite medium. The lower frequency mode has not been observed before, and is interpreted as a surface acoustic mode, which propagates between adjacent spheres through a decaying portion of the excitation in the fluid.

It is important to understand the diffusion sun light in sea ice as this interaction exerts a strong influence over the weather in polar regions and over the growth of microbial communities in the sub-ice water column. Sea ice is a granular composite of ice, brine, air and at low temperatures precipitated salts, in which the proportion and disposition of these components vary with depth, with temperature and thermal history. It is demonstrated that by using a simple in situ technique, supported by Monto Carlo simulations, the diffusive transport of light through a weakly absorbing composite such as sea ice can be characterised. The radiation field both within and emergent from the ice is found to reflect the anisotropic structure of the ice, in particular, the scattering is found to be highly anisotropic so that the light is channelled predominantly vertically. The technique will be illustrated with experimental results collected in McMurdo Sound, Antarctica.

A T-matrix formalism is used to calculate local electric fields around clusters of prolate ellipsoids in the long wavelength regime. The calculations are performed as a function of interparticle distance as well as angle of orientation. The observed red shifts in the resonant wavelengths of the characteristic peaks are shown to obey an exponential relationship as a function of interparticle separation and a sinusoidal relationship as a function of angle of rotation of the ellipsoid. The behavior of the cluster is discussed and the two effects, of separation and rotation, are compared.

We review the origins of the magnetoresistance in granular metals with emphasis on the quantum coherence effects arising from the interference of electrons traveling by different paths. We discuss the maximum in the magnetoresistance expected from scaling arguments and observed in granular aluminum. Two theories of the magnetoresistance in the variable range hopping regime, one based on the magnetic-field induced shift of the mobility edge and the other dealing with ‘directed’ hopping, are compared with experiments.

We have studied the electrical transport behavior of sputter deposited Nix(SiO2)100−x thin films between room temperature and 100 mK and, at selected temperatures, in applied magnetic fields up to 6 T. As the Ni concentration x is reduced, the resistivity increases systematically. At a Ni concentration (nominal) of about x–70 atomic percent (38 volume percent) the room temperature coefficient of resistivity changes sign. For Ni concentrations greater than 70 percent the resistance first decreases with temperature then increases logarithmically at, low temperatures. This increase becomes smaller and the resistivity minimum moves to progressively lower temperatures as the Ni concentration increases. In films with less than x–70 percent Ni, the resistivity has a temperature dependence of the form ρ(T)–ρo exp \(To/T)α] between room temperature and about 5 K. The exponent a is about 1/2 and To increases with decreasing Ni content. Below 1 K, however, the resistivity increases much less rapidly, with a temperature dependence independent of Ni concentration. In all films the magnetoresistance is small and negative.

A quantum percolation model is introduced to study the magnetoconductance of granular metal films. This model incorporates the granular property of the films and enables us to study the magnetoconductance in the strong scattering regime. Our calculations show a sign change in magnetoconductance as the temperature varies. There also exist oscillations in the magnetoconductance as the magnetic field is increased. Both observations are consistent with some recent experimental data.

In all applications and experimental setups one has to do measurements on finite samples with some average properties. Due to statistical fluctuations in the realization of the specific sample one has, there will be a spread in the measured properties. In this paper we consider electrical conduction in a two-phase material, where the two phases have different conductivities. We study the size dependence of the fluctuations in the effective conductivity and give the dependence of the sample size and the dependence of the resistance ratio, especially when the latter is close to one. A simple model and numerical simulations are presented.

A General Effective Media (GEM) equation is used to quantitatively describe the resistivity of an Fe304-eccogel composite system as a function of the relative volume fractions. The two percolation morphology parameters (øc and t) characterise the microstructure. Preliminary models, also based on the GEM equation, are used to describe the positive temperature coefficient of resistivity (PTC) and the piezoresistivity (uniaxial pressure) of the composite when the composition is near the percolation threshold.

Part of the work described below was delivered as an invited talk by one of us (A.K.) at the special symposium to honour Dr. Ben Abeles for his 65th birthday. During the questions part of my talk, I was asked by Ben Abeles: ‘what about magnetoresistance…’. I answered that this is a complicated issue and I don't have time to discuss this matter. After my talk Ben explained that he always asks this question because his thesis was on magnetoresistance measurements. I remembered this question and decided that this paper would be an excellent place give to the answer. Hence section IV.2 is specialy dedicated to Dr. Ben Abeles.

A simple effective spherical cluster model of generalized susceptibility enhancements in disordered monodisperse suspensions of conducting spheres is compared with experimental measurements of reduced permittivity and conductance. Good agreement with experiment is obtained by treating the suspension in the Clausius-Mossotti approximation as a mixture of isolated spheres and compact spherical metallized clusters.