Christine Andraud

Entropic analysis of random morphologies

When the random morphology of ramified or percolating clusters exhibit local fluctuations, the framework of the theory of random percolation with its critical exponents and fractal dimension is still not enough to describe the disorder and the optical properties. We propose an alternative concept: the configuration entropy, that we compare to the multifractal analysis on computer simulated morphologies. At the percolation threshold, the entropy undergoes a maximum and its optimum length a minimum. In contrast with the multifractal analysis, the configuration entropy gives unambiguous results, relatively independent of the finite size of the image.

Scalar Kirchhoff's model for light scattering from dielectric random rough surfaces

In this paper, the Kirchhoff scalar approach is investigated for scattering from rough dielectric surfaces. Our aim is to derive expressions simpler than in the vector formalism in order to introduce surface scattering in scalar problems or to simplify some complicated problems, for applications. In transmission, expressions similar to those for reflection are derived with a first-order development of the local normal component of the transmitted wavevector versus the slope. The variations of reflection and transmission coefficients with local angle of incidence are also introduced in our calculations. The domain of validity of the model is discussed. The predictions of our treatment are in good agreement with published data. In particular we give a correct account of interesting effects such as the attenuation of the refractive index contrast already observed by Nieto-Vesperinas et al.

ENTROPIC AND MULTIFRACTAL ANALYSIS OF DISORDERED MORPHOLOGIES

We propose the configuration entropy as an efficient tool of characterization of the disorder of random morphologies and as a pertinent morphological parameter for describing the optical properties. When increasing the size of observation of an image, it undergoes a maximum at a characteristic length which is the optimum length at which the image must be observed to get the maximum information. When applied to computer simulated images, the configuration entropy is more powerful, less ambiguous and less sensitive to the finite size of images than the generalized fractal dimension.

Radiative transfer calculations in multilayer systems with smooth or rough interfaces

Abstract A very general discrete-ordinate method is presented for radiative transfer calculations in plane-parallel systems with partially reflecting interfaces. It is the natural extension of existing treatments for atmospheres (like DISORT) to account for changes of refractive index (Fresnel interfaces). The system under study is made of several dielectric layers, each layer containing spherical particles which produce anisotropic scattering (Mie scatterers). Incident light can be either collimated at normal or oblique incidence, or diffuse. A reflecting substrate can be added to the system. A procedure can be used to calculate the scattered fluxes at arbitrary angles, from the fluxes firstly obtained at a fixed set of polar angles. An efficient matrix formalism allows one to consider various boundary conditions: smooth or rough (scattering) interfaces. Surface scattering is introduced through a combination of Kirchhoffs expressions (for the specular reflection attenuation) and a geometrical optics model (for the scattering lobe). Comparisons with previous models and examples of simulations are presented. The main limitation of the method seems to be the approximate account for the polarization in this scalar treatment.

Absorption in multiple-scattering systems of coated spheres

We derive formulas for rigorous transfer matrix calculations of absorption in multiple-coherent-scattering systems in which the scatterers are multiply coated spheres (not necessarily concentric). Any of the spherical coatings, cores, or host media may be composed of absorbing materials. For a nonabsorbing host media, the total absorption may be deduced from overall energy conservation. A more detailed description of the absorption is obtained through formulas yielding the absorption within individual scatterers and/or coatings. We present some illustrative applications of these formulas to the design of heterogeneous coated-sphere media exhibiting enhanced absorption.

A model of the angular distribution of light scattered by multilayered media

Abstract A model for calculating the spatial distribution of light flux scattered from multilayered inhomogeneous media, with index of refraction mismatches between layers, is described. By separating volume and surface properties, a compact matrix formulation is constructed for the solution of this problem, based on the application of the Discrete Ordinate Method to solve the Radiative Transfer Equation. Results are compared with those obtained with other techniques in order to evaluate the accuracy and efficiency of the proposed method. An optimization of the numerical procedure has been achieved, allowing application of the method to systems with a large number of slabs.

Catastrophe theory interpretation of multiple peaks produced by light scattering from very rough dielectric surfaces

Abstract Dielectric rough surfaces, which scatter light with several maxima of intensity, are investigated in the framework of the geometrical optics approach. We consider surfaces between two media of refractive indices n1 and n2+ik2. In this case, previous works notice two maxima in the plane of incidence: near the Brewster angle (p-polarization), or near the critical angle (if n1>n2). New effects are predicted here: three maxima in the plane of incidence near the Brewster and the critical angles (with n1>n2 in p-polarization); and two maxima in the cross-polarized components, near the critical angle (if n1>n2). We show that such “multiple maxima” effects disappear when k2 increases. We demonstrate that the transition is accounted for rigorously by Thoms catastrophe theory and corresponds to a cusp catastrophe.

Model of light scattering that includes polarization effects by multilayered media

We present a model for calculating the angular distribution of light, including polarization effects from multilayered inhomogeneous media, with an index of refraction mismatch between layers. The model is based on the resolution of the radiative transfer equation by the discrete ordinate method. Comparisons with previous simpler models and examples of simulations are presented.

Void and grain resonances in discontinuous silver thin films close to the percolation threshold

An optical study of discontinuous metallic thin films has permitted us to observe simultaneously two resonant phenomena in media close to the percolation threshold. In addition to the well known metal grain resonance, a weaker resonance appears in the UV spectrum. This phenomenon, the presence of both resonances in a single sample, has seldom been pointed out. We demonstrate experimentally, on a silver percolating film, that this resonance is due to the presence of voids in the thin metal layer. We introduce a new model for the calculation of the optical properties of heterogeneous media, based on an entropic analysis of the actual medium, which accounts fairly well for both phenomena.

Absorption in multiple scattering systems of coated spheres: design applications

We illustrate the utility of some recently derived transfer matrix methods for electromagnetic scattering calculations in systems composed of coated spherical scatterers. Any of the spherical coatings, cores, or host media may be composed of absorbing materials. Our formulae permit the calculation of local absorption in either orientation fixed or orientation averaged situations. We introduce methods for estimating the macroscopic transport properties of such media, and show how our scattering calculations can permit ‘design’ optimization of macroscopic properties.