Singularity of the dyadic Green's function for heterogeneous dielectrics.

For heterogeneous media with piecewise constant complex permittivity on regular domains, we show that the dyadic Green's function has the same singular part as the corresponding free space dyadic Green's function on every domain of constant permittivity. We give two important applications of this property, namely the distorted-wave Born approximation for composite media and the calculation of the single photon decay rate in spontaneous emission.

Separation of surface and volume effects in scattering from heterogeneous rough surfaces: derivation of a splitting rule.

We give theoretical support to the splitting rule, which was recently observed numerically for the scattering from heterogeneous rough surfaces. Under certain general conditions, the incoherent intensity of a composite medium with a rough interface is the sum of the incoherent intensity of the rough homogeneous surface with an effective permittivity and the incoherent intensity of the same composite medium below a flat interface. The coherent intensity is merely that of the rough effective homogeneous surface. The effective permittivity is given accurately by the Bruggemann mixing rule, provided that the scale of fluctuations in the volume is small with respect to the electromagnetic wavelength.

Influence of multiple scattering on the resolution of an imaging system: a Cramér-Rao analysis.

We revisit the notion of resolution of an imaging system in the light of a probabilistic concept, the Cramér-Rao bound (CRB). We show that the CRB provides a simple quantitative estimation of the accuracy one can expect in measuring an unknown parameter from a scattering experiment. We then investigate the influence of multiple scattering on the CRB for the estimation of the interdistance between two objects in a typical two-sphere scattering experiments. We show that, contrarily to a common belief, the occurence of strong multiple scattering does not automatically lead to a resolution enhancement.

Effective-medium theory for finite-size aggregates.

We propose an effective-medium theory for random aggregates of small spherical particles that accounts for the finite size of the embedding volume. The technique is based on the identification of the first two orders of the Born series within a finite volume for the coherent field and the effective field. Although the convergence of the Born series requires a finite volume, the effective constants that are derived through this identification are shown to admit of a large-scale limit. With this approach we recover successively, and in a simple manner, some classical homogenization formulas: the Maxwell Garnett mixing rule, the effective-field approximation, and a finite-size correction to the quasi-crystalline approximation (QCA). The last formula is shown to coincide with the usual low-frequency QCA in the limit of large volumes, while bringing substantial improvements when the dimension of the embedding medium is of the order of the probing wavelength. An application to composite spheres is discussed.

Second-order perturbation theory for scattering from heterogeneous rough surfaces.

We propose a model to calculate scattering from inhomogeneous three-dimensional, rough surfaces on top of a stratified medium. The roughness is made up of an ensemble of deposits with various shapes and permittivities whose heights remain small with respect to the wavelength of the incident light. This geometry is encountered in the remote sensing of soil surfaces, or in optics wherever there are contaminated planar components. Starting from a volume-integral equation involving the Green's tensor of the stratified medium, we derive a height-perturbative expansion up to second-order. Our formulation, which depends explicitly on the profiles of each deposit and on the Fresnel coefficients of the layered substrate, accounts for double-scattering events and permits an evaluation of depolarization in the plane of incidence. Comparisons with rigorous calculations in the simplified case of two-dimensional geometries are presented. It is shown that the second-order scattering term can be much more important for heterogeneous surfaces than for their homogeneous counterparts.