We give a rigorous and original derivation of the Maxwell-Garnett mixing rule in the dynamical regime for a composite dielectric random medium with small spherical inclusions. For certain configurations of scatterers, we show that contrarily to the common belief, the Maxwell-Garnett formula can remain very accurate at a high concentration of scatterers and incorporate multiple-scattering effects as well as attenuation of the mean field. We provide a realistic numerical example for which this is the case
In the coupled dipole method, a three-dimensional scattering object is discretized over a lattice into a set of polarizable units that are coupled self-consistently. Starting from the volume integral equation for the field, we show that performing the integration of the free-space field susceptibility tensor over the lattice cell dramatically improves the accuracy of the method when the permittivity of the object is large. This integration, done without any approximation, allows us to define a prescription for the polarizability used in the coupled dipole method. Our derivation is not restricted to any particular shape of the scatterer or to a cubic discretization lattice.
We simulate a total internal reflection tomography experiment in which an unknown object is illuminated by evanescent waves and the scattered field is detected along several directions. We propose a full-vectorial three-dimensional nonlinear inversion scheme to retrieve the map of the permittivity of the object from the scattered far-field data. We study the role of the solid angle of illumination, the incident polarization, and the position of the prism interface on the resolution of the images. We compare our algorithm with a linear inversion scheme based on the renormalized Born approximation and stress the importance of multiple scattering in this particular configuration. We analyze the sensitivity to noise and point out that using incident propagative waves together with evanescent waves improves the robustness of the reconstruction.
Optical diffraction tomography (ODT) is a recent imaging technique that combines the experimental methods of phase microscopy and synthetic aperture with the mathematical tools of inverse scattering theory. We show experimentally that this approach permits us to obtain the map of permittivity of highly scattering samples with axial and transverse resolutions that are much better than that of a microscope with the same numerical aperture.
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