Light Scattering from 3-D Nanoscale Disordered Media

Abstract

Random volume and surface scattering is a topic, which has been studied in many domains such as optical wave propagation in turbulent media, plasmonics and surface optics. Useful phenomena in the optical range can be produced by random media with randomly rough surfaces. Designing these disordered slabs with rough surfaces can produce new optical com- ponents, which can transmit or scatter optical fleld with specifled angular, spatial or spectral properties. Understanding how light interacts with disordered matter is a fundamental issue in optoelectronics and photonics and has huge consequences in communications, imaging and sensing. In this paper, we consider a three-dimensional disordered medium with randomly rough interfaces. This structure describes a device based on metallic nanoparticles embedded in insula- tors or dielectric media. We present a theory of transport based on the Bethe-Salpeter equation. The calculation of the intensities scattered by the considered structure for the ladder and most- crossed contributions is given by a Green tensor, which satisfles a Bethe-Salpeter equation. Random media have attracted much attention, not only in electromagnetic wave propagation, but also in solid-state physics. The governing equation can be written in the form of a Bethe- Salpeter equation. The problem is then reduced to flnd a good approximation to the solution of this equation. For a three-dimensional system composed of a random medium bounded by two randomly rough surfaces, the Bethe-Salpeter is constructed in order that the medium and the boundaries are treated on the same footing. This unifled Bethe-Salpeter equation enables us to obtain a general expression, whatever the choice of the scattering operators used at the boundaries. The Quasi-Crystalline Coherent Potential Approximation (QC-CPA) is taken into account for the contribution of the random medium, which is made of spherical particles of given permittivity in a homogeneous background medium. The boundaries are described by random functions. In (1{ 4), we developped a general formalism based on Green functions to calculate the difiuse intensity. With these Green functions, we can separate the contributions of the surfaces and the volume. The procedure is to write the Maxwell equations as an integral form with the help of the Green functions and to apply the Wigner transform to the derived equation. Starting from the wave equation, we are able to take into account new contributions to the scattered intensity such as enhanced backscattering and the correlations between the scatterers which can not be introduced by the phenomenological radiometric approach. We use an unifled approach to describe how the waves interact with the randomly rough boundaries. The main advantage of this approach is that the equations we obtained are very similar to the equations used to describe the electromagnetic waves scattered by an inflnite random medium.