Chapter 1.5.6 - Special Methods of Wave Diffaraction

Abstract

This chapter discusses numerical methods of increasing complexity that are able to solve a wide variety of problems of scattering, including scattering from a single object, scattering by a set of randomly or periodically placed scattering objects and scattering by an arbitrary set of scatterers located below a random interface separating two dielectric materials. The same kinds of problem may be solved using well-known methods like boundary or volume finite element methods and finite-difference time-domain (FDTD), but it appears that the methods described here are very efficient and attractive in many practical problems. A generalization of these methods to 3D problems of scattering is straightforward from a pure theoretical viewpoint, but very costly for the numerical implementation. It is worth noting that some of these generalizations have been achieved, for instance, the use of fictitious sources method for 3D scatterers, the use of the S-matrix method for a set of spheres, and the use of the boundary integral equation for scattering from randomly rough surfaces. The numerical programs are much more difficult to implement than those devoted to 2D objects but progress in the modeling of 3D objects is necessary for many practical applications like the study of doped or nondoped photonic crystals, precise treatment of sea or ground scattering, and remote sensing for buried objects.