Scattering as a Boundary Value Problem

Abstract

If we speak about scattering in this book it is tacitly meant that we consider the interaction of a plane electromagnetic wave with a three-dimensional structure. The latter is characterized by its dielectric property, and the geometry of its boundary surface. A corresponding scattering theory interrelates the asymptotic free states before and after the interaction of the primary incoming plane wave with the scattering structure, whereas the incoming plane wave represents the asymptotic free state before the interaction. If we know the asymptotic free state after the interaction we can derive and define quantities which are appropriate to measure. Moreover, we restrict our considerations to the steady state of scattering with an assumed time dependence of \(exp(-i\omega t)\). The asymptotic free states correspond in this case to spatial distances large compared to a characteristic distance of the scattering structure, i.e., we look at the free states in the far field. Due to this understanding of scattering we have to consider processes taking place at different spatial scales. These are the interaction between the incoming plane wave and the scatterer on the local scale of the scatterer, and the behaviour of the electromagnetic fields in the nonlocal far-field. An exception is only made in Chap. 6, when we examine the near-field of a two-dimensional, ideal metallic grating