ABSTRACT
In Sections 7.5 through 7.7 of Volume 1, we discussed radiation, scattering, and diffraction from a theoretical viewpoint. These classes of problems are called exterior problems in the sense that the field region of interest includes the sphere of infinite radius. However, we assume that the sources and obstructing objects/scatterers can all be included in a sphere of finite radius (in three-dimensional problems). Theoretical and implied boundary conditions at the radius r equal to infinity are called Sommerfeld radiation boundary conditions; in simple language, they state that at infinity you can have only outgoing waves. Two-dimensional versions of these boundary conditions (BC) are given in Example 17.3 of Section 17.4.2.
