Completeness of a set of modes connected with the electromagnetic field of a homogeneous sphere embedded in an infinite medium

Publisher Website
Google Scholar
Abstract
The mode decomposition of the electromagnetic field connected with a sphere is considered. The sphere is embedded in an infinite medium. The continuity requirements of the field across the surface of the sphere lead to a certain set of so called natural modes, which can be calculated explicitly if the radial part of the electric field strength inside the sphere equals zero. The completeness of the radial parts of these modes, which is a set of spherical Bessel functions, is sometimes erroneously deduced from Sturm-Liouville theory. This theory, however, cannot be used to show the completeness because the continuity conditions of the field lead to a boundary value problem with a boundary condition which explicitly depends on the eigenvalue. The completeness of this set of functions, which is necessary to solve an initial value problem, will be shown.

This publication has 13 references indexed in Scilit: