Green’s function methods

Abstract

In the previous three chapters we described the solution of Maxwell’s equations for the total electromagnetic field of arbitrary and weakly guiding fibers in terms of the bound and radiation modes of the fiber. The need to use a superposition of all these modes is not always the most straightforward procedure, particularly in the case of single-mode fibers when only the fundamental mode is of interest. Here we provide background information on the alternative method of Green’s functions [1–3] to supplement their application to the perturbation problems of Chapter 18 and to the radiation problems for the current sources of Chapter 21. In the latter, the method is equivalent to first calculating the fields due to a single point current dipole and then constructing the fields of the current distribution by superposition. For an arbitrary distribution, however, this may be no easier than using an eigenfunction expansion. In other words, the advantages in using either Green’s functions or eigenfunction expansions depends on the particular problem in question.