Radiation in spherically symmetric structures. I. The coupled-amplitude equations for vector spherical waves

A scalar Green’s-function technique is used to derive coupled-amplitude equations for electromagnetic waves propagating in a three-dimensional structure with a radially varying refractive index. The vector nature of the problem is discussed and a method is outlined for reducing the vector wave equations to characteristic scalar equations. These scalar equations are then solved via an exact coupled-amplitude formalism, and closed-form solutions are compared with numerical results for the particular case of a spherical Bragg region. The derivation of the coupled-amplitude equations for vector spherical waves is a significant portion of the calculation, described in the companion paper [Sullivan and Hall, following paper, Phys. Rev. A 50, 2708 (1994)], of the radiative effects due to the presence of a spherical Bragg structure. Furthermore, the formulation is a powerful complement to previously developed Debye potential and transfer-matrix methods.