RESUMO
A difference equation obtained for the reassociated Green dyadic formalism is exploited to obtain solutions for the case of a multilayered dielectric medium: Computation of limits as layers become progressively thinner leads to a parallel development for the case of a dielectric varying continuously in a single direction. A demonstration example then shows how discrete and continuous techniques can be combined into a hybrid formulation. Finally, numerical computations are presented for the simple case of a dipole, illustrating convergence of the difference equation solutions to the differential equation solution.
RESUMO
The problem of molecular fluorescence in the vicinity of a gradient-index medium is studied theoretically through classical modeling of a radiating dipole. A previously developed formulation involving the Green dyadic for an inhomogeneous medium is applied to the present problem. Normalized lifetimes for the admolecules are calculated and compared with those for a homogeneous medium. The results are illustrated by numerical examples assuming certain simple forms for the index profile.
