A recursive transfer-matrix solution for a dipole radiating inside and outside a stratified sphere

Fast and numerically stable transfer-matrix solution is presented for the classical electromagnetics problem of a dipole radiating inside and outside a stratified sphere consisting of concentric spherical shells. There is no limitation on the dipole position, the number of the concentric shells, the shell medium, or on the sphere radius. Electromagnetic fields are determined anywhere in the space, the time-averaged angular distribution of the radiated power, the total radiated power, Ohmic losses due to an absorbing shell, and Green's function are calculated. An absorbing, optically active, and ultrathin (≲10 nm) metallic shell (core), characterized by a nonlocal dielectric function, are all allowed. The classical results are then applied to inelastic light scattering (fluorescence and Raman), the radiative and nonradiative normalized decay rates, and frequency shift. Using correspondence principle, the radiative decay rate is calculated from the Poynting vector, whereas the nonradiative decay rate is calculated from the Ohmic losses inside a sphere absorptive shell. Numerical stability of our method and limitations of classical description of decay rates are addressed. The importance of grouping various radiative and nonradiative decay mechanisms into local and nonlocal decay rates is emphasized. Further possible extensions of the theory presented here to the case of an arbitrary multilayered (axially symmetric) particle and to the classical problem of a radiating quadrupole in the presence of a multilayered particle are briefly outlined. Various applications for chemical speciation, LIDAR, fluorescent microscopy, engineering of decay rates, identification of biological particles, and monitoring specific cell functions are envisaged. Computer program is freely available at http://www.wave-scattering.com.