Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power

TLDR: In this paper, a relation between the normalized radiated powers radiated by magnetic and electric dipoles is established, and the authors show that the classical results for the radiated power yield the correct normalized spontaneous emission rates from an excited atomic state for electric and magnetic dipole transitions, respectively.

Abstract: Expressions for the total power radiated by magnetic and electric dipoles of arbitrary orientation located in a medium 1 at distance z0 from the interface to a homogeneous or planar stratified medium 2 are derived. A relation between the normalized powers radiated by magnetic and electric dipoles is established. For a homogeneous loss-free medium 2, curves of the normalized powers L(z0)/L∞ radiated by magnetic and electric dipoles versus the normalized distance z0/λ1 are presented for different values of the relative refractive index n = n2/n1 as the only parameter. The computer calculations are compared with analytical expressions derived for small and large distances. For n > 1, the contribution of the evanescent waves to the radiated power is calculated separately. We show that the classical results for the normalized radiated power yield the correct normalized spontaneous emission rates from an excited atomic state for electric and magnetic dipole transitions, respectively. We point out that the results for the electric dipole also give the change of the total power scattered by a small dielectric scattering particle when it is placed close to an interface.