Evaluation of local field effect on theI13∕24lifetimes in Er-doped silica-hafnia planar waveguides

Abstract

The spontaneous emission SE rate 0 of the free atom in vacuum is due to the interaction of the free ion with the electromagnetic vacuum fluctuation. 1 When the atom is embedded in a medium, the SE rate suffers a modification because of the changes in the density of electromagnetic states and because of the electromagnetic fields generated by the other atoms in its neighborhood. In an inhomogeneous system containing interfaces, mirrors, and cavities, the two effects cannot be easily separated. However, in a homogeneous system described by the refractive index n, the density of electromagnetic states simply increases by a factor of n 3 with respect to the vacuum level. In the past few years, a lot of theoretical and experimental papers have been focused on the study of the local field effect on emitting ions embedded in dielectric media. 2–8 In an absorption process, the total electromagnetic field, consisting of the sum of the electric field of the incident light Elight and the electric field of the dipole induced by the presence of other atomic species Edip ,i s called the effective field Eef f Eef f= Elight+ Edip. All these effects produce a modification of the decay rate that may be expected to be modified to