The influence of photonic mode density on the luminescence of erbium-doped optical materials

Erbium doped optical materials have been widely researched and many applications have been demonstrated. According to the Fermi golden rule, the spontaneous emission rate from excited level |i> to lower level |j> is Γ_ij ∝ |M_ij|² ρ(ν _ij), where M_ij is the matrix element related to the two energy levels, ρ_ij is the optical density and is also known as the photon mode density (PMD). The concept of PMD was put forward by Purcell in 1946, and is a quantity determined by the environment aound the rare earth ions. The radiative performance of a rare earth(RE) doped material is decided not only by the wave function of the energy level that the rare earth ions are located, but also by the environment of the RE ions, i.e., the PMD. In various materials, the state of the host (crystal, glass or glass ceramics), the composition of the host with same state (for examples, the different glasses), the doping of metal into the host, and the surface plasmon portions (SPP) arised from the metal gratings or nanoparticals on the host, will all change the optical density of the materials, Thus the PMD are different. In this paper, we summarized the influence of the PMD on the luminescence of erbium doped materials for above indicated cases. Especially, we reported the difference of the luminescence performance of the erbium doped phosphate glass ceramics and its precursor glass, from which, we can find that even the composition of both glass ceramics and glass are the same, the luminescence performance are quite different due to the different PMD. Another example we illustrate in this paper is to use SPP to change the PMD. When RE doped glass is coated with a thin metal film or islands, SPP mode will be generated under special condition. We summarized the recent progress on the field, and also demonstrated the enhancement of fluorescence in the visible wavelengths and 1.5μm wavelength, from which, we can think that the SPP changes the PMD of the material and the emission rate is modified.