We consider the lifetime of a phosphor layer situated near a metallic film. We first make general observations of the effect of the plasmons on the lifetime and quantum efficiency of the luminescent ions in the phosphor layer and on the role of the plasmons in the emission process. The effect of the plasmons in the excitation process and on the total luminescence from the system is also discussed. We then derive an expression for the lifetime of the optical ions interacting with the surface plasmon modes using the Einstein A and B coefficient formalism, which requires a determination of the mode density of the surface plasmons. Because the surface plasmons represent a 2-dimensional system, a length parameter must be introduced into the expression of the mode density. We derive this parameter using a semi-classical approach, and show its dependence on the dielectric constants of the system and on the distance from the metallic layer. Recently there has been considerable interest on utilizing surface plasmons in metallic thin films to enhance internal quantum efficiency of luminescent materials [1][2][3][4][5][6][7][8][9][10][11][12] and light emitting diodes (LED).
13-22The most important effect of the surface plasmons on luminescent ions is on their lifetime in the excited state which could contribute to improving the internal quantum efficiency of luminescent materials in the form of a slab or a layer. In this paper, we have studied how the change in the excited state lifetime of the radiating atoms could be described using the dispersion relations of the surface plasmons. The lifetime of an excited ion, τ as measured by the decay measurements consists of two components, radiative lifetime,τ R and nonradiative lifetime, τ N R the reciprocals of which are additive,The radiative lifetime of an ion depends on the transition moments of the ion, i.e., the matrix element of the electric dipole and quadrupole moments or magnetic moments between the excited and ground state wavefunctions of the radiating ions. Normally the radiative lifetime is a characteristic of the optical ion and does not change unless the wavefunctions of the optical ions are perturbed. On the other hand, nonradiative lifetime is associated with the relaxation of the excited state to phonons, lattice defects and impurities with a loss of the excited state energy. It is sometimes possible to increase the nonradiative lifetime by controlling the purity of the material, operating temperature, better material processing etc., thus decreasing the probability of nonradiative relaxation of the ion. From Eq. 1, it can be shown that when the nonradiative lifetime increases, the lifetime of the excited state increases. This increase in lifetime usually results in an increase of the internal quantum efficiency.If a new nonradiative pathway is opened, the nonradiative lifetime will decrease. It will not always decrease the internal quantum efficiency if the transferred energy is not completely lost as it is in the case of phonons. Such could be the case for s...