Diffusion of localized optical excitations and trap emission in ruby

Abstract

Using the critical percolation conductance method the energy-dependent diffusion coefficient associated with thermally assisted transfer of the R₁ line excitation between single Cr³⁺ ions with strain-induced randomness has been calculated in the ⁴A₂ to E(²E) transition energies. For localized states sufficiently far away from the mobility edge the energy transfer is dominated by dipolar interactions, while very close to the mobility edge it is determined by short-range exchange interactions. Using the above energy-dependent diffusion coefficient a macroscopic diffusion equation is solved for the rate of light emission by Cr³⁺ ion-pair traps to which single-ion excitations are transferred. The dipolar mechanism leads to good agreement with recent measurements of the pair emission rate by Koo et al. (Phys. Rev. Lett., vol.35, p.1669 (1975)) right up to the mobility edge.