On the Temperature Dependence of Transition Intensities of Rare-Earth Ions: A Modified Judd-Ofelt Theory

Abstract

We report on a modification of the Judd-Ofelt theory accounting for thermal populations of Stark sub-levels of the multiplets involved in transitions in absorption and emission. The calculations require the data on the crystal-field splitting, the irreducible representations of Stark sub-levels and the selection rules for electric-dipole transitions. Simple formulas for absorption oscillator strengths and probabilities of radiative spontaneous transitions are obtained. The application of the proposed model allowed us to remove the contradiction between the transition intensities in absorption and emission (3H6 ↔ 3F4) for Tm3+-doped crystals. It was also used to explain the experimental temperature dependences of luminescence lifetimes of the 3F4 Tm3+ manifold in two widely used laser crystals, LiYF4 and Y3Al5O12. The case of Yb3+ ions featuring a small number of crystal-field sub-levels is also considered.

Keywords: Judd-Ofelt theory, rare-earth ions, transition intensities, luminescence lifetime