Method for estimating the Stark splitting of rare-earth ions from the measured cross-section spectra

A method to estimate the Stark levels of the rare-earth ions doped in a laser medium from the measured emission and absorption cross-sections is proposed. The method is based on the McCumber theory, which can calculate the emission/absorption cross-sections from the given Stark levels. By fitting the calculated emission/absorption spectra to the measured ones through a numerical optimization process, the Stark levels of the RE ions can be determined. As examples, the Stark levels of the laser-emission-related manifolds of Er³⁺ and Yb³⁺ ions in a gain fiber and two doped glasses have been determined by the proposed method. The data were then used to analyze the temperature-dependent population of the Stark levels. This method avoids the difficulties in direct measurement of the Stark levels in a cryogenic temperature environment. It is important to the evaluation of the thermal load, distribution, and design of the thermal management system of high-power fiber lasers and amplifiers.