Group chain scheme analysis of the energy levels in laser crystals

Abstract

A method for crystal-field energy level analysis was proposed which used the group chain scheme introduced by Butler. The ratios of crystal-field parameter calculated by a simple point charge model was used as a constraint condition, which turned out to be the same or essentially the same as those obtained by a superposition model or other models and the absolute values of these ratios can be seen as a measure of the degree of symmetry distortion of the system. As an example, the situation of D3 symmetry was studied. By using this fitting technique to obtain values for the parameters, only one minimum was found for each of the cases studied. The eigenfunctions obtained have obvious symmetry properties and the low-symmetry distortion of the system can easily be seen from the ratios Cmu k/C0k. Therefore, the crystal-field analysis is not only a formalism but also a real physical insight. The crystal field for Nd3+:YAl3(BO3)4 and NdAl3(BO3)4 crystals was analysed in detail.