A short review of theoretical and empirical models for characterization of optical materials doped with the transition metal and rare earth ions

In this paper, a brief retrospective review of the main developments in crystal field theory is provided. We have examined how different crystal field models are applied to solve the problems that arise in the spectroscopy of optically active ions. Attention is focused on the joint application of crystal field and density functional theory (DFT) based models, which takes advantages of strong features of both individual approaches and allows for obtaining a complementary picture of the electronic properties of a doped crystal with impurity energy levels superimposed onto the host band structure.