50th anniversary of the Judd-Ofelt theory: An experimentalist's view of the formalism and its application

The theory on the intensities of 4f→4f transitions introduced by B.R. Judd and G.S. Ofelt in 1962 has become a centerpiece in rare-earth optical spectroscopy over the past five decades. Many fundamental studies have since explored the physical origins of the Judd-Ofelt theory and have proposed numerous extensions to the original model. A great number of studies have applied the Judd-Ofelt theory to a wide range of rare-earth-doped materials, many of them with important applications in solid-state lasers, optical amplifiers, phosphors for displays and solid-state lighting, upconversion and quantum-cutting materials, and fluorescent markers. This paper takes the view of the experimentalist who is interested in appreciating the basic concepts, implications, assumptions, and limitations of the Judd-Ofelt theory in order to properly apply it to practical problems. We first present the formalism for calculating the wavefunctions of 4f electronic states in a concise form and then show their application to the calculation and fitting of 4f→4f transition intensities. The potential, limitations and pitfalls of the theory are discussed, and a detailed case study of LaCl₃:Er³⁺ is presented.