Judd–Ofelt theory

Judd–Ofelt theory is a theory in physical chemistry describing the intensity of electron transitions within the 4f shell of rare-earth ions in solids and solutions.

The theory was introduced independently in 1962 by Brian R. Judd of the University of California, Berkeley, and PhD candidate George S. Ofelt at Johns Hopkins University. Their work was published in Physical Review and the Journal of Chemical Physics, respectively. Judd and Ofelt did not meet until 2003 at a workshop in Lądek-Zdrój, Poland.

Judd and Ofelt's work was cited approximately 2000 times between 1962 and 2004. Brian M. Walsh of NASA Langley places Judd and Ofelt's theory at the "forefront" of a 1960s revolution in spectroscopic research on rare-earth ions.

Theory
The theory is a powerful theoretical framework used to predict and analyze the intensities of electronic transitions within the 4f electron shell of rare-earth ions in solid-state materials. The transitions, which are parity forbidden in free ions, are made partially allowed in a solid matrix due to the effects of the crystal field. This field induces a mixing of electronic states, allowing transitions that would not occur in an isolated ion. The theory quantitatively describes this mixing using three phenomenological parameters, denoted as $$\Omega_\lambda$$ (where $$\lambda = 2, 4, 6$$). These parameters account for the asymmetric nature of the crystal field and enable the calculation of transition probabilities, oscillator strengths, and radiative lifetimes of excited states, which are crucial for the development of various photonic devices such as lasers and optical amplifiers.

The theory is named after Brian G. Judd and George S. Ofelt, who independently developed it in 1962. It has become a standard tool in the field of lanthanide spectroscopy, providing insights into the optical properties of rare earth-doped materials and aiding in the design of materials for color display systems, fluorescent lamps, and lasers.

Application software
Judd–Ofelt intensity parameters from absorption spectrum of any lanthanide can be calculated by the RELIC application software. Judd–Ofelt intensity parameters and derived quantities (oscillator strengths, radiative transition probabilities, luminescence branching ratios, excited state radiative lifetimes, and estimates of quantum efficiencies) from the emission spectrum of Eu3+ doped compounds, can be obtained by the JOES application software. Theoretical Judd-Ofelt intensity parameters for Eu3+ can be obtained using the LUMPAC software. Additionally, the JOYSpectra web platform provides these parameters for all Ln3+ ions.