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.^[1][2][3]

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.^[2] Their work was published in Physical Review and the Journal of Chemical Physics, respectively.^[4][5] Judd and Ofelt did not meet until 2003 at a workshop in Lądek-Zdrój, Poland.^[1]

Judd and Ofelt's work was cited approximately 2000 times between 1962 and 2004.^[1] 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.^[2]

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 ${\displaystyle \Omega _{\lambda }}$ (where ${\displaystyle \lambda =2,4,6}$). 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.^[6]

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.^[7]

Application software

Judd–Ofelt intensity parameters from absorption spectrum of any lanthanide can be calculated by the RELIC application software.^[3] 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.^[8][9] Theoretical Judd-Ofelt intensity parameters for Eu³⁺ can be obtained using the LUMPAC software.^[10] Additionally, the JOYSpectra web platform provides these parameters for all Ln³⁺ ions.^[11][12]

Bibliography of the research by Judd and Ofelt supporting the theory

Author	Title	Year
Brian Judd	Optical Absorption Intensities of Rare-Earth Ions[13]	1962
George S. Olfelt	Intensities of Crystal Spectra of Rare-Earth Ions[14]	1962

See also

• Parity (physics)
• Bert Broer
• Otto Laporte
• Giulio Racah
• John Hasbrouck Van Vleck
• Eugene Wigner
• Brian Garner Wybourne

References

1. Walsh, Brian M. (June 2005). Judd–Ofelt Theory: Principles and Practices (slideshow). The International School of Atomic and Molecular Spectroscopy. Erice, Italy. Retrieved 18 November 2015.
2. Walsh, Brian M. "Chapter 21: Judd-Ofelt theory: Principles and practices". In Di Bartolo, B.; Forte, O. (eds.). Advances in Spectroscopy for Lasers and Sensing. Springer Netherlands. pp. 403–433. Retrieved 18 November 2015.
3. Hehlen, Markus P.; Brik, Mikhail G.; Krämer, Karl W. (April 2013). "50th anniversary of the Judd–Ofelt theory: An experimentalist's view of the formalism and its application". Journal of Luminescence. 136: 221–239. Bibcode:2013JLum..136..221H. doi:10.1016/j.jlumin.2012.10.035.
4. Judd, B. R. (1962). "Optical Absorption Intensities of Rare-Earth Ions". Phys. Rev. 127 (3): 750. Bibcode:1962PhRv..127..750J. doi:10.1103/PhysRev.127.750.
5. Ofelt, G. S. (1962). "Intensities of Crystal Spectra of Rare-Earth Ions". J. Chem. Phys. 37 (3): 511. Bibcode:1962JChPh..37..511O. doi:10.1063/1.1701366.
6. "One-photon rare earth optical transitions: recent theoretical developments". Digital Commons @ Andrews University. Retrieved 6 November 2023.
7. "Judd-Ofelt theory: principles and practices". SearchWorks catalog at Stanford University. Retrieved 6 November 2023.
8. Ćirić, Aleksandar; Stojadinović, Stevan; Sekulić, Milica; Dramićanin, Miroslav D. (January 2019). "JOES: An application software for Judd-Ofelt analysis from Eu³⁺ emission spectra". Journal of Luminescence. 205: 351–356. doi:10.1016/j.jlumin.2018.09.048. S2CID 105828989.
9. "JOES – Judd-Ofelt from emission spectrum Software – OMAS Group".
10. Dutra, José Diogo L.; Bispo, Thiago D.; Freire, Ricardo O. (2014). "LUMPAC lanthanide luminescence software: Efficient and user friendly". Journal of Computational Chemistry. 35 (10): 772–775. doi:10.1002/jcc.23542.
11. Moura Jr., Renaldo T.; Carneiro Neto, Albano N.; Aguiar, Eduardo C.; Santos-Jr., Carlos V.; de Lima, Ewerton M.; Faustino, Wagner M.; Teotonio, Ercules E.S.; Brito, Hermi F.; Felinto, Maria C.F.C.; Ferreira, Rute A.S.; Carlos, Luís D.; Longo, Ricardo L.; Malta, Oscar L. (2021). "JOYSpectra: A web platform for luminescence of lanthanides". Opt. Mater.: X. 11: 100080. doi:10.1016/j.omx.2021.100080.
12. "JOYSpectra a web platform for luminescence of lanthanides".
13. Judd, B. R. (1962). "OPTICAL ABSORPTION INTENSITIES OF RARE-EARTH IONS". {{cite journal}}: Cite journal requires |journal= (help)
14. Ofelt, G. S. (1 August 1962). "Intensities of Crystal Spectra of Rare-Earth Ions". Journal of Chemical Physics. 37: 511–520. doi:10.1063/1.1701366. ISSN 0021-9606.