We show in this article the improvements which can be obtained in the description of the luminescence properties of Pr3+ doped materials by using an extension of the Judd-Ofelt theory in order to relax some strong selection rules and approximations of the standard formalism and to better account for the influence of the 4f5d excited electronic configuration. The demonstration is made by re-examining the case of Pr3+:YAG, a well known luminescent and laser crystal with a very low energy 4f5d absorption band. Our extension thus provides a better agreement between calculated and measured absorption intensities, especially for the hypersensitive 3 H4 $\rightarrow$ 3 P2 transition. A comparison is made with the results obtained in the case of Pr3+:ZBLAN, a laser fluoride glass with much higher 4f5d absorption levels. Our investigation also gives the opportunity, in the case of Pr3+:YAG, to provide more complete and more reliable absorption and emission data than reported in the past literature and to exploit these data to better address the question of laser operation at various emission wavelengths. It is thus demonstrated that laser operation should be possible with improved laser performance at 488 nm, 616 nm and 744 nm, as it was already achieved in the past, but also at 566 nm and 931 nm by using appropriate laser cavities and laser mirrors.We show in this article the improvements which can be obtained in the description of the luminescence properties of Pr3+ doped materials by using an extension of the Judd-Ofelt theory in order to relax some strong selection rules and approximations of the standard formalism and to better account for the influence of the 4f5d excited electronic configuration. The demonstration is made by re-examining the case of Pr3+:YAG, a well known luminescent and laser crystal with a very low energy 4f5d absorption band. Our extension thus provides a better agreement between calculated and measured absorption intensities, especially for the hypersensitive 3 H4 $\rightarrow$ 3 P2 transition. A comparison is made with the results obtained in the case of Pr3+:ZBLAN, a laser fluoride glass with much higher 4f5d absorption levels. Our investigation also gives the opportunity, in the case of Pr3+:YAG, to provide more complete and more reliable absorption and emission data than reported in the past literature and to exploit these data to better address the question of laser operation at various emission wavelengths. It is thus demonstrated that laser operation should be possible with improved laser performance at 488 nm, 616 nm and 744 nm, as it was already achieved in the past, but also at 566 nm and 931 nm by using appropriate laser cavities and laser mirrors.

physics.atom-phCross-listedarXiv:2604.21374Apr 24, 2026

Calculations of cross sections of resonant two-photon transitions to the second excited 4f5d state in Pr3+:Y3Al5O12using density matrix theory

Zhenwen Dai, Jing‐yao Liu, Siyuan Zhang

The density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 × 10-50 cm4 s which is very close to the previous experimental value 4 × 10-50 cm4 s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.The density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 × 10-50 cm4 s which is very close to the previous experimental value 4 × 10-50 cm4 s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.

Journal of Physics Condensed MatterOct 5, 19990 citations

Resonant Two-Photon Transitions

Pavel A Apanasevich, G. I. Timofeeva

Journal of Applied SpectroscopyMay 1, 20184 citations

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3 P2 transition. A comparison is made with the results obtained in the case of Pr3+:ZBLAN, a laser fluoride glass with much higher 4f5d absorption levels. Our investigation also gives the opportunity, in the case of Pr3+:YAG, to provide more complete and more reliable absorption and emission data than reported in the past literature and to exploit these data to better address the question of laser operation at various emission wavelengths. It is thus demonstrated that laser operation should be possible with improved laser performance at 488 nm, 616 nm and 744 nm, as it was already achieved in the past, but also at 566 nm and 931 nm by using appropriate laser cavities and laser mirrors.