Table 1.
Matrix Elements and Magnetic-Dipole Line Strengths for Praseodymium (III)
Transition | | |
---|
| 10.538 | 0.3929 |
| 0.005 | 0.0002 |
| 0.126 | 0.0047 |
| 0.068 | 0.0025 |
Table 2.
Measured Mean Wavelengths, Integrated Absorption Cross Sections, and Oscillator Strengths of Ions in ZBLA Glasses
Transition | (nm) | () | () |
---|
| 4668.4 | 14.6 | 26.9 |
| 2231.4 | 28.7 | 65.1 |
| 1968.7 | 85.1 | 248.1 |
, | 2035.6 | 113.8 | 310.2 |
| 1556.9 | 115.7 | 539.2 |
| 1446 | 45.2 | 244.9 |
| 1525.7 | 160.9 | 781.4 |
| 1007.1 | 2.5 | 28.1 |
| 588.4 | 5.5 | 179.4 |
| 481.4 | 3.9 | 190.3 |
| 468.6 | 5.7 | 293.2 |
| 460.1 | 2.5 | 133.4 |
, | 466.0 | 8.2 | 426.5 |
| 443.3 | 14.5 | 835.1 |
Table 3.
Judd–Ofelt Parameters Calculated for Different Sets of Transitions Included in the Fit (Referred to as Nos. 1 to 8) Using Both Standard and Normalized Methods ( Transition Excluded)
Transition | Levels Included |
---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Average |
---|
| | | | | | | | | |
| | × | | | × | × | | × | |
| | × | | | × | × | | × | |
, | × | | × | × | | | × | | |
| | | × | | × | | × | × | |
| | | × | | × | | × | × | |
| × | × | | × | | × | | | |
| × | × | × | × | × | × | × | × | |
| × | × | × | × | × | × | × | × | |
| × | × | × | × | × | × | × | × | |
| | | | × | | × | × | × | |
| | | | × | | × | × | × | |
, | × | × | × | | × | | | | |
| | | | | | | | | |
| 1.55 | 1.36 | 0.50 | 5.21 | 1.17 | 1.55 | 20.79 | 0.92 | |
| 4.37 | 4.36 | 5.56 | 4.11 | 5.67 | 4.12 | 4.12 | 5.00 | |
| 4.59 | 4.62 | 4.34 | 4.43 | 4.18 | 4.68 | 3.38 | 4.52 | |
| 0.49 | 0.43 | 0.52 | 0.47 | 0.49 | 0.38 | 1.03 | 0.39 | |
| 1.09 | 1.66 | 0.30 | 0.99 | 1.68 | 1.56 | 1.97 | 1.76 | |
| 3.65 | 3.67 | 3.97 | 3.84 | 3.66 | 3.87 | 3.99 | 3.99 | |
| 7.05 | 6.42 | 5.52 | 7.07 | 5.25 | 6.44 | 5.39 | 5.44 | |
| 0.40 | 0.37 | 0.42 | 0.36 | 0.39 | 0.33 | 0.38 | 0.34 | |
Table 4.
Theoretical Branching Ratios and Lifetimes for Transitions from , , and Levels, Calculated with Judd–Ofelt Parameters No 2, 5, 6, 8, and Average
| | Branching Ratio (%) |
---|
| | 2 | 5 | 6 | 8 | Average |
---|
Em. Level | Final Level | Std | N | Std | N | Std | N | Std | N | Std | N |
---|
| | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | |
| 2.1 | 1.8 | 2.3 | 1.9 | 2 | 2 | 2 | 2 | | |
| 12.4 | 10.9 | 13.6 | 11.2 | 12 | 11 | 13 | 11 | | |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | |
| 13.7 | 17.2 | 9.8 | 18.1 | 16 | 16 | 9 | 18 | | |
| 12.8 | 18.5 | 9.7 | 15.6 | 13 | 18 | 12 | 15 | | |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | |
| | 59.0 | 51.6 | 64.6 | 53.2 | 57 | 53 | 63 | 54 | | |
| () | 38.8 | 40.3 | 32.6 | 41.7 | 40.3 | 39.4 | 36.6 | 38.9 | | |
| | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | |
| 0.3 | 0.3 | 0.2 | 0.3 | 0 | 0.3 | 0 | 0 | | |
| 1.2 | 1 | 1.3 | 1 | 1 | 1 | 1 | 1 | | |
| 11.2 | 9.6 | 12.4 | 9.9 | 11 | 10 | 12 | 10 | | |
| 16.2 | 16.8 | 15.1 | 17.7 | 17 | 16 | 14 | 18 | | |
| 6.0 | 7.2 | 4.6 | 7.6 | 7 | 7 | 4 | 7 | | |
| 8.2 | 11.6 | 6.3 | 9.9 | 9 | 11.4 | 8 | 10 | | |
| 35.1 | 34.9 | 35.9 | 34.0 | 34 | 35.3 | 37 | 34 | | |
| | 21.8 | 18.6 | 24.2 | 19.4 | 21 | 19 | 24 | 20 | | |
| | 39.5 | 40.1 | 33.6 | 42 | 40.3 | 39.3 | 37.5 | 39.5 | | |
| | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | |
| 2.6 | 3.3 | 2.2 | 3 | 3 | 3 | 2 | 3 | | |
| 50.1 | 48.8 | 51.0 | 49.4 | 50 | 49 | 50.5 | 50 | | |
| 34.6 | 35.1 | 34.3 | 34.9 | 35 | 35 | 35 | 35 | | |
| 0.2 | 0.2 | 0.1 | 0.1 | 0 | 0 | 0 | 0 | | |
| 2.1 | 2.6 | 1.8 | 2.4 | 2 | 3 | 2 | 2 | | |
| 1.3 | 1.2 | 1.3 | 1.2 | 1 | 1 | 1.2 | 1 | | |
| 0.3 | 0.3 | 0.3 | 0.3 | 0 | 0 | 0.3 | 0 | | |
| | 8.8 | 8.5 | 9 | 8.6 | 9 | 9 | 9 | 9 | | |
| () | 163.5 | 153.5 | 144 | 169.4 | 167.5 | 150 | 153 | 159 | | |
| | Std | N | Std | N | Std | N | Std | N | Std | N |
Table 5.
Experimental Branching Ratios, Is the Integrated Intensity Calculated from the Calibrated Experimental Emission Spectra, and Is the Ratio
Transition | | | Integrated Intensity (au.nm) | | Ratios | Branching Ratios (%) |
---|
| 890.8 | | 1.7 | | 0.16 | 10 |
| 719.3 | | 1.9 | | 0.18 | 9 |
| 635.7 | | 4.7 | | 0.45 | 19 |
| 604.6 | | 6.8 | | 0.63 | 26 |
| 538.1 | | 1.3 | | 0.13 | 4 |
| 483.3 | | 10.4 | | 1 | 32 |
Table 6.
Emission Cross Section Calculated for Visible Transitions of Ions with Füchtbauer–Ladenburg Formula, Using Judd–Ofelt Results, with McCumber Method and with Experimental Branching Ratios and Lifetimes
| | Calculated Emission Cross Section () |
---|
| | Füchtbauer–Ladenburg (average) | | |
---|
Transition | Wavelength (nm) | Std | Norm | McCumber | Exp. and |
---|
| 479.1 | | | 2.2 | 2.4 |
| 535.3 | | | | |
| 519.9 | 0 | 0 | | 3.8 |
| 602.1 | | | | 5.3 |
| 634.6 | | | | 7.2 |