Laura Agazzi,1,*
Kerstin Wörhoff,1
Andreas Kahn,2
Matthias Fechner,2
Günter Huber,2
and Markus Pollnau1
1Integrated Optical MicroSystems (IOMS) Group, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, AE Enschede 7500, The Netherlands
2Institute of Laser-Physics, University of Hamburg, Luruper Chaussee 149, Hamburg 22761, Germany
Laura Agazzi, Kerstin Wörhoff, Andreas Kahn, Matthias Fechner, Günter Huber, and Markus Pollnau, "Spectroscopy of upper energy levels in an Er3+-doped amorphous oxide," J. Opt. Soc. Am. B 30, 663-677 (2013)
A spectroscopic study of the population mechanisms in erbium-doped amorphous aluminum oxide up to the levels is performed. Via luminescence decay measurements, absorption and emission spectra, and a Judd–Ofelt analysis, we determine luminescence lifetimes, radiative and nonradiative decay-rate constants, and branching ratios of the intermanifold transitions. With a continuous-wave pump-probe technique, the excited-state absorption (ESA) spectrum is recorded between 900 and 1800 nm and the cross sections of the ESA transitions , , and are determined. The microparameters and efficiencies of resonant and phonon-assisted energy-migration and energy-transfer upconversion (ETU) processes among ions occurring from the first and second excited states are evaluated. From the ratio of the and luminescence intensities as a function of concentration, we prove the existence and quantify the macroscopic ETU coefficient of the two-phonon-assisted ETU process .
Sergio A. Vázquez-Córdova, Shanmugam Aravazhi, Alexander M. Heuer, Christian Kränkel, Yean-Sheng Yong, Sonia M. García-Blanco, Jennifer L. Herek, and Markus Pollnau Opt. Mater. Express 9(12) 4782-4795 (2019)
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Mean Wavelengths, Values of Reduced Matrix Elements [23,24], Refractive Indices, Integrated Absorption Cross Sections, and Measured and Calculated Absorption Line Strengths for the Absorption Transitions of in
Transition from
[nm]
[]
[]
[]
1512.5
0.0195
0.1173
1.4316
1.651
45.570
1.6700
1.6821
976.0
0.0282
0.0003
0.3953
1.659
7.8623
0.4437
0.4784
800.0
0
0.1733
0.0099
1.664
3.9168
0.2686
0.1340
657.8
0
0.5354
0.4618
1.669
10.169
0.8447
0.8868
545.2
0
0
0.2211
1.679
4.6332
0.4607
0.2423
523.2
0.7125
0.4125
0.0925
1.682
14.287
1.4768
1.4752
Table 2.
Reduced Matrix Elements [23,24], Predicted Fluorescence Line Strengths, Radiative Decay-Rate Constants, and Radiative Branching Ratios of in
Transition
State Energy []
[]
→
6500
0.0195
0.1173
1.4316
1.682
97.81
1.000
→
3600
0.0331
0.1708
1.0864
1.362
15.96
0.115
10,100
0.0282
0.0003
0.3953
4.763
123.17
0.885
→
2150
0.0030
0.0674
0.1271
0.192
0.58
0.005
5750
0.0004
0.0106
0.7162
0.793
45.88
0.378
12,250
0.0000
0.1732
0.0099
0.134
74.94
0.617
→
2900
0.1279
0.0059
0.0281
0.290
1.72
0.002
5050
0.0704
0.0112
1.2839
1.522
60.23
0.057
8650
0.0101
0.1533
0.0714
0.203
40.29
0.038
15,150
0.0000
0.5354
0.4619
0.887
947.72
0.902
→
3200
6100
0.0000
0.0788
0.2542
0.335
59.53
0.034
8250
0.0000
0.0042
0.0739
0.084
36.96
0.021
11,850
0.0000
0.0000
0.3462
0.379
494.85
0.280
18,350
0.0000
0.0000
0.2211
0.242
1173.52
0.665
→
4000
0.3629
0.0224
0.0022
0.569
9.56
0.003
6900
0.2077
0.0662
0.2858
0.675
58.30
0.020
9050
0.0357
0.1382
0.0371
0.193
37.60
0.013
12,650
0.0230
0.0611
0.0527
0.136
72.39
0.025
19,150
0.7125
0.4123
0.0925
1.475
2722.24
0.939
Table 3.
Energy Gaps to the Next Lower Levels, Total Radiative Decay-Rate Constants, Radiative and Luminescence Lifetimes, and Nonradiative Decay-Rate Constants of the Lowest Five Excited States of in . The and Levels are Treated as a Single, Thermally Coupled Levela
Excited State
[]
[]
[ms]
[ms]
[]
6061
97.815
10.22
7.55
34.603 (calc.)
3263
139.129
7.19
0.060
(calc.)
1911
121.392
8.24
0.0016 (est.)
(est.)
2377
1049.955
0.95
0.006 (est.)
(est.)
2810
1764.863
0.57
0.0126
(calc.)
The index (calc.) indicates that the nonradiative decay-rate constants are calculated via Eq. (11) with known radiative and luminescence lifetimes; the index (est.) indicates that the nonradiative decay-rate constants and luminescence lifetimes are estimated via the energy-gap analysis in Fig. 4 and the subsequent use of Eq. (11), respectively
Table 4.
ESA Transitions, Corresponding Peak Wavelengths, Peak Cross Sections, and Comparison between the Measured Integrated ESA Cross Sections and Those Calculated by the J–O Formalism
ESA Transition
Peak Wavelength [nm]
Peak ESA Cross Section []
[]
[]
1692
2.53
11.653
13.150
1143
1.51
7.648
4.075
979
1.71
7.171
4.219
Table 5.
Microparameters of Energy Migration within, and ETU from, the First and Second Excited States, Calculated with Eq. (21) and the Measured Donor Emission and either Donor GSA or Acceptor ESA Spectraa
The fourth column refers to the overlap integral explained in Section 5.A, as calculated with the ESA spectrum shifted by toward the emission spectrum, and the last column lists the values appearing in Eq. (22), where for the first excited state the value obtained with the shifted ESA spectrum is used. The second row refers to microparameters of energy migration and ETU from the level obtained from the evaluation of luminescence decay curves in [3]
Table 6.
Values of the Macroscopic ETU Coefficients Taken from [3], Along with the Calculations of and with Eq. (22), and Derived from the Analysis of the Ratio under 1480 nm Pumping, for the Four Concentrations Considered in this Study
Effective Population Densities and Relative Excited Population Densities under the Experimental Conditions of the ESA Measurements of Section 4, for the Example of
Level
Active Ions () []
Quenched Ions () []
Total () []
(1)
0.712
(2)
0.232
(5)
0.056
Tables (7)
Table 1.
Mean Wavelengths, Values of Reduced Matrix Elements [23,24], Refractive Indices, Integrated Absorption Cross Sections, and Measured and Calculated Absorption Line Strengths for the Absorption Transitions of in
Transition from
[nm]
[]
[]
[]
1512.5
0.0195
0.1173
1.4316
1.651
45.570
1.6700
1.6821
976.0
0.0282
0.0003
0.3953
1.659
7.8623
0.4437
0.4784
800.0
0
0.1733
0.0099
1.664
3.9168
0.2686
0.1340
657.8
0
0.5354
0.4618
1.669
10.169
0.8447
0.8868
545.2
0
0
0.2211
1.679
4.6332
0.4607
0.2423
523.2
0.7125
0.4125
0.0925
1.682
14.287
1.4768
1.4752
Table 2.
Reduced Matrix Elements [23,24], Predicted Fluorescence Line Strengths, Radiative Decay-Rate Constants, and Radiative Branching Ratios of in
Transition
State Energy []
[]
→
6500
0.0195
0.1173
1.4316
1.682
97.81
1.000
→
3600
0.0331
0.1708
1.0864
1.362
15.96
0.115
10,100
0.0282
0.0003
0.3953
4.763
123.17
0.885
→
2150
0.0030
0.0674
0.1271
0.192
0.58
0.005
5750
0.0004
0.0106
0.7162
0.793
45.88
0.378
12,250
0.0000
0.1732
0.0099
0.134
74.94
0.617
→
2900
0.1279
0.0059
0.0281
0.290
1.72
0.002
5050
0.0704
0.0112
1.2839
1.522
60.23
0.057
8650
0.0101
0.1533
0.0714
0.203
40.29
0.038
15,150
0.0000
0.5354
0.4619
0.887
947.72
0.902
→
3200
6100
0.0000
0.0788
0.2542
0.335
59.53
0.034
8250
0.0000
0.0042
0.0739
0.084
36.96
0.021
11,850
0.0000
0.0000
0.3462
0.379
494.85
0.280
18,350
0.0000
0.0000
0.2211
0.242
1173.52
0.665
→
4000
0.3629
0.0224
0.0022
0.569
9.56
0.003
6900
0.2077
0.0662
0.2858
0.675
58.30
0.020
9050
0.0357
0.1382
0.0371
0.193
37.60
0.013
12,650
0.0230
0.0611
0.0527
0.136
72.39
0.025
19,150
0.7125
0.4123
0.0925
1.475
2722.24
0.939
Table 3.
Energy Gaps to the Next Lower Levels, Total Radiative Decay-Rate Constants, Radiative and Luminescence Lifetimes, and Nonradiative Decay-Rate Constants of the Lowest Five Excited States of in . The and Levels are Treated as a Single, Thermally Coupled Levela
Excited State
[]
[]
[ms]
[ms]
[]
6061
97.815
10.22
7.55
34.603 (calc.)
3263
139.129
7.19
0.060
(calc.)
1911
121.392
8.24
0.0016 (est.)
(est.)
2377
1049.955
0.95
0.006 (est.)
(est.)
2810
1764.863
0.57
0.0126
(calc.)
The index (calc.) indicates that the nonradiative decay-rate constants are calculated via Eq. (11) with known radiative and luminescence lifetimes; the index (est.) indicates that the nonradiative decay-rate constants and luminescence lifetimes are estimated via the energy-gap analysis in Fig. 4 and the subsequent use of Eq. (11), respectively
Table 4.
ESA Transitions, Corresponding Peak Wavelengths, Peak Cross Sections, and Comparison between the Measured Integrated ESA Cross Sections and Those Calculated by the J–O Formalism
ESA Transition
Peak Wavelength [nm]
Peak ESA Cross Section []
[]
[]
1692
2.53
11.653
13.150
1143
1.51
7.648
4.075
979
1.71
7.171
4.219
Table 5.
Microparameters of Energy Migration within, and ETU from, the First and Second Excited States, Calculated with Eq. (21) and the Measured Donor Emission and either Donor GSA or Acceptor ESA Spectraa
The fourth column refers to the overlap integral explained in Section 5.A, as calculated with the ESA spectrum shifted by toward the emission spectrum, and the last column lists the values appearing in Eq. (22), where for the first excited state the value obtained with the shifted ESA spectrum is used. The second row refers to microparameters of energy migration and ETU from the level obtained from the evaluation of luminescence decay curves in [3]
Table 6.
Values of the Macroscopic ETU Coefficients Taken from [3], Along with the Calculations of and with Eq. (22), and Derived from the Analysis of the Ratio under 1480 nm Pumping, for the Four Concentrations Considered in this Study
Effective Population Densities and Relative Excited Population Densities under the Experimental Conditions of the ESA Measurements of Section 4, for the Example of