The indices of refraction, thermal variations of refractive indices, and thermal expansion coefficients were measured for the gadolinium garnets Gd3Sc2Ga3O12 (GSGG) and Gd3Sc2Al3O12 The variation of these properties with trivalent chromium doping was investigated for GSGG. The refractive indices were determined by the minimum-deviation technique, with indices fitted to a five-parameter Sellmeier formula. The thermal coefficients were measured by an interferometric technique using simultaneous Twyman–Green and Fizeau interferometry.
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Refractive Indices of Undoped GSGG (Material Progress Sample MP-15) with Respect to Air at 26.0°C ± 0.4°Ca
λ (Å)
n
Δn (105)
4 046.56 Hg
2.01416
−1
4 358.33 Hg
2.00175
2
4 678.15 Cd
1.99190
−2
4 799.91 Cd
1.98867
2
5 085.82 Cd
1.98214
2
5 460.74 Hg
1.97522
0
5 893. Na
1.96895
−4
6 438.47 Cd
1.96276
0
7 800.27 Rb
1.95266
−1
7 947.60 Rb
1.95183
2
8 521.13 Cs
1.94906
2
8 943.46 Cs
1.94732
2
10 640.00 Xe arc + interference filter
1.94203
−2
The Sellmeier coefficients from least-squares fitting are as follows: A = 3.743782, B = 4.4263165 × 10−10, C = 4.3240392 × 109, D = 1.067490 × 106, E = 1.558170 × 106.
Table 2
Refractive Indices of Cr:GSGG (Union Carbide) with Respect to Aira
The Sellmeier coefficients from least-squares fitting are as follows: A = 3.733247, B = 5.0094229 × 10−10, C = 1.3971234 × 1010, D = 4.531561 × 105, E = 2.326604 × 106.
Measurement not used in Sellmeier fit.
Table 3
Refractive Indices of Cr:GSAG (Union Carbide) with Respect to Air at T = 26.0 ± 0.4°Ca
The Sellmeier coefficients from least-squares fitting are as follows: A = 3.523287, B = 4.0659107 × 10−10, C = 5.2328206 × 1010, D = 3.959125 × 105, E = 1.736132 × 106.
Not used in fit.
Table 4
Refractive Indices of Undoped GGG (Union Carbide) with Respect to Aira
λ (Å)
n
Δn (105)
4 046.56 Hg
2.01503
0
4 358.33 Hg
2.00256
3
4 678.15 Cd
1.99271
−2
4 799.91 Cd
1.98954
−3
5 085.82 Cd
1.98300
0
5 460.74 Hg
1.97609
3
5 790.66 Hg
1.97121
0
6 438.47 Cd
1.96379
0
7 800.27 Rb
1.95385
−1
7 947.60 Rb
1.95305
0
8 521.13 Cs
1.95032
1
8 943.46 Cs
1.94862
1
10 640.00 Xe arc + interference filter
1.94343
−1
The Sellmeier coefficients from least-squares fitting are as follows: A = 3.749719, B = 4.3238166 × 10−10, C = 3.9509089 × 109, D = 1.048372 × 106, E = 1.855744 × 105.
Table 5
Refractive Indices of Undoped GGG:Ca, Zr (Sample MP-18) with Respect to Aira
λ (Å)
n
Δn (105)
4 046.56 Hg
2.01166
−1
4 358.33 Hg
1.99905
0
4 678.15 Cd
1.98900
2
4 799.91 Cd
1.98580
−1
5 085.82 Cd
1.97913
5
5 460.74 Hg
1.97220
−1
5 893. Na
1.96588
−5
6 438.47 Cd
1.95968
−3
7 800.27 Rb
1.94951
1
7 947.60 Rb
1.94871
1
8 521.13 Cs
1.94593
3
8 943.46 Cs
1.94420
2
10 640.00 Xe arc + interference filter
1.93894
−2
The Sellmeier coefficients from least-squares fitting are as follows: A = 3.731373 B = 4.4090956 × 10−10, C = 4.0534369 × 109, D = 1.014311 × 106, E = 2.311652 × 106.
Table 6
Thermal Change of Refractive Index of GSGG (Material Progress Sample MP-15) with Respect to Vacuuma
λ (Å)
n
ΔTT (°C)
ΔTF (°C)
αL (10−6/°C)
αn (10−6/°C)
4 416
1.99996
0.9310
0.6897
7.25
6.73
6 328
1.96401
1.5172
1.0690
7.30
5.48
11 520
1.93944
3.1497
2.1508
7.41
4.66
Average:
7.32 ± 0.06
L = 1.145 cm.
Table 7
Thermal Change of Refractive Index of Cr:GSGG (Union Carbide) with Respect to Vacuuma
λ (Å)
n
ΔTT (°C)
ΔTF (°C)
αL (10−6/°C)
αn (10−6/°C)
11 520
1.93944
4.0310
2.8527
7.32
5.59
4.1935
2.9355
7.29
5.25
4.6296
3.0741
7.55
5.32
Average:
7.39 ± 0.11
5.39 ± 0.14
L = 0.808 cm.
Table 8
Thermal Change of Refractive Index of Cr:GSAG (Union Carbide Sample) with Respect to Vacuuma
λ (Å)
n
ΔTT (°C)
ΔTF (°C)
αL (10−6/°C)
αn (10−6/°C)
11 520
1.93944
5.5298
3.3444
7.14
2.17
5.6688
3.2166
8.12
1.56
4.5364
3.2782
5.11
4.39
5.0714
3.1429
7.31
2.60
Average:
6.92 ± 0.91
2.68 + 0.86
L = 0.9538 cm.
Table 9
Thermal Change of Refractive Index of Nd:CZGGG (Material Progress Sample MP-18) with Respect to Vacuuma
λ (Å)
n
ΔTT (°C)
ΔTF (°C)
αL (10−6/°C)
αn (10−6/°C)
6 328
1.96094
1.2308
0.9423
6.45
7.58
11 520
1.93627
2.4310
1.7586
7.41
6.43
Average:
6.93 ± 0.5
L = 1.22 cm.
Table 10
Comparison of Thermal Expansion and Thermo-Optic Coefficients for Garnets in the 35–40°C Range
Refractive Indices of Undoped GSGG (Material Progress Sample MP-15) with Respect to Air at 26.0°C ± 0.4°Ca
λ (Å)
n
Δn (105)
4 046.56 Hg
2.01416
−1
4 358.33 Hg
2.00175
2
4 678.15 Cd
1.99190
−2
4 799.91 Cd
1.98867
2
5 085.82 Cd
1.98214
2
5 460.74 Hg
1.97522
0
5 893. Na
1.96895
−4
6 438.47 Cd
1.96276
0
7 800.27 Rb
1.95266
−1
7 947.60 Rb
1.95183
2
8 521.13 Cs
1.94906
2
8 943.46 Cs
1.94732
2
10 640.00 Xe arc + interference filter
1.94203
−2
The Sellmeier coefficients from least-squares fitting are as follows: A = 3.743782, B = 4.4263165 × 10−10, C = 4.3240392 × 109, D = 1.067490 × 106, E = 1.558170 × 106.
Table 2
Refractive Indices of Cr:GSGG (Union Carbide) with Respect to Aira
The Sellmeier coefficients from least-squares fitting are as follows: A = 3.733247, B = 5.0094229 × 10−10, C = 1.3971234 × 1010, D = 4.531561 × 105, E = 2.326604 × 106.
Measurement not used in Sellmeier fit.
Table 3
Refractive Indices of Cr:GSAG (Union Carbide) with Respect to Air at T = 26.0 ± 0.4°Ca
The Sellmeier coefficients from least-squares fitting are as follows: A = 3.523287, B = 4.0659107 × 10−10, C = 5.2328206 × 1010, D = 3.959125 × 105, E = 1.736132 × 106.
Not used in fit.
Table 4
Refractive Indices of Undoped GGG (Union Carbide) with Respect to Aira
λ (Å)
n
Δn (105)
4 046.56 Hg
2.01503
0
4 358.33 Hg
2.00256
3
4 678.15 Cd
1.99271
−2
4 799.91 Cd
1.98954
−3
5 085.82 Cd
1.98300
0
5 460.74 Hg
1.97609
3
5 790.66 Hg
1.97121
0
6 438.47 Cd
1.96379
0
7 800.27 Rb
1.95385
−1
7 947.60 Rb
1.95305
0
8 521.13 Cs
1.95032
1
8 943.46 Cs
1.94862
1
10 640.00 Xe arc + interference filter
1.94343
−1
The Sellmeier coefficients from least-squares fitting are as follows: A = 3.749719, B = 4.3238166 × 10−10, C = 3.9509089 × 109, D = 1.048372 × 106, E = 1.855744 × 105.
Table 5
Refractive Indices of Undoped GGG:Ca, Zr (Sample MP-18) with Respect to Aira
λ (Å)
n
Δn (105)
4 046.56 Hg
2.01166
−1
4 358.33 Hg
1.99905
0
4 678.15 Cd
1.98900
2
4 799.91 Cd
1.98580
−1
5 085.82 Cd
1.97913
5
5 460.74 Hg
1.97220
−1
5 893. Na
1.96588
−5
6 438.47 Cd
1.95968
−3
7 800.27 Rb
1.94951
1
7 947.60 Rb
1.94871
1
8 521.13 Cs
1.94593
3
8 943.46 Cs
1.94420
2
10 640.00 Xe arc + interference filter
1.93894
−2
The Sellmeier coefficients from least-squares fitting are as follows: A = 3.731373 B = 4.4090956 × 10−10, C = 4.0534369 × 109, D = 1.014311 × 106, E = 2.311652 × 106.
Table 6
Thermal Change of Refractive Index of GSGG (Material Progress Sample MP-15) with Respect to Vacuuma
λ (Å)
n
ΔTT (°C)
ΔTF (°C)
αL (10−6/°C)
αn (10−6/°C)
4 416
1.99996
0.9310
0.6897
7.25
6.73
6 328
1.96401
1.5172
1.0690
7.30
5.48
11 520
1.93944
3.1497
2.1508
7.41
4.66
Average:
7.32 ± 0.06
L = 1.145 cm.
Table 7
Thermal Change of Refractive Index of Cr:GSGG (Union Carbide) with Respect to Vacuuma
λ (Å)
n
ΔTT (°C)
ΔTF (°C)
αL (10−6/°C)
αn (10−6/°C)
11 520
1.93944
4.0310
2.8527
7.32
5.59
4.1935
2.9355
7.29
5.25
4.6296
3.0741
7.55
5.32
Average:
7.39 ± 0.11
5.39 ± 0.14
L = 0.808 cm.
Table 8
Thermal Change of Refractive Index of Cr:GSAG (Union Carbide Sample) with Respect to Vacuuma
λ (Å)
n
ΔTT (°C)
ΔTF (°C)
αL (10−6/°C)
αn (10−6/°C)
11 520
1.93944
5.5298
3.3444
7.14
2.17
5.6688
3.2166
8.12
1.56
4.5364
3.2782
5.11
4.39
5.0714
3.1429
7.31
2.60
Average:
6.92 ± 0.91
2.68 + 0.86
L = 0.9538 cm.
Table 9
Thermal Change of Refractive Index of Nd:CZGGG (Material Progress Sample MP-18) with Respect to Vacuuma
λ (Å)
n
ΔTT (°C)
ΔTF (°C)
αL (10−6/°C)
αn (10−6/°C)
6 328
1.96094
1.2308
0.9423
6.45
7.58
11 520
1.93627
2.4310
1.7586
7.41
6.43
Average:
6.93 ± 0.5
L = 1.22 cm.
Table 10
Comparison of Thermal Expansion and Thermo-Optic Coefficients for Garnets in the 35–40°C Range