Beat Zysset, Ivan Biaggio, and Peter Günter, "Refractive indices of orthorhombic KNbO3. I. Dispersion and temperature dependence," J. Opt. Soc. Am. B 9, 380-386 (1992)
We have measured the refractive indices of potassium niobate in the orthorhombic phase at six different temperatures between 22 and 180°C in the wavelength range 400–3400 nm. Sellmeier coefficients are determined by using a two-term oscillator model with an IR correction term. The temperature-dependent spontaneous polarization and the quadratic polarization optical coefficients are obtained from the index data. For practical purposes the temperature dependence can be well approximated by a polynomial expansion of degree 2.
Mario Bertolotti, Victor Bogdanov, Aldo Ferrari, Andrei Jascow, Natalia Nazorova, Alexander Pikhtin, and Luigi Schirone J. Opt. Soc. Am. B 7(6) 918-922 (1990)
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Refractive Indices of KNbO3 at Selected Wavelengths (22°C)
Wavelength (nm)
na
nb
nc
0.430
2.4145
2.4974
2.2771
0.488
2.3527
2.4187
2.2274
0.514
2.3337
2.3951
2.2121
0.633
2.2801
2.3296
2.1687
0.860
2.2372
2.2784
2.1338
1.064
2.2195
2.2576
2.1194
1.500
2.1992
2.2341
2.1029
2.000
2.1832
2.2159
2.0899
2.500
2.1674
2.1981
2.0771
3.000
2.1498
2.1785
2.0630
Table 2
Sellmeier Coefficients for Orthorhombic KNbO3 at Six Temperaturesa
Temp (°C)
S1 (m−2)
S2 (m−2)
E1 (eV)
E2 (eV)
D (m−2)
KNbO3a-Axis Sellmeier Coefficients
22
2.005519 × 1013
1.498408 × 1014
4.802660
9.604319
2.517432 × 1010
50
2.027475 × 1013
1.52338 × 1014
4.793250
9.717225
2.514857 × 1010
75
1.933691 × 1013
1.504971 × 1014
4.754501
9.573709
2.514893 × 1010
100
1.660832 × 1013
1.420508 × 1014
4.667575
9.043137
2.51586 × 1010
140
1.604692 × 1013
1.407942 × 1014
4.630086
8.958690
2.508202 × 1010
180
1.389662 × 1013
1.372157 × 1014
4.529961
8.658983
2.511282 × 1010
KNbO3b-Axis Sellmeier Coefficients
22
1.937347 × 1013
1.354992 × 1014
4.545782
9.049686
2.845018 × 1010
50
2.06625 × 1013
1.441607 × 1014
4.568340
9.493910
2.827127 × 1010
75
2.006891 × 1013
1.427868 × 1014
4.549368
9.396314
2.80751 × 1010
100
1.437713 × 1013
1.233481 × 1014
4.397290
8.187495
2.79633 × 1010
140
1.887445 × 1013
1.388675 × 1014
4.510746
9.164866
2.771253 × 1010
180
2.21202 × 1013
1.628852 × 1014
4.574790
10.349864
2.762299 × 1010
KNbO3c-Axis Sellmeier Coefficients
22
1.60917 × 1013
1.654431 × 1014
4.857787
10.356684
1.943289 × 1010
50
1.824447 × 1013
1.811303 × 1014
4.905359
11.095552
1.945428 × 1010
75
1.756954 × 1013
1.766712 × 1014
4.868314
10.878384
1.95288 × 1010
100
1.40194 × 1013
1.584156 × 1014
4.728256
9.910805
1.968455 × 1010
140
1.648284 × 1013
1.677579 × 1014
4.792351
10.463581
1.982648 × 1010
180
2.147866 × 1013
2.156493 × 1014
4.904956
12.548861
2.004523 × 1010
The model assumes two UV oscillators and an IR correction term [see Eq. (2)]. The model represents the refractive indices in the wavelength range 400–3400 nm.
Table 3
Comparison of Quadratic Polarization Optic Coefficients of KNbO3 from Optical (at 546 nm) and Electro-Optical Measurements (m4/C2)
g44, g11 − g12, and spontaneous polarization Ps (C/cm2) obtained by solving Eqs. (5) for room temperature.
Values obtained with a least-squares fit over the whole temperature range, assuming Ps(T = 22°C) = 0.41 C/cm2.
Table 5
Coefficients of the Polynomial Expansion [Eq. (6)] for the Temperature Dependence of the Refractive Indices of KnbO3 at Three Wavelengths
Wavelength (nm)
Axes
C0
C1 (1/°C)
C2 [1/(°C)2]
435.83
a
2.4053
0.58 × 10−4
2.0 × 10−7
b
2.4877
−0.29 × 10−4
6.1 × 10−8
c
2.2683
1.10 × 10−4
3.4 × 10−7
1064
a
2.2190
0.20 × 10−4
7.9 × 10−3
b
2.2583
−0.35 × 10−4
1.5 × 10−8
c
2.1181
0.55 × 10−4
1.9 × 10−7
3000
a
2.1494
0.18 × 10−4
6.7 × 10−8
b
2.1790
−0.23 × 10−4
6.6 × 10−9
c
2.0619
0.48 × 10−4
1.6 × 10−7
Tables (5)
Table 1
Refractive Indices of KNbO3 at Selected Wavelengths (22°C)
Wavelength (nm)
na
nb
nc
0.430
2.4145
2.4974
2.2771
0.488
2.3527
2.4187
2.2274
0.514
2.3337
2.3951
2.2121
0.633
2.2801
2.3296
2.1687
0.860
2.2372
2.2784
2.1338
1.064
2.2195
2.2576
2.1194
1.500
2.1992
2.2341
2.1029
2.000
2.1832
2.2159
2.0899
2.500
2.1674
2.1981
2.0771
3.000
2.1498
2.1785
2.0630
Table 2
Sellmeier Coefficients for Orthorhombic KNbO3 at Six Temperaturesa
Temp (°C)
S1 (m−2)
S2 (m−2)
E1 (eV)
E2 (eV)
D (m−2)
KNbO3a-Axis Sellmeier Coefficients
22
2.005519 × 1013
1.498408 × 1014
4.802660
9.604319
2.517432 × 1010
50
2.027475 × 1013
1.52338 × 1014
4.793250
9.717225
2.514857 × 1010
75
1.933691 × 1013
1.504971 × 1014
4.754501
9.573709
2.514893 × 1010
100
1.660832 × 1013
1.420508 × 1014
4.667575
9.043137
2.51586 × 1010
140
1.604692 × 1013
1.407942 × 1014
4.630086
8.958690
2.508202 × 1010
180
1.389662 × 1013
1.372157 × 1014
4.529961
8.658983
2.511282 × 1010
KNbO3b-Axis Sellmeier Coefficients
22
1.937347 × 1013
1.354992 × 1014
4.545782
9.049686
2.845018 × 1010
50
2.06625 × 1013
1.441607 × 1014
4.568340
9.493910
2.827127 × 1010
75
2.006891 × 1013
1.427868 × 1014
4.549368
9.396314
2.80751 × 1010
100
1.437713 × 1013
1.233481 × 1014
4.397290
8.187495
2.79633 × 1010
140
1.887445 × 1013
1.388675 × 1014
4.510746
9.164866
2.771253 × 1010
180
2.21202 × 1013
1.628852 × 1014
4.574790
10.349864
2.762299 × 1010
KNbO3c-Axis Sellmeier Coefficients
22
1.60917 × 1013
1.654431 × 1014
4.857787
10.356684
1.943289 × 1010
50
1.824447 × 1013
1.811303 × 1014
4.905359
11.095552
1.945428 × 1010
75
1.756954 × 1013
1.766712 × 1014
4.868314
10.878384
1.95288 × 1010
100
1.40194 × 1013
1.584156 × 1014
4.728256
9.910805
1.968455 × 1010
140
1.648284 × 1013
1.677579 × 1014
4.792351
10.463581
1.982648 × 1010
180
2.147866 × 1013
2.156493 × 1014
4.904956
12.548861
2.004523 × 1010
The model assumes two UV oscillators and an IR correction term [see Eq. (2)]. The model represents the refractive indices in the wavelength range 400–3400 nm.
Table 3
Comparison of Quadratic Polarization Optic Coefficients of KNbO3 from Optical (at 546 nm) and Electro-Optical Measurements (m4/C2)
g44, g11 − g12, and spontaneous polarization Ps (C/cm2) obtained by solving Eqs. (5) for room temperature.
Values obtained with a least-squares fit over the whole temperature range, assuming Ps(T = 22°C) = 0.41 C/cm2.
Table 5
Coefficients of the Polynomial Expansion [Eq. (6)] for the Temperature Dependence of the Refractive Indices of KnbO3 at Three Wavelengths