Bernard Bendow, Peter D. Gianino, Yet-Ful Tsay, and Shashanka S. Mitra, "Pressure and Stress Dependence of the Refractive Index of Transparent Crystals," Appl. Opt. 13, 2382-2396 (1974)
The pressure derivative of the refractive index (dn/dP) and the elastooptic constants (pij) in the transparent frequency regime of semiconducting and ionic crystals are investigated theoretically. The electronic contribution to dn/dP of semiconductors is obtained by carrying out pseudopotential calculations of the band structure as a function of hydrostatic pressure, and the results compared with experiment. The lattice contribution to dn/dP is obtained by relating dn/dP to changes in the effective ionic charge and the phonon spectrum as functions of pressure. As for the pij, we perform a detailed application of the theory of Humphreys and Maradudin to calculate these for a variety of cubic crystals as functions of frequency in the transparent regime. The parameters required in the calculation are determined from improved prescriptions, which relate various microscopic functions to experimental data on the pressure dependence of phonon frequencies. The theoretical results are checked employing a relation between dn/dP and the pij. Overall, one finds that frequency dispersion is most important for the ionic materials and is generally negligible for the more highly covalent materials.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Parameters for Calculation of Lattice dn/dP in Ionic Crystalsa
Material
∊0
∊∞
∊S*
eT*
ω0(cm−1)
r0(Å)
K (10−6/bar)
(10−6/bar)
(10−6/bar)
LiF
8.81
1.9
0.87
1.13
306
2.01
1.49
0.29
3.98
LiCl
12.0
2.7
0.73
1.14
191
2.57
3.36
0.26
8.23
LiBr
13.2
3.2
0.68
1.18
159
2.75
4.20
0.42
10.25
NaF
5.1
1.7
0.93
1.15
244
2.31
2.15
0.65
5.25
NaCl
5.9
2.25
0.74
1.05
164
2.81
4.17
1.29
10.18
NaBr
6.4
2.6
0.70
1.07
134
2.98
5.02
1.70
12.35
NaI
6.6
2.91
0.71
1.16
117
3.23
6.62
3.05
16.42
KF
5.5
1.5
0.88
1.03
190
2.67
3.28
−0.19
7.94
KCl
4.85
2.13
0.81
1.11
142
3.14
5.75
2.16
14.43
KBr
4.9
2.3
0.76
1.09
113
3.29
6.76
3.2
17.04
KI
5.1
2.7
0.71
1.11
101
3.53
8.85
6.7
22.66
RbF
6.5
1.9
0.95
1.23
156
2.82
3.82
−0.45
9.47
RbCl
4.90
2.2
0.84
1.18
116
3.27
6.4
2.01
16.38
RbBr
4.90
2.3
0.84
1.20
88
3.43
7.7
3.1
19.71
RbI
5.50
2.6
0.75
1.15
75
3.66
9.45
3.4
24.57
MgO
9.64
3.0
1.76
2.94
400
2.10
0.596
−0.29
1.95
CaO
11.1
3.33
1.76
3.10
295
2.41
1.00
−1.05
3.52
AgCl
12.3
4.0
0.71
1.42
103
2.78
2.45
−0.25
7.48
AgBr
13.1
4.6
0.70
1.54
80
2.89
2.47
−0.13
7.83
deT*/dP and dω0/dP calculated from theoretical values of γ as described in the text. Existing experimental values generally agree with the theory within ~20% [see, e.g., J. R. Ferraro, S. S. Mitra, and A. Quattrochi, J. Appl. Phys. 42, 3677 (1971)].
Table IV
Parameters for Calculation of Lattice dn/dP in Semiconductors
Material
∊0
∊∞
∊S*
∊T*
ω0(cm−1)
r0(Å)
K (10−6/bar)
(10−6/bar)
(10−6/bar)
GaP
10.18
8.46
0.59
2.04
367
2.36
1.13
0.41
1.18
GaAs
12.9
10.9
0.50
2.16
269
2.45
1.34
−0.16
1.74
GaSb
15.69
14.44
0.33
2.15
230
2.65
1.77
0.07
2.12
AlSb
11.21
9.88
0.48
2.30
319
2.66
1.69
0.35
2.03
ZnS
8.3
5.0
0.92
2.15
271
2.35
1.39
−0.99
2.78
ZnSe
9.2
6.1
0.75
2.03
207
2.46
1.7
−1.25
2.81
ZnTe
10.38
7.8
0.62
2.00
177
2.63
2.0
−2.61
3.12
CdTe
10.2
7.1
0.77
2.35
141
2.81
2.36
—
—
deT*/dP and dω0/dP deduced from experimental values of γ from Raman spectra under hydrostatic pressure: GaP, ZnS, ZnSe, and ZnTe from S. S. Mitra, O. Brafman, W. B. Daniels, and R. K. Crawford, Phys. Rev. 168, 942(1969) others from C. J. Buchenauer, F. Cerdeira, and M. Cardona, in Light Scattering Spectra of Solids, M. Balkanski, Ed. (Flammarion, Paris, France, 1971).
Table V
dn/dP at Selected Wavelengths
Crystal
dn/dP ×1012 (cm2/dyne)
Electronic Values
3.9 μm
10.6 μm
LiF
0.198
0.166
−0.457
LiCl
0.358
0.315
−0.076
LiBr
0.347
0.312
0.020
NaF
0.398
0.391
0.267
NaCl
1.170
1.166
1.114
NaBr
1.570
1.567
1.541
NaI
2.140
2.142
2.144
KF
0.585
0.554
0.303
KCl
1.820
1.819
1.801
KBr
2.440
2.442
2.450
KI
3.850
3.858
3.904
RbCl
2.240
2.238
2.220
RbBr
3.000
3.001
3.001
RbI
4.250
4.250
4.248
ZnS
0.872
0.880
0.905
ZnSe
0.914
0.919
0.943
GaP
0.582
0.571
0.466
GaAs
−1.585
−1.590
−1.634
Table VI
Interionic Potential and Moment Function Parameters for Ionic Crystals
Parameters for Calculation of Lattice dn/dP in Ionic Crystalsa
Material
∊0
∊∞
∊S*
eT*
ω0(cm−1)
r0(Å)
K (10−6/bar)
(10−6/bar)
(10−6/bar)
LiF
8.81
1.9
0.87
1.13
306
2.01
1.49
0.29
3.98
LiCl
12.0
2.7
0.73
1.14
191
2.57
3.36
0.26
8.23
LiBr
13.2
3.2
0.68
1.18
159
2.75
4.20
0.42
10.25
NaF
5.1
1.7
0.93
1.15
244
2.31
2.15
0.65
5.25
NaCl
5.9
2.25
0.74
1.05
164
2.81
4.17
1.29
10.18
NaBr
6.4
2.6
0.70
1.07
134
2.98
5.02
1.70
12.35
NaI
6.6
2.91
0.71
1.16
117
3.23
6.62
3.05
16.42
KF
5.5
1.5
0.88
1.03
190
2.67
3.28
−0.19
7.94
KCl
4.85
2.13
0.81
1.11
142
3.14
5.75
2.16
14.43
KBr
4.9
2.3
0.76
1.09
113
3.29
6.76
3.2
17.04
KI
5.1
2.7
0.71
1.11
101
3.53
8.85
6.7
22.66
RbF
6.5
1.9
0.95
1.23
156
2.82
3.82
−0.45
9.47
RbCl
4.90
2.2
0.84
1.18
116
3.27
6.4
2.01
16.38
RbBr
4.90
2.3
0.84
1.20
88
3.43
7.7
3.1
19.71
RbI
5.50
2.6
0.75
1.15
75
3.66
9.45
3.4
24.57
MgO
9.64
3.0
1.76
2.94
400
2.10
0.596
−0.29
1.95
CaO
11.1
3.33
1.76
3.10
295
2.41
1.00
−1.05
3.52
AgCl
12.3
4.0
0.71
1.42
103
2.78
2.45
−0.25
7.48
AgBr
13.1
4.6
0.70
1.54
80
2.89
2.47
−0.13
7.83
deT*/dP and dω0/dP calculated from theoretical values of γ as described in the text. Existing experimental values generally agree with the theory within ~20% [see, e.g., J. R. Ferraro, S. S. Mitra, and A. Quattrochi, J. Appl. Phys. 42, 3677 (1971)].
Table IV
Parameters for Calculation of Lattice dn/dP in Semiconductors
Material
∊0
∊∞
∊S*
∊T*
ω0(cm−1)
r0(Å)
K (10−6/bar)
(10−6/bar)
(10−6/bar)
GaP
10.18
8.46
0.59
2.04
367
2.36
1.13
0.41
1.18
GaAs
12.9
10.9
0.50
2.16
269
2.45
1.34
−0.16
1.74
GaSb
15.69
14.44
0.33
2.15
230
2.65
1.77
0.07
2.12
AlSb
11.21
9.88
0.48
2.30
319
2.66
1.69
0.35
2.03
ZnS
8.3
5.0
0.92
2.15
271
2.35
1.39
−0.99
2.78
ZnSe
9.2
6.1
0.75
2.03
207
2.46
1.7
−1.25
2.81
ZnTe
10.38
7.8
0.62
2.00
177
2.63
2.0
−2.61
3.12
CdTe
10.2
7.1
0.77
2.35
141
2.81
2.36
—
—
deT*/dP and dω0/dP deduced from experimental values of γ from Raman spectra under hydrostatic pressure: GaP, ZnS, ZnSe, and ZnTe from S. S. Mitra, O. Brafman, W. B. Daniels, and R. K. Crawford, Phys. Rev. 168, 942(1969) others from C. J. Buchenauer, F. Cerdeira, and M. Cardona, in Light Scattering Spectra of Solids, M. Balkanski, Ed. (Flammarion, Paris, France, 1971).
Table V
dn/dP at Selected Wavelengths
Crystal
dn/dP ×1012 (cm2/dyne)
Electronic Values
3.9 μm
10.6 μm
LiF
0.198
0.166
−0.457
LiCl
0.358
0.315
−0.076
LiBr
0.347
0.312
0.020
NaF
0.398
0.391
0.267
NaCl
1.170
1.166
1.114
NaBr
1.570
1.567
1.541
NaI
2.140
2.142
2.144
KF
0.585
0.554
0.303
KCl
1.820
1.819
1.801
KBr
2.440
2.442
2.450
KI
3.850
3.858
3.904
RbCl
2.240
2.238
2.220
RbBr
3.000
3.001
3.001
RbI
4.250
4.250
4.248
ZnS
0.872
0.880
0.905
ZnSe
0.914
0.919
0.943
GaP
0.582
0.571
0.466
GaAs
−1.585
−1.590
−1.634
Table VI
Interionic Potential and Moment Function Parameters for Ionic Crystals
Add to BibSonomy