Classical linear crystal optics

Glazer, A. M.; Cox, K. G.

doi:10.1107/97809553602060000633

International Tables for Crystallography (2006). Vol. D. ch. 1.6, pp. 150-177
https://doi.org/10.1107/97809553602060000633

Chapter 1.6. Classical linear crystal optics

1.6. Classical linear crystal optics (pp. 150-177) | html | pdf | chapter contents |
A. M. Glazer and K. G. Cox
- 1.6.1. Introduction (p. 150) | html | pdf |
- 1.6.2. Generalized optical, electro-optic and magneto-optic effects (pp. 150-152) | html | pdf |
  - 1.6.2.1. Spontaneous polarization (pp. 150-151) | html | pdf |
  - 1.6.2.2. Dielectric polarization $[\varepsilon_o \chi_{ij}E_j^\omega]$ (p. 151) | html | pdf |
  - 1.6.2.3. Optical rotation (gyration) $[\varepsilon_o\chi_{ij\ell}\nabla_{\ell}E_j^{\omega}]$ (p. 151) | html | pdf |
  - 1.6.2.4. Quadratic electric effect $[\varepsilon_o\chi_{ijk}E_j^{\omega_1}E_k^{\omega_2}]$ (p. 151) | html | pdf |
  - 1.6.2.5. Linear electro-optic effect $[\varepsilon_o\chi_{ijk}E_j^{\omega_1}E_k^{\omega_2}]$ (p. 151) | html | pdf |
  - 1.6.2.6. Sum/difference frequency generation (two-wave mixing) $[\varepsilon_o\chi_{ijk}E_j^{\omega_1}E_k^{\omega_2}]$ (p. 151) | html | pdf |
  - 1.6.2.7. Quadratic electro-optic effect $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}E_k^{\omega_2}E_\ell^{\omega_3}]$ (p. 151) | html | pdf |
  - 1.6.2.8. Electric-field induced second harmonic generation $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}E_k^{\omega_2}E_\ell^{\omega_3}]$ (p. 151) | html | pdf |
  - 1.6.2.9. Four-wave mixing $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}E_k^{\omega_2}E_\ell^{\omega_3}]$ (pp. 151-152) | html | pdf |
  - 1.6.2.10. Faraday rotation $[\varepsilon_o\chi_{ijk}E_j^{\omega_1}B_k^{\omega_2}]$ (p. 152) | html | pdf |
  - 1.6.2.11. Quadratic magneto-optic effect $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}B_k^{\omega_2}B_\ell^{\omega_3}]$ (p. 152) | html | pdf |
  - 1.6.2.12. Linear photoelastic effect $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}T_{k\ell}^{\omega_2}]$ (p. 152) | html | pdf |
  - 1.6.2.13. Linear acousto-optic effect $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}T_{k\ell}^{\omega_2}]$ (p. 152) | html | pdf |
- 1.6.3. Linear optics (pp. 152-154) | html | pdf |
  - 1.6.3.1. The fundamental equation of crystal optics (pp. 152-153) | html | pdf |
  - 1.6.3.2. The optical indicatrix (pp. 153-154) | html | pdf |
  - 1.6.3.3. The dielectric impermeability tensor (p. 154) | html | pdf |
- 1.6.4. Practical observation of crystals (pp. 154-166) | html | pdf |
  - 1.6.4.1. The polarizing microscope (pp. 154-155) | html | pdf |
  - 1.6.4.2. Specimen preparation (p. 155) | html | pdf |
  - 1.6.4.3. The indicatrix as an aid to practical microscopy (p. 155) | html | pdf |
  - 1.6.4.4. Vibration directions (pp. 155-156) | html | pdf |
  - 1.6.4.5. Measuring refractive indices (pp. 156-157) | html | pdf |
  - 1.6.4.6. Determination of linear birefringence (pp. 157-158) | html | pdf |
  - 1.6.4.7. Identification of polarization colours (p. 158) | html | pdf |
  - 1.6.4.8. Fringe counting (pp. 158-159) | html | pdf |
  - 1.6.4.9. Fast and slow vibration directions (pp. 159-160) | html | pdf |
  - 1.6.4.10. Other methods of measuring birefringence (p. 160) | html | pdf |
  - 1.6.4.11. Interference figures (pp. 160-161) | html | pdf |
  - 1.6.4.12. Uniaxial figures (pp. 161-162) | html | pdf |
  - 1.6.4.13. Biaxial figures (pp. 162-165) | html | pdf |
  - 1.6.4.14. Orientation studies (pp. 165-166) | html | pdf |
  - 1.6.4.15. Absorption colours (p. 166) | html | pdf |
  - 1.6.4.16. Dispersion (p. 166) | html | pdf |
- 1.6.5. Optical rotation (pp. 166-172) | html | pdf |
  - 1.6.5.1. Introduction (pp. 166-167) | html | pdf |
  - 1.6.5.2. The dielectric tensor and spatial dispersion (pp. 167-168) | html | pdf |
  - 1.6.5.3. Symmetry of effective dielectric tensor (p. 168) | html | pdf |
  - 1.6.5.4. Gyration tensor (p. 168) | html | pdf |
  - 1.6.5.5. Optical rotation along the optic axis of a uniaxial crystal (pp. 168-170) | html | pdf |
  - 1.6.5.6. Optical rotation perpendicular to the optic axis of a uniaxial crystal (pp. 170-172) | html | pdf |
- 1.6.6. Linear electro-optic effect (pp. 172-173) | html | pdf |
  - 1.6.6.1. Primary and secondary effects (p. 172) | html | pdf |
  - 1.6.6.2. Example of LiNbO₃ (pp. 172-173) | html | pdf |
- 1.6.7. The linear photoelastic effect (pp. 173-176) | html | pdf |
  - 1.6.7.1. Introduction (pp. 173-174) | html | pdf |
  - 1.6.7.2. Spontaneous strain in BaTiO₃ (pp. 174-175) | html | pdf |
  - 1.6.7.3. The acousto-optic effect (pp. 175-176) | html | pdf |
- 1.6.8. Glossary (p. 176) | html | pdf |
- References | html | pdf |
- Figures
  - Fig. 1.6.3.1. The optical indicatrix (p. 153) | html | pdf |
  - Fig. 1.6.3.2. Positive and negative uniaxial indicatrix (p. 153) | html | pdf |
  - Fig. 1.6.3.3. Biaxial indicatrix, showing the two optic axes and corresponding circular cross sections (p. 154) | html | pdf |
  - Fig. 1.6.4.1. A thin section of a rock containing the minerals aegirine (elongated crystals) and eudyalite (the matrix) viewed in plane-polarized light in two positions at right angles to each other (p. 155) | html | pdf |
  - Fig. 1.6.4.2. Successive sections across the optical path of the microscope (p. 157) | html | pdf |
  - Fig. 1.6.4.3. Plot of retardation, R, versus wavelength, showing how polarization colours are formed (p. 157) | html | pdf |
  - Fig. 1.6.4.4. A quartz wedge between crossed Nicols (p. 158) | html | pdf |
  - Fig. 1.6.4.5. (a) Photomicrograph between crossed polars of a thin section of rock containing large olivine crystals set in a fine-grained matrix (p. 158) | html | pdf |
  - Fig. 1.6.4.6. Polarization colours versus thickness (p. 159) | html | pdf |
  - Fig. 1.6.4.7. Three birefringence images of industrial diamond viewed along [111] taken with the rotating analyser system (p. 161) | html | pdf |
  - Fig. 1.6.4.8. Formation of the interference figure (p. 161) | html | pdf |
  - Fig. 1.6.4.9. (a) Centred uniaxial optic axis figure of a crystal with low birefringence (p. 162) | html | pdf |
  - Fig. 1.6.4.10. (a) Vibration directions of an oblique ray passing through calcite, viewed relative to the indicatrix (p. 162) | html | pdf |
  - Fig. 1.6.4.11. (a) Centred optic axis figure of quartz (uniaxial) (p. 163) | html | pdf |
  - Fig. 1.6.4.12. (a) The Biot–Fresnel construction illustrated on the stereographic projection (p. 163) | html | pdf |
  - Fig. 1.6.4.13. (a) Illustration of the formation of crossed isogyres when the optic axial plane of a biaxial figure lies N–S (p. 163) | html | pdf |
  - Fig. 1.6.4.14. (a) Drawing of biaxial optic axis figures set in the 45° position with the optic axial plane set NW–SE (p. 164) | html | pdf |
  - Fig. 1.6.4.15. (a) Acute bisectrix figure of a biaxial crystal with $[2V \simeq 40]$ ° (p. 164) | html | pdf |
  - Fig. 1.6.5.1. Fresnel's explanation of optical rotation (p. 167) | html | pdf |
  - Fig. 1.6.5.2. Real and imaginary birefringence as a function of wavelength (p. 167) | html | pdf |
  - Fig. 1.6.5.3. The principle of superposition (p. 170) | html | pdf |
  - Fig. 1.6.6.1. (a) Symmetry elements of point group 3m (p. 173) | html | pdf |
  - Fig. 1.6.7.1. (a) Symmetry elements of point group $[{\bar 4}3m]$ (p. 174) | html | pdf |
- Tables
  - Table 1.6.2.1. Summary of linear and nonlinear optical properties (p. 150) | html | pdf |
  - Table 1.6.3.1. Symmetry constraints on the optical indicatrix (p. 154) | html | pdf |
  - Table 1.6.5.1. Symmetry constraints (see Section 1.1.4.10 ) on the gyration tensor $[g_{ij}]$ (p. 169) | html | pdf |
  - Table 1.6.6.1. Symmetry constraints (see Section 1.1.4.10 ) on the linear electro-optic tensor $[r_{ij}]$ (contracted notation) (p. 171) | html | pdf |
  - Table 1.6.7.1. Symmetry constraints on the linear elasto-optic (strain-optic) tensor $[p_{ij}]$ (contracted notation) (see Section 1.1.4.10.6 ) (p. 175) | html | pdf |

Chapter 1.6. Classical linear crystal optics

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