Section: 12 | Elasto-Optic, Electro-Optic, and Magneto-Optic Constants |
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Additional Information
One or more tables in this document differ to those in the book. This is due to space restrictions in the book.
Summary of table differences
The table 'TABLE 9. Elasto-Optic Coefficients: Garnets' has one or more different columns to those in the book version.
The table 'TABLE 3. Elasto-Optic Coefficients: Hexagonal Crystals (mmc, 6mm)' has one or more different columns to those in the book version.
The table 'TABLE 4. Elasto-Optic Coefficients: Trigonal Crystals (3m, 32, 3̅m)' has one or more different columns to those in the book version.
The table 'TABLE 7. Elasto-Optic Coefficients: Orthorhombic Crystals (222, m22, mmm)' has one or more different columns to those in the book version.
The table 'Kerr Constants of Ferroelectric Crystals' has one or more different columns to those in the book version.
The table 'Kerr Constant K (at 589 nm and Room Temperature); Static Dielectric Constant ε; Melting Point tm; and Normal Boiling Point tb of Selected Liquids' has one or more different columns to those in the book version.
The table 'Verdet Constants for KDP-Type Crystalsa' has one or more different columns to those in the book version.
How to Cite this Reference
The recommended form of citation is:
John R. Rumble, ed., CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), CRC Press/Taylor & Francis, Boca Raton, FL.
If a specific table is cited, use the format: "Physical Constants of Organic Compounds," in CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), John R. Rumble, ed., CRC Press/Taylor & Francis, Boca Raton, FL.


When a crystal is subjected to a stress field, an electric field, or a magnetic field, the resulting optical effects are in general dependent on the orientation of these fields with respect to the crystal axes. It is useful, therefore, to express the optical properties in terms of the refractive index ellipsoid (or indicatrix):






ε is the dielectric constant or permeability; the quantity Bij is called impermeability.

A crystal exposed to a stress S will show a change of its impermeability. The photoelastic (or elasto-optic) constants, Pijkl , are defined by


where n is the refractive index and Skl are the strain tensor elements; the Pijkl are the elements of a 4th rank tensor.

When a crystal is subjected to an electric field E , two possible changes of the refractive index may occur depending on the symmetry of the crystal.

  1. All materials, including isotropic solids and polar liquids, show an electro-optic birefringence (Kerr effect) which is proportional to the square of the electric field, E :
    where Ek and El are the components of the electric field and pk and pl the electric polarizations. The coefficients Kijkl are the quadratic electro-optic coefficients, while the constants gijkl are known as the Kerr constants.
  2. The other electro-optic effect only occurs in the 20 piezo-electric crystal classes (no center of symmetry). This effect is known as the Pockels effect. The optical impermeability changes linearly with the static field
    The coefficients rij,k have the name (linear) electro-optic coefficients.
  3. The values of the electro-optic coefficients depend on the boundary conditions. If the superscripts T and S denote, respectively, the conditions of zero stress (free) and zero strain (clamped) one finds:


    where ejk = (∂Tk /∂Ej )S and djk = (∂Sk/∂Ej)T are the appropriate piezo-electric coefficients.

    The interaction between a magnetic field and a light wave propagating in a solid or in a liquid gives rise to a rotation of the plane of polarization. This effect is known as Faraday rotation. It results from a difference in propagation velocity for left and right circular polarized light.

    The Faraday rotation, θF, is linearly proportional to the magnetic field H:

    θF = VlH

    where l is the light path length and V is the Verdet constant (minutes/oersted·cm).

    For ferromagnetic, ferrimagnetic, and antiferromagnetic materials the magnetic field in the above expression is replaced by the magnetization M and the magneto-optic coefficient in this case is known as the Kund constant K:

    Specific Faraday rotation F = KM

    In the tables below the Faraday rotation is listed at the saturation magnetization per unit length, together with the absorption coefficient α, the temperature T, the critical temperature TC (or TN ), and the wavelength of the measurement.

    In the tables that follow, the properties are presented in groups:

    • Elasto-optic coefficients (photoelastic constants)
    • Linear electro-optic coefficients (Pockels constants)
    • Quadratic electro-optic coefficients (Kerr constants)
    • Magneto-optic coefficients:
      • Verdet constants
      • Faraday rotation parameters

    Within each group, materials are classified by crystal system or physical state. References are given at the end of each group of tables.


    TABLE 1. Elasto-Optic Coefficients: Cubic Crystals (43m, 432, m3m)

    NameSynonymFormulaλ/µm p 11 p 12 p 44 p 11 - p 12 Ref.
    Continued on next page...
    Ammonium chlorideSal ammoniacNH4Cl0.5890.1420.2450.042-0.1039
    Cadmium tellurideCdTe1.06-0.152-0.017-0.057-0.13510
    Calcium fluorideFluoriteCaF20.60a0.0380.2260.0254-0.18311
    Carbon (diamond)DiamondC0.565b-0.2780.123-0.161-0.38513
    Copper(I) bromideCuprous bromideCuBr0.6330.0720.195-0.083-0.12312
    Copper(I) chlorideNantokiteCuCl0.6330.1200.250-0.082-0.13012
    Copper(I) iodideMarshiteCuI0.6330.0320.151-0.068-0.11912
    Gallium arsenideGaAs1.15-0.165-0.140-0.072-0.02515
    Gallium phosphideGaP0.633-0.151-0.082-0.074-0.06915
    Lithium chlorideLiCl0.589-0.0177-0.04073
    Lithium fluorideLiF0.5890.020.13-0.045-0.115
    Potassium bromideKBr0.5890.2120.165-0.0220.0475
    Potassium chlorideSylviteKCl0.6330.220.16-0.0250.064
    Potassium fluorideKF0.5460.260.20-0.0290.061
    Potassium iodideKI0.5900.2120.1710.0416
    Rubidium bromideRbBr0.5890.2930.185-0.0340.1087,8

    • a0.55 to 0.65 μm.
    • b0.540 to 0.589 μm.

    Page 1 of 12

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