Section: 12 | Elasto-Optic, Electro-Optic, and Magneto-Optic Constants |

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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 t_m; and Normal Boiling Point t_b of Selected Liquids' has one or more different columns to those in the book version.
The table 'Verdet Constants for KDP-Type Crystals^a' has one or more different columns to those in the book version.

How to Cite this Reference

ELASTO-OPTIC, ELECTRO-OPTIC, AND MAGNETO-OPTIC CONSTANTS

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):

$\frac{x^{2}}{n_{x}^{2}} + \frac{y^{2}}{n_{y}^{2}} + \frac{z^{2}}{n_{z}^{2}} = 1$

$\sum_{i j} B_{i j} x_{i} y_{j} = 1 (i, j = 1, 2, 3)$

where

$B_{i j} = {[\frac{1}{ε}]}_{i j} = {[\frac{1}{n^{2}}]}_{i j}$

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

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

$Δ {[\frac{1}{ε}]}_{i j} = Δ {[\frac{1}{n^{2}}]}_{i j} = \sum_{k l} P_{i j k l} S_{k l}$

where n is the refractive index and S_kl are the strain tensor elements; the P_ijkl 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.

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 :
$Δ {[\frac{1}{n^{2}}]}_{i j} = \sum_{k} K_{i j k l} E_{k} E_{l} = \sum_{k, l = 1, 2, 3} g_{i j k l} p_{k} p_{l}$
where E_k and E_l are the components of the electric field and p_k and p_l the electric polarizations. The coefficients K_ijkl are the quadratic electro-optic coefficients, while the constants g_ijkl are known as the Kerr constants.
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
$Δ {[\frac{1}{n^{2}}]}_{i j} = \sum_{k} r_{i j, k} E_{k}$
The coefficients r_ij,k have the name (linear) electro-optic coefficients.

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:

$r_{i j}^{T} = r_{i j}^{S} + q_{i k}^{E} e_{j k} = r_{i j}^{S} + P_{i k}^{E} d_{j k}$

where e_jk = (∂T_k /∂E_j )_S and d_jk = (∂S_k/∂E_j)_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, θ_F, is linearly proportional to the magnetic field H:

θ_F = 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 T_C (or T_N ), 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.

ELASTO-OPTIC COEFFICIENTS (PHOTOELASTIC CONSTANTS)

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

Name	Synonym	Formula	λ/µm	p ₁₁	p ₁₂	p ₄₄	p ₁₁ - p ₁₂	Ref.
Continued on next page...
Ammonium chloride	Sal ammoniac	NH₄Cl	0.589	0.142	0.245	0.042	-0.103	9
Cadmium telluride		CdTe	1.06	-0.152	-0.017	-0.057	-0.135	10
Calcium fluoride	Fluorite	CaF₂	0.60^a	0.038	0.226	0.0254	-0.183	11
Carbon (diamond)	Diamond	C	0.565^b	-0.278	0.123	-0.161	-0.385	13
Copper(I) bromide	Cuprous bromide	CuBr	0.633	0.072	0.195	-0.083	-0.123	12
Copper(I) chloride	Nantokite	CuCl	0.633	0.120	0.250	-0.082	-0.130	12
Copper(I) iodide	Marshite	CuI	0.633	0.032	0.151	-0.068	-0.119	12
Gallium arsenide		GaAs	1.15	-0.165	-0.140	-0.072	-0.025	15
Gallium phosphide		GaP	0.633	-0.151	-0.082	-0.074	-0.069	15
Germanium		Ge	3.39	-0.151	-0.128	-0.072	-0.023	14
KRS-5		Tl(Br,I)	0.633	-0.140	0.149	-0.0725	-0.289	18,20
KRS-6		Tl(Br,Cl)	0.633	-0.451	-0.337	-0.164	-0.114	19,20
Lithium chloride		LiCl	0.589			-0.0177	-0.0407	3
Lithium fluoride		LiF	0.589	0.02	0.13	-0.045	-0.11	5
Potassium bromide		KBr	0.589	0.212	0.165	-0.022	0.047	5
Potassium chloride	Sylvite	KCl	0.633	0.22	0.16	-0.025	0.06	4
Potassium fluoride		KF	0.546	0.26	0.20	-0.029	0.06	1
Potassium iodide		KI	0.590	0.212	0.171		0.041	6
Rubidium bromide		RbBr	0.589	0.293	0.185	-0.034	0.108	7,8

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

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