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

Page of 12
Type a page number and hit Enter.
/12
Back to Search Results
Type a page number and hit Enter.
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.

# 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):

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

or

$\sum _{ij}{B}_{ij}{x}_{i}{y}_{j}=1\text{\hspace{0.17em}}\left(i,j=1,2,3\right)$

where

${B}_{ij}={\left[\frac{1}{\epsilon }\right]}_{ij}={\left[\frac{1}{{n}^{2}}\right]}_{ij}$

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

$\Delta {\left[\frac{1}{\epsilon }\right]}_{ij}=\Delta {\left[\frac{1}{{n}^{2}}\right]}_{ij}=\sum _{kl}{P}_{ijkl}{S}_{kl}$

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 :
$\Delta {\left[\frac{1}{{n}^{2}}\right]}_{ij}=\sum _{k}{K}_{ijkl}{E}_{k}{E}_{l}=\sum _{k,l=1,2,3}{g}_{ijkl}{p}_{k}{p}_{l}$
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
$\Delta {\left[\frac{1}{{n}^{2}}\right]}_{ij}=\sum _{k}{r}_{ij,k}{E}_{k}$
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:

${r}_{ij}^{\text{T}}={r}_{ij}^{\text{S}}+{q}_{ik}^{\text{E}}{e}_{jk}={r}_{ij}^{\text{S}}+{P}_{ik}^{\text{E}}{d}_{jk}$

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

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)

## 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 0.60a 0.038 0.226 0.0254 -0.183 11 Carbon (diamond) Diamond C 0.565b -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.

Page 1 of 12
1/12

Entry Display
This is where the entry will be displayed

#### Other ChemNetBase Products

 You are not within the network of a subscribing institution.Please sign in with an Individual User account to continue.Note that Workspace accounts are not valid.

Confirm Log Out
Are you sure?
Your personal workspace allows you to save and access your searches and bookmarks.

Are you sure?

 You have entered your Individual User account sign in credentials instead of Workspace credentials. While using this network, a personal workspace account can be created to save your bookmarks and search preferences for later use. Click the help icon for more information on the differences between Individual User accounts and Workspace accounts.
My Account

 Username Title [Select]DrProfMissMrsMsMrMx [Select]DrProfMissMrsMsMrMx First Name (Given) Last Name (Family) Email address

Searching for Chemicals and Properties

The CRC Handbook of Chemistry and Physics (HBCP) contains over 700 tables in over 450 documents which may be divided into several pages, all categorised into 17 major subject areas. The search on this page works by searching the content of each page individually, much like any web search. This provides a challenge if you want to search for multiple terms and those terms exist on different pages, or if you use a synonym/abbreviation that does not exist in the document.

We use metadata to avoid some of these issues by including certain keywords invisibly behind each table. Whilst this approach works well in many situations, like any web search it relies in the terms you have entered existing in the document with the same spelling, abbreviation etc.

Since chemical compounds and their properties are immutable, a single centralised database has been created from all chemical compounds throughout HBCP. This database contains every chemical compound and over 20 of the most common physical properties collated from each of the >700 tables. What's more, the properties can be searched numerically, including range searching, and you can even search by drawing a chemical structure. A complete list of every document table in which the compound occurs is listed, and are hyperlinked to the relevant document table.

The 'Search Chemicals' page can be found by clicking the flask icon in the navigation bar at the top of this page. For more detailed information on how to use the chemical search, including adding properties, saving searches, exporting search results and more, click the help icon in to top right of this page, next to the welcome login message.

Below is an example of a chemical entry, showing its structure, physical properties and document tables in which it appears.

We have developed this cookie policy (the “Cookie Policy”) in order to explain how we use cookies and similar technologies (together, “Cookies”) on this website (the “Website”) and to demonstrate our firm commitment to the privacy of your personal information.

The first time that you visit our Website, we notify you about our use of Cookies through a notification banner. By continuing to use the Website, you consent to our use of Cookies as described in this Cookie Policy. However, you can choose whether or not to continue accepting Cookies at any later time. Information on how to manage Cookies is set out later in this Cookie Policy.

Cookies are small text files containing user IDs that are automatically placed on your computer or other device by when you visit a website. The Cookies are stored by the internet browser. The browser sends the Cookies back to the website on each subsequent visit, allowing the website to recognise your computer or device. This recognition enables the website provider to observe your activity on the website, deliver a personalised, responsive service and improve the website.

## Cookies We Use and Their Purpose

‘Strictly Necessary’ Cookies enable you to move around the Website and use essential features. For example, if you log into the Website, we use a Cookie to keep you logged in and allow you to access restricted areas, without you having to repeatedly enter your login details. If you are registering for or purchasing a product or service, we will use Cookies to remember your information and selections, as you move through the registration or purchase process.

Strictly Necessary Cookies are necessary for our Website to provide you with a full service. If you disable them, certain essential features of the Website will not be available to you and the performance of the Website will be impeded.

‘Performance’ Cookies collect information about how you use our Website, for example which pages you visit and if you experience any errors. These Cookies don’t collect any information that could identify you – all the information collected is anonymous. We may use these Cookies to help us understand how you use the Website and assess how well the Website performs and how it could be improved.

‘Functionality’ Cookies enable a website to provide you with specific services or a customised experience. We may use these Cookies to provide you with services such as watching a video or adding user comments. We may also use such Cookies to remember changes you make to your settings or preferences (for example, changes to text size or your choice of language or region) or offer you time-saving or personalised features.

You can control whether or not Functionality Cookies are used, but disabling them may mean we are unable to provide you with some services or features of the Website.

## First and Third Party Cookies

The Cookies placed on your computer or device include ‘First Party’ Cookies, meaning Cookies that are placed there by us, or by third party service providers acting on our behalf. Where such Cookies are being managed by third parties, we only allow the third parties to use the Cookies for our purposes, as described in this Cookie Policy, and not for their own purposes.

You always have a choice over whether or not to accept Cookies. When you first visit the Website and we notify you about our use of Cookies, you can choose not to consent to such use. If you continue to use the Website, you are consenting to our use of Cookies for the time being. However, you can choose not to continue accepting Cookies at any later time. In this section, we describe ways to manage Cookies, including how to disable them.

You can manage Cookies through the settings of your internet browser. You can choose to block or restrict Cookies from being placed on your computer or device. You can also review periodically review the Cookies that have been placed there and disable some or all of them.

Please be aware that if you choose not to accept certain Cookies, it may mean we are unable to provide you with some services or features of the Website.

In order to keep up with changing legislation and best practice, we may revise this Cookie Policy at any time without notice by posting a revised version on this Website. Please check back periodically so that you are aware of any changes.

## Questions or Concerns

You can also contact the Privacy Officer for the Informa PLC group at [email protected].

Here is a list of cookies we have defined as 'Strictly Necessary':

### Taylor and Francis 'First Party' Cookies

JSESSIONID

Here is a list of the cookies we have defined as 'Performance'.

_ga

_gid

_gat

Accessibility

The Voluntary Product Accessibility Template (VPAT) is a self-assessment document which discloses how accessible Information and Communication Technology products are in accordance with global standards.

The VPAT disclosure templates do not guarantee product accessibility but provide transparency around the product(s) and enables direction when accessing accessibility requirements.

Taylor & Francis has chosen to complete the International version of VPAT which encompasses Section 508 (US), EN 301 549 (EU) and WCAG2.1 (Web Content Accessibility Guidelines) for its products.