# What's the difference between photoelastic constant, photoelastic coefficient and the acousto-optic coefficient

I'm reading a few papers about how the optical properties of materials change when a under stress or a force acts upon them. I seem to be encountering the following three terms:

1. Photoelastic constant
2. Photoelastic coefficient
3. Acousto-optic coefficient

Is there a difference between these three terms, as they seem to be used in context of describing very similar phenomena? Also, does Acousto-optic constant exist?

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Is my answer below not sufficient, would you like more clarification? –  daaxix Jan 1 '13 at 18:12

Photoelastic constant

I've typically seen this as part of the optical property list of glass or other optical materials. It predicts the birefringence. It is also called the stress-optic constant (Defined in Mueller, THE THEORY OF PHOTOELASTICITY, 1938): $$B=\frac{n_p - n_n}{p}$$ where $p$ is the pressure, $n_n$ is the index of refraction normal to the direction of pressure (with a ${\bf{k}}$-vector normal to the pressure direction), and $n_p$ is the index of refraction parallel to the pressure direction. This equation is for a non-crystalline material, you get two constants and two equations for a uniaxial crystal for example.

Photoelastic coefficient

I found a few papers where this was used to mean photoelastic constant.

I also found a definition for photoelastic coefficient in Properties of Group-IV, III-V and II-VI Semiconductors by Adachi : $$\alpha_{pe} = \frac{\Delta\epsilon_{ij}}{X}$$ for a uniaxial crystal where "$\Delta\epsilon_{ij}$ is the change in the dielectric constant parallel and perpendicular to the direction of stress $X$."

In this definition they are using the dielectric constant (aka the permittivity) instead of the index of refraction. This means that the units will be different between the two definitions, but they are basically measuring the same thing in the optical regime (where $\mu \approx 1$, $\mu$ is the permeability).

A lot of materials (other than glasses) papers seem to use this definition.

Acousto-optic coefficient

The only reference that I could find to the above term was in a conference paper for CLEO/Pacific Rim 2001 :

Sound Field Measurement through the Acousto-Optic Effect of Air by using Laser Doppler Velocimeter by Nakamura.

This paper is so terse that I cannot figure out what he is actually calling the Acousto-optic coefficient. I have never heard this term before.

I found another definition from a thesis from Moscow State University here : MOROZOV Thesis

$$\gamma = \frac{\partial n}{\partial p}$$ where $n = n(p)$ is the pressure dependent index of refraction and $p$ is the pressure, which is the differential case of the stress-optic coefficient.

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Hey daaxix, thanks for the thoroughly researched answer :) –  user714852 Jan 4 '13 at 20:21