I am attempting to estimate the elasto-optic coefficients ($p_{11}$ and $p_{12}$) of $\mathrm{TiO}_2$ and $\mathrm{ZrO}_2$, where $p_{11}$ and $p_{12}$ refer to the elements of a strain-optic tensor for a homogeneous material as given in Hocker (Fiber-optic sensing of pressure and temperature, 1979).
I have found a document which specifies that the longitudinal elasto-optic coefficient ($p_{12}$) can be estimated using the Lorentz-Lorenz relation that it gives as
$$p_{12} = \frac{(n^2 - 1)(n^2 + 2)}{3n^4}$$
however no reference is given, and other sources give the Lorentz-Lorenz relation as something rather different. For example Wikipedia says that the equation relates the refractive index of a substance to its polarizability and gives it as
$$\frac{n^2 - 1}{n^2 + 2} = \frac{4\pi}{3}N\alpha$$
which bares only a vague relation to the earlier equation.
Does anyone know of any other ways in which to estimate the elasto-optic coefficients of a material?
