I would like to calculate the performance of an optical phase modulator, in which a varying electric field across a crystal modulates the effective refractive index of light passing through the crystal.
The effect depends on the crystal orientation, polarization (i.e. direction of the E-field of the optical beam), and the direction of the applied electric field. The dependence on these vectors is encoded into the electro-optic coefficients, which form the electro-optic tensor.
My question: How do I apply these coefficients to give the magnitude of the electro-optical effect (in radians of optical phase per applied volt of potential difference) when the light is polarized in direction $i$, propagating in direction $j$, with an applied electric field in direction $k$? In short, how do I use the electro-optical coefficients?
For concreteness, I am interested in lithium niobate. A datasheet gives the coefficients as: