Inside the EoM

Inside an Electro optic modulator is a birefringent crystal. One of the more popular crystals to be used in EoMs are lithium niobate (LiNb0_{3}) doped with magnesium oxide (MgO). The magnesium oxide is there to prevent optical damage that can occur with high energy light in the bluish green frequencies. The Index of refraction of this crystal is n_{o} = 2.29  and the linear electro optic coefficient r = 30.9. I could not find any information on R the quadratic electro optic coefficient. Inside the EoM, the crystal has a parallel plate capacitor across it as shown below.

This capacitor allows for a voltage controlled uniform electric field. There is a well-known simple relationship

(1)   \begin{equation*} E=\frac{V}{d} \end{equation*}

Where V is the voltage d is the distance between the plates and E is the electric field strength which points from the positive to negative plate. This gives us a direct relationship between the electric field and the applied voltage. This can be used in determining required voltage to obtain specific types of modulations.