Page "Electro-optic modulator" Paragraph 5

Note that the electric field can be created by placing a parallel plate capacitor across the crystal.

Since the field inside a parallel plate capacitor depends linearly on the potential, the index of refraction depends linearly on the field ( for crystals where Pockels effect dominates ), and the phase depends linearly on the index of refraction, the phase modulation must depend linearly on the potential applied to the EOM.