The Pockels effect is a linear electro-optic effect: in a non-centrosymmetric crystal an applied field changes the refractive indices by Δn = ½ n³ r E. Two polarization components then accumulate a phase difference Γ = π V/Vπ. Between crossed polarizers at 45 degrees the transmitted fraction is T = sin²(Γ/2) (parallel: cos²(Γ/2)), which makes the cell either an amplitude modulator or a fast optical switch.

Half-wave voltage: transverse geometry Vπ = λ d / (n³ r L), longitudinal Vπ = λ / (2 n³ r). Coefficients used are typical literature values (LiNbO3 r33 30.8, KDP r63 10.5, GaAs r41 1.5, BBO r22 2.2 pm/V) with a single index each; dispersion and the exact tensor orientation are ignored. The 3D lab uses a fixed illustrative Vπ of 2000 V, so numbers differ by design.

Biasing at V = Vπ/2 places the operating point on the steepest, most linear part of the curve; large drive amplitudes compress the peaks, which the 3rd/1st harmonic readout quantifies. Not modelled: crystal natural birefringence, temperature drift, capacitance-limited bandwidth.