Electro-optic effect of lithium niobate in piezoelectric resonance

The electro-optic (EO) effect of a lithium niobate (LN) single crystal was analyzed around a piezoelectric resonance frequency. The EO-coefficient of the LN resonator was measured as a function of frequency. The EO-coefficient around piezoelectric resonance frequency varied with a maximum and a minimum in the frequency dependence. To explain the frequency dependence of the EO-coefficient, three effects were considered: (1) the intrinsic EO-effect excluding the effect of piezoelectric resonance, (2) the change of optical pass length due to piezoelectric displacement, and (3) the photo-elastic effect due to piezoelectric strain. The maximum of the EO-coefficient corresponded to the maximum of piezoelectric displacement at the resonance frequency, while the minimum was caused by the phase-lag between applied sinusoidal electric field and piezoelectric displacement. A new equation including the three effects as well as the phase-lag was formulated to represent the EO-effect of piezoelectric crystals. The equation gave a good agreement in the fitting of calculation to the observation.