Beam deflection based on the composition gradient and quadratic electro-optic effect of unpoled tetragonal SBN crystal

Abstract

SBN crystals are excellent electro-optic materials, generally known for exhibiting a prominent linear electro-optic effect in the tetragonal phase. In this work, an SBN crystal with a composition gradient along the growth direction was prepared with the Czochralski method from an incongruently melting composition. Using the Mach-Zehnder interferometry technique, the unpoled tetragonal phase SBN crystal was confirmed to exhibit a quadratic electro-optic effect, with the coefficient measured to be approximately 10⁻¹⁵ m²/V². The quadratic EO effect was mainly attributed to the high symmetry introduced by the randomly distributed domain structures. However, the poling effect of a high applied voltage can align the dipoles in each microdomain in the same direction, leading to the transition of the crystal from a quadratic EO effect to a linear one. A beam deflection system utilizing the composition gradient and quadratic electro-optic (EO) effect was established. At lower voltages, the deflection angle exhibited a parabolic increase with the applied voltage, while at higher voltages, it decreases due to the poling effect. A maximum deflection angle of 10 mrad was obtained by applying 880 V/mm on an SBN crystal with the dimension of 5.8 mm × 2 mm × 1 mm. A theoretical model that accounts for both the gradient of the intrinsic refractive index and the EO effect was constructed. The derived expression for the deflection angle's dependence on the applied voltage demonstrated that the deflection angle resulting from the quadratic EO effect is considerably greater than that produced by the linear EO effect.