Cascading second-order nonlinearities in noncentrosymmetric crystals contributing to higher-order nonlinear effects is a common way to enhance the intrinsic weak high-order nonlinearity, which has much larger value than the direct higher-order nonlinear process. Normally they are carried out by optical methods with pretty high incident pump intensity. The Kerr electro-optic (EO) effect, though with a low Kerr EO coefficient, exists in any symmetry medium. Therefore, if the effective Kerr EO coefficient can be largely enhanced by cascading ways, it will extend the potential applications and also open up a new direction of electrically controlled third-order nonlinearities, especially in noncentrosymmetric medium.

In this work, we proposed a new scheme of controlling second-harmonic generation by enhanced Kerr electro-optic nonlinearity.We designed a structure that can implement the cascaded Pockels effect and second-harmonic generationsimultaneously. The energy coupling between the fundamental lights of different polarizations led to a large nonlinearphase shift and, thus, an effective electro-optic nonlinear refractive index. The effective nonlinearity can beeither positive or negative, causing the second-harmonic spectra to move toward the coupling center, which, inturn, offered us a way to measure the effective electro-optic nonlinear refractive index. The correspondingenhanced Kerr electro-optic nonlinearity is more than three orders of magnitude higher than the intrinsic value.These results open a door to manipulate the nonlinear phase by applying an external electric field instead of lightintensity in noncentrosymmetric crystals.
This work was published on Photonics Research.

G. Z. Li, Y. P. Chen, H. W. Jiang, and X. F. Chen, “Enhanced kerr electro-optic nonlinearity and its applicationin controlling second-harmonic generation,” Photon. Res. 3, 168–172 (2015).