Electro-optic coefficient measurement of a K(H_1-xD_x)₂PO₄ crystal based on χ⁽²⁾ nonlinear optical technology

We present a novel method utilizing the χ⁽²⁾ nonlinear optical technology, which can realize high precision measurement of linear electro-optic (EO) coefficients of nonlinear materials. By applying the linear EO effect to the nonlinear optical process, the theoretical model of this measurement method was established, and the calculation formula of the linear EO coefficient was given. In the proof-of-principle experiment, by introducing an external electric field into the fourth harmonic generation (FHG) process, we comprehensively obtained the linear EO coefficients of K(H_1-xD_x)₂PO₄ crystals and revealed the relationship between deuterium content (x) and EO coefficient (γ₆₃): γ₆₃ = -9.789 - 16.53x. Meanwhile, the stability of FHG was greatly improved, and the angular range of efficiency stability was increased to 4.4 times in maximum. This work not only systematically demonstrates the FHG characteristics of KDP-family crystals, which provides a good reference for the deep ultraviolet laser generation, but also offers a new way to measure the basic parameters of nonlinear optical materials.