We derive a numerical method based on coupled density functional theory and effective Hamiltonian schemes to calculate the linear and quadratic electro-optic response of ferroelectrics at finite temperature and in different frequency ranges. By applying the developed method to ${\mathrm{BaTiO}}_3$, we successfully resolve apparent discrepancies in the experimental literature that reported a linear or quadratic electro-optic response when visible or terahertz radiation was employed to measure the optical index, respectively. We further demonstrate that (and explain why), in the case of the ${\mathrm{Ba}}_{1-\mathrm{x}}{\mathrm{Sr}}_{\mathrm{x}}{\mathrm{TiO}}_3$ disordered solid solutions, structural phase transitions not only lead to larger linear electro-optic constants, as previously demonstrated in the literature, but also significantly enhance the quadratic electro-optic constants.

中文翻译：

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BaTiO3 和 (Ba,Sr)TiO3 固溶体中从线性到二次电光行为的交叉

我们推导了一种基于耦合密度泛函理论和有效哈密顿格式的数值方法，用于计算铁电体在有限温度和不同频率范围下的线性和二次电光响应。通过应用所开发的方法${\mathrm{钛酸钡}}_3$，我们成功解决了实验文献中的明显差异，这些文献报告了当使用可见光或太赫兹辐射分别测量光学指数时出现线性或二次电光响应。我们进一步证明（并解释原因），在${巴}_{1-\mathrm{X}}{锶}_{\mathrm{X}}{\mathrm{二氧化钛}}_3$在无序固溶体中，结构相变不仅会导致更大的线性电光常数（如文献中所证明的），而且还会显着增强二次电光常数。