从准相位匹配的基本原理出发，提出了一种研究周期极化介质中二阶非线性的三波互作用现象的分析方法——矢量叠加法。这种方法利用了相互作用的电场矢量叠加的特征曲线，清晰地描绘出晶体内部产生的倍频光的电场变化规律。该方法描述物理现象清晰，结果简洁直观，不仅与经典的傅里叶变换方法结果相一致，而且也可以用于分析周期极化结构中各种误差对倍频效率的影响。它还为准相位匹配技术新的实现方法奠定了理论基础。

A new method of analyzing three waves interaction in nonlinear periodically poled crystals(PP-crystals)on the theorem of quasi-phase-matching,called the vector superposing method is presented. By using of the characteristic curve of interactive electric field,this method can clearly illustrate the principle of the electric field changing in the second harmonic generation process inside the nonlinear PP-crystals. The method can not only describe the physics phenomenon clearly but also get concise results. These results are similar with former Fourier's transform and can be used to research the influence of various errors for the efficiency of SHG in ferroelectric domain-inverted gratings .The method also establishes the theoretical foundation for realizing the new method of QPM.