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由于晶体的折射率主轴与其晶体物理主轴有着不同的配对方式，其三阶有效非线性系数计算公式将发生变化．考虑到配对方式的影响，首次得到变换后的三阶非线性系数的矩阵形式，然后推导出了任意配对方式下，晶体主平面上三阶有效非线性系数的最一般解析表达式．
Since the principal axis of the refractive index of the crystal has a different pairing pattern with its physical principal axis of the crystal, the formula for calculating the third-order effective nonlinear coefficient will vary. Considering the effect of pairing mode, the matrix form of the transformed third-order nonlinear coefficients is obtained for the first time. Then the most general analytical expression of the third-order effective nonlinear coefficients on the principal plane of the crystal under any pairing mode is deduced.