当各向异性晶体介电主轴坐标系与入射光波所在平面坐标系取向不同时, 讨论折射光波场强E的问题变得比较复杂, 但是这种情形对于许多双轴晶体的非线性光学现象具有重要影响。在上述两坐标系任意取向的前提下, 讨论了平面波从各向同性介质入射到各向异性晶体后, 其折射光波电场强度E的大小和方向的一般表达式, 证明了折射光波电场强度的方向和大小可以通过求解一元四次方程和电磁场边界条件而得到。对于一些特殊的入射光波方向和具有特殊对称性的晶体, 折射光波电场强度E的方向与光波法线方向垂直, 也就此特殊情况进行了讨论。利用所得结果, 可以讨论两束折射光波能量的分配关系。

When the principal dielectric axes of the anisotropic crystals and the axes built for describing the direction of incident lightwave are different,discussing about the electric field E of the refracted light wave becomes a complex problem. But it is important for some phenomena of nonlinear optics in biaxial crystals. After a plane wave propagating from an isotropic medium into an anisotropic crystal without any restriction on the orientation of the axes above, general expressions about the direction and amplitude of the refracted light wave’s electric field E are given. The result proves that E can be got by solving a quartic equation and using the boundary conditon of electromagnetic field. When the incident light wave takes some special direction or propagate into some symmetrical crystals, the E of the refracted light wave is perpendicular to the direction of the unit wave normal. That is a special case and also be discussed. The results can be used to discuss the distribution of energy between the two refracted light waves.