为了用琼斯矢量更明确地表示双折射晶体入射光和折射光的偏振状态, 利用波法线椭球和物质方程, 将入射光和折射光的电场矢量均视为由o振动和e振动两个方向的分量叠加而成, 并将之投影到垂直于和平行于入射面的两个方向上。其中, 入射光和折射光电场分量之间的关系用菲涅耳方程中的透射系数表示。考虑到e光电场矢量与电位移矢量的差别, 对菲涅耳方程进行了一定的修正以满足e光的边界条件。最终给出了入射光和折射光电场矢量的琼斯矢量形式。并通过具体的数值计算说明, 菲涅耳方程修正前后e光的透射系数有一定的差别, 且e光的电场矢量和电位移矢量之间的分裂不可忽略。

In order to express the polarization states of the incident and refracted rays of a birefringent crystal more accurately by Jones vectors, with the aid of ellipsoid of wave normals and material equations, the electric fields of incident and refracted beams are considered as combination of o component and e component which can be decomposed into directions parallel and perpendicular to the incident plane. The relationship between electric components of incident and refracted waves is expressed by transmission coefficients from Fresnel equations. Considering the differences between the electric field vector and displacement vector of e ray, Fresnel equations are modified to meet the boundary conditions. Finally, Jones vectors for the electric fields of the incident and refracted rays are obtained. And numerical examples are given to show that there is difference between conventional and modified transmission coefficients, and the difference between the electric field vector and displacement vector of e ray cannot be neglected.