Abstract: In order to analyze the energy loss of a beam at crystal surfaces, a method was proposed to calculate the corresponding reflectivity and transmissivity. According to the electromagnetic boundary conditions and the phase matching conditions, reflection and refraction of a beam incident from a crystal upon an isotropic medium were studied, and the Fresnel formulas at the interface between the crystal and the isotropic medium were deduced. As the orientation of optical axis is arbitrary, the polarization states and the amplitudes of the o ray and e ray and the refracted ray were given, and the theoretical expressions of the reflectivity and the transmissivity representing energy relations between the rays were obtained, which provide a theoretical basis for developing and applying crystal devices. Numerical simulations show that the results are accordant with conservation of energy; electrical field or magnetic field of the ray refracted to the isotropic medium does not parallel to the electric field or the magnetic field of original incident ray; the direction of optical axis and the magnitude of incident angle have a great effect on the energy and the polarization direction of the refracted ray.

Key words: Uniaxial crysta ,  Boundary condition ,  Transmissivity ,  Reflectivity

摘要： 为了分析光在晶体界面的能量损失,给出了一种求解反射率和透射率的方法。分析了光从单轴晶体
入射到各向同性介质表面时的折射和反射,根据在界面处电磁场的边界条件和位相匹配条件,得到了在晶体界面的
菲涅耳公式。在晶体光轴取向任意的条件下,给出了反射的o光、e光以及折射光的偏振状态和振幅以及表明各光
束间能量关系的折射率和反射率的理论表达式,为晶体器件特性的研究提供了有力的理论工具。数值模拟表明,所
得结果满足能量守恒;射入各向同性介质中光的电场(或磁场)与原入射光的电场(或磁场)不再平行;光轴的取向和
入射角的大小对折射光的偏振方向和能量有重大影响。

关键词: 单轴晶体 , 边界条件 , 透射率 , 反射率