二维平面光栅角色散公式的完整解析形式及分析

在矢量衍射理论基础上给出了任意入射状态下二维平面光栅的光栅方 程，推导出二维平面光栅角色散公式的完整解析形式，确立了二维平面光栅衍射极角 角色散（第一类角色散）和衍射方位角角色散（第二类角色散）的概念. 通过二维平面光栅 衍射极角和衍射方位角角色散的理论分析和数值计算，阐明了当入射波矢偏离光栅法线时， 衍射光斑阵列发生畸变的机理，并明确指出了引起衍射方位角角色散的突变、导致衍射光斑 阵列剧烈变化的条件，因而具有理论上的意义. 在实际应用方面，以晶体和量子点 的x射线衍射、低能电子衍射和反射式高能电子衍射为关键词：二维平面光栅衍射极角角色散衍射方位角角色散晶体电子衍射

The complete analytical form and analysis on angular dispersion formula of two-dimensional grating

On the basis of the vector diffraction theory,the equation of two-dimensional grating in arbitrary angle of incidence is given,the complete analytical form of angular dispersion formula of two-dimensional grating is firstly deduced,and the concept of angular dispersion of diffractive polar angle (ADDPA)(the first kind angular dispersion) and angular dispersion of diffractive azimuthal angle (ADDAA) (the second kind angular dispersion) are established. In addition,according to theoretical analysis and numerical method on ADDPA and ADDAA of two-dimensional grating,the mechanism that diffraction spot array generates distortion is explained when the incidence wave has an angular deviation from the grating normal. Moreover,the conditions for causing mutation of ADDAA and leading to the dramatic change of diffraction spot array are also determined. This work,therefore,is of great importance in basic theory research. In practical application,taking x-ray diffraction,low-energy electron diffraction and reflection high-energy electron diffraction of crystal and quantum dot for example,we may take advantage of the above formula to test,analyze and explain the structure of a crystal lattice and the crystal growth process, then we can find new methods of characterizing crystal structure.