摘要
采用矢量理论处理了多台阶位相光栅的衍射问题。用半数值的方法把微分方程转化成广义本征值方程。在利用纵向边值关系作模式匹配时，引入了模式变换阵、反射系数阵和透射系数阵，从而获得了计算电磁场振幅系数阵的递推公式，最后求出任意偏振状态下各级透射波和反射波的衍射效率。采用此法设计的程序极大地减少了运算量，计算稳定可靠，可快速地在微机上计算具有任意多个台阶光栅的衍射问题，从而为用矢量衍射迭代方法设计二元光学元件提供了一种快速简便的算法。所得结论与标量衍射理论有较大差异。
A vector theory for diffraction of multi step phase grating is presented. The half numerical method converts differential equation into generalized eigenvalue equation. At matching the boundary conditions in the longitudinal direction, a mode conversion matrix is introduced together with the reflection and transmission coefficient matrices. The iteration formula of the amplitude coefficient of the electric field are derived out. Finally the diffraction efficiency for each order of the transmission wave and the reflection wave are obtained in the any polarization.The computer program developed from the method has much less amount of calculation so that it can work on PC fast and stable. The method presented in this paper provides a simple fast algorithm to design binary optical element by vector diffraction. The results show that the scalar theory results differ greatly with that of the vector theory in the certain condition.
出处
《光学学报》
EI
CAS
CSCD
北大核心
1997年第12期1652-1659,共8页
Acta Optica Sinica
基金
中国工程物理研究院第二研究所和国家教委回国人员基金
关键词
矢量理论
多台阶位相光栅
二元光学
光栅衍射
vector theory, multi step phase grating, binary optical, half numerical method, mode conversion matrix, reflection coefficient matrix, transmission coefficient matrix.
