一种综合处理光栅矢量衍射的新方法

理论上将Waterman -Rayleigh方法 (WRM) ,傅立叶模方法 (FMM)和坐标变换法 (CM)巧妙结合 ,吸收了三者各自处理多分层光栅的优点 ,摒弃了各自的缺点 ,简化了理论推导。采用WRM方法的形式来表示电磁场 ,以便省去对本征值和本征矢的数值计算时间 ;采用FMM对物理量作矩阵表述 ,以便实现理论推导的简洁性 ,规范性 ;采用CM的坐标变换 ,以便简化对边界条件的匹配 ;在作Fourier展开时采用“逆规则” ,以保持方法的快速收敛性 ;在对多分层光栅的递推计算中 ,采用反射透射系数阵算法 (RTCM) ,以便克服由于层与层之间厚度变大所带来的数值不稳定性 ,同时提高计算速度。总之 ,这种综合处理光栅问题的方法不仅物理概念清晰 ,计算简洁 ,速度快 ,而且准确性 ,稳定性和收敛性均令人满意。

A synthetical method to vector diffraction

We integrate Waterman-Rayleigh method (WRM),Fourier Model method (FMM),and C Method properly into our new method-WFCM,which assimilates their advantages to operate multilayer-coated gratings.WRM,FMM and C Method are used to describe electric and magnetic fields,to express the physical quantities with matrix form and to transform tangent quantities of electric and magnetic fields for the sake of saving the numerical computation time of eigenvalues and eigenvectors,simplifying theoretical deductions and the boundary condition respectively;The Fourier factorization theory is applied to achieve the good numerical convergence of our method;The reflection and transmission coefficient matrix method (RTCM) is also used to save the computation time and overcome numerical values instability brought by the added layers.In all,the method,which synthetically deals with multilayer-coated gratings,is clear in physical concept,compact in expression form and excellent in numerical stability and convergence.