光栅形状反演的数值方法  

Numerical Method to Reconstruction of Grating

作　　者：张晔[1,2] 马云云[1] 

机构地区：[1]吉林大学数学研究所,长春130012 [2]北华大学数学学院,吉林吉林132013

出　　处：《吉林大学学报（理学版）》2012年第4期654-662,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10431030)

摘　　要：提出一种光栅形状反演的数值算法.考虑利用一个入射波和在光栅上部一条直线Γb上的散射场反演单周期良导体光栅的形状,先利用Dirichlet-to-Neumann映射得到散射场在Γb上的法向导数值,再应用求解椭圆方程初值问题的谱方法求解Helmholtz方程Cauchy问题,得到Γb以下的全场,最后逐点寻找全场的零点并连接,得到的曲线即为反演的光栅形状.数值结果表明该方法可行、有效.The authors proposed a numerical method to reconstruct the grating profile. We considered the reconstrution of the grating profile by the incident plane wave and the scattered waves measured on Γb, which is a straight line above the grating. First, we obtained the normal derivatives of the scattered waves on Γb via the Dirichlet-to-Neumann map. Then we got the total field below Γb by means of solving the Cauchy problem of the Helmholtz equation, which is changed into an initial value problem. The initial value problem was sol,/ed by the spectral method which is used to solve the initial value problem of the elliptic equation. Finally, we used the curve, which is composed of the zeros of the total field, to approximate the grating profile. The numerical results show that the method is effective.

关 键 词：HELMHOLTZ方程 初值问题 不适定问题 正则化方法 光栅 

分 类 号：O241.3[理学—计算数学]