Use of Fourier series in the analysis of discontinuous periodic structures
Use of Fourier series in the analysis of discontinuous periodic structures
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DOI：
10.1364/josaa.13.001870
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发表时间：
1996-09-01
影响因子：
1.9
通讯作者：
Li, LF
中科院分区：
文献类型：
--
作者：
Li, LF
Lalanne和Morris最近对耦合波方法的重新表述[J. Opt. Sec. Am. A 13，779（1996）]和Granet和Guizal [J. Opt. Am. A 13，1019（1996）]，该方法大大提高了TM偏振金属光栅法的收敛性，本文给出了坚实的数学基础。新的公式收敛速度更快，因为它一致地满足光栅区域的边界条件，而旧的公式这样做，只有非均匀。给出了具有跳跃间断的函数乘积的傅里叶系数因式分解的数学定理。本文的结果适用于任何数值工作，需要的产品的不连续周期函数的傅立叶分析。(C)1996年美国光学学会。
The recent reformulation of the coupled-wave method by Lalanne and Morris [J. Opt. Sec. Am. A 13, 779 (1996)] and by Granet and Guizal [J. Opt. Sec. Am. A 13, 1019 (1996)], which dramatically improves the convergence of the method for metallic gratings in TM polarization, is given a firm mathematical foundation in this paper. The new formulation converges faster because it uniformly satisfies the boundary conditions in the grating region, whereas the old formulations do so only nonuniformly. Mathematical theorems that govern the factorization of the Fourier coefficients of products of functions having jump discontinuities are given. The results of this paper are applicable to any numerical work that requires the Fourier analysis of products of discontinuous periodic functions. (C) 1996 Optical Society of America.