傅里叶级数
不连续性分类
跳跃
系列(地层学)
傅里叶变换
傅里叶分析
趋同(经济学)
数学分析
数学
周期边界条件
边值问题
物理
应用数学
生物
古生物学
经济
量子力学
经济增长
标识
DOI:10.1364/josaa.13.001870
摘要
The recent reformulation of the coupled-wave method by Lalanne and Morris [ J. Opt. Soc. Am. A13, 779 ( 1996)] and by Granet and Guizal [ J. Opt. Soc. Am. A13, 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.
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