Recently two variants of a pseudospectral modal method were developed for analyzing lamellar diffraction gratings: [J. Lightwave Technol. 27, 5151 (2009)] and [J. Opt. Soc. Am. A 28, 613 (2011)]. Both of them divide the computational domain into nonoverlapping subdomains and replace the spatial derivative in the Helmoltz equation by a differentiation matrix at the Chebyshev collocation points. The authors of the second reference claim that their method is more robust and accurate because they match the Fourier coefficient at the interfaces between the layers and drop some computed eigenmodes. We challenge these two ideas. Instead, we numerically demonstrate that by keeping all computed eigenmodes and by also numerically computing eigenmodes in homogeneous regions, the pseudospectral method performs better.
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机译：最近，开发了一种用于分析层状衍射光栅的伪光谱模态方法的两种变体：光波技术。 27，5151（2009）]和[J.选择。 Soc。上午。 A 28，613（2011）]。它们都将计算域划分为不重叠的子域，并用切比雪夫搭配点上的微分矩阵替换Helmoltz方程中的空间导数。第二篇参考文献的作者声称，他们的方法更加健壮和准确，因为它们在层之间的界面处匹配了傅立叶系数，并丢弃了一些计算的本征模。我们挑战这两个想法。取而代之的是，我们通过数值方法证明了，通过在同质区域中保留所有计算的本征模并且还通过数值计算本征模，伪谱方法的性能更好。
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