Abstract

We mathematically prove and numerically demonstrate that the source of the convergence problem of the anal ytical modal method and the Fourier modal method for modeling some lossless metal-dielectric lamellar gratings in TM polarization recently reported by Gundu and Mafi [J. Opt. Soc. Am. A 27, 1694 (2010)] is the existence of irregular field singularities at the edges of the grating grooves. We show that Fourier series are incapable of representing the transverse electric field components in the vicinity of an edge of irregular field singularity; therefore, any method, not necessarily of modal type, using Fourier series in this way is doomed to fail. A set of precise and simple criteria is given with which, given a lamellar grating, one can predict whether the conventional implementation of a modal method of any kind will converge without running a convergence test.

© 2011 Optical Society of America

Field singularities at lossless metal–dielectric arbitrary-angle edges and their ramifications to the numerical modeling of gratings

Lifeng Li
J. Opt. Soc. Am. A 29(4) 593-604 (2012)

Treatment of nonconvergence of Fourier modal method arising from irregular field singularities at lossless metal-dielectric right-angle edges

Yanpeng Mei, Haitao Liu, and Ying Zhong
J. Opt. Soc. Am. A 31(4) 900-906 (2014)

Treatment of nonconvergence of the Fourier modal method and C method arising from field hypersingularities at lossless metal–dielectric arbitrary-angle edges

Junda Zhu, Haitao Liu, and Ying Zhong
J. Opt. Soc. Am. A 33(5) 845-853 (2016)

Fourier-matching pseudospectral modal method for diffraction gratings

Dawei Song, Lijun Yuan, and Ya Yan Lu
J. Opt. Soc. Am. A 28(4) 613-620 (2011)

Numerical study on the spectroscopic ellipsometry of lamellar gratings made of lossless dielectric materials

Koki Watanabe, Jaromı́r Pištora, Martin Foldyna, Kamil Postava, and Jaroslav Vlček
J. Opt. Soc. Am. A 22(4) 745-751 (2005)