High order integral equation method for diffraction gratings

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)734-740
Journal / PublicationJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number5
Publication statusPublished - May 2012
Externally publishedYes


Conventional integral equation methods for diffraction gratings require lattice sum techniques to evaluate quasiperiodic Green's functions. The boundary integral equation Neumann-to-Dirichlet map (BIE-NtD) method in Wu and Lu [J. Opt. Soc. Am. A 26, 2444 (2009)], [J. Opt. Soc. Am. A 28, 1191 (2011)] is a recently developed integral equation method that avoids the quasi-periodic Green's functions and is relatively easy to implement. In this paper, we present a number of improvements for this method, including a revised formulation that is more stable numerically, and more accurate methods for computing tangential derivatives along material interfaces and for matching boundary conditions with the homogeneous top and bottom regions. Numerical examples indicate that the improved BIE-NtD map method achieves a high order of accuracy for in-plane and conical diffractions of dielectric gratings. © 2012 Optical Society of America.