Conventional integral equation methods for diffraction gratings require lattice sum techniques to evaluate quasi-periodic 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
Diffraction and Gratings
Original Manuscript: January 3, 2012
Manuscript Accepted: January 26, 2012
Published: April 19, 2012
Wangtao Lu and Ya Yan Lu, "High order integral equation method for diffraction gratings," J. Opt. Soc. Am. A 29, 734-740 (2012)