For analyzing diffraction gratings, a new method is developed based on dividing one period of the grating into homogeneous subdomains and computing the Neumann-to-Dirichlet (NtD) maps for these subdomains by boundary integral equations. For a subdomain, the NtD operator maps the normal derivative of the wave field to the wave field on its boundary. The integral operators used in this method are simple to approximate, since they involve only the standard Green’s function of the Helmholtz equation in homogeneous media. The method retains the advantages of existing boundary integral equation methods for diffraction gratings but avoids the quasi-periodic Green’s functions that are expensive to evaluate.
© 2009 Optical Society of America
Original Manuscript: August 18, 2009
Revised Manuscript: September 23, 2009
Manuscript Accepted: September 24, 2009
Published: October 27, 2009
Yumao Wu and Ya Yan Lu, "Analyzing diffraction gratings by a boundary integral equation Neumann-to-Dirichlet map method," J. Opt. Soc. Am. A 26, 2444-2451 (2009)