Abstract

Differential theory is said to be difficult to apply to surface-relief gratings made of metals with very high conductivity even though the formulation follows Li’s Fourier factorization rules. Recently, Popov et al. [J. Opt. Soc. Am. 21, 199 (2004) ] pointed out this difficulty and explained that its origin is related to the inversion of Toeplitz matrices constructed by the permittivity distribution inside the groove region. The current paper provides information about the differential theory for highly conducting gratings and considers the numerical instability problems. A stable calculation for lossless gratings is described, based on the extrapolation technique with the assumption of small losses.

© 2006 Optical Society of America

Differential theory: application to highly conducting gratings

Evgeny Popov, Boris Chernov, Michel Nevière, and Nicolas Bonod
J. Opt. Soc. Am. A 21(2) 199-206 (2004)

Differential theory of gratings made of anisotropic materials

Koki Watanabe, Roger Petit, and Michel Nevière
J. Opt. Soc. Am. A 19(2) 325-334 (2002)

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)

Study of the numerical artifacts in differential analysis of highly conducting gratings

Amin Khavasi, Khashayar Mehrany, and Amir M. Jazayeri
Opt. Lett. 33(2) 159-161 (2008)

Numerical integration schemes used on the differential theory for anisotropic gratings

Koki Watanabe
J. Opt. Soc. Am. A 19(11) 2245-2252 (2002)