Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited

Abstract

I report significant improvements to the differential method of Chandezon et al. [ J. Opt. Soc. Am. 72, 839– 846 ( 1982)]. The R-matrix propagation algorithm is used to remove completely the previously existing limitations on the total coating thickness and on the total number of coated layers. I analyze the symmetry properties of the eigenvalue problem that arises in the differential formalism and use them to speed up the numerical computation. The time needed for computing the eigensolutions of coated gratings in a conical mount is reduced to little more than what is needed for gratings in a classical mount. For gratings with dielectric coatings or gratings with symmetrical profiles the need to invert certain matrices appearing in the formalism is eliminated. Numerical results show that it is possible to make nearly 100% efficient surface-relief reflection gratings in a Littrow mount by the use of dielectric materials only.