Une nouvelle mbthode d'ktude theorique des reseaux de diffraction et son application numkrique RESUME : Nous presentons un nouveau formalisme de la diffraction par un reseau, tres different de ceux actuellement utilises. I1 se caracterise par I'utilisation d'un systeme d e coordonnees de translation qui permet, apres emploi des equations de Maxwell en coordonnees curvilignes, d'aboutir a un systeme d'equations differentielles a coefficients constants. L'application numerique est fondee sur le calcul matriciel elementaire. Le programme est teste a l'aide de criteres numeriques et par comparaison des resultats avec ceux issus de la methode integrale.

We present a new formalism for the diffraction of an electromagnetic plane wave by a multicoated grating. Its basic feature lies in the use of a coordinate system that maps all the interfaces onto parallel planes. Using Maxwell's equations in this new system leads to a linear system of differential equations with constant coefficients whose solution is obtained through the calculation of the eigenvalues and eigenvectors of a matrix in each medium. Through classical criteria, our numerical results have been found generally to be accurate to within 1%. The serious numerical difficulties encountered by the previous differential formalism for highly conducting metallic gratings completely disappear, whatever the optical region. Furthermore, our computer code provides accurate results for metallic gratings covered by many modulated dielectric coatings or for highly modulated gratings. We give two kinds of applications. The first concerns the use of dielectric coatings on a modulated metallic substrate to minimize the absorption of energy. Conversely, the second describes the use of highly modulated metallic gratings to increase this absorption.

The coordinate-transformation-based differential method of Chandezon et al. [J. Opt. (Paris) 11, 235 (1980); J. Opt. Soc. Am. 72, 839 (1982)] (the C method) is one of the simplest and most versatile methods for modeling surface-relief gratings. However, to date it has been used by only a small number of people, probably because, traditionally, elementary tensor theory is used to formulate the method. We reformulate the C method without using any knowledge of tensor, thus, we hope, making the C method more accessible to optical engineers.

No abstract

Abstract-The goal of the present paper is two folded. The first, the methodological one, is the complementation of well established in diffraction theory of gratings C method with certain elements of spectral theory and the development of interactive numerical algorithm that made feed back conjunction between diffraction and spectral problems. As a natural result the second goal appeared: the appearing of such tool for numerical experiments resulted in profound qualitative and quantitative study of rather peculiar phenomena in resonant scattering from periodic surface. Special attention has been paid to the investigation of electromagnetic waves diffraction from periodic boundaries of material with single and double negative parameters.

In a recent Letter to the Editor (1995 Pure Appl. Opt. 4 1-5), the differential formalism of Chandezon et al (the C method) was extended to treat layered gratings in which the profiles of the medium interfaces within the same grating are different from each other. Numerical experiments have shown that a computer program based on the recipe given in the Letter gives excellent numerical results for diffraction efficiencies. However, a crucial assumption was implicitly used without justification. In this paper, we examine this assumption and comment on its validity. In addition, we suggest two alternative ways to extend the C method, and show that one of them is as effective as the recipe given in the Letter.

No abstract

The extension of C method, combined with idea of Tikhonov's regularization is proposed. The regularizing algorithm for numerical solution of electromagnetic wave diffraction by the boundary of dielectric media is developed. This algorithm is based on the solution of the system linear algebraic equations of C method as subject of regularizing method of A. N. Tikhonov. The numerical calculations of scattered field in the case of E-polarization are presented. The efficiency and reliability of the method for the solution of the problems of boundary shape reconstruction have been proved and demonstrated numerically for several situations.