Jean Chandezon

Rigorous and efficient grating-analysis method made easy for optical engineers

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.

Improvement of the coordinate transformation method for surface-relief gratings with sharp edges

The coordinate transformation method for modeling surface-relief gratings is reformulated with use of the recent results [ J. Opt. Soc. Am. A13, 1870 ( 1996)] on the Fourier factorization of products that contain discontinuous periodic functions. The matrix operator of the eigenvalue problem in the traditional formulation is modified following the correct Fourier factorization procedures. In addition, a new and simpler matrix operator is derived. Both the modified old operator and the new operator greatly improve the convergence of the coordinate transformation method for gratings whose profiles have sharp edges.

Scattering by a periodically corrugated dielectric layer with non-identical faces

A new approach is proposed for analysis of scattering by a periodically corrugated dielectric layer with non-identical faces. The method combines the simultaneous use of several different coordinate systems and the generalized S-matrix formalism. The program has been tested by comparisons with results given by the integral method.

Coordinate transformation method as applied to asymmetric gratings with vertical facets

The differential formalism introduced by J. Chandezon during the seventies has been successfully applied to the study of waveguides and to diffraction problems. Until now it was believed that the method could be applied only if the interfaces between media were described by graphs of functions. We show that an eigenoperator formulation of the method allows one to solve a larger set of profiles. This theoretical result is applied to gratings having a vertical facet.

Differential covariant formalism for solving Maxwell's equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces

A rigorous differential method describing the diffraction properties of lossy periodic surfaces is presented. A nonorthogonal coordinate system and a covariant formalism of Maxwells equation are used simplifying boundary conditions expression. Only one eigenvalue system, unique for the TE and TM polarizations even for an oblique incidence, needs to be solved. Thus the numerical treatment is very efficient and CPU requirements significantly reduced. Numerical results are successfully compared with those obtained by an integral method using the boundary element method (BEM) as a numerical procedure. >

C-Method: Several Aspects of Spectral Theory of Gratings

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.

Extension of the C method to nonhomogeneous media: application to nonhomogeneous layers with parallel modulated faces and to inclined lamellar gratings

The differential formalism of Chandezon was extended to nonhomogeneous media. In contrast to the case of homogeneous media, we were led to a different eigenvalue problem for each polarization. As an illustration, we analyzed diffraction by a sinusoidal piecewise-homogeneous modulated layer and by an inclined lamellar grating. Results were validated by comparison with the rigorous coupled-wave analysis.

New perturbation theory of diffraction gratings and its application to the study of ghosts

A new perturbation method for the diffraction of a plane wave by a grating with periodic imperfections is presented. The originality of the method lies in the fact that the perturbation occurs on a reference profile that is not a plane but a grating. First, the diffraction by a reference grating is treated. At this stage Maxwell’s equations are used in covariant form written in a nonorthogonal coordinate system fitted to the surface geometry. Second, the periodic errors are taken into account. The tensorial formalism permits the elaboration of this two-roughness-level model. The grating profile appears only through two fundamental functions. The variations of these functions under the effect of variation in the profile are expanded in power series of the perturbation parameter v1. v1 represents the maximum of the derivative of the function describing the perturbation. By using this formalism, we determine the efficiencies.

Conical diffraction of a plane wave by an inclined parallel-plate grating

We present a rigorous differential method describing the conical diffraction of an electromagnetic plane wave by an inclined parallel-plate grating. Above and below the grating, the fields are written with the use of Rayleigh’s expansion. Inside the grating, Maxwell’s equations are used in covariant form, written in a nonorthogonal coordinate system. Therefore the expression of boundary conditions on the perfectly conducting walls as well as on the planes delimiting the grating becomes simplified. In the classical diffraction case the numerical results compared successfully with those obtained with a Wiener–Hopf method [IEEE Trans. Antennas Propag.36, 1424 (1988)].

MATHEMATICAL MODELING OF ELECTROMAGNETIC WAVE SCATTERING BY WAVY PERIODIC BOUNDARY BETWEEN TWO MEDIA

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.