Gérard Granet

Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization

A new implementation of the coupled-wave method for TM polarization is proposed. We use a second-order differential operator established by Neviere together with a scattering-matrix approach. Thus we obtain for metallic gratings a convergence rate as quick as that in TE polarization.

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.

Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution

The lamellar grating problem is reformulated through the concept of adaptive spatial resolution. We introduce a new coordinate system such that spatial resolution is increased around the discontinuities of the permittivity function. We derive a new eigenproblem that we solve by using Fourier expansions for both the field and the coefficients of Maxwell’s equations. We provide numerical evidence that highly improved convergence rates can be obtained.

Polarization independence of a one-dimensional grating in conical mounting

We demonstrate theoretically a polarization-independent guided-mode resonant filter with only a one dimensional grating. A rigorous method, the modal method by Fourier expansion, is used to compute the diffracted efficiencies of the grating. Wave-vector analysis fails to correctly design a polarization-independent structure. We show that a rigorous analysis of the resonances must be employed to obtain such a device; using a pole approach, we study the effects of grating parameters on the resonances of both polarizations.

Generalization of the coordinate transformation method with application to surface-relief gratings

The coordinate-transformation-based differential method, initially used by Chandezon et al. for modeling surface-relief gratings, is now known as a powerful rigorous formalism for solving diffraction problems. We explain a coordinate transformation that generalizes the original one, and we extend the formulation to a wide class of monodimensional surface shapes. The boundary-value problem turns on the same eigenvalue problem for the TE and TM polarizations.

Corrections to “Simple and Accurate Analytical Model of Planar Grids and High-Impedance Surfaces Comprising Metal Strips or Patches” [Jun 08 1624-1632]

In the above titled paper (ibid., vol. 56, no. 6, pp. 1624-1632, Jun. 08), there were mistakes in equations (16) and (17). The corrections are presented here.

Polynomial modal analysis of slanted lamellar gratings

The problem of diffraction by slanted lamellar dielectric and metallic gratings in classical mounting is formulated as an eigenvalue eigenvector problem. The numerical solution is obtained by using the moment method with Legendre polynomials as expansion and test functions, which allows us to enforce in an exact manner the boundary conditions which determine the eigensolutions. Our method is successfully validated by comparison with other methods including in the case of highly slanted gratings.

A scattering matrix interpolation from perturbation method: application to scatterometry for profile control

The scatterometric and electromagnetic signatures of a pattern are computing with the perturbation method combined with the Fourier Modal Method (FMM) in order to reduce computational time. In electromagnetic point of view, the grating is characterized by its scattering matrix which allows the computation of the reflection and transmission coefficient. A slight variation of profile parameters or electrical ones provides a small fluctuation of the scattering matrix, consequently, an analytical expression of the local behavior of its eigenvectors and eigenvalues can be obtained by using a perturbation method.

Optimal architecture of a neural network for a high precision in ellipsometric scatterometry

Neural networks (NN) have received a great deal of interest over the last few years. They are being applied accross a wide range of problems in pattern recognition, artificial intelligence, and classification as well as in the inverse problem of scatterometry. Optical scatterometry is a non-direct characterization method that has been widely employed in the semiconductor industry for critical dimensions control. It is based on the analysis of the light scattered from periodic structures. This analysis consists of the resolution of an inverse problem in order to determine the parameters defining the geometrical shape of the structure. In this work, we will study the performances of the NN according to various internal parameters when it is applied to solve the scattered problem. This will allow us to examine how a NN reacts and to select the optimal configuration of these parameters leading to a rapid and accurate characterization.