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Proceedings Paper

Scattering matrix approach to multilayer crossed gratings diffraction
Author(s): Gérard Granet
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Paper Abstract

It has already been shown that the dif- ferential method of Chandezon is well suited for analysing multilayer diffraction gratings [1]. Lifeng Li has reported significant improvments to this method [2] . He used the R-matrix propagation algo- rithm to remove the limitation on the layer thickness and on the number of layers. As far as we are con- cerned, we have allowed for different interface pro- files within the grating structure although all must share the same periodicity [3]. Preist et al have done it also [4]. Boundary conditions were expressed with the scattering matrix approach which is an alterna- tive to the R-matrix approach. The aim of this paper is to analyze multi- layer crossed gratings with the Chandezon method and the S-matrix formulation. It consists of a genera- lization of the formalism already used for 2D multi- coated gratings. The basic features lies in the use of a coordinate system that maps the interface onto a plane. In the new frame, the structure is analogous to a planar stratified medium. As in the 2D case, we are led to a linear system of differential equations whose solution is obtained through the calculation of the ei- genvalues and eigenvectors of a matrix dependant on the geometry and on the index of the medium. As an example, we shall consider cases where "anomalies" in the diffracted efficiencies occur, that is when a suitable phase matching between the incident wave and the guided wave is achieved.

Paper Details

Date Published: 1 September 1996
PDF: 2 pages
Proc. SPIE 2778, 17th Congress of the International Commission for Optics: Optics for Science and New Technology, 27785C (1 September 1996); doi: 10.1117/12.2299075
Show Author Affiliations
Gérard Granet, Institut National des Telecommunications (France)


Published in SPIE Proceedings Vol. 2778:
17th Congress of the International Commission for Optics: Optics for Science and New Technology
Joon-Sung Chang; Jai-Hyung Lee; ChangHee Nam, Editor(s)

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