Justification of matrix truncation in the modal methods of diffraction gratings
- 1 January 1999
- journal article
- Published by IOP Publishing in Journal of Optics A: Pure and Applied Optics
- Vol. 1 (4), 531-536
- https://doi.org/10.1088/1464-4258/1/4/320
Abstract
In the Fourier modal method (FMM) and Chandezon method for modelling diffraction gratings, the reduction method is used to obtain approximate numerical solutions of certain matrix eigenvalue problems in the infinite Fourier space. However, at least in the optics literature to date, the legitimacy of using the reduction method in these situations has not been carefully studied. By using the classical theory of determinants of infinite order, I show that the solutions of the eigenvalue problems with truncated matrices tend to the exact solutions as the matrix order increases; thus the use of the reduction method is legitimate. This conclusion is valid for any permittivity variations (continuous or discontinuous) in the case of the FMM, and for any permissible grating profiles (smooth or edgy) in the case of the Chandezon method.Keywords
This publication has 21 references indexed in Scilit:
- Rigorous coupled-wave analysis of planar-grating diffractionJournal of the Optical Society of America, 1981
- Rigorous diffraction theory for transmission phase gratings with deep rectangular groovesJournal of the Optical Society of America, 1978
- Modal Theory of Spatially Periodic MediaIEEE Transactions on Microwave Theory and Techniques, 1977
- Theory of Periodic Dielect WaveguidesIEEE Transactions on Microwave Theory and Techniques, 1975
- Diffraction by thick, periodically stratified gratings with complex dielectric constantJournal of the Optical Society of America, 1973
- Diffraction of a Plane Wave at a Sinusoidally Stratified Dielectric GratingJournal of the Optical Society of America, 1966
- SCATTERING OF ELECTROMAGNETIC WAVES BY A SINUSOIDALLY STRATIFIED HALF-SPACE: II. DIFFRACTION ASPECTS AT THE RAYLEIGH AND BRAGG WAVELENGTHSCanadian Journal of Physics, 1966
- SCATTERING OF ELECTROMAGNETIC WAVES BY A SINUSOIDALLY STRATIFIED HALF-SPACE: I. FORMAL SOLUTION AND ANALYTIC APPROXIMATIONSCanadian Journal of Physics, 1966
- Transverse Magnetic Wave Propagation in Sinusoidally Stratified Dielectric MediaIEEE Transactions on Microwave Theory and Techniques, 1965
- Wave Propagation in Sinusoidally Stratified Dielectric MediaIEEE Transactions on Microwave Theory and Techniques, 1964