12 December 1984 Modal Expansion Method For Dielectric Gratings With Rectangular Grooves
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Abstract
An exact method of analyzing the dielectric gratings with rectangular grooves is presented. The most common of rigorous approaches are the expansion-methods such as coupled-wave approaches and modal approaches, which expand the fields in terms of space harmonics based on the Floquet's theorem. However, these methods are not rigorous in the strict sence for the numerical analysis of dielectric gratings with rectangular grooves, since in the case of rectangular shapes the Fourier series sometimes fails to converge with the increase of the number of order in the expansion. In this paper, a rigorous numerical method for rectangular-groove gratings is presented by using modal expansion in terms of modal functions consisting of the Bloch waves inside the periodic stratified media. The convergence of the solutions in this method is very rapid with the increase of the truncation size retained in the calculation, moreover the accuracy of the solutions can be checked by the energy-conservation and the square-errors of the electromagnetic fields on the boundaries. The scattering problems for both E-mode and H-mode polarizations are treated.
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Jiro Yamakita, Jiro Yamakita, Katsu Rokushima, Katsu Rokushima, "Modal Expansion Method For Dielectric Gratings With Rectangular Grooves", Proc. SPIE 0503, Application, Theory, and Fabrication of Periodic Structures, DiffractionGratings, and Moire Phenomena II, (12 December 1984); doi: 10.1117/12.944838; https://doi.org/10.1117/12.944838
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