Abstract

Analysis of highly conducting binary gratings in TM polarization has been problematic as the Fourier factorization fails and thus unwanted numerical artifacts appear. The Legendre polynomial expansion method (LPEM) is employed here, and the erroneous harsh variations attributed to the violation of the inverse rule validity in applying the Fourier factorization are filtered out. In this fashion, stable and artifact-free numerical results are obtained. The observed phenomenon is clearly demonstrated via several numerical examples and is explained by inspecting the transverse electromagnetic field profile.

© 2009 Optical Society of America

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References

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2008 (2)

2007 (2)

2006 (1)

2004 (1)

1996 (1)

1995 (1)

Bonod, N.

Chernov, B.

Gaylord, T. K.

Grann, E. B.

Jahromi, A. K.

Jazayeri, A. H.

Khavasi, A.

Li, L.

Lyndin, N. M.

Mehrany, K.

Moharam, M. G.

Nevière, M.

Parriaux, O.

Pommet, D. A.

Popov, E.

Rashidian, B.

Tishchenko, A. V.

Watanabe, K.

J. Opt. Soc. Am. A (6)

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

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Figures (8)

Fig. 1
Fig. 1

Geometry of a typical binary grating.

Fig. 2
Fig. 2

Minus-first reflected order versus the groove width g obtained by using (a) the RCWA with N = 35 and (b) the LPEM with N = 35 and M = 7 (solid curve) and the extrapolation technique based on the RCWA with N = 60 (dashed curve) for the grating shown in Fig. 1 illuminated by a TM polarized plane wave at θ = 30 ° and with the vacuum wavelength λ = 632.8 nm . Other parameters in Fig. 1 are d = Λ G = 500 nm , n c = 1 , n s = 10 j .

Fig. 3
Fig. 3

Minus-first reflected order versus the truncation order ( N ) obtained by LPEM with M = 8 (solid curve), M = 7 (dashed curve), and M = 6 (dotted curve). The groove width of the grating is fixed at g = 250 nm . The reference value is obtained by using the extrapolation technique based on the RCWA with N = 150 applied to a slightly lossier structure.

Fig. 4
Fig. 4

Spatial distribution of H y calculated by (a) RCWA with N = 35 (b), LPEM with N = 35 and M = 7 , and (c) by RCWA with N = 35 applied to a slightly lossier structure with n s = 0.05 10 j . The groove width of the grating is fixed at g = 360.4 nm .

Fig. 5
Fig. 5

Minus-first reflected order versus the truncation order ( N ) obtained by LPEM with M = 10 (solid curve), M = 9 (dashed curve), and M = 8 (dotted curve). The groove width of the grating is g = 252 nm and its thickness is d = 1 μ m . The reference value is obtained by using an extrapolation technique based on RCWA with N = 150 applied to a slightly lossier structure.

Fig. 6
Fig. 6

Spatial distribution of H y calculated by LPEM with N = 29 and M = 10 applied to the lossless metallic grating with n s = 10 j . The groove width of the grating is fixed at g = 252.4 nm and its thickness is d = 1 μ m .

Fig. 7
Fig. 7

Spatial distribution of H y calculated by LPEM with N = 40 and M = 10 applied to the lossless metallic grating with n s = 10 j . The groove width of the grating is fixed at g = 252.4 nm and its thickness is d = 1 μ m .

Fig. 8
Fig. 8

Spatial distribution of H y calculated by RCWA with N = 35 applied to a slightly lossier structure with n s = 0.05 10 j . The groove width of the grating is once again fixed at g = 252.4 nm and the grating thickness is d = 1 μ m .

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