Abstract

The Fourier modal method equipped with the concept of adaptive spatial resolution (FMMASR) is shown to be naturally more stable than the classical Fourier modal method toward spurious modes that appear with metallic structures. It is demonstrated that this stability can be further improved by reformulating the eigenvalue problem of the FMMASR.

© 2009 Optical Society of America

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References

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2008

2007

2004

2002

1999

1996

1978

K. Knop, J. Opt. Soc. Am. A. 68, 1206 (1978).
[CrossRef]

Bonod, N.

Chernov, B.

Granet, G.

Guizal, B.

Honkanen, M.

Jazayeri, A. H.

Khavasi, A.

Knop, K.

K. Knop, J. Opt. Soc. Am. A. 68, 1206 (1978).
[CrossRef]

Lalanne, P.

Li, L.

Lyndin, N. M.

Meherany, K.

Morris, G. M.

Nevière, M.

Parriaux, O.

Popov, E.

Tishchenko, A. V.

Vallius, T.

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Figures (5)

Fig. 1
Fig. 1

Geometry of the diffraction problem. The parameters are those of [7]: λ = 0.6328 μ m , d = 0.5 μ m , h = 0.5 μ m , θ = 30 ° , ε i n = 1 , and ε o u t = ε = 100 .

Fig. 2
Fig. 2

−1 reflected order versus the filling ratio computed with (a) the FMM and (b) the classical ASRFMM. The retained number of Fourier coefficients is 31 and the number of sampling points is 400.

Fig. 3
Fig. 3

Same as in Fig. 2, computed with the new formulation of the ASRFMM given by Eq. (2). The retained number of Fourier coefficients is 31 and the number of sampling points is 400.

Fig. 4
Fig. 4

Same as in Fig. 2, computed with (a) the classical ASRFMM and (b) the new formulation of the ASRFMM. 31 Fourier coefficients and 2000 sampling points were used.

Fig. 5
Fig. 5

−1 reflected order for a small thickness grating of h = 0.005 μ m , computed with the classical FMM and 51 Fourier coefficients (continuous curve), with the old ASRFMM (thin dotted curve), and with the new ASRFMM (thick dashed curve) with 41 Fourier coefficients. In all cases N s = 400 .

Equations (4)

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d 2 H z d y 2 = γ 2 H z = b 1 { α a 1 α k 0 2 f } H z ,
d 2 H z d y 2 = γ 2 H z = 1 / ε 1 { f 1 α ε 1 f 1 α k 0 2 I d } H z ,
x ( u ) = F ( u ) = a 1 + a 2 u + a 3 2 π sin   2 π [ u u l 1 u l u l 1 ] ,
u l 1 u u l ,

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