Abstract

A numerical scattering calculation method for defective gratings is proposed. This method is based on an integral equation method that computes a difference-field distribution, which is the difference between the scattering fields with and without the defect, and it is possible to simulate the arbitrary (finite) size and shape of a defect in the grating without any limitation. A calculation example is also presented to demonstrate the fast convergence and high accuracy of this method.

© 2012 Optical Society of America

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References

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  1. K. Hattori and J. Nakayama, IEICE Trans. Electron. E90-C, 312 (2007).
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  3. P. Lalanne and E. Silberstein, Opt. Lett. 25, 1092 (2000).
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  4. K. Trotskovsky and Y. Leviatan, J. Opt. Soc. Am. A 28, 502 (2011).
    [CrossRef]
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    [CrossRef]
  6. M. Tanaka and K. Tanaka, J. Opt. Soc. Am. A 15, 101 (1998).
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  7. N. Morita, IEEE Trans. Antennas Propag. 26, 261 (1978).
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  8. Y. Nakata and M. Koshiba, J. Opt. Soc. Am. A 7, 1494 (1990).
    [CrossRef]
  9. C. Brebbia, The Boundary Element Method for Engineers (Pentech, 1978).

2011 (1)

2007 (1)

K. Hattori and J. Nakayama, IEICE Trans. Electron. E90-C, 312 (2007).
[CrossRef]

2005 (1)

S. Wilcox, L. C. Botten, R. C. McPhedran, C. G. Poulton, and C. M. Sterke, Phys. Rev. E 71056606 (2005).
[CrossRef]

2002 (1)

H. Ammari and G. Bao, Adv. Comput. Math. 16, 99 (2002).
[CrossRef]

2000 (1)

1998 (1)

1990 (1)

1978 (1)

N. Morita, IEEE Trans. Antennas Propag. 26, 261 (1978).
[CrossRef]

Ammari, H.

H. Ammari and G. Bao, Adv. Comput. Math. 16, 99 (2002).
[CrossRef]

Bao, G.

H. Ammari and G. Bao, Adv. Comput. Math. 16, 99 (2002).
[CrossRef]

Botten, L. C.

S. Wilcox, L. C. Botten, R. C. McPhedran, C. G. Poulton, and C. M. Sterke, Phys. Rev. E 71056606 (2005).
[CrossRef]

Brebbia, C.

C. Brebbia, The Boundary Element Method for Engineers (Pentech, 1978).

Hattori, K.

K. Hattori and J. Nakayama, IEICE Trans. Electron. E90-C, 312 (2007).
[CrossRef]

Koshiba, M.

Lalanne, P.

Leviatan, Y.

McPhedran, R. C.

S. Wilcox, L. C. Botten, R. C. McPhedran, C. G. Poulton, and C. M. Sterke, Phys. Rev. E 71056606 (2005).
[CrossRef]

Morita, N.

N. Morita, IEEE Trans. Antennas Propag. 26, 261 (1978).
[CrossRef]

Nakata, Y.

Nakayama, J.

K. Hattori and J. Nakayama, IEICE Trans. Electron. E90-C, 312 (2007).
[CrossRef]

Poulton, C. G.

S. Wilcox, L. C. Botten, R. C. McPhedran, C. G. Poulton, and C. M. Sterke, Phys. Rev. E 71056606 (2005).
[CrossRef]

Silberstein, E.

Sterke, C. M.

S. Wilcox, L. C. Botten, R. C. McPhedran, C. G. Poulton, and C. M. Sterke, Phys. Rev. E 71056606 (2005).
[CrossRef]

Tanaka, K.

Tanaka, M.

Trotskovsky, K.

Wilcox, S.

S. Wilcox, L. C. Botten, R. C. McPhedran, C. G. Poulton, and C. M. Sterke, Phys. Rev. E 71056606 (2005).
[CrossRef]

Adv. Comput. Math. (1)

H. Ammari and G. Bao, Adv. Comput. Math. 16, 99 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

N. Morita, IEEE Trans. Antennas Propag. 26, 261 (1978).
[CrossRef]

IEICE Trans. Electron. (1)

K. Hattori and J. Nakayama, IEICE Trans. Electron. E90-C, 312 (2007).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Lett. (1)

Phys. Rev. E (1)

S. Wilcox, L. C. Botten, R. C. McPhedran, C. G. Poulton, and C. M. Sterke, Phys. Rev. E 71056606 (2005).
[CrossRef]

Other (1)

C. Brebbia, The Boundary Element Method for Engineers (Pentech, 1978).

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Figures (5)

Fig. 1.
Fig. 1.

Cross-sectional geometry of a defective grating. The period of the grating T=4λ, w=0.5T, h=0.2T, and r=0.15T. The refractive indices inside and outside the grating are 2.5 and 1.0 (lossless dielectrics).

Fig. 2.
Fig. 2.

Integral paths of DFBEM. C0, surface of groove pattern. C1, boundary between the grating and the defect. C2, surface of the defect. An arbitrary shape can be set for C2.

Fig. 3.
Fig. 3.

(a) Base field (field for nondefective grating). (b) Difference field (difference in the field between nondefective and defective grating cases). (c) Total field [field of the defective grating obtained by addition of (a) and (b)]. Since the incident wave is p polarization, these are the z components of magnetic fields.

Fig. 4.
Fig. 4.

Far-field distribution calculated by DFBEM. Vertical arrows are base-field components. The solid curve is the differential field components. These units are not unified.

Fig. 5.
Fig. 5.

Convergence of field at P in Fig. 1. The lateral axis is the length of the discretized region. In the calculation of relative error, the true value (intensity at L=) was estimated by exponential fitting of the data in 1L29.

Equations (3)

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ft(ρ)=C0[G1(ρ;ρ)ft(ρ)nft(ρ)G1(ρ;ρ)n]dl+C1[G1(ρ;ρ)ft(ρ)nft(ρ)G1(ρ;ρ)n]dl,
ft(ρ)+fs1(ρ)=C0[G1(ρ;ρ)[ft(ρ)+fs1(ρ)]n[ft(ρ)+fs1(ρ)]G1(ρ;ρ)n]dl+C2[G1(ρ;ρ)[ft(ρ)+fs1(ρ)]n[ft(ρ)+fs1(ρ)]G1(ρ;ρ)n]dl.
fs1(ρ)=C0[G1(ρ;ρ)fs1(ρ)nfs1(ρ)G1(ρ;ρ)n]dl+C2[G1(ρ;ρ)[ft(ρ)+fs1(ρ)]n[ft(ρ)+fs1(ρ)]G1(ρ;ρ)n]dlC1[G1(ρ;ρ)ft(ρ)nft(ρ)G1(ρ;ρ)n]dl.

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