Abstract

We demonstrate the accuracy of the finite-element method to calculate the diffraction efficiencies of an arbitrarily shaped crossed grating in a multilayered stack illuminated by an arbitrarily polarized plane wave under oblique incidence. The method has been validated by using classical cases found in the literature. Finally, to illustrate the independence of our method with respect to the shape of the diffractive object, we present the global energy balance resulting from the diffraction of a plane wave by a lossy thin torus crossed grating.

© 2009 Optical Society of America

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2008

Y. Ould Agha, F. Zolla, A. Nicolet, and S. Guenneau, Compel 27, 95 (2008).
[CrossRef]

2007

2004

A. Nicolet, S. Guenneau, C. Geuzaine and F. Zolla, J. Comput. Appl. Math. 168, 321 (2004).
[CrossRef]

1998

1997

L. Li, J. Opt. Soc. Am. A 14, 2758 (1997).
[CrossRef]

T. V. Yioultsis and T. D. Tsiboukis, IEEE Trans. Magn. 33, 1812 (1997).
[CrossRef]

1995

P. Dular, A. Nicolet, A. Genon, and W. Legros, IEEE Trans. Magn. 31, 1356 (1995).
[CrossRef]

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 1068 (1995).
[CrossRef]

1994

R. Petit and F. Zolla, J. Electromagn. Waves Appl. 8, 1 (1994).
[CrossRef]

1993

R. Bräuer and O. Bryngdahl, Opt. Commun. 100, 1 (1993).
[CrossRef]

O. P. Bruno and F. Reitich, J. Opt. Soc. Am. A 10, 2551 (1993).
[CrossRef]

1992

1979

G. H. Derrick, R. C. McPhedran, D. Maystre, and M. Nevière, Appl. Phys. B 18, 39 (1979).
[CrossRef]

1978

D. Maystre and M. Nevière, J. Opt. (Paris) 9, 301 (1978).

Baylard, C.

Bräuer, R.

R. Bräuer and O. Bryngdahl, Opt. Commun. 100, 1 (1993).
[CrossRef]

Bruno, O. P.

Bryngdahl, O.

R. Bräuer and O. Bryngdahl, Opt. Commun. 100, 1 (1993).
[CrossRef]

Commandré, M.

Demésy, G.

Derrick, G. H.

G. H. Derrick, R. C. McPhedran, D. Maystre, and M. Nevière, Appl. Phys. B 18, 39 (1979).
[CrossRef]

Dular, P.

P. Dular, A. Nicolet, A. Genon, and W. Legros, IEEE Trans. Magn. 31, 1356 (1995).
[CrossRef]

Fossati, C.

Gaylord, T. K.

Genon, A.

P. Dular, A. Nicolet, A. Genon, and W. Legros, IEEE Trans. Magn. 31, 1356 (1995).
[CrossRef]

Geuzaine, C.

A. Nicolet, S. Guenneau, C. Geuzaine and F. Zolla, J. Comput. Appl. Math. 168, 321 (2004).
[CrossRef]

Granet, G.

Grann, E. B.

Greffet, J. J.

Guenneau, S.

Y. Ould Agha, F. Zolla, A. Nicolet, and S. Guenneau, Compel 27, 95 (2008).
[CrossRef]

A. Nicolet, S. Guenneau, C. Geuzaine and F. Zolla, J. Comput. Appl. Math. 168, 321 (2004).
[CrossRef]

Kerwien, N.

Legros, W.

P. Dular, A. Nicolet, A. Genon, and W. Legros, IEEE Trans. Magn. 31, 1356 (1995).
[CrossRef]

Li, L.

Maystre, D.

G. H. Derrick, R. C. McPhedran, D. Maystre, and M. Nevière, Appl. Phys. B 18, 39 (1979).
[CrossRef]

D. Maystre and M. Nevière, J. Opt. (Paris) 9, 301 (1978).

McPhedran, R. C.

G. H. Derrick, R. C. McPhedran, D. Maystre, and M. Nevière, Appl. Phys. B 18, 39 (1979).
[CrossRef]

Moharam, M. G.

Nevière, M.

G. H. Derrick, R. C. McPhedran, D. Maystre, and M. Nevière, Appl. Phys. B 18, 39 (1979).
[CrossRef]

D. Maystre and M. Nevière, J. Opt. (Paris) 9, 301 (1978).

Nicolet, A.

Y. Ould Agha, F. Zolla, A. Nicolet, and S. Guenneau, Compel 27, 95 (2008).
[CrossRef]

G. Demésy, F. Zolla, A. Nicolet, M. Commandré, and C. Fossati, Opt. Express 15, 18089 (2007).
[CrossRef] [PubMed]

A. Nicolet, S. Guenneau, C. Geuzaine and F. Zolla, J. Comput. Appl. Math. 168, 321 (2004).
[CrossRef]

P. Dular, A. Nicolet, A. Genon, and W. Legros, IEEE Trans. Magn. 31, 1356 (1995).
[CrossRef]

Osten, W.

Ould Agha, Y.

Y. Ould Agha, F. Zolla, A. Nicolet, and S. Guenneau, Compel 27, 95 (2008).
[CrossRef]

Petit, R.

R. Petit and F. Zolla, J. Electromagn. Waves Appl. 8, 1 (1994).
[CrossRef]

Pommet, D. A.

Rafler, S.

Reitich, F.

Ruoff, J.

Schuster, T.

Tsiboukis, T. D.

T. V. Yioultsis and T. D. Tsiboukis, IEEE Trans. Magn. 33, 1812 (1997).
[CrossRef]

Urbach, H. P.

Versaevel, P.

Wachters, A. J.

Wei, X.

Yioultsis, T. V.

T. V. Yioultsis and T. D. Tsiboukis, IEEE Trans. Magn. 33, 1812 (1997).
[CrossRef]

Zolla, F.

Y. Ould Agha, F. Zolla, A. Nicolet, and S. Guenneau, Compel 27, 95 (2008).
[CrossRef]

G. Demésy, F. Zolla, A. Nicolet, M. Commandré, and C. Fossati, Opt. Express 15, 18089 (2007).
[CrossRef] [PubMed]

A. Nicolet, S. Guenneau, C. Geuzaine and F. Zolla, J. Comput. Appl. Math. 168, 321 (2004).
[CrossRef]

R. Petit and F. Zolla, J. Electromagn. Waves Appl. 8, 1 (1994).
[CrossRef]

Appl. Phys. B

G. H. Derrick, R. C. McPhedran, D. Maystre, and M. Nevière, Appl. Phys. B 18, 39 (1979).
[CrossRef]

Compel

Y. Ould Agha, F. Zolla, A. Nicolet, and S. Guenneau, Compel 27, 95 (2008).
[CrossRef]

IEEE Trans. Magn.

T. V. Yioultsis and T. D. Tsiboukis, IEEE Trans. Magn. 33, 1812 (1997).
[CrossRef]

P. Dular, A. Nicolet, A. Genon, and W. Legros, IEEE Trans. Magn. 31, 1356 (1995).
[CrossRef]

J. Comput. Appl. Math.

A. Nicolet, S. Guenneau, C. Geuzaine and F. Zolla, J. Comput. Appl. Math. 168, 321 (2004).
[CrossRef]

J. Electromagn. Waves Appl.

R. Petit and F. Zolla, J. Electromagn. Waves Appl. 8, 1 (1994).
[CrossRef]

J. Opt. (Paris)

D. Maystre and M. Nevière, J. Opt. (Paris) 9, 301 (1978).

J. Opt. Soc. Am. A

Opt. Commun.

R. Bräuer and O. Bryngdahl, Opt. Commun. 100, 1 (1993).
[CrossRef]

Opt. Express

Opt. Lett.

Other

G. Demésy, Ph.D. thesis (Université Aix-Marseille, 2009).

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Figures (2)

Fig. 1
Fig. 1

Setup of the problem and notation.

Fig. 2
Fig. 2

Set of diffractive patterns studied in this Letter: (a) lossless pyramid, (b) circular aperture in a lossy layer, (c) lossy torus.

Tables (2)

Tables Icon

Table 1 Diffraction Efficiencies for the Pyramidal Grating

Tables Icon

Table 2 Energy Balance of the Problem (Fig. 2)

Equations (8)

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A 0 = ( cos Ψ cos θ cos ϕ sin Ψ sin ϕ ) x + ( cos Ψ cos θ sin ϕ + sin Ψ cos ϕ ) y ( cos Ψ sin θ ) z ) ,
M ε r , μ r ( E ) curl ( μ r 1 curl E ) + k 0 2 ε r E = 0 ,
ξ r ( x , y , z ) { ξ + for z > h ξ g ( x , y , z ) for h > z > 0 ξ for z < 0 } ,
ξ 1 ( x , y , z ) { ξ + for z > 0 ξ for z < 0 } ,
E 0 0 ( x , y , z ) { E 0 for z > h 0 for z < h } .
M ε 1 , μ 1 ( E 1 ) = 0
M ε r , μ r ( E 2 d ) = M ε r , μ r ( E 1 ) = M ε r ε 1 , μ r μ 1 ( E 1 ) ,
n = 1 + 1 m = 1 + 1 R n , m + n = 2 + 2 m = 2 + 2 T n , m + Q = R + T + Q = 0.26761 + 0.29110 + 0.44148 = 1.00019 .

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