Abstract

We show that the difference in the effective medium properties of perfectly or finitely conducting short-period gratings is because for finitely conducting gratings it is possible to completely homogenize the electromagnetic field vector components, contrary to perfectly conducting gratings. As a consequence, for aluminum in the microwave domain, two possible effective media can be found, depending on whether the feature dimensions are much larger or shorter than the depth of field penetration inside the metal.

© 2007 Optical Society of America

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References

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2007 (1)

T. Mackay, J. Nanophotonics 1, 019501 (2007).
[CrossRef]

2005 (1)

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, J. Opt. A, Pure Appl. Opt. 7, S97 (2005).
[CrossRef]

2004 (1)

T. Mackay and A. Lakhtakia, Opt. Commun. 234, 35 (2004).
[CrossRef]

1997 (1)

1985 (1)

G. Bouchitte and R. Petit, Electromagnetics 5, 17 (1985).
[CrossRef]

1982 (2)

M. G. Moharam and T. K. Gaylord, J. Opt. Soc. Am. 72, 1385 (1982).
[CrossRef]

R. McPhedran, L. Botten, M. Craig, M. Nevière, and D. Maystre, Opt. Acta 29, 289 (1982).
[CrossRef]

1981 (2)

C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, Opt. Acta 28, 1087 (1981).
[CrossRef]

1978 (1)

P. Yeh, Opt. Commun. 26, 289 (1978).
[CrossRef]

1977 (1)

1904 (1)

J. C. Maxwell-Garnet, Philos. Trans. R. Soc. London, Ser. A 203, 385 (1904).
[CrossRef]

Electromagnetics (1)

G. Bouchitte and R. Petit, Electromagnetics 5, 17 (1985).
[CrossRef]

J. Nanophotonics (1)

T. Mackay, J. Nanophotonics 1, 019501 (2007).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, J. Opt. A, Pure Appl. Opt. 7, S97 (2005).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Opt. Acta (3)

C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, Opt. Acta 28, 1087 (1981).
[CrossRef]

R. McPhedran, L. Botten, M. Craig, M. Nevière, and D. Maystre, Opt. Acta 29, 289 (1982).
[CrossRef]

Opt. Commun. (2)

T. Mackay and A. Lakhtakia, Opt. Commun. 234, 35 (2004).
[CrossRef]

P. Yeh, Opt. Commun. 26, 289 (1978).
[CrossRef]

Philos. Trans. R. Soc. London, Ser. A (1)

J. C. Maxwell-Garnet, Philos. Trans. R. Soc. London, Ser. A 203, 385 (1904).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Reflectivity as a function of the period for three different lamellae materials, p.c., aluminum in the MW, and in the visible. Substrate, cladding, and grooves are air, and the grating height is h = λ 4 . Normal incidence is in TM polarization. Labeled points are analyzed in Fig. 2. Empty circle represents the reflectivity level of a homogeneous layer of the same thickness with anisotropic permittivity ( ε ¯ x = 2 , ε ¯ y = ε ¯ z = ) and anisotropic permittivity ( μ ¯ x = 1 , μ ¯ y = μ ¯ z = 1 2 ) . The full circle represents the homogeneous layer with anisotropic permittivity and isotropic permeability ( μ ¯ x = μ ¯ y = μ ¯ z = 1 ) . The inset represents schematically the diffraction grating.

Fig. 2
Fig. 2

X dependence of the z component of the magnetic field for three different groove periods, labeled in Fig. 1, calculated at the middle height of the lamellae ( y = h 2 ) .

Fig. 3
Fig. 3

Variation of the normalized plasmon surface wave propagation constant k p k 0 as a function of the period-to-wavelength ratio d λ for a lamellar grating with metallic substrate, and groove depth h = λ 6 . Dashed line, perfect conductivity; dotted curve, real part of k p k 0 for aluminum grating in the MW ( ε 2 = 10 5 + i 10 7 ) ; solid curve, its imaginary part.

Equations (3)

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ε ¯ x = ε 1 ε 2 f 1 ε 2 + f 2 ε 1 ε 2 ε 1 f 1 .
μ ¯ z = μ 1 .
μ ¯ z , p.c. = f 1 μ 1 .

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