Abstract

Enhanced transmission through subwavelength slit gratings and hole arrays is studied in view of its application in the far-infrared and microwave domains. Because for perfectly conducting gratings, plasmon resonances are not expected to produce an enhanced transmission, other kinds of resonance, such as Fabry-Perot, waveguide-mode, and cavity-mode resonances, are studied. The possibility of reaching 100% transmittivity for some particular wavelengths is established when two superimposed identical gratings are used while each of them transmits approximately 1% off resonance. A similar transmission is obtained with hole arrays. The study of the field map inside the groove region allows our establishing the nature of the resonance, that is involved. Comparison of the bandwidth with respect to the wavelength or incidence given by various kinds of resonance is presented.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. Z. Bomzon, V. Kleiner, E. Hasman, “Computer-generated space-variant polarization elements with subwavelength metal stripes,” Opt. Lett. 26, 33–35 (2001).
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    [CrossRef]
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  12. A. P. Hibbins, J. R. Sambles, C. R. Lawrence, D. M. Robinson, “Remarkable transmission of microwaves through a wall of long metallic bricks,” Appl. Phys. Lett. 79, 2844–2846 (2001).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. M. Nevière, E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, New York, 2003).
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    [CrossRef]

2003 (2)

N. Bonod, S. Enoch, L. Li, E. Popov, M. Neviere, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11, 482–490 (2003), http://www.opticsexpress.org .
[CrossRef] [PubMed]

B. Gralak, M. De Dood, G. Tayeb, S. Enoch, D. Maystre, “Theoretical study of photonic bandgaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

2002 (1)

S. Enoch, E. Popov, M. Neviére, R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A Pure Appl. Opt. 4, S83–S87 (2002).
[CrossRef]

2001 (4)

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, D. M. Robinson, “Remarkable transmission of microwaves through a wall of long metallic bricks,” Appl. Phys. Lett. 79, 2844–2846 (2001).
[CrossRef]

Z. Bomzon, V. Kleiner, E. Hasman, “Computer-generated space-variant polarization elements with subwavelength metal stripes,” Opt. Lett. 26, 33–35 (2001).
[CrossRef]

N. Bokor, R. Shechter, N. Davidson, A. Frieseman, E. Hasman, “Achromatic phase retarder by slanted illumination of a dielectric grating with period comparable with the wavelength,” App. Opt. 40, 2076–2080 (2001).
[CrossRef]

E. Popov, M. Nevière, “Maxwell equations in Fourier space: fast converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886–2894 (2001).
[CrossRef]

1999 (2)

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, “The coupling of microwave radiation to surface plasmon polaritons and guided modes via dielectric gratings,” J. Appl. Phys. 87, 2677–2683 (1999).
[CrossRef]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, “Grating-coupled surface plasmons at microwave frequency,” J. Appl. Phys. 86, 1791–1795 (1999).
[CrossRef]

1998 (2)

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

1997 (1)

1996 (1)

1986 (2)

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986).
[CrossRef]

1985 (1)

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated grating,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

1981 (1)

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

1978 (1)

K. Knop, “Reflection grating polarizer for the infrared,” Opt. Commun. 26, 281–283 (1978).
[CrossRef]

1941 (1)

1902 (1)

R. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).

Adams, J. L.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Andrewartha, J. R.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Biswas, R.

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

Bokor, N.

N. Bokor, R. Shechter, N. Davidson, A. Frieseman, E. Hasman, “Achromatic phase retarder by slanted illumination of a dielectric grating with period comparable with the wavelength,” App. Opt. 40, 2076–2080 (2001).
[CrossRef]

Bomzon, Z.

Bonod, N.

Botten, I. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Botten, L. C.

R. C. McPhedran, G. H. Derrick, L. C. Botten, “Theory of crossed grating,” in Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics, R. Petit, ed. (Springer-Verlag, Berlin, 1980), p. 249.

Bouchitté, G.

R. Petit, G. Bouchitté, “Replacement of a very fine grating by a stratified layer, homogenization techniques, and multiple-scale method theory,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moiré Phenomena 431, J. Lerner, ed., Proc. SPIE815, 25–31 (1988).
[CrossRef]

Bur, J.

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

Craig, M. S.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Davidson, N.

N. Bokor, R. Shechter, N. Davidson, A. Frieseman, E. Hasman, “Achromatic phase retarder by slanted illumination of a dielectric grating with period comparable with the wavelength,” App. Opt. 40, 2076–2080 (2001).
[CrossRef]

De Dood, M.

B. Gralak, M. De Dood, G. Tayeb, S. Enoch, D. Maystre, “Theoretical study of photonic bandgaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

Derrick, G. H.

R. C. McPhedran, G. H. Derrick, L. C. Botten, “Theory of crossed grating,” in Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics, R. Petit, ed. (Springer-Verlag, Berlin, 1980), p. 249.

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Enoch, S.

N. Bonod, S. Enoch, L. Li, E. Popov, M. Neviere, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11, 482–490 (2003), http://www.opticsexpress.org .
[CrossRef] [PubMed]

B. Gralak, M. De Dood, G. Tayeb, S. Enoch, D. Maystre, “Theoretical study of photonic bandgaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

S. Enoch, E. Popov, M. Neviére, R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A Pure Appl. Opt. 4, S83–S87 (2002).
[CrossRef]

Fano, U.

Flemming, J. G.

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

Frieseman, A.

N. Bokor, R. Shechter, N. Davidson, A. Frieseman, E. Hasman, “Achromatic phase retarder by slanted illumination of a dielectric grating with period comparable with the wavelength,” App. Opt. 40, 2076–2080 (2001).
[CrossRef]

Gaylord, T. K.

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Gralak, B.

B. Gralak, M. De Dood, G. Tayeb, S. Enoch, D. Maystre, “Theoretical study of photonic bandgaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

Hasman, E.

N. Bokor, R. Shechter, N. Davidson, A. Frieseman, E. Hasman, “Achromatic phase retarder by slanted illumination of a dielectric grating with period comparable with the wavelength,” App. Opt. 40, 2076–2080 (2001).
[CrossRef]

Z. Bomzon, V. Kleiner, E. Hasman, “Computer-generated space-variant polarization elements with subwavelength metal stripes,” Opt. Lett. 26, 33–35 (2001).
[CrossRef]

Hetherington, D. L.

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

Hibbins, A. P.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, D. M. Robinson, “Remarkable transmission of microwaves through a wall of long metallic bricks,” Appl. Phys. Lett. 79, 2844–2846 (2001).
[CrossRef]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, “The coupling of microwave radiation to surface plasmon polaritons and guided modes via dielectric gratings,” J. Appl. Phys. 87, 2677–2683 (1999).
[CrossRef]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, “Grating-coupled surface plasmons at microwave frequency,” J. Appl. Phys. 86, 1791–1795 (1999).
[CrossRef]

Ho, K. M.

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

Kleiner, V.

Knop, K.

K. Knop, “Reflection grating polarizer for the infrared,” Opt. Commun. 26, 281–283 (1978).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Theory of dielectric waveguides,” in Integrated Optics, T. Tamir, ed. (Springer, Berlin, 1975), Chap. 2.
[CrossRef]

Kurtz, S. R.

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

Lawrence, C. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, D. M. Robinson, “Remarkable transmission of microwaves through a wall of long metallic bricks,” Appl. Phys. Lett. 79, 2844–2846 (2001).
[CrossRef]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, “Grating-coupled surface plasmons at microwave frequency,” J. Appl. Phys. 86, 1791–1795 (1999).
[CrossRef]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, “The coupling of microwave radiation to surface plasmon polaritons and guided modes via dielectric gratings,” J. Appl. Phys. 87, 2677–2683 (1999).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Li, L.

Lin, S. Y.

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

Mashev, L.

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated grating,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Maystre, D.

B. Gralak, M. De Dood, G. Tayeb, S. Enoch, D. Maystre, “Theoretical study of photonic bandgaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

McPhedran, R. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

R. C. McPhedran, G. H. Derrick, L. C. Botten, “Theory of crossed grating,” in Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics, R. Petit, ed. (Springer-Verlag, Berlin, 1980), p. 249.

Moharam, M. G.

Neviere, M.

Neviére, M.

S. Enoch, E. Popov, M. Neviére, R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A Pure Appl. Opt. 4, S83–S87 (2002).
[CrossRef]

Nevière, M.

Petit, R.

R. Petit, G. Bouchitté, “Replacement of a very fine grating by a stratified layer, homogenization techniques, and multiple-scale method theory,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moiré Phenomena 431, J. Lerner, ed., Proc. SPIE815, 25–31 (1988).
[CrossRef]

R. Petit, “A tutorial introduction,” in Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics, R. Petit, ed. (Springer-Verlag, Berlin, 1980), p. 12.

Popov, E.

N. Bonod, S. Enoch, L. Li, E. Popov, M. Neviere, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11, 482–490 (2003), http://www.opticsexpress.org .
[CrossRef] [PubMed]

S. Enoch, E. Popov, M. Neviére, R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A Pure Appl. Opt. 4, S83–S87 (2002).
[CrossRef]

E. Popov, M. Nevière, “Maxwell equations in Fourier space: fast converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886–2894 (2001).
[CrossRef]

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated grating,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

M. Nevière, E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, New York, 2003).

Reinisch, R.

S. Enoch, E. Popov, M. Neviére, R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A Pure Appl. Opt. 4, S83–S87 (2002).
[CrossRef]

Robinson, D. M.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, D. M. Robinson, “Remarkable transmission of microwaves through a wall of long metallic bricks,” Appl. Phys. Lett. 79, 2844–2846 (2001).
[CrossRef]

Sambles, J. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, D. M. Robinson, “Remarkable transmission of microwaves through a wall of long metallic bricks,” Appl. Phys. Lett. 79, 2844–2846 (2001).
[CrossRef]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, “The coupling of microwave radiation to surface plasmon polaritons and guided modes via dielectric gratings,” J. Appl. Phys. 87, 2677–2683 (1999).
[CrossRef]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, “Grating-coupled surface plasmons at microwave frequency,” J. Appl. Phys. 86, 1791–1795 (1999).
[CrossRef]

Shechter, R.

N. Bokor, R. Shechter, N. Davidson, A. Frieseman, E. Hasman, “Achromatic phase retarder by slanted illumination of a dielectric grating with period comparable with the wavelength,” App. Opt. 40, 2076–2080 (2001).
[CrossRef]

Sigalas, M. M.

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

Smith, B. K.

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

Tayeb, G.

B. Gralak, M. De Dood, G. Tayeb, S. Enoch, D. Maystre, “Theoretical study of photonic bandgaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Wood, R.

R. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).

Zubrzycki, W.

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

App. Opt. (1)

N. Bokor, R. Shechter, N. Davidson, A. Frieseman, E. Hasman, “Achromatic phase retarder by slanted illumination of a dielectric grating with period comparable with the wavelength,” App. Opt. 40, 2076–2080 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, D. M. Robinson, “Remarkable transmission of microwaves through a wall of long metallic bricks,” Appl. Phys. Lett. 79, 2844–2846 (2001).
[CrossRef]

J. Appl. Phys. (2)

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, “Grating-coupled surface plasmons at microwave frequency,” J. Appl. Phys. 86, 1791–1795 (1999).
[CrossRef]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, “The coupling of microwave radiation to surface plasmon polaritons and guided modes via dielectric gratings,” J. Appl. Phys. 87, 2677–2683 (1999).
[CrossRef]

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

S. Enoch, E. Popov, M. Neviére, R. Reinisch, “Enhanced light transmission by hole arrays,” J. Opt. A Pure Appl. Opt. 4, S83–S87 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Nature (2)

S. Y. Lin, J. G. Flemming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelength,” Nature 394, 251–253 (1998).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Opt. Acta (2)

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Opt. Commun. (2)

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated grating,” Opt. Commun. 55, 377–380 (1985).
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K. Knop, “Reflection grating polarizer for the infrared,” Opt. Commun. 26, 281–283 (1978).
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Opt. Express (1)

Opt. Lett. (1)

Philos. Mag. (1)

R. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4, 396–402 (1902).

Phys. Rev. E (1)

B. Gralak, M. De Dood, G. Tayeb, S. Enoch, D. Maystre, “Theoretical study of photonic bandgaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003).
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Other (5)

R. Petit, “A tutorial introduction,” in Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics, R. Petit, ed. (Springer-Verlag, Berlin, 1980), p. 12.

M. Nevière, E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, New York, 2003).

H. Kogelnik, “Theory of dielectric waveguides,” in Integrated Optics, T. Tamir, ed. (Springer, Berlin, 1975), Chap. 2.
[CrossRef]

R. Petit, G. Bouchitté, “Replacement of a very fine grating by a stratified layer, homogenization techniques, and multiple-scale method theory,” in Application and Theory of Periodic Structures, Diffraction Gratings, and Moiré Phenomena 431, J. Lerner, ed., Proc. SPIE815, 25–31 (1988).
[CrossRef]

R. C. McPhedran, G. H. Derrick, L. C. Botten, “Theory of crossed grating,” in Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics, R. Petit, ed. (Springer-Verlag, Berlin, 1980), p. 249.

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Figures (19)

Fig. 1
Fig. 1

Schematic representation of a double-grating structure consisting of two identical grid gratings.

Fig. 2
Fig. 2

(a) Transmission through a single or a double-grating structure. d = 1, c = 0.5, t = 0.5, lamellae thickness is 0.5, and refractive index n L = i250; all units are in centimeters. (b) Transmission through a single grating in TE or TM polarization [same parameters as in (a)].

Fig. 3
Fig. 3

Schematic representation of two types of a one-dimensional slit grating: (a) a double grating with a continuous dielectric layer in the middle, called the grating-waveguide configuration, and (b) a grating-cavity configuration.

Fig. 4
Fig. 4

Transmission as a function of the lamellae width (c) and middle-layer thickness (t) in centimeters for the grating represented in Fig. 3(a).

Fig. 5
Fig. 5

Electric field maps corresponding to different working points of Fig. 4: (a) point 1a with c = 0.02, (b) point 2a with c = 0.2, and (c) point 1b with c = 0.7.

Fig. 6
Fig. 6

Electric field maps corresponding to different working points along curve 3 of Fig. 4: (a) point 3a with c = 0.02, (b) point 3b with c = 0.1, (c) point 3c with c = 0.3, and (d) point 3d with c = 0.7.

Fig. 7
Fig. 7

Transmission as a function of the lamellae width (c) and middle-layer thickness (t) in centimeters for the grating represented in Fig. 3(b).

Fig. 8
Fig. 8

Electric field maps corresponding to the working point 1B of Fig. 7.

Fig. 9
Fig. 9

Electric field maps corresponding to different working points along curves 3 and 4 of Fig. 7: (a) point 3A, (b) point 3B, and (c) point 4B.

Fig. 10
Fig. 10

Transmission corresponding to working points 1b of Fig. 4 and 1B of Fig. 7: (a) as a function of the wavelength and (b) as a function of the angle of incidence.

Fig. 11
Fig. 11

Transmission corresponding to the working point 3d of Fig. 4: (a) as a function of the wavelength and (b) as a function of the angle of incidence.

Fig. 12
Fig. 12

Spectral (12a) and angular (12b) dependences of transmission at the working point 4B of Fig. 7.

Fig. 13
Fig. 13

Comparison of the influence of the period between the cavity modes and the waveguide modes. (a) Schematic representations of the cavity-type grating. (b) Influence of the period d of the cavity-type grating on the transmission as a function of the wavelength. (c) Influence of the period d of the one-dimensional double grating on the transmission as a function of the wavelength.

Fig. 14
Fig. 14

Schematic representation of the woodpile gratings. The parameters are period d = 1 cm, c = 0.7 cm, t = 0.715 cm, t 1 = 0.1 cm, the optical index of the metal is n m = i 104, and the structure is lying in vacuum.

Fig. 15
Fig. 15

Transmission of the woodpile grating of Fig. 14 in normal incidence.

Fig. 16
Fig. 16

Schematic representation of the biperiodic gratings. (a) Perspective view of the double grating with a continuous dielectric layer in the middle. (b) Section of the unit cell (along any of the periodicity axes) of the double grating with a continuous dielectric layer in the middle (slab type). (c) Section of the unit cell (along any of the periodicity axes) of the cavity-type grating. The parameters are d = 1 cm, c = 0.5 cm, t = 0.22 cm, t 1 = 0.1 cm, w = 0.9 cm, n 2 = 3.47, the optical index of the metal is n m = i 250, and the structure is lying in vacuum.

Fig. 17
Fig. 17

Transmission of the slab-type grating [Fig. 16(b)] in normal incidence.

Fig. 18
Fig. 18

Transmission of the cavity-type grating [Fig. 16(c)] in normal incidence.

Fig. 19
Fig. 19

Transmission of the slab-type grating [Fig. 16(b)] for λ = 1.4968 cm (solid curve) and of the cavity-type grating [Fig. 16(c)] for λ = 1.4802 cm (dashed curve).

Tables (1)

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Table 1 Values of the Resonant Thickness of the Dielectric Layer Corresponding to Curve 3 of Fig. 4 When nLc → 0

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

2πn2λ2-p2πd2=mπt2.
2πλ n2t=π,
2πλ n2t=2π,
2πλn22-λd21/2t=π.
sin θi=γgλ2π±λd.

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