Abstract

Extremely shallow lamellar metallic gratings are shown to totally absorb incident light inside a wide angular interval. The full absorption still holds at the homogeneization limit when the period tends toward zero. It is shown that a lamellar grating, illuminated in normal incidence and in transerve magnetic polarization with a period lower than 1/, of the vacuum wavelength behaves like a dielectric one with a high refractive index. The full absorption is then not due to the excitation of surface plasmon but either to Fabry-Perot resonance or Brewster effect, depending on the corrugated layer thickness.

© 2009 Optical Society of America

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  1. R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phylos. Mag. 4, 396-402 (1902).
  2. U. Fano, "The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld’s waves)," J. Opt. Soc. Am. 31, 213-222 (1941).
    [CrossRef]
  3. D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, "Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering," Phys. Rev. Lett. 45, 355-358 (1980).
    [CrossRef]
  4. R. Reinisch and M. Nevière, "Electromagnetic theory of diffraction in nonlinear optics and surface-enhanced nonlinear optical effects," Phys. Rev. B 28, 1870-1885 (1983).
    [CrossRef]
  5. W. L. Barnes, A. Dereux, T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-829 (2003).
    [CrossRef] [PubMed]
  6. M. C. Hutley and D. Maystre, "Total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976).
    [CrossRef]
  7. M. Nevière, D. Maystre, R. C. McPhedran, G. H. Derrick and M. C. Hutley, "On the total absorption of unpolarized monochromatic light," Proceedings of the ICO-11 Conference, Madrid, Spain, pp. 609-612 (1978).
  8. E. Popov, D. Maystre, R. C. McPhedran, M. Nevière, M. C. Hutley, and G. H. Derrick, "Total absorption of unpolarized light by crossed gratings," Opt. Express 16, 6146-6155 (2008).
    [CrossRef] [PubMed]
  9. E. Popov, S. Enoch, G. Tayeb, M. Nevière, B. Gralak, and N. Bonod, "Enhanced transmission due to non-plasmon resonances in one and two dimensional gratings," Appl. Opt. 43, 999-1008 (2004).
    [CrossRef] [PubMed]
  10. T. V. Teperik, F. J. García De Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, "Omnidirectional absorption in nanostuctured metal surfaces," Nat. Photonics 2, 299-301 (2008).
    [CrossRef]
  11. N. Bonod and E. Popov, "Total light absorption in a wide range of incidence by nanostructured metals without plasmons," Opt. Lett. 33, 2398-2400 (2008).
    [CrossRef] [PubMed]
  12. P. M. Ajayan, "Experimental observation of an extremely dark material made by a low-density nanotube array," Nano. Lett. 8, 446 (2008).
    [CrossRef] [PubMed]
  13. V. G. Kravets, F. Schedin, and A. N. Grigorenko, "Plasmonic blackbody: Almost complete absorption of light in nanostructured metallic coatings," Phys. Rev. B 78, 205405 (2008).
    [CrossRef]
  14. J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Rios, "Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light," Phys. Rev. Lett. 100, 066408 (2008).
    [CrossRef] [PubMed]
  15. S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
    [CrossRef]
  16. E. I. Krupitsky and B. C. Chernov, "Rigorous analysis of arbitrary slanted volume holographic gratings," (in Russian), Proc. IX All-Union School of Holography, Leningrad, 1977, pp 84-95.
  17. M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982).
    [CrossRef]
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    [CrossRef]
  19. G. Granet and B. Guizal, "Efficient implementation of the coupled-wave method for metallic gratings in TM polarization," J. Opt. Soc. Am. A 13, 1019-1023 (1996).
    [CrossRef]
  20. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).
    [CrossRef]
  21. M. Nevère and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, New York, 2003).
  22. E. D. Palik, ed. Handbook of Optical Constants of Solids (Academic Press, 1985)
  23. http://www.luxpop.com/
  24. R. C. McPhedran, L. C. Botten, M. Craig, M. Nevière, and D. Maystre, "Lossy lamellar gratings in the quasistatic limit," Opt. Acta 29, 289-312 (1982).
    [CrossRef]
  25. G. Bouchitte and R. Petit, "Homogenization techniques as applied in the electromagnetic theory of gratings," Electromagnetics 5, 17-36 (1985).
    [CrossRef]
  26. E. Popov and S. Enoch, "Mystery of the double limit in homogenisation of finitely or perfectly conducting periodic structures," Opt. Lett. 32, 3441-3443 (2007).
    [CrossRef] [PubMed]
  27. J. C. Maxwell-Garnet, "Colors in metal glasses and in metallic films," Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904).
    [CrossRef]
  28. A. D. Yaghjian, "Electric dyadic Green's functions in the source region," Proc. IEEE 68, 248-263, (1980).
    [CrossRef]
  29. M. Nevière, "The homogeneous problem," in Electromagnetic theory of gratings, R. Petit, ed., (Springer-Verlag, 1980), Chap. 5.

2008

E. Popov, D. Maystre, R. C. McPhedran, M. Nevière, M. C. Hutley, and G. H. Derrick, "Total absorption of unpolarized light by crossed gratings," Opt. Express 16, 6146-6155 (2008).
[CrossRef] [PubMed]

T. V. Teperik, F. J. García De Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, "Omnidirectional absorption in nanostuctured metal surfaces," Nat. Photonics 2, 299-301 (2008).
[CrossRef]

N. Bonod and E. Popov, "Total light absorption in a wide range of incidence by nanostructured metals without plasmons," Opt. Lett. 33, 2398-2400 (2008).
[CrossRef] [PubMed]

P. M. Ajayan, "Experimental observation of an extremely dark material made by a low-density nanotube array," Nano. Lett. 8, 446 (2008).
[CrossRef] [PubMed]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, "Plasmonic blackbody: Almost complete absorption of light in nanostructured metallic coatings," Phys. Rev. B 78, 205405 (2008).
[CrossRef]

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Rios, "Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light," Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

2007

2004

2003

W. L. Barnes, A. Dereux, T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-829 (2003).
[CrossRef] [PubMed]

1996

1985

G. Bouchitte and R. Petit, "Homogenization techniques as applied in the electromagnetic theory of gratings," Electromagnetics 5, 17-36 (1985).
[CrossRef]

1983

R. Reinisch and M. Nevière, "Electromagnetic theory of diffraction in nonlinear optics and surface-enhanced nonlinear optical effects," Phys. Rev. B 28, 1870-1885 (1983).
[CrossRef]

1982

R. C. McPhedran, L. C. Botten, M. Craig, M. Nevière, and D. Maystre, "Lossy lamellar gratings in the quasistatic limit," Opt. Acta 29, 289-312 (1982).
[CrossRef]

M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982).
[CrossRef]

1980

A. D. Yaghjian, "Electric dyadic Green's functions in the source region," Proc. IEEE 68, 248-263, (1980).
[CrossRef]

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, "Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering," Phys. Rev. Lett. 45, 355-358 (1980).
[CrossRef]

1976

M. C. Hutley and D. Maystre, "Total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976).
[CrossRef]

1975

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

1941

1904

J. C. Maxwell-Garnet, "Colors in metal glasses and in metallic films," Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904).
[CrossRef]

1902

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phylos. Mag. 4, 396-402 (1902).

Abdelsalam, M.

T. V. Teperik, F. J. García De Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, "Omnidirectional absorption in nanostuctured metal surfaces," Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Ajayan, P. M.

P. M. Ajayan, "Experimental observation of an extremely dark material made by a low-density nanotube array," Nano. Lett. 8, 446 (2008).
[CrossRef] [PubMed]

Barbara, A.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Rios, "Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light," Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-829 (2003).
[CrossRef] [PubMed]

Bartlett, P. N.

T. V. Teperik, F. J. García De Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, "Omnidirectional absorption in nanostuctured metal surfaces," Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Baumberg, J. J.

T. V. Teperik, F. J. García De Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, "Omnidirectional absorption in nanostuctured metal surfaces," Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

Bonod, N.

Borisov, A. G.

T. V. Teperik, F. J. García De Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, "Omnidirectional absorption in nanostuctured metal surfaces," Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Botten, L. C.

R. C. McPhedran, L. C. Botten, M. Craig, M. Nevière, and D. Maystre, "Lossy lamellar gratings in the quasistatic limit," Opt. Acta 29, 289-312 (1982).
[CrossRef]

Bouchitte, G.

G. Bouchitte and R. Petit, "Homogenization techniques as applied in the electromagnetic theory of gratings," Electromagnetics 5, 17-36 (1985).
[CrossRef]

Craig, M.

R. C. McPhedran, L. C. Botten, M. Craig, M. Nevière, and D. Maystre, "Lossy lamellar gratings in the quasistatic limit," Opt. Acta 29, 289-312 (1982).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-829 (2003).
[CrossRef] [PubMed]

Derrick, G. H.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-829 (2003).
[CrossRef] [PubMed]

Enoch, S.

Fano, U.

García De Abajo, F. J.

T. V. Teperik, F. J. García De Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, "Omnidirectional absorption in nanostuctured metal surfaces," Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Gaylord, T. K.

Genack, A. Z.

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, "Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering," Phys. Rev. Lett. 45, 355-358 (1980).
[CrossRef]

Gersten, J. I.

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, "Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering," Phys. Rev. Lett. 45, 355-358 (1980).
[CrossRef]

Gralak, B.

Gramila, T. J.

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, "Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering," Phys. Rev. Lett. 45, 355-358 (1980).
[CrossRef]

Granet, G.

Grigorenko, A. N.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, "Plasmonic blackbody: Almost complete absorption of light in nanostructured metallic coatings," Phys. Rev. B 78, 205405 (2008).
[CrossRef]

Guizal, B.

Hutley, M. C.

Kravets, V. G.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, "Plasmonic blackbody: Almost complete absorption of light in nanostructured metallic coatings," Phys. Rev. B 78, 205405 (2008).
[CrossRef]

Lalanne, P.

Le Perchec, J.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Rios, "Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light," Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

Li, L.

López-Rios, T.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Rios, "Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light," Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

Maxwell-Garnet, J. C.

J. C. Maxwell-Garnet, "Colors in metal glasses and in metallic films," Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904).
[CrossRef]

Maystre, D.

E. Popov, D. Maystre, R. C. McPhedran, M. Nevière, M. C. Hutley, and G. H. Derrick, "Total absorption of unpolarized light by crossed gratings," Opt. Express 16, 6146-6155 (2008).
[CrossRef] [PubMed]

R. C. McPhedran, L. C. Botten, M. Craig, M. Nevière, and D. Maystre, "Lossy lamellar gratings in the quasistatic limit," Opt. Acta 29, 289-312 (1982).
[CrossRef]

M. C. Hutley and D. Maystre, "Total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976).
[CrossRef]

McPhedran, R. C.

E. Popov, D. Maystre, R. C. McPhedran, M. Nevière, M. C. Hutley, and G. H. Derrick, "Total absorption of unpolarized light by crossed gratings," Opt. Express 16, 6146-6155 (2008).
[CrossRef] [PubMed]

R. C. McPhedran, L. C. Botten, M. Craig, M. Nevière, and D. Maystre, "Lossy lamellar gratings in the quasistatic limit," Opt. Acta 29, 289-312 (1982).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Nevière, M.

E. Popov, D. Maystre, R. C. McPhedran, M. Nevière, M. C. Hutley, and G. H. Derrick, "Total absorption of unpolarized light by crossed gratings," Opt. Express 16, 6146-6155 (2008).
[CrossRef] [PubMed]

E. Popov, S. Enoch, G. Tayeb, M. Nevière, B. Gralak, and N. Bonod, "Enhanced transmission due to non-plasmon resonances in one and two dimensional gratings," Appl. Opt. 43, 999-1008 (2004).
[CrossRef] [PubMed]

R. Reinisch and M. Nevière, "Electromagnetic theory of diffraction in nonlinear optics and surface-enhanced nonlinear optical effects," Phys. Rev. B 28, 1870-1885 (1983).
[CrossRef]

R. C. McPhedran, L. C. Botten, M. Craig, M. Nevière, and D. Maystre, "Lossy lamellar gratings in the quasistatic limit," Opt. Acta 29, 289-312 (1982).
[CrossRef]

Peng, S. T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

Petit, R.

G. Bouchitte and R. Petit, "Homogenization techniques as applied in the electromagnetic theory of gratings," Electromagnetics 5, 17-36 (1985).
[CrossRef]

Popov, E.

Quémerais, P.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Rios, "Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light," Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

Reinisch, R.

R. Reinisch and M. Nevière, "Electromagnetic theory of diffraction in nonlinear optics and surface-enhanced nonlinear optical effects," Phys. Rev. B 28, 1870-1885 (1983).
[CrossRef]

Schedin, F.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, "Plasmonic blackbody: Almost complete absorption of light in nanostructured metallic coatings," Phys. Rev. B 78, 205405 (2008).
[CrossRef]

Sugawara, Y.

T. V. Teperik, F. J. García De Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, "Omnidirectional absorption in nanostuctured metal surfaces," Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Tamir, T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

Tayeb, G.

Teperik, T. V.

T. V. Teperik, F. J. García De Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, "Omnidirectional absorption in nanostuctured metal surfaces," Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Weitz, D. A.

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, "Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering," Phys. Rev. Lett. 45, 355-358 (1980).
[CrossRef]

Wood, R. W.

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phylos. Mag. 4, 396-402 (1902).

Yaghjian, A. D.

A. D. Yaghjian, "Electric dyadic Green's functions in the source region," Proc. IEEE 68, 248-263, (1980).
[CrossRef]

Appl. Opt.

Electromagnetics

G. Bouchitte and R. Petit, "Homogenization techniques as applied in the electromagnetic theory of gratings," Electromagnetics 5, 17-36 (1985).
[CrossRef]

IEEE Trans. Microwave Theory Tech.,

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nano. Lett.

P. M. Ajayan, "Experimental observation of an extremely dark material made by a low-density nanotube array," Nano. Lett. 8, 446 (2008).
[CrossRef] [PubMed]

Nat. Photonics

T. V. Teperik, F. J. García De Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, "Omnidirectional absorption in nanostuctured metal surfaces," Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-829 (2003).
[CrossRef] [PubMed]

Opt. Acta

R. C. McPhedran, L. C. Botten, M. Craig, M. Nevière, and D. Maystre, "Lossy lamellar gratings in the quasistatic limit," Opt. Acta 29, 289-312 (1982).
[CrossRef]

Opt. Commun.

M. C. Hutley and D. Maystre, "Total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976).
[CrossRef]

Opt. Express

Opt. Lett.

Philos. Trans. R. Soc. London, Ser. A

J. C. Maxwell-Garnet, "Colors in metal glasses and in metallic films," Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904).
[CrossRef]

Phylos. Mag.

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phylos. Mag. 4, 396-402 (1902).

Phys. Rev. B

R. Reinisch and M. Nevière, "Electromagnetic theory of diffraction in nonlinear optics and surface-enhanced nonlinear optical effects," Phys. Rev. B 28, 1870-1885 (1983).
[CrossRef]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, "Plasmonic blackbody: Almost complete absorption of light in nanostructured metallic coatings," Phys. Rev. B 78, 205405 (2008).
[CrossRef]

Phys. Rev. Lett.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Rios, "Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light," Phys. Rev. Lett. 100, 066408 (2008).
[CrossRef] [PubMed]

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, "Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering," Phys. Rev. Lett. 45, 355-358 (1980).
[CrossRef]

Proc. IEEE

A. D. Yaghjian, "Electric dyadic Green's functions in the source region," Proc. IEEE 68, 248-263, (1980).
[CrossRef]

Other

M. Nevière, "The homogeneous problem," in Electromagnetic theory of gratings, R. Petit, ed., (Springer-Verlag, 1980), Chap. 5.

M. Nevière, D. Maystre, R. C. McPhedran, G. H. Derrick and M. C. Hutley, "On the total absorption of unpolarized monochromatic light," Proceedings of the ICO-11 Conference, Madrid, Spain, pp. 609-612 (1978).

E. I. Krupitsky and B. C. Chernov, "Rigorous analysis of arbitrary slanted volume holographic gratings," (in Russian), Proc. IX All-Union School of Holography, Leningrad, 1977, pp 84-95.

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

E. D. Palik, ed. Handbook of Optical Constants of Solids (Academic Press, 1985)

http://www.luxpop.com/

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Figures (14)

Fig. 1.
Fig. 1.

Sketch of lamellar diffraction gratings, together with the coordinate system and notations: grating with 1D (a) and 2D (b) periodicity.

Fig. 2.
Fig. 2.

Reflectivity of the grating sketched in Fig. 1(b) as a function of the groove depth h and the channel c. Period d = 60 nm (a), 120 nm (b), wavelength λ = 457 nm, normal incidence, arbitrary polarization.

Fig. 3.
Fig. 3.

Angular dependence of the reflectivity of the grating sketched in Fig. 2. Two fundamental polarizations with respect to the plane of incidence, λ = 457 nm, TE case with the angle between the plane of incidence and the incident electric field vector Φ = 90°, and TM case with Φ = 0. (a) d = 60 nm, c = 15 nm, and h = 21.5 nm, (b) d = 120 nm, c = 30 nm, and h = 27.5 nm.

Fig. 4.
Fig. 4.

Spectral dependence of the reflectivity in normal incidence and arbitrary polarization for the grating with 2D periodicity. Same parameters as in Figs. 3(a) and 3(b).

Fig. 5.
Fig. 5.

Reflectivity of a grating with 1D periodicity (as given in Fig. 1(a)). (a) Groove depth dependence with period d = 60 nm, wavelength 457 nm, normal incidence. (b) Angular dependence for different periods and groove depth, with c/d = 1/6.

Fig. 6.
Fig. 6.

The effective permittivity along the extraordinary axis as given by Eqs. (3) and (4) as a function of c/d and λ. (a) Re( ε ¯ x), black line for Re(ε̅x) =0 and the hatched zone for Re( ε ¯ x) <0, (b) Im( ε ¯ x).

Fig. 7.
Fig. 7.

Reflectivity of a homogenous layer with optical index equal to 5.29 + i 1.62 on a silver substrate as a function of the layer thickness. Normal incidence with λ = 457 nm.

Fig. 8.
Fig. 8.

Reflectivity of an anisotropic homogeneous layer with thickness 6.2 nm deposited on a silver substrate: (a) spectral dependence in normal incidence, both polarizations, (b) angular dependence for λ = 457 nm, polarizations as indicated in the figure.

Fig. 9.
Fig. 9.

The reflection and the interference factors (real and imaginary parts) of R as given in Eq. (6), for a homogeneous layer with effective permittivity given by Eq. (3), with f = 0.18165, λ = 0.457 μm, and silver substrate. Permeabilities are equal to 1.

Fig. 10.
Fig. 10.

Reflectivity as a function of the groove depth (a) in normal incidence (TM polarization) for a 1D grating having different λ/d ratio, compared with the reflectivity of a plane homogeneous layer (asterisks) with indexes given in the text. λ = 457 nm, c/d = 1/6. (b) spectral dependence for the same λ/d ratios with h = 7.6 nm

Fig. 11.
Fig. 11.

Trajectory of the pole of the scattering matrix, above the cut in the complex plane presented by a green line, or the corresponding zero of the reflection order below the cut, as a function of the groove depth (given in nm) for a homogeneous anisotropic layer obtained by a 1D periodic grating with c/d = 1/6 and λ = 456 nm. (a) the entire trajectory, (b) zoom close to α0 = 1.

Fig. 12.
Fig. 12.

Reflectivity of a homogeneous anisotropic layer (a) and of 1D grating (d = 60 nm, c = 10 nm) as a function of the angle of incidence and groove depth. Wavelength 456 nm, TM polarization.

Fig. 13.
Fig. 13.

Trajectory of the pole of the scattering matrix, or the corresponding zero of the reflection order below the cut, as a function of the groove depth (given in nm) for a 1D periodic grating with c/d = 1/7 and λ = 456 nm.

Fig. 14.
Fig. 14.

Light intensity on one period of a 1D grating when illuminated in oblique incidence, θ = sin-1(0.65) (see Fig. 13) in TM polarization, with d = 60 nm, h = 16 nm, c/d = 1/7 and λ = 456 nm..

Equations (9)

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ε ̅ x = d ( d c ) / ε m + c / ε a
ε ̅ y = ε ̅ z = ( d c ) d ε m + c d ε a
ε ̅ y = ε ̅ z = ε a ( 1 + f ) ε m + ( 1 f ) ε a ( 1 f ) ε m + ( 1 + f ) ε a ,
ε ̅ y = f ε m + ( 1 f ) ε a ,
f = ( 1 c d ) 2
R = R refl . + R interf . r 12 + t 12 t 21 r 23 exp ( 2 ik 2 h ) r 21 r 23
α p ( h = 0 ) = ± ε m ε a / ( ε m + ε a ) ,
r 12 = β 1 / ε 1 β 2 / ε 2 β 1 / ε 1 + β 2 / ε 2 ,
α p , aniso = ε 1 ε ̅ y ε 1 ε ̅ x ε 1 2 ε ̅ x ε ̅ y

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