Abstract

Using a rigorous electromagnetic analysis of two-dimensional (or crossed) gratings, we account, in a first step, for the enhanced transmission of a sub-wavelength hole array pierced inside a metallic film, when plasmons are simultaneously excited at both interfaces of the film. Replacing the hole array by a continuous metallic film, we then show that resonant extraordinary transmission can still occur, provided the film is modulated. The modulation may be produced in both a one-dimensional and a two dimensional geometry either by periodic surface deformation or by adding an array of high index pillars. Transmittivity higher than 80% is found when surface plasmons are excited at both interfaces, in a symmetric configuration.

© 2002 Optical Society of America

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References

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  1. 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]
  2. U. Schröter, D. Heitmann, �??Surface-plasmon-enhanced transmission through metallic gratings,�?? Phys. Rev. B 58, 15419-15421 (1998)
    [CrossRef]
  3. M. M. J. Treacy, �??Dynamical diffraction in metallic optical gratings,�?? Appl. Phys. Lett. 75, 606-608 (1999)
    [CrossRef]
  4. J. A. Porto, F. T. Garcia-Vidal, J. B. Pendry, �??Transmission resonances on metallic gratings with very narrow slits,�?? Phys. Rev. Lett. 83, 2845-2848 (1999)
    [CrossRef]
  5. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, H. J. Lezec, �??Surface plasmons enhance optical transmission through sub-wavelength holes,�?? Phys. Rev. B 58, 6779-6782 (1998)
    [CrossRef]
  6. T. Lopez-Rios, D. Mendoza, J. J. Garcia-Vidal, J. Sanchez-Dehesa, B. Pannetier, �??Surface shape resonances in lamellar metallic gratings,�?? Phys. Rev. Lett. 81, 665-668 (1998)
    [CrossRef]
  7. Ph. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, K. D. Möller, �??One-mode model and Airy-like formulae for one-dimensional metallic gratings,�?? J. Opt. A: Pure Appl. Opt. 2, 48-51 (2000)
    [CrossRef]
  8. M. M. J. Treacy, �??Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,�?? Phys. Rev. B 66, 195105-1 �?? 195105-10 (2002
    [CrossRef]
  9. Q. Cao, Ph. Lalanne, �??Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,�?? Phys. Rev. Lett. 88, 057403-1 �?? 057403-4 (2002)
    [CrossRef] [PubMed]
  10. E. Popov, M. Nevière, S. Enoch, R. Reinisch, �??Theory of light transmission through subwavelength periodic hole arrays,�?? Phys. Rev. B 62, 16100-16108 (2000)
    [CrossRef]
  11. S. Enoch, E. Popov, M. Nevière, R. Reinisch, �??Enhanced light transmission by hole arrays,�?? J. Opt. A: Pure and Appl. Opt. 4, S83-S87 (2002)
    [CrossRef]
  12. L. Martin-Moreno, F. J. Garcia Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, �??Theory of extraordinary optical transmission through subwavelength hole arrays,�?? Phys. Rev. Lett. 86, 1114-1117 (2001)
    [CrossRef] [PubMed]
  13. L. Salomon, F. Grillot, A. Zayats, and F. de Fornel, �??Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,�?? Phys. Rev. Lett. 86, 1110-1113 (2001)
    [CrossRef] [PubMed]
  14. A. Krishman, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolf, J. Pendry, L. Martin-Moreno, and J. J. Garcia-Vidal, �??Evanescently-coupled surface resonance in surface plasmon enhanced transmission,�?? Opt. Commun. 200, 1-7 (2001)
    [CrossRef]
  15. M. Nevière, E. Popov, R. Reinisch, and G. Vitrant, Electromagnetic Resonances in Nonlinear Optics (Gordon and Breach Sci. Publ., Amsterdam, 2000) and the references cited therein
  16. M. Nevière and R. reinisch, �??Electromagnetic study of the surface-plasmon-resonance contribution to surface-enhanced Raman scattering,�?? Phys. Rev. B 26, 5043-5048 (1982)
    [CrossRef]
  17. R. Reinisch and M. Nevière, �??Electromagnetic theory of diffraction in nonlinear optics and surfaceenhanced nonlinear optical effects,�?? Phys. Rev. B 28, 1870-1885 (1983)
    [CrossRef]
  18. I. Avrutsky, Y. Zhao, V. Kochergin, �??Surface-plasmon-assisted resonant tunneling of light through a periodically corrugated thin metal film,�?? Opt. Lett. 25, 595-597 (2000)
    [CrossRef]
  19. American Institute of Physics Handbook, 2nd edition (Mc Graw-Hill, New-York, 1963)
  20. L. Li, �??New formulation of the Fourier-modal method for crossed surface-relief gratings,�?? J. Opt. Soc. Am. A 14, 2758-2769 (1997)
    [CrossRef]
  21. L. Li, �??Formulation and comparison of two recursive matrix algorithm for modeling layered diffraction gratings,�?? J. Opt. Soc. Am. A 13, 1024-1035 (1996)
    [CrossRef]
  22. M. Nevière, E. Popov, Light propagation in periodic media; differential theory and design (Marcel Dekker, New York, 2003)
  23. R. Gruhlke, W. Hod, and D. Hall, �??Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film,�?? Phys. Rev. Lett. 56, 2838-2841 (1986)
    [CrossRef] [PubMed]
  24. U. Schröter and D. Heitmann, �??Grating couplers for surface plasmons excited on thin films in the Kretschmann-Raether configuration,�?? Phys. Rev. B 60, 4992-4999 (1999)
    [CrossRef]
  25. Z. Zhu and T. Brown, �??Nonperturbative analysis of cross coupling in corrugated metal films,�?? J. Opt. Soc. Am. A 17, 1798-1806 (2000)
    [CrossRef]
  26. R.C. McPhedran, G. H. Derrick, L. C. Botten, �??Theory of Crossed Gratings,�?? in Electromagnetic Theory of Gratings, R. Petit ed. (Springer-Verlag, Berlin, 1980), pp. 227-276

Appl. Phys. Lett.

M. M. J. Treacy, �??Dynamical diffraction in metallic optical gratings,�?? Appl. Phys. Lett. 75, 606-608 (1999)
[CrossRef]

J. Opt. A: Pure and Appl. Opt.

S. Enoch, E. Popov, M. Nevière, R. Reinisch, �??Enhanced light transmission by hole arrays,�?? J. Opt. A: Pure and Appl. Opt. 4, S83-S87 (2002)
[CrossRef]

J. Opt. A: Pure Appl. Opt.

Ph. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, K. D. Möller, �??One-mode model and Airy-like formulae for one-dimensional metallic gratings,�?? J. Opt. A: Pure Appl. Opt. 2, 48-51 (2000)
[CrossRef]

J. Opt. Soc. Am. A

Nature

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. Commun.

A. Krishman, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolf, J. Pendry, L. Martin-Moreno, and J. J. Garcia-Vidal, �??Evanescently-coupled surface resonance in surface plasmon enhanced transmission,�?? Opt. Commun. 200, 1-7 (2001)
[CrossRef]

Opt. Lett.

Phys. Rev. B

U. Schröter and D. Heitmann, �??Grating couplers for surface plasmons excited on thin films in the Kretschmann-Raether configuration,�?? Phys. Rev. B 60, 4992-4999 (1999)
[CrossRef]

M. Nevière and R. reinisch, �??Electromagnetic study of the surface-plasmon-resonance contribution to surface-enhanced Raman scattering,�?? Phys. Rev. B 26, 5043-5048 (1982)
[CrossRef]

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

E. Popov, M. Nevière, S. Enoch, R. Reinisch, �??Theory of light transmission through subwavelength periodic hole arrays,�?? Phys. Rev. B 62, 16100-16108 (2000)
[CrossRef]

U. Schröter, D. Heitmann, �??Surface-plasmon-enhanced transmission through metallic gratings,�?? Phys. Rev. B 58, 15419-15421 (1998)
[CrossRef]

M. M. J. Treacy, �??Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,�?? Phys. Rev. B 66, 195105-1 �?? 195105-10 (2002
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, H. J. Lezec, �??Surface plasmons enhance optical transmission through sub-wavelength holes,�?? Phys. Rev. B 58, 6779-6782 (1998)
[CrossRef]

Phys. Rev. Lett.

T. Lopez-Rios, D. Mendoza, J. J. Garcia-Vidal, J. Sanchez-Dehesa, B. Pannetier, �??Surface shape resonances in lamellar metallic gratings,�?? Phys. Rev. Lett. 81, 665-668 (1998)
[CrossRef]

Q. Cao, Ph. Lalanne, �??Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,�?? Phys. Rev. Lett. 88, 057403-1 �?? 057403-4 (2002)
[CrossRef] [PubMed]

J. A. Porto, F. T. Garcia-Vidal, J. B. Pendry, �??Transmission resonances on metallic gratings with very narrow slits,�?? Phys. Rev. Lett. 83, 2845-2848 (1999)
[CrossRef]

R. Gruhlke, W. Hod, and D. Hall, �??Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin film,�?? Phys. Rev. Lett. 56, 2838-2841 (1986)
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, �??Theory of extraordinary optical transmission through subwavelength hole arrays,�?? Phys. Rev. Lett. 86, 1114-1117 (2001)
[CrossRef] [PubMed]

L. Salomon, F. Grillot, A. Zayats, and F. de Fornel, �??Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,�?? Phys. Rev. Lett. 86, 1110-1113 (2001)
[CrossRef] [PubMed]

Other

M. Nevière, E. Popov, R. Reinisch, and G. Vitrant, Electromagnetic Resonances in Nonlinear Optics (Gordon and Breach Sci. Publ., Amsterdam, 2000) and the references cited therein

M. Nevière, E. Popov, Light propagation in periodic media; differential theory and design (Marcel Dekker, New York, 2003)

American Institute of Physics Handbook, 2nd edition (Mc Graw-Hill, New-York, 1963)

R.C. McPhedran, G. H. Derrick, L. C. Botten, �??Theory of Crossed Gratings,�?? in Electromagnetic Theory of Gratings, R. Petit ed. (Springer-Verlag, Berlin, 1980), pp. 227-276

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Figures (7)

Fig. 1.
Fig. 1.

Transmittance as a function of wavelength in micrometers

Fig. 2.
Fig. 2.

Transmittivity as a function of wavelength for a continuous modulated silver film

Fig. 3.
Fig. 3.

Same as Fig. 2, but with 0.07 µm thickness. The red curve represents the sum of reflected and transmitted efficiency

Fig. 4.
Fig. 4.

Maximum of transmission for a silver layer as a function of the layer thickness for four different structures: plane layer (green curve), sinusoidal grating (groove depth h=18 nm is constant for thicknesses greater than 150 nm) with an identical substrate and superstrate material (black curve), grating hole array (violet curve),11 and a symmetrical prism coupler with 2 µm air gap (blue curve)

Fig. 5.
Fig. 5.

Light transmission of a two-dimensionally corrugated sinusoidal film as a function of the wavelength and the modulation depth.

Fig. 6.
Fig. 6.

Schematical representation of a plane metallic layer with a periodical array of dielectric pillars

Fig.7.
Fig.7.

Light transmission of a two-dimensional dielectric pillar grating on a plane silver film as a function of the wavelength and the pillar height.

Equations (1)

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y = h 4 [ sin ( Kx ) + sin ( Kz ) ]

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