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A New Look at Grating Theories Through the Extraordinary Optical Transmission Phenomenon

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Plasmonics

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 167))

Abstract

The electromagnetic properties of subwavelength metallic surfaces are due to two kinds of elementary distinct waves: the famous surface plasmon polariton and the quasi-cylindrical wave, which are both scattered by the subwavelength indentations as they propagate on the metal. The ab initio microscopic description of the electromagnetic properties starting from the sole knowledge of the elementary waves launched in between the indentation has a long history in grating theories. We review the evolution of the ideas and the fundamental principles that govern these waves and their impacts. For the sake of illustration, the emblematic case of a metal surface perforated by a subwavelength-hole array, which exhibits remarkable transmission properties, is taken to illustrate our purpose.

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References

  1. T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Extraordinary optical transmission through sub-wavelength hole arrays. Nature 391, 667–669 (1998)

    Article  ADS  Google Scholar 

  2. H. Bethe, Theory of diffraction by small holes. Phys. Rev. 66, 163–182 (1944)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. A. Roberts, Electromagnetic theory of diffraction by a circular aperture in a thick, perfectly conducting screen. J. Opt. Soc. Am A 4, 1970–1983 (1987)

    Article  ADS  Google Scholar 

  4. C. Genet, M.P. van Exter, J.P. Woerdman, Fano-type interpretation of red shifts and red tails in hole array transmission spectra. Opt. Commun. 225, 331–336 (2003)

    Article  ADS  Google Scholar 

  5. F. Przybilla, A. Degiron, C. Genet, T.W. Ebbesen, F. de Leon-Perez, J. Bravo-Abad, F. Garcia-Vidal, L. Martin-Moreno, Efficiency and finite size effects in enhanced transmission through subwavelength apertures. Opt. Express 16, 9571–79 (2008)

    Article  ADS  Google Scholar 

  6. C. Genet, T.W. Ebbesen, Light in tiny holes. Nature 445, 39–46 (2007)

    Article  ADS  Google Scholar 

  7. J.V. Coe, J.M. Heer, S. Teeters-Kennedy, H. Tian, K.R. Rodriguez, Extraordinary transmission of metal films with arrays of subwavelength holes. Ann. Rev. Phys. Chem. 59, 179–202 (2008)

    Article  ADS  Google Scholar 

  8. E. Ozbay, Plasmonics: merging photonics and electronics at nanoscale dimensions. Science 311, 189–193 (2006)

    Article  ADS  Google Scholar 

  9. R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980)

    Book  Google Scholar 

  10. H.T. Liu, P. Lalanne, Microscopic model for the extraordinary optical transmission. Nature 452, 728 731 (2008)

    Google Scholar 

  11. 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)

    Article  ADS  Google Scholar 

  12. Lord Rayleigh, On the dynamical theory of gratings. Proc. R. Soc. (London) A79, 399–416 (1907)

    ADS  Google Scholar 

  13. R.H. Ritchie, Plasma losses by fast electrons in thin films. Phys. Rev. 106, 874–881 (1957)

    Article  MathSciNet  ADS  Google Scholar 

  14. A. Hessel, A.A. Oliner, A new theory of Wood’s anomalies on optical gratings. Appl. Opt. 4, 1275–97 (1965)

    Google Scholar 

  15. D. Maystre, General study of grating anomalies from electromagnetic surface modes. in Electromagnetic Surface Modes, ed. by A.D. Boardman, Chapter 17 (Wiley, New York, 1982)

    Google Scholar 

  16. E. Popov, Light diffraction by relief gratings. Prog. Opt. 31, 141–187 (1993)

    Google Scholar 

  17. H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, L. Martin-Moreno, F.J. Garcia-Vidal, T.W. Ebbesen, Beaming light from a subwavelength aperture. Science 297, 820–822 (2002)

    Article  ADS  Google Scholar 

  18. V. Twersky, On a multiple scattering theory of the finite grating and the Wood anomaly. J. Appl. Phys. 23, 1099–1118 (1952)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. J.J.A. Porto, F.J. Garcia-Vidal, J.B. Pendry, Transmission resonances on metallic gratings with very narrow slits. Phys. Rev. Lett. 83, 2845–2848 (1999)

    Article  ADS  Google Scholar 

  20. P. Lalanne, J.P. Hugonin, S. Astilean, M. Palamaru, K.D. Möller, One-mode model and airy-like formulae for 1D metallic gratings. J. Opt. A: Pure Appl. Opt. 2, 48–51 (2000)

    Article  ADS  Google Scholar 

  21. S. Astilean, P. Lalanne, M. Palamaru, Light transmission through metallic channels much smaller than the wavelength. Opt. Commun. 175, 265–273 (2000)

    Article  ADS  Google Scholar 

  22. M.M.J. Treacy, Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings. Phys. Rev. B 66, 195105 (2002)

    Article  ADS  Google Scholar 

  23. Q. Cao, P. Lalanne, Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits. Phys. Rev. Lett. 88, 057403 (2002)

    Article  ADS  Google Scholar 

  24. P. Lalanne, J.P. Hugonin, H.T. Liu, B. Wang, A microscopic view of the electromagnetic properties of sub-metallic surfaces. Surf. Sci. Rep. 64, 453–469 (2009)

    Article  Google Scholar 

  25. D. Maystre, A. L. Fehrembach and E. Popov, Plasmonic antiresonance through subwavelength hole arrays, J. Opt. Soc. Am. A 28, 342–355 (2011)

    Article  Google Scholar 

  26. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, H.J. Lezec, The optical response of nanostructured surfaces and the composite diffracted evanescent wave model. Nat. Phys. 2, 262–267 (2006)

    Article  Google Scholar 

  27. I. Zenneck, Propagation of plane electromagnetic waves along a plane conducting surface and its bearing on the theory of transmission in wireless telegraphy. Ann. Phys. 23, 846–866 (1907)

    Article  MATH  Google Scholar 

  28. A. Sommerfeld, The broadening of the waves and the wireless telegraph. Ann. der Physik 28, 665–36 (1909)

    Article  ADS  MATH  Google Scholar 

  29. A. Sommerfeld, The propagation of waves in wireless telegraphy. Ann. der Physik 81, 1135–1153 (1926)

    Article  ADS  MATH  Google Scholar 

  30. K.A. Norton, Propagation of radio waves over a plane earth. Nature 135, 954–955 (1935)

    Article  ADS  Google Scholar 

  31. K.A. Norton, The propagation of radio waves over the surface of the earth and in the upper atmosphere. Proc. IRE 24, 1367–1387 (1936) and 1203–1236 (1937)

    Google Scholar 

  32. R.E. Collin, Hertzian dipole radiating over a lossy earth or sea: some early and late 20th-century controversies. IEEE Antennas Propag. Mag. 46, 64–79 (2004)

    Article  ADS  Google Scholar 

  33. A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon Press, Oxford, 1966)

    Google Scholar 

  34. P. Lalanne, J.P. Hugonin, Interaction between optical nano-objects at metallo-dielectric interfaces. Nat. Phys. 2, 551–556 (2006)

    Article  Google Scholar 

  35. L. Aigouy, P. Lalanne, J.P. Hugonin, G. Julié, V. Mathet, M. Mortier, Near-field analysis of surface waves launched at nano-slit apertures. Phys. Rev. Lett. 98, 153902 (2007)

    Article  ADS  Google Scholar 

  36. W. Dai, C.M. Soukoulis, Theoretical analysis of the surface wave along a metal-dielectric interface. Phys. Rev. B 80, 155407 (2009)

    Article  ADS  Google Scholar 

  37. A.Y. Nikitin, S.G. Rodrigo, F.J. Garcia-Vidal, L. Martin-Moreno, In the diffraction shadow: Norton waves versus surface plasmon polaritons in the optical region. New J. Phys. 11, 123020 (2009)

    Article  ADS  Google Scholar 

  38. F.J. Garcia-Vidal, L. Martin-Moreno, T.W. Ebbesen, L. Kuipers, Light passing through subwavelength apertures. Rev. Mod. Phys. 82, 729–787 (2010)

    Article  ADS  Google Scholar 

  39. E. Popov, M. Nevière, S. Enoch, R. Reinisch, Theory of light transmission through subwavelength periodic hole arrays. Phys. Rev. B 62, 16100 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  41. P. Lalanne, J.C. Rodier, J.P. Hugonin, Surface plasmons of metallic surfaces perforated by nanohole arrays. J. Opt. A: Pure Appl. Opt 7, 422–426 (2005)

    Article  ADS  Google Scholar 

  42. H.T. Liu, P. Lalanne, A comprehensive microscopic model of the extraordinary optical transmission. J. Opt. Soc. Am. A 27, 2542–2550 (2010)

    Article  ADS  Google Scholar 

  43. X. Huang, M.L. Brongersma, Rapid computation of light scattering from aperiodic plasmonic structures, Phys. Rev. B 84, 245120 (2011)

    Article  ADS  Google Scholar 

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Acknowledgments

Haitao Liu acknowledges financial supports from the Natural Science Foundation of China (No. 10804057), from the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No. 708021), and from the Program for New Century Excellent Talents in University (No. NCET-08-0289). Jean Paul Hugonin and Pierre Chavel are acknowledged for fruitful discussions and for careful readings of the manuscript.

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Lalanne, P., Liu, H. (2012). A New Look at Grating Theories Through the Extraordinary Optical Transmission Phenomenon. In: Enoch, S., Bonod, N. (eds) Plasmonics. Springer Series in Optical Sciences, vol 167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28079-5_3

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  • DOI: https://doi.org/10.1007/978-3-642-28079-5_3

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