OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 3 — Mar. 1, 2004
  • pp: 456–463

Transmission through single subwavelength apertures in thin metal films and effects of surface plasmons

Tuomas Vallius, Jari Turunen, Masud Mansuripur, and Seppo Honkanen  »View Author Affiliations

JOSA A, Vol. 21, Issue 3, pp. 456-463 (2004)

View Full Text Article

Acrobat PDF (469 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The existing analyses on extraordinary optical transmission through apertures on a metal screen have been carried out assuming perfect conductivity or by examining arrays of closely spaced holes with subwavelength dimensions. We present an electromagnetic analysis of a single hole (modeled by use of an array of distant holes) in a finitely conducting metal membrane, applying no approximations. We demonstrate that finite conductivity is not of remarkable importance with small hole-diameter-to-wavelength ratios in the absence of strong resonances. However, if the angle of incidence of a plane wave is such that surface plasmons are excited, substantial enhancement of the transmittance can be observed, and the effect of finite conductivity will no longer be negligible. Our analysis also reveals that transmission of small apertures in highly conducting membranes can be described by approximate analytical formulas if surface waves are not excited, but with poor conductors the full electromagnetic analysis should be applied.

© 2004 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1960) Diffraction and gratings : Diffraction theory
(240.6680) Optics at surfaces : Surface plasmons

Tuomas Vallius, Jari Turunen, Masud Mansuripur, and Seppo Honkanen, "Transmission through single subwavelength apertures in thin metal films and effects of surface plasmons," J. Opt. Soc. Am. A 21, 456-463 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature 391, 667–669 (1998).
  2. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998).
  3. U. Schröter and D. Heitmann, “Surface-plasmon-enhanced transmission through metallic gratings,” Phys. Rev. B 58, 15419–15421 (1998).
  4. M. M. J. Treacy, “Dynamical diffraction in metallic optical gratings,” Appl. Phys. Lett. 75, 606–608 (1999).
  5. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
  6. T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B 16, 1743–1748 (1999).
  7. I. Avrutsky, Y. Zhao, and V. Kochergin, “Surface-plasmon-assisted resonant tunneling of light through a periodically corrugated thin metal film,” Opt. Lett. 25, 595–597 (2000).
  8. E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
  9. S. Astilean, P. Lalanne, and M. Palamaru, “Light transmission through metallic channels much smaller than the wavelength,” Opt. Commun. 175, 265–273 (2000).
  10. L. Martín-Moreno, F. J. García-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).
  11. Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 0574031–0574034 (2002).
  12. P. Lalanne, C. Sauvan, J.-P. Hugonin, J. C. Rodier, and P. Chavel, “Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,” Phys. Rev. B 68, 125404 (2003).
  13. N. Bonod, S. Enoch, L. Li, E. Popov, and M. Nevière, “Resonant optical transmission through thin metallic films with and without holes,” Opt. Express 11, 482–490 (2003).
  14. A. Moreau, G. Granet, F. I. Baida, and D. Van Labeke, “Light transmission by subwavelength square coaxial aperture arrays in metallic films,” Opt. Express 11, 1131–1136 (2003).
  15. R. C. McPhedran, G. H. Derrick, and L. C. Botten, “Theory of crossed gratings,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 227–276.
  16. V. Kettunen, M. Kuittinen, J. Turunen, and P. Vahimaa, “Spectral filtering with finitely conducting inductive grids,” J. Opt. Soc. Am. A 15, 2783–2785 (1998).
  17. J. R. Sambles, “More than transparent,” Nature 391, 641–642 (1998).
  18. T. Thio, H. J. Lezec, and T. W. Ebbesen, “Strongly enhanced optical transmission through subwavelength holes in metal films,” Physica B 279, 90–93 (2000).
  19. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001).
  20. M. Mansuripur, The Physical Principles of Magneto-Optical Recording (Cambridge U. Press, Cambridge, 1995).
  21. J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Wiley-VCH, Berlin, 1997).
  22. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163–182 (1944).
  23. C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 18, 35–100 (1954).
  24. A. Sommerfeld, “Mathematische theorie der diffraction,” Math. Ann. 47, 317–374 (1896).
  25. G. Mie, “Beitrage zur optik truber median, speziell kolloidaler metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
  26. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
  27. K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am. 68, 1206–1210 (1978).
  28. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
  29. F. J. García de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10, 1475–1484 (2002).
  30. E. Noponen and J. Turunen, “Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles,” J. Opt. Soc. Am. A 11, 2494–2502 (1994).
  31. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997).
  32. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
  33. P. Dansas and N. Paraire, “Fast modeling of photonic bandgap structures by use of a diffraction-grating approach,” J. Opt. Soc. Am. A 15, 1586–1598 (1998).
  34. P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
  35. P. Lalanne, “Improved formulation of the coupled-wave method for two-dimensional gratings,” J. Opt. Soc. Am. A 14, 1592–1598 (1997).
  36. B. Layet and M. R. Taghizadeh, “Analysis of gratings with large periods and small features by stitching the electromagnetic field,” Opt. Lett. 21, 1508–1510 (1996).
  37. T. Vallius, V. Kettunen, M. Kuittinen, and J. Turunen, “Step-discontinuity approach for non-paraxial diffractive optics,” J. Mod. Opt. 48, 1195–1210 (2001).
  38. E. Silberstein, P. Lalanne, J.-P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865–2875 (2001).
  39. Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London Ser. A 79, 399–416 (1907).
  40. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, New York, 1988).
  41. J. Turunen and A. T. Friberg, “Self-imaging and propagation-invariance in electromagnetic fields,” Pure Appl. Opt. 2, 51–60 (1993).
  42. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article

OSA is a member of CrossRef.

CrossCheck Deposited