OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 7 — Jul. 1, 2006
  • pp: 1608–1615

Approximate model for surface-plasmon generation at slit apertures

P. Lalanne, J. P. Hugonin, and J. C. Rodier  »View Author Affiliations

JOSA A, Vol. 23, Issue 7, pp. 1608-1615 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (543 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a semianalytical model that quantitatively predicts the scattering of light by a single subwavelength slit in a thick metal screen. In contrast to previous theoretical works related to the transmission properties of the slit, the analysis emphasizes the generation of surface plasmons at the slit apertures. The model relies on a two-stage scattering mechanism, a purely geometric diffraction problem in the immediate vicinity of the slit aperture followed by the launching of a bounded surface-plasmon wave on the flat interfaces surrounding the aperture. By comparison with a full electromagnetic treatment, the model is shown to provide accurate formulas for the plasmonic generation strength coefficients, even for metals with a low conductivity. Limitations are outlined for large slit widths ( > λ ) or oblique incidence ( > 30 ° ) when the slit is illuminated by a plane wave.

© 2006 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction
(260.2110) Physical optics : Electromagnetic optics
(260.3910) Physical optics : Metal optics

ToC Category:
Diffraction and Gratings

Original Manuscript: September 23, 2005
Manuscript Accepted: November 10, 2005

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Approximate model for surface-plasmon generation at slit apertures," J. Opt. Soc. Am. A 23, 1608-1615 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. Thio, K. M. Pellerin, R. A. Linke, T. W. Ebbesen, and H. J. Lezec, 'Enhanced light transmission through a single subwavelength aperture,' Opt. Lett. 26, 1972-1974 (2001). [CrossRef]
  2. F. I. Baida and D. Van Labeke, 'Light transmission by subwavelength annular aperture arrays in metallic films,' Opt. Commun. 209, 17-22 (2002). [CrossRef]
  3. K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, 'Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,' Phys. Rev. Lett. 92, 183901 (2004). [CrossRef] [PubMed]
  4. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, 'Beaming light from a subwavelength aperture,' Science 297, 820-822 (2002). [CrossRef] [PubMed]
  5. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. 't Hooft, D. Lenstra, and E. R. Eliel, 'Plasmon-assisted two-slit transmission: Young's experiment revisited,' Phys. Rev. Lett. 94, 053901 (2005). [CrossRef] [PubMed]
  6. H. Bethe, 'Theory of diffraction by small holes,' Phys. Rev. 66, 163-182 (1944). [CrossRef]
  7. C. J. Bouwkamp, 'Diffraction theory,' Rep. Prog. Phys. 17, 35-100 (1954). [CrossRef]
  8. 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). [CrossRef]
  9. R. Wannemacher, 'Plasmon-supported transmission of light through nanometric holes in metallic thin films,' Opt. Commun. 195, 107-118 (2001). [CrossRef]
  10. S. H. Chang, S. K. Gray, and G. C. Schatz, 'Surface-plasmon generation and light transmission by isolated nanoholes and nanohole arrays in thin metal films,' Opt. Express 13, 3150-3165 (2005). [CrossRef] [PubMed]
  11. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, 'Transmission of light through slit aperture in metallic films,' Opt. Express 12, 6106-6121 (2004). [CrossRef] [PubMed]
  12. P. Lalanne, J. C. Rodier, and J. P. Hugonin, 'Surface plasmons of metallic surfaces perforated by nanohole arrays,' J. Opt. A Pure Appl. Opt. 7, 422-426 (2005). [CrossRef]
  13. L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S.-H. Chang, S. K. Gray, G. C. Schatz, D. E. Brown, and C. W. Kimball, 'Surface plasmons at single nanoholes in Au films,' Appl. Phys. Lett. 85, 467-469 (2004). [CrossRef]
  14. H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, 'Fluorescence imaging of surface plasmon fields,' Appl. Phys. Lett. 80, 404-406 (2002). [CrossRef]
  15. P. Lalanne, J. P. Hugonin, and J. C. Rodier, 'Theory of surface plasmon generation at nanoslit apertures,' Phys. Rev. Lett. 95, 263902 (2005). [CrossRef]
  16. Inaccuracies due to numerical truncation in the modal expansions are inevitable in numerics but they are kept at a low level. We estimate that the scattering coefficients are calculated with a relative accuracy better than 1%.
  17. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985), Part II.
  18. P. W. Wei, H. L. Chou, Y. R. Cheng, C. H. Wei, W. Fann, and J. O. Tegenfeldt, 'Beaming effect of optical near-field in multiple metallic slits with nanometric linewidth and micrometer pitch,' Opt. Commun. 253, 198-204 (2005). [CrossRef]
  19. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, 'Transmission of light through slit apertures in metallic films,' Opt. Express 12, 6106-6121 (2004). [CrossRef] [PubMed]
  20. 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). [CrossRef]
  21. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, 'Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,' J. Opt. Soc. Am. A 12, 1068-1076 (1995). [CrossRef]
  22. Ph. Lalanne and G. M. Morris, 'Highly improved convergence of the coupled-wave method for TM polarization,' J. Opt. Soc. Am. A 13, 779-784 (1996). [CrossRef]
  23. G. Granet and B. Guizal, 'Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,' J. Opt. Soc. Am. A 13, 1019-1023 (1996). [CrossRef]
  24. L. Li, 'Mathematical reflections on the Fourier modal method in grating theory,' in Mathematical Modeling in Optical Science, Frontiers in Applied Mathematics, G.Bao, L.Cowsar, and W.Masters, eds. (Society for Industrial and Applied Mathematics, 2001), pp. 111-139. [CrossRef]
  25. J. P. Bérenger, 'A perfectly matched layer for the absorption of electromagnetic waves,' J. Comput. Phys. 114, 185-200 (1994). [CrossRef]
  26. J. P. Hugonin and P. Lalanne, 'Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,' J. Opt. Soc. Am. A 22, 1844-1849 (2005). [CrossRef]
  27. C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).
  28. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  29. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).
  30. Ph. Lalanne, J. P. Hugonin, S. Astilean, M. Palamaru, and K. D. Möller, 'One-mode model and Airy-like formulae for 1D metallic gratings,' J. Opt. A Pure Appl. Opt. 2, 48-51 (2000). [CrossRef]
  31. This approximation amounts to considering that the slit is narrow enough so that all modes are evanescent except the fundamental one; see Ref. for a discussion of this approximation with respect to the metallic film thickness h.
  32. Standard techniques, like the adaptive Simpson quadrature method implemented with the function quad in MATLAB (MathWorks, Inc.), can be used.
  33. H. Lochbihler and R. A. Depine, 'Highly conducting wire gratings in the resonance domain,' Appl. Opt. 32, 3459-3465 (1993). [CrossRef] [PubMed]

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  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited