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Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission


A metal film perforated by a regular array of subwavelength holes shows unexpectedly large transmission at particular wavelengths, a phenomenon known as the extraordinary optical transmission (EOT) of metal hole arrays1. EOT was first attributed to surface plasmon polaritons, stimulating a renewed interest in plasmonics2,3,4 and metallic surfaces with subwavelength features5,6,7. Experiments soon revealed that the field diffracted at a hole or slit is not a surface plasmon polariton mode alone8. Further theoretical analysis9 predicted that the extra contribution, from quasi-cylindrical waves10,11,12,13, also affects EOT. Here we report the experimental demonstration of the relative importance of surface plasmon polaritons and quasi-cylindrical waves in EOT by considering hole arrays of different hole densities. From the measured transmission spectra, we determine microscopic scattering parameters which allow us to show that quasi-cylindrical waves affect EOT only for high densities, when the hole spacing is roughly one wavelength. Apart from providing a deeper understanding of EOT, the determination of microscopic scattering parameters from the measurement of macroscopic optical properties paves the way to novel design strategies.

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Figure 1: Sample design.
Figure 2: Measured transmission spectra (solid curves) and the fitted SPP model (red dashed curves).


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

    Article  ADS  CAS  Google Scholar 

  2. Yanik, A. A. et al. An optofluidic nanoplasmonic biosensor for direct detection of live viruses from biological media. Nano Lett. 10, 4962–4969 (2010)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  3. Oulton, R. F. et al. Plasmon lasers at deep subwavelength scale. Nature 461, 629–632 (2009)

    Article  ADS  CAS  Google Scholar 

  4. Atwater, H. A. & Polman, A. Plasmonics for improved photovoltaic devices. Nature Mater. 9, 205–213 (2010)

    Article  ADS  CAS  Google Scholar 

  5. Barnes, W. L., Dereux, A. & Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 424, 824–830 (2003)

    Article  ADS  CAS  Google Scholar 

  6. García de Abajo, F. J. Light scattering by particle and hole arrays. Rev. Mod. Phys. 79, 1267–1290 (2007)

    Article  ADS  Google Scholar 

  7. García-Vidal, F. J., Martín-Moreno, L., Ebbesen, T. W. & Kuipers, L. Light passing through subwavelength apertures. Rev. Mod. Phys. 82, 729–787 (2010)

    Article  ADS  Google Scholar 

  8. Gay, G. et al. The optical response of nanostructured surfaces and the composite diffracted evanescent wave model. Nature Phys. 2, 262–267 (2006)

    Article  ADS  CAS  Google Scholar 

  9. Liu, H. T. & Lalanne, P. Microscopic theory of the extraordinary optical transmission. Nature 452, 728–731 (2008)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  13. Nikitin, A. Y., García-Vidal, F. J. & Martín-Moreno, L. Surface electromagnetic field radiated by a subwavelength hole in a metal film. Phys. Rev. Lett. 105, 073902 (2010)

    Article  ADS  Google Scholar 

  14. Nikitin, A., Yu, Rodrigo, S. G., García-Vidal, F. J. & Martín-Moreno, L. In the diffraction shadow: Norton waves versus surface plasmon polaritons in the optical region. N. J. Phys. 11, 123020 (2009)

    Article  Google Scholar 

  15. Gan, C. H., Lalouat, L., Lalanne, P. & Aigouy, L. Optical quasicylindrical waves at dielectric interfaces. Phys. Rev. B 83, 085422 (2011)

    Article  ADS  Google Scholar 

  16. Barnes, W. L., Murray, W. A., Dintinger, J., Devaux, E. & Ebbesen, T. W. Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film. Phys. Rev. Lett. 92, 107401 (2004)

    Article  ADS  CAS  Google Scholar 

  17. Stolwijk, D. et al. Enhanced coupling of plasmons in hole arrays with periodic dielectric antennas. Opt. Lett. 33, 363–365 (2008)

    Article  ADS  CAS  Google Scholar 

  18. Yin, L. et al. Subwavelength focusing and guiding of surface plasmons. Nano Lett. 5, 1399–1402 (2005)

    Article  ADS  CAS  Google Scholar 

  19. Lalanne, P., Sauvan, C., Hugonin, J. P., Rodier, J. C. & Chavel, P. Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures. Phys. Rev. B 68, 125404 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Born, M. & Wolf, E. Principles of Optics (Pergamon, 1986)

    Google Scholar 

  22. Palik, E. D. Handbook of Optical Constants of Solids 286–295 (Academic, 1985)

    Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  24. van der Molen, K. L. et al. Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: experiment and theory. Phys. Rev. B 72, 045421 (2005)

    Article  ADS  Google Scholar 

  25. van Beijnum, F., Rétif, C., Smiet, C. B. & van Exter, M. P. Transmission processes in random patterns of subwavelength holes. Opt. Lett. 36, 3666–3668 (2011)

    Article  ADS  CAS  Google Scholar 

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We acknowledge E. R. Eliel for discussions. H.L. acknowledges a Poste Rouge fellowship from CNRS and the 973 Program (2013CB328701). This work is part of the research program of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO).

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Authors and Affiliations



F.v.B. was the primary researcher on the project; he designed the experiment and wrote the paper. With C.B.S., F.v.B. conducted the experiments and analysed the data. C.R. made the samples. H.L., P.L. and M.P.v.E. made essential contributions to interpreting the results and writing the manuscript.

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Correspondence to Frerik van Beijnum.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains a more elaborate discussion of the theoretical framework used in the main article. It contains the extension of the SPP model, which includes the quasi-cylindrical wave, and explains the discrepancy found between the SPP model and the experimental data for the q=1 sample. (PDF 258 kb)

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van Beijnum, F., Rétif, C., Smiet, C. et al. Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission. Nature 492, 411–414 (2012).

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