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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).


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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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