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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 7 — Apr. 3, 2006
  • pp: 2552–2572

Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique

J.M. Brok and H.P. Urbach  »View Author Affiliations

Optics Express, Vol. 14, Issue 7, pp. 2552-2572 (2006)

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We discuss a mode expansion technique to rigorously model the diffraction from three-dimensional pits and holes in a perfectly conducting layer with finite thickness. On the basis of our simulations we predict extraordinary transmission through a single hole, caused by the Fabry-Perot effect inside the hole. Furthermore, we study the fundamental building block for extraordinary transmission through hole arrays: two and three holes. Coupled electromagnetic surface waves, the perfect conductor equivalent of a surface plasmon, are found to play a key role in the mutual interaction between two or three holes.

© 2006 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1960) Diffraction and gratings : Diffraction theory

ToC Category:
Diffraction and Gratings

Original Manuscript: January 27, 2006
Revised Manuscript: March 16, 2006
Manuscript Accepted: March 16, 2006
Published: April 3, 2006

J. M. Brok and H. P. Urbach, "Extraordinary transmission through 1, 2 and 3 holes in a perfect conductor, modelled by a mode expansion technique," Opt. Express 14, 2552-2572 (2006)

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  21. Here and henceforth the square root of a complex number z is defined such that for real z > 0 we have √z > 0 and √z = +i√z, with the branch cut along the negative real axis.
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  23. Although υ¯α(x,y) is real, we include the conjugation for consistency of the notation.
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  26. <other>. Although the ± for α4 now does not have anything to do with the propagation direction, for consistency, we stick to this notation. </other>
  27. The reader might wonder why we do not use the sine and cosine form always instead of using the exponential form only for | γz/kp|< ε. However, for large and purely imaginary γz, the functions cos (γzz) and sin (γzz) increase exponentially with |z|, which is not very convenient for numerical implementation.
  28. The interaction integral also has some other properties that can save a lot of computation time. These properties are outside the scope of this paper.
  29. This routine is a multi-dimensional adaptive quadrature over a hyper-rectangle. For a description, see the internet link: http://www.nag.com/nagware/mt/doc/d01fcf.html.

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