Abstract
Extraordinary transmission has been recently measured in a parallel plate waveguide (PPWG) through a metal strip with a patterned 1-D periodic array of circular holes, the metal strip being embedded inside the PPWG. Wood's anomaly and the extraordinary transmission peak (EOT) were detected for transverse electric (TE) mode excitation at frequencies higher than those found for TEM mode excitation. In this paper we provide an explanation for this frequency shift by decomposing the problem of a TE mode impinging on the 1-D array of holes into two problems of plane waves impinging obliquely on 2-D periodic arrays of holes. By then solving the integral equation for the electric field on the surface of the holes, the origin of the frequency shift is proved both mathematically and physically in terms of the symmetries present in the system.
Highlights
With the experimental discovery of extraordinary optical transmission (EOT) in the late nineteen nineties [1], it was unveiled that the transmission through small holes could be accomplished by taking advantage of periodicity, largely overcoming the predictions of Bethe’s single aperture theory [2]
For a perfect electric conductors (PECs) screen with a 2-D array of holes under normal incidence conditions, the first Wood’s anomaly is expected to appear at a frequency for which λ0 = max(a, b). This corresponds to the Wood’s anomaly experimentally detected in [15] for a parallel plate waveguide (PPWG) under transverse electromagnetic (TEM) excitation since this problem is equivalent to the EOT problem of a 2-D periodic array of holes under normal incidence [17]
Note that total transmission does not occur in the EOT peaks associated with the Wood’s anomalies for which a/λ0 > 1, which is due to the fact that some diffracted modes have already been launched at those frequencies and are capturing part of the energy of the original incident wave
Summary
With the experimental discovery of extraordinary optical transmission (EOT) in the late nineteen nineties [1], it was unveiled that the transmission through small holes could be accomplished by taking advantage of periodicity, largely overcoming the predictions of Bethe’s single aperture theory [2]. In this paper we present an approach to understand the origin of the EOT peak frequency shift in PPWG under TE1 mode excitation This theory is based on the decomposition of the problem into two problems of EOT through a 2-D periodic array of symmetric holes under oblique plane wave excitation. Our approach provides new physical insight into the origin of Wood’s anomalies and proposes a highly efficient analysis tool for the numerical study of structures supporting EOT phenomena. It only requires the solution of a small system of equations to obtain accurate results as opposite to other numerical methods such as coupled-mode method ( known as mode-matching). This singular behavior cannot be handled by the expansion modes used in the coupled-mode method presented in [15]
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