Scattering resonances on a fast-wave structure

Abstract

This investigation is concerned with the scattering resonances, or generalized Wood's anomalies, that are exhibited on a fast-wave structure. In the past, all similar efforts have confined their attention to structures supporting a basic slow wave along the surface. In the frequency range <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\frac{1}{2}&lt;a/\lambda&lt;1</tex> , such structures exhibit only one anomaly as compared to two for the fast-wave type. The reason for this difference lies in the fact that in the above frequency range only the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = - 1</tex> space harmonic radiates away from the slow-wave structure while both the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = 0</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = - 1</tex> radiate from the other. In other words, the number of scattering resonances is exactly equal to the number of leaky waves supported by the structure under the same conditions of periodicity. The fast-wave structure analyzed here in detail consists of a parallel-plate waveguide perturbed by a series of periodic, parallel slits in the top plate. In the range <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a/\lambda&lt;\frac{1}{2}</tex> , the plane-wave scattering problem is considered for both <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> mode polarizations, and the anomalies are found to manifest themselves as a rapid variation in the phase of the reflection coefficient. When <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a/\lambda&lt;\frac{1}{2}</tex> there are no higher-order diffracted waves, and the magnitude of the reflection coefficient is, therefore, fixed at unity. The relative periodicity is next extended to the range <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\frac{1}{2}&lt;a/\lambda&lt;1</tex> El, and the scattering problem considered for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> mode polarization. The periodicity is now such that both the reflected wave and the first higher-order diffracted wave propagate transversely. Under such circumstances, it is convenient to use a scattering description for the fields, and the anomalies may then be observed as rapid variations in both the magnitude and phase of the scattering coefficients. The relation to the role played by the Rayleigh wavelength in the classical Wood's anomalies on optical reflection gratings is also considered.