Summary
International Symposium on Antennas and Propagation
2010
Session Number:3TE2
Session:
Number:3TE2-4
Spectral-Domain Formulation of Electromagnetic Scattering from Circular Cylinder Located near Periodically Corrugated Surface
Koki WATANABE,
pp.-
Publication Date:2010/11/23
Online ISSN:2188-5079
Summary:
Periodic structures are widely used in microwave, millimeter-wave, and optical wave regions, and many analytical and numerical approaches have been developed to analyze the scattering from periodic structures. When a plane-wave illuminates a perfectly periodic structure, the Floquet theorem asserts that the scattered fields are pseudo-periodic (namely, each field component is a product of a periodic function and an exponential phase factor). This implies that the scattered fields have discrete spectra in the wavenumber space. The field components can be therefore expressed in the generalized Fourier series expansions, and the analysis region can be reduced to only one periodicity cell. Then most of the approaches for periodic structures are based on the Floquet theorem. However, when the structural periodicity is broken even if locally, the Floquet theorem is no longer applicable and the analysis region has to generally cover all the scattering structure under consideration. This paper presents an approach in spectral-domain for the electromagnetic scattering problem of an imperfectly periodic structure, in which a circular cylinder is located near a periodically corrugated surface. The fields in imperfectly periodic structures have continuous spectra, and an artificial discretization in the wavenumber space is necessary for numerical computation. When perfectly periodic structures are illuminated by incident fields with continuous spectra, the spectra of scattered fields are known to have infinite number of non-smooth points in the wavenumber space, which are called the Wood anomalies. They do not vanish if the structural periodicity is locally collapsed, and should be taken into account on the discretization in the wavenumber space. The present approach uses the pseudo-periodic Fourier transform (PPFT) [1] to consider the discretization scheme in the wavenumber space. PPFT converts an arbitrary function into a pseudo-periodic one, and the transformed function can be expressed in the generalized Fourier series expansion. Then the conventional formulations for perfectly periodic structures based on the Floquet theorem can be applied to analyze the scattering problem of imperfectly periodic structures. The transformed function has also a periodic property in terms of the transform parameter, which is related to the wavenumber, and the analysis region in the spectral domain is reduced to the Brillouin zone. Therefore, the discretization scheme in terms of the transform parameter can be considered inside the Brillouin zone.