High-frequency multiple diffraction by a flat strip: Higher order asymptotics

By including correction terms in inverse powers of the wavenumber
k
, one may hope to extend the range of applicability of multiple edge diffracted geometrical theory of diffraction (GTD) to lower frequencies, and also to extend thereby the range of validity of the corresponding time domain solutions. The correction can be applied to each of the surface rays in the hierarchy that has been proposed by us recently as a model for multiple interaction between parallel edges separated by a plane surface segment on a two-dimensional perfectly conducting scatterer. The surface rays, which were found to explain the structure of the complex resonances in transient scattering, are excited for each interaction by equivalent line sources, dipole line sources, and their derivatives, with strengths determined from the asymptotic expansion of the edge diffracted field. This procedure is applied in detail to
E
- and
H
- polarized plane wave scattering by a perfectly conducting flat strip, up to quadruple diffraction, including consistent
O(k^{-2})
corrections with respect to the dominant term. The procedure is applied also to generate corrected multiple diffracted individual surface ray fields, which lead to an improved equation for the complex resonances in the "layer" synthesized in the complex frequency plane by a surface ray of a particular order. Inclusion of the low frequency corrections reduces further the already small discrepancy between the ray optically calculated low frequency resonances and those computed numerically by the moment method.