Wavefront and resonance analysis of scattering by a perfectly conducting flat strip

Abstract

Wavefronts and resonances form alternative descriptions for transient scattering by targets, with the former most effective at early observation times and the latter most effective at later times. Wavefronts can be employed to synthesize resonances, and both constituents can be combined self-consistently within a hybrid format that seeks to exploit the best features of each. These aspects are illustrated here for the special case of impulsive plane wave scattering by a perfectly conducting flat strip. Since the multiple diffracted wavefront fields are found by geometrical theory of diffraction (GTD) asymptotics, the example also highlights the detrimental effects caused by approximations confined essentially to the high frequencies in the incident signal spectrum. Despite these inadequacies (present for impulsive signals but not for those with low frequency cutoff), the analysis and numerical comparisons confirm the wavefront-resonance equivalence, with inclusion of the branch cut integral due to the two-dimensional geometry of the scatterer; the role of the "entire function" in, and the poor convergence of, the resonance expansion at early times, the improved convergence achieved by delayed resonance series turn-on in a hybrid format; and the internal consistency of that format. Moreover, the GTD approximations are adequate for accurate synthesis of the resonance frequencies.