Diffraction theory of frequency- and time-domain scattering by weakly aperiodic truncated thin-wire gratings

Abstract

An arbitrarily illuminated truncated nonuniform thin-wire grating produces a scattered field that can be synthesized by superposition of the fields radiated by the currents induced on each wire element. For weak departures from periodicity and for quasi-plane-wave conditions of incidence the combined effect of the individual induced radiations exhibits beam structure that can be interpreted in terms of truncated locally adapted Floquet modes plus Floquet-modulated edge diffractions that are due to the truncations. This interpretation is tied directly to the fields produced by a truncated aperture source distribution, provided that this distribution bears the local Floquet-mode (FM) imprint. The equivalence between the two formulations is established by Poisson summation, which converts the finite sum of individually radiated scattered fields into a series of truncated wave spectra (the Floquet modes) plus truncation contributions (the edge diffractions). The analysis is carried out for two-dimensional geometries, with reliance on high-frequency asymptotics applied first to the Poisson spectral integrals in the frequency domain and subsequently to the Fourier inversion into the time domain. The result is a new hybrid diffracted-ray–FM algorithm valid throughout the near, intermediate, and far zones of the total grating aperture in the frequency domain and yielding time-domain Floquet modes with novel features and interpretation. The quality of the ray-mode algorithm is assessed by comparison with reference data generated by direct numerical techniques. Because the diffraction-oriented analysis clarifies the spectral connection between individually radiated fields that are due to localized sources and globally radiated fields that are due to the collective effect of these sources, the resulting algorithm may be helpful in the design of frequency- and time-domain grating components for the control of radiative coupling.