Time-domain wave-oriented data processing of scattering by nonuniform truncated gratings

Abstract

In a companion paper [ J. Opt. Soc. Am. A11, 2675 ( 1994)] we investigated wave-oriented processing techniques that extract from frequency-domain (FD) scattering data for nonuniform truncated thin-wire or strip gratings the wave phenomenology that ties features in data to scattering mechanisms that are responsible for these features. The resulting observable-based parameterization (OBP) should be useful for construction of wave-based algorithms aimed, through forward and backward propagation routines, at design, classification, and imaging. The processing strategy projects the data, which are assembled on an elevated track at height z parallel to the grating-plane coordinate x, onto the (x, kx) phase-space subdomain by means of windowed Fourier transforms; here kx is the spatial spectral wave number corresponding to x. The (x, kx) phase-space distributions and their information content for various grating configurations are analyzed in detail and are related to previously derived analytic scattering models based on truncated local Floquet modes (FM’s) and on FM-modulated edge diffractions. We explore time-domain (TD) wave-oriented processing techniques for scattering by truncated gratings produced by a pulsed incident plane wave. By spatial–temporal resolution, the TD data base adds to the FD processing options. Time (t)–frequency (ω) phase-space distributions implemented through windowed transforms extract from TD data new TD phenomenology, TD-OBP, that differs fundamentally from that in the frequency domain: strongly dispersive TD-FM’s with prolonged time-varying frequency response ωm(t), where m is the FM index, and temporally well-resolved weakly dispersive impulselike edge diffractions. These phenomenologies extracted from the TD scattering data are interpreted in terms of, and shown to be in agreement with, previously developed analytic TD scattering models. The (t, ω) processing is applied to pulsed plane-wave scattering data produced for various grating configurations by previously calibrated numerical reference codes and reveals the changes in (t, ω) footprints that are attributable to departures from strict canonical truncated periodicity. Short-pulse TD excitation is found to resolve the element structure within each scattering cell directly, in contrast to (t, ω) processing, in which element-structure information is tied indirectly to the FM excitation strengths.