David Kralj

Dispersive modes in the time domain: analysis and time-frequency representation

Four algorithms for time-frequency (TF) distributions are considered for the processing and interpretation of dispersive time-domain (TD) data: the short-time Fourier transform, frequency and time-domain wavelets, and a new ARMA-based representation. The TF resolutions of the various distributions are discussed and compared with reference to results for the scattered fields from a chirped finite grating excited by a pulsed plane wave. The processing in the TF phase space extracts TD phenomenology, in particular the instantaneous dispersion relation /spl minus/ with its associated time-dependent frequencies-descriptive of the local TD Floquet modes on the chirped truncated grating.<<ETX>>

Wave-oriented signal processing of dispersive time-domain scattering data

Phase-space data processing is receiving increased attention because or its potential for furnishing new discriminants relating to classification and identification of targets and other scattering environments. Primary emphasis has been on time-frequency processing because of its impact on transient, especially wideband, short-pulse excitations. Here, we investigate the windowed Fourier transform, the wavelet transform, and model based superresolution algorithms within the context of a fully quantified and calibrated test problem investigated by us previously: two-dimensional (2-D) short-pulse plane wave scattering by a finite periodic array of perfectly conducting coplanar flat strips. Because the forward problem has been fully calibrated and parametrized, some quantitative measures can be assigned with respect to the tradeoffs of these time-frequency algorithms, yielding tentative performance assessments of the tested processing algorithms.

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

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.

Picosecond-pulse and millimeter-wave spectroscopy of barium ferrite

Transmission measurements of a barium ferrite pressed-powder sample have been made with an optically switched picosecond-pulse spectrometer. By comparison to millimeter-wave spectroscopy of the same sample, features related to the ferrimagnetic resonance have been identified in the pulse spectrum. Time-domain spectra predicted from models of the permeability indicate significant discrepancies with the experimental short-pulse line shape.

Frequency-domain scattering by nonuniform truncated arrays: wave-oriented data processing for inversion and imaging

We previously presented an asymptotic diffraction theory for time-harmonic and transient scattering by arbitrarily illuminated truncated nonuniform thin-wire gratings [ J. Opt. Soc. Am. A11, 1291 ( 1994)]. We parameterized and interpreted the results in terms of scattered truncated Floquet modes (FM’s) and Floquet-modulated edge diffraction, which generalize the constructs of the conventional geometric theory of diffraction (GTD). We also demonstrated that numerical implementation of the FM–GTD algorithm yields results that compare very well with data computed from rigorously based numerical reference solutions. We enlarge the previous frequency-domain numerical data base for gratings to scattering by truncated arrays whose elements are arbitrarily oriented strips rather than thin-wire filaments and also to arrays whose element locations depart from truncated periodicity in a random rather than an orderly manner. We show that the FM–GTD parameterization of the scattered field remains applicable under these generalized conditions. With a view toward inversion and imaging, our principal purpose is the application of space-wave-number phase-space processing techniques to extract the footprints of truncated nonuniform periodicity from the scattered-field data. Because the processing is tied to the wave physics, we refer to this procedure as wave-oriented data processing. Implementation involves projection onto appropriate phase-space subdomains and the generation of space–wave-number phase-space distributions by windowed Fourier transforms. It is found that this form of processing in the frequency domain highlights effects of truncation and perturbed periodicity but is not very sensitive to the structure of the array elements (i.e., wires versus strips). In a companion paper [ J. Opt. Soc. Am. A11, 2685 ( 1994)] we perform phase-space processing in the time domain, show how the time-domain FM-GTD phenomenology is revealed through time-frequency distributions, and show also how short-pulse excitation enhances the sensitivity with respect to element structure by means of spatial–temporal resolution.

Photoconductively switched antennas for measuring target resonances

Coplanar‐strip horn antennas are switched photoconductively to generate picosecond bursts of freely propagating electromagnetic energy with bandwidth covering 15–75 GHz. The antennas are fabricated on GaAs grown by molecular beam epitaxy at low substrate temperatures. These antennas are used to perform transient scattering measurements from slit‐coupled circular and coaxial cavities; Prony’s method [IEEE Trans. Antennas Propagat. 23, 777 (1975)] is used to extract cavity resonances from the measured late‐time scattered signal.

Short-pulse propagation in a hollow waveguide: analysis, optoelectronic measurement, and signal processing

An asymptotic analysis is performed for short-pulse propagation in a hollow waveguide. It is demonstrated that each time-domain mode supported by the guide is characterized by a time-dependent frequency which, as time proceeds, approaches the modal cutoff frequency. This phenomenon is demonstrated experimentally by performing short-pulse optoelectronic measurements for the case of rectangular waveguide. In these measurements a short-pulse laser is used to switch planar antennas photoconductively, generating freely propagating waveforms with instantaneous bandwidth from 15-75 GHz. Time-frequency signal processing is performed on the measured data, the results of which are in close agreement with the predictions of the asymptotic analysis. >

DISPERSION CURVES AND TRANSMISSION SPECTRA OF A TWO-DIMENSIONAL PHOTONIC BAND-GAP CRYSTAL : THEORY AND EXPERIMENT

An on‐shell method that combines plane‐wave and finite‐difference techniques for the calculation of dispersion curves and transmission spectra for electromagnetic fields in photonic band‐gap crystals is presented. The overall problem is decomposed into a field problem of determining the plane‐wave scattering from an individual crystalline layer and a conventional one‐dimensional network problem of combining this scattering to obtain the band structure of the entire crystal or the scattering properties of a crystal with a finite thickness. Results of the calculation are compared with experimental data measured using ultrawideband microwave pulses for a two‐dimensional photonic band‐gap crystal.

Wideband dispersion measurements of water in reflection and transmission

Planar antennas are switched photoconductively to generate picosecond bursts of freely-propagating radiation with usable spectral amplitudes from 5 to 85 GHz. This radiation is used to perform reflection and transmission measurements on materials, with experimental results presented for the complex index of refraction of water. We compare the relative merits of time-domain reflection and transmission material measurements and present new deconvolution techniques for extracting frequency-domain information from time-domain measurements. >

Characterization of layered dielectrics with short electromagnetic pulses

The use of picosecond duration bursts of electromagnetic radiation to study short-pulse wave propagation in layered dieletric materials is discussed. The radiation is generated using planar antennas that are switched photoconductively. The measurements are compared with time- and frequency-domain theoretical data. Issues associated with the windowing of time-domain results for highly resonant structures are addressed, as well as how the derived frequency domain data are influenced by the windowed Fourier transform. The accuracy of the time-domain results suggest that this technique may be a useful tool for characterizing layered materials. >