Stratified Dispersive Media Research Articles

Parameter Estimation of Damped Power-Law Phase Signals via a Recursive and Alternately Projected Matrix Pencil Method

We propose a novel algorithm based on the matrix pencil method to estimate the parameters of a class of signals modeled as damped power-law phase signals. This class arises primarily from the electromagnetic probing of dispersive geological and civil engineering materials as a consequence of the universal dielectric response. When stratified media are considered, direct application of conventional matrix-shifting methods is hindered not only by the nonlinear frequency dependency which destroys the desired shift-invariance property of the data matrix, but also by the stratified structure of the medium which introduces a cumulative effect. In this regard, the proposed algorithm restores recursively the Vandermonde structure of one mode vector at a time by means of a spline-interpolation technique and then orthogonally projects it to filter out its contribution before passing to another. The algorithm is tested on simulated and experimental data resulting from the probing of a stratified dispersive medium, and its performance is assessed against the Cramer-Rao lower bound. For the example of experimental data, collected from concrete cores by means of a cylindrical transition line, the permittivities at the reference frequency and the dispersion indices are determined using the new algorithm and compared with those of a nonlinear optimization scheme.

Parameter estimation of dispersive media using the matrix pencil method with interpolated mode vectors

A modified matrix pencil method (MPM) inspired by interpolated arrays is proposed for the problem of parameter estimation in dispersive media obeying a frequency power law. A direct consequence of the arising dispersive signal model is that the Hankel prediction matrix can no longer be expressed using the Vandermonde decomposition, which hinders the direct application of all matrix-shifting techniques including the MPM. This is remedied by restoring the Vandermonde structure of the mode vectors via two different interpolation procedures. The first procedure is two dimensional, whereas the second one is one dimensional and iterative. The two versions of the interpolated algorithm are tested on simulated data representing radar acquisitions over a stratified dispersive medium, and their performance is assessed against the CramerRao lower bound. The obtained results indicate that the iterative interpolation procedure affords the optimal performance of its two-dimensional counterpart at a reduced computational burden.

Interpolation-based matrix pencil method for parameter estimation of dispersive media in civil engineering

In this paper, we propose a modified matrix pencil method for the problem of time delay estimation in dispersive media obeying a particular frequency power law, namely, the constant- Q model. Being based on a Vandermonde decomposition of the prediction matrix, the matrix pencil method produces biased estimates when applied directly to data of the constant- Q model. The proposed approach allows to compensate for the bias inherent to the classical method by restoring the Vandermonde structure via a spline-interpolation technique. The restoration involves an iterative procedure where each iteration selects a set of interpolated samples depending on the value of the quality factor of the previous iteration. The algorithm is tested on simulated data representing radar acquisitions over a stratified dispersive medium, and its performance is assessed against the Cramér–Rao lower bound.

FDTD scattered field formulation for scatterers in stratified dispersive media

We introduce a simple scattered field (SF) technique that enables finite difference time domain (FDTD) modeling of light scattering from dispersive objects residing in stratified dispersive media. The introduced SF technique is verified against the total field scattered field (TFSF) technique. As an application example, we study surface plasmon polariton enhanced light transmission through a 100 nm wide slit in a silver film.

Numerical solution of nonlinear wave equations in stratified dispersive media

Nonlinear wave motion in dispersive media is solved numerically. The model applies to laser propagation in a relativistic plasma. The latter causes, besides dispersion, nonlinear effects due to relativistic mass variation in the presence of strong laser pulses. A new variant of the Gautschi-type integrator for reducing the number of time steps is proposed as a fast solver for such nonlinear wave-equations. In order to reduce the number of spatial grid points, a physically motivated quasi-envelope approach (QEA) is introduced. The new method turns out to reduce the computational time significantly compared to the standard leap-frog scheme.

Diffusion approximation in space-time geometrical optics

A Fokker-Planck equation that describes the diffusion of a quasi-monochromatic wave packet in a stratified dispersive medium with random inhomogeneities is derive from the ray equations of space-time geometrical optics. The equation obtained does not have limitations on the angle of scattering or on the random field that determines the inhomogeneities of a medium. The Fokker-Planck equation in question includes all equations considered earlier in the quasi-static approximation as particular cases. The solution of the problem connected with the investigation of statistical properties of wave packets that propagate in an averagely homogeneous nondispersive medium, is given as an example of a practical application.

Aerial and Buried Wires above Stratified Dispersive Media

This paper discusses plane wave reflection and transmission characteristics for soils which are modeled as plane, stratified media with frequency-dependent constitutive parameters. Values selected for soil conductivity and electrical permittivity in each layer of soil were based upon measurements of water content as a function of depth obtained from U.S. Geological Survey data. Currents induced by plane wave illumination are calculated for long wires above and below ground. The results are compared to those obtained from simplified soil models which ignore the frequency-dependence of the constitutive parameters. Currents calculated for buried and aerial wires with near grazing incidence were found to display a strong dependence upon details of the soil model due to attenuation and reflections which occur during wave propagation through stratified, conductive media.

Light propagation in a stratified dispersive medium

Light propagation in a stratified dispersive medium

Reflection of pulses at oblique incidence from stratified dispersive media

The reflection coefficient is calculated at normal and oblique incidence for a sine-squared pulse with the middle layer having a frequency dependent complex permittivity. The two important results of the theoretical investigation are the importance of the frequency dependence of the complex dielectric constant in pulse propagation studies as well as the unique effect that occurs at some angles of incidence at parallel polarization in which the power from the second interface exceeds the primary reflection from the first interface.

Transient radiation in a plane stratified dispersive medium. II. Exponential profile, plasma slab, and plasma gap

In a previous paper by the authors, a similarity principle was derived for a class of transient diffraction problems in cold, lossless, isotropic, plane stratified plasmas. In this paper, the similarity principle will be utilized to obtain exact closed-form solutions to three specific problems; the problems of an impulsive point magnetic dipole (the current density is a delta function in space and time) in the presence of (1) a continuously varying plane stratified plasma with an exponential electron density profile, (2) a grounded plasma slab, and (3) a grounded plasma gap. In the case of the exponential electron density profile, the solution to the problem suggests a new type of approximation to cases where the profile is slowly varying but otherwise arbitrary. In the case of the slab and gap problems an interpretation will be given in terms of multiply-reflected rays within the slab. The gap problem is particularly interesting because, if the impulsive time dependence of the source were replaced by a harmonic time dependence, this problem would be distinguished by the presence of a surface wave. Thus an examination of the gap problem serves to illustrate the role played by the surface wave in the transient case.

Transient radiation in a plane stratified dispersive medium. I. Half-space configuration

In this paper a similarity principle will be derived for a class of transient diffraction problems in cold, lossless, isotropic plane stratified plasmas. The similarity principle will be utilized to obtain an exact closed-form solution to the problem of a magnetic current source whose density is a delta function (in space and time) situated either in or above a homogeneous plasma half-space. This solution will be interpreted in terms of rays and group velocity. An independent solution to the half-space problem will also be obtained using asymptotic techniques. Exact and asymptotic solutions will be compared and discussed.