Inhomogeneous Lossy Medium Research Articles

Perfectly Matched Layers for time-harmonic transverse electric wave propagation in cylindrical and toroidal gyrotropic media

In this paper we implement the stretched-coordinate Perfectly Matched Layer (PML) technique in [28] to emulate full power absorption outside the simulation domain for time-harmonic electromagnetic wave propagation in presence of gyrotropic dielectric tensor and curved geometry relevant for magnetized plasma devices. We recall the PML formulation as an artificial inhomogeneous lossy medium, following the stretching into the complex plane of a general system of three orthogonal curvilinear coordinates. We apply the general method in cylindrical and toroidal geometries. We then assess this technique in a simple case combining gyrotropy and coordinate curvature. Our test problem analytically quantifies the reflection of Transverse Electric (TE) cylindrical eigenmodes in a gyrotropic medium by a radial PML in cylindrical geometry. The obtained reflection coefficient involves wave, PML and geometric parameters at the PML location. The new coefficient generalizes the one obtained earlier with Cartesian coordinates, and becomes equivalent when the effects of the local cylindrical curvature at the PML (stretched) location can be neglected. These curvature effects are outlined and the limitations they impose on the properties of the PML are quantified as a function of the relevant parameters. Peculiarities related to the gyrotropy are also highlighted. Finite element calculations of the test problem in two-dimensional cylindrical geometry are exploited to verify these properties numerically. Indications are finally given on how to choose the PML parameters in order to obtain a minimal wave reflection at given numerical cost, taking into account errors associated with the numerical scheme.

Optimization of Sensor Network Topology in Deployed in Inhomogeneous Lossy Media

This paper presents optimization of wireless sensor network (WSN) topology for forest fire detection. The sensors for this purpose are deployed in forest, grassland and open space, which have different attenuation properties in electromagnetic waves. For this reason, routers which receive signals from sensors and send them to the base station must be deployed considering these differences. In this work, we develop an optimization method for WSN topology based on simulated annealing considering the differences in the attenuation property. The vegetation data are taken from Landsat data. Using the present method, the necessary number of routers for full connection of the sensors deployed in diverse, irregular environments can be estimated.

Propagation in Finite Lossy Media: <newline/>An Application to WBAN

The Wireless Body Area Network (WBAN) has become an important part of the wireless communication world in the past decade leading to the need for efficient antennas for In-, On- and Off-Body links. The design of such antennas depends critically on the understanding of their interaction with the host body, and thus on the propagation of waves in inhomogeneous lossy media of finite dimensions. To this aim, we propose a simplified spherical multishell model of the lossy body, and study its interaction with elementary sources placed within or on the latter.

Focusing time harmonic scalar fields in non-homogenous lossy media: Inverse filter vs. constrained power focusing optimization

Two strategies to focus time harmonic scalar fields in known inhomogeneous lossy media are compared. The first one is the Inverse Filter (IF) method, which faces the focusing task as the synthesis of a nominal field. The second one is the Constrained Power Focusing Optimization (CPFO) method, which tackles the problem in terms of constrained mask constrained power optimization. Numerical examples representative of focusing in noninvasive microwave hyperthermia are provided to show that CPFO is able to outperform IF, thanks to the additional degrees of freedom arising from the adopted power synthesis formulation.

A General Three-Dimensional Tensor FDTD-Formulation for Electrically Inhomogeneous Lossy Media Using the Z-Transform

A general three-dimensional tensor finite-difference time-domain (TFDTD) formulation is derived to model electrically inhomogeneous lossy media of arbitrary shapes. The time domain representation of electric losses is achieved using Z-transforms. The regular cubical grid structure is maintained everywhere in the calculation domain by defining a 3-D face-fraction based 3 x 3 permittivity tensor on the interfaces that describes the relationship between the (known) average flux density vector and the (unknown) local electric field vector. For electrically lossy media, this tensor is complex in the frequency domain. However, it can be modified for use with the Z-transform. Only this modified real form is inverted, then transformed from the frequency into the Z-domain, and finally into the time domain. Furthermore, a local interface matrix is used to describe the relationship between the local electric field in the grid node and its counterpart on the other side of the interface. This matrix is complex in the frequency domain for lossy media. By applying the Z-transform, this matrix can also be transformed into the time domain using only real modified matrix elements. The accuracy of the method is confirmed by comparisons with analytical solutions.

Multidomain pseudospectral time-domain simulations of scattering by objects buried in lossy media

A multidomain pseudospectral time-domain (PSTD) method with a newly developed well-posed PML is introduced as an accurate and flexible tool for the modeling of electromagnetic scattering by 2-D objects buried in an inhomogeneous lossy medium. Compared with the previous single-domain Fourier PSTD method, this approach allows for an accurate treatment of curved geometries with subdomains, curvilinear mapping, and high-order Chebyshev polynomials. The effectiveness of the algorithm is confirmed by an excellent agreement between the numerical results and analytical solutions for perfectly conducting as well as permeable dielectric cylinders. The algorithm has been applied to model various ground-penetrating radar (GPR) applications involving curved objects in a lossy half space with an undulating surface. This multidomain PSTD algorithm is potentially a very useful tool for simulating antennas near complex objects and inhomogeneous media.

Simultaneous reconstruction of approximate profiles of an inhomogeneous lossy medium through a collocation method

In this paper a one-dimensional inverse-scattering problem is considered. Two approximate inversion formulae are derived. Using these formulae, approximate permittivity and conductivity profiles of an inhomogeneous lossy medium are simultaneously generated from the partial knowledge of the reflection coefficient in the frequency domain. These formulae are deduced through the application of linear transformations to two nonlinear differential equations for the reflection coefficient in the frequency domain. Discrete versions of the inversion formulae are also developed. The transformed equations for the reflection coefficient in the frequency domain are applicable irrespective of whether the derivative of the unknown permittivity profile exists. An example to demonstrate these approximate inversion formulae is given.

Inverse scattering method for one-dimensional inhomogeneous lossy medium by using a microwave networking technique

The formulation of reflection coefficients from an inhomogeneous lossy medium illuminated by TE and TM waves is approximately derived, in closed form, by using a microwave network method. From the formulation, a novel inverse scattering scheme to reconstruct simultaneously the permittivity and conductivity profiles, is proposed. This scheme is suitable for both continuous and discontinuous profiles, under both the weak scattering and strong scattering conditions. It has also been shown that when the conductivity of the medium equals zero, the reconstructed result of this scheme will reduce to the one formulated by Ladouceur and Jordan (1985). Numerical and closed-form reconstruction examples show the validity of the scheme.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonlinear differential equation for the reflection coefficient of an inhomogeneous lossy medium and its inverse scattering solutions

Nonlinear differential equations for the reflection coefficients of an inhomogeneous lossy medium illuminated by both TE-polarized and TM-polarized electromagnetic plane waves are derived using a microwave networking technique, which can be approximately solved by a nonlinear renormalization method. Considering the equivalent microwave network of the permittivity profile discontinuity at the interface of free space with the medium, two novel inverse scattering solutions for the permittivity profile and the conductivity profile are further investigated in closed forms. Closed-form and numerical reconstruction examples show the availability of this scheme.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Inverse scattering method for one‐dimensional inhomogeneous lossy medium using linear prediction method

AbstractA method of solution based on a linear prediction method is presented for an inverse scattering problem in which the permittivity ε(x) and the conductivity s̀(x) in a one‐dimensional inhomogeneous lossy material are estimated from the reflected and transmitted waves. The present method is shown in the following manner. First, from Maxwell's equation governing the medium, coupled equations for the forward and backward waves are derived which subsequently are discretized. In the discretized coupled equations, the permittivity ε(x) and the conductivity s̀(x) are included as coupling potentials. Also, if these discretized coupled equations are used, the transmitted and reflected waves for the incident impulse are an AR and an ARMA process, respectively. Their AR and MA parameters are closely related to the coupling potentials. Hence, from the reflected and transmitted waves for the incident impulse, the permittivity and permeability of the medium can be determined via the coupling potentials. To confirm the validity of the forementioned method, several computer simulations have been carried out.

Direct and inverse scattering in the time domain for a dissipative wave equation. III. Scattering operators in the presence of a phase velocity mismatch

The direct scattering problem for an inhomogeneous lossy medium is examined for the one-dimensional case in which the phase velocity profile is discontinuous at the boundaries of the medium. Scattering operators (or impulse responses) and propagation operators are defined and equations that govern their behavior are developed. Knowledge of the scattering kernels for one round trip in the medium implies that the scattering kernels can be determined on any time interval. Numerical examples are presented. It is also shown that this scattering problem is reducible to one in which there are no phase velocity mismatches. This reduction provides considerable numerical advantage in the solution of the direct scattering problem. The inverse problem is examined in a companion paper.

Direct acoustic scattering for one-dimensional lossy media

The scattering of acoustic waves by inhomogeneities within a one-dimensional lossy medium is investigated. The inhomogeneities may be spatial variations in the attenuation coefficient of the lossy medium and/or variations in its density and wave velocity. The frequency dependence of the attenuation coefficient is modeled after loss mechanisms governed by viscosity, heat conduction, and single and multiple relaxation processes. Two methods previously developed for lossless media—the transmission matrix method and the forward scattering or impediography method—are extended to treat the determination of the reflection and transmission coefficients of an inhomogeneous lossy medium. These scattering coefficients are numerically determined for several one-dimensional media with varying density and attenuation profiles.

The overall sink strength of an inhomogeneous lossy medium. Part II: variational estimates

Trial fields generated by trial polarizations are substituted into the classical variational principles for the model system introduced in Part I. The resulting expressions are simplified by discarding certain terms which vanish quadratically at the actual solution, to yield a ‘Hashin-Shtrikman’ variational principle for the system under consideration. Substitution of simple configuration-dependent trial polarizations yields expressions that are identical with those obtained from the QCA in Part I. This demonstrates that the self-consistent QCA has an interpretation in terms of a variational principle and, furthermore, that the self-consistent prescription of Willis (1983, 1984) in fact produces a bound. The opposite bound can also be obtained by choosing the sink parameter of the comparison medium to be that of the inclusions. Results are presented for two cases, both assuming Percus-Yevick statistics. The bounds are usefully close when k 1 2 k 2 2 = ;10 ; the self-consistent QCA lies between them but the simple Brailsford-Bullough estimate does not. The case k 1 2 k 2 2 = ;10 6 is also discussed, as a model for voids in a lossy matrix.

The overall sink strength of an inhomogeneous lossy medium. Part I: self-consistent estimates

Steady-state diffusion in a medium containing a continuous distribution of sinks is considered. The medium comprises a matrix, with sink strength k 2 2 , which contains a random array of identical spherical inclusions, with sink strength k 1 2 . On a macroscopic scale, the medium appears homogeneous, with uniform sink strength k ̃ 2 . This work is devoted to the estimation of the overall sink strength k ̃ 2 , in terms of k 1 2, k 2 2 and the statistics of the distribution of the inclusions. Part I discusses three distinct schemes of self-consistent type. One is based upon a simple embedding procedure and makes no explicit allowance for spatial correlations. The other two make use, in different ways, of the quasicristalline approximation (QCA). Part II develops variational principles which yield bounds for k ̃ 2 . The self-consistent estimates are interpreted relative to the variational formulation and explicit numerical results are presented.

Wave propagation and profile inversion in lossy inhomogeneous media

Using the Lagrangian approach, a time-domain analysis of wave propagation in an inhomogeneous lossy medium is described. We consider a half-space problem (x ≥ 0) in which the medium is plane stratified in the direction of propagation and can be modeled by a piecewise uniform lossy transmission line. A method of profile inversion which is based directly upon quantities measured in time at the sending end boundary is presented. The problem of uniqueness is discussed. For a given medium, computer simulation results obtained by using the known reflected waves at the boundary x = 0 are shown.

Local properties of radiation in lossy media

In lossless inhomogeneous media the ray-optical description of the propagation and scattering of electromagnetic waves exhibits the local and sequential properties of these phenomena. The extension of ray optics to lossy inhomogeneous media does not exhibit such properties, in general, since the equations defining the paths of rays connecting real source and observation points yield complex values of the space coordinates, i.e., complex rays. The purpose of this paper is to clarify the local and sequential propagation characteristics of fields in an inhomogeneous lossy medium, and to assertain the significance of the complex rays. The simplest configuration suited to this purpose is a planar interface between homogeneous lossless and lossy half-spaces. By studying the shadowing effects produced at an observation point by sampling windows placed in planes crossed by the field, one finds the region through which the field principally propagates to the observation point, and there-from the local and sequential properties. The results give physical meaning to complex rays and should provide a basis for a description of propagation and scattering in lossy media that avoids the use of complex space.