Funda Akleman

A novel finite-difference time-domain wave propagator

A novel time-domain wave propagator is introduced. A two-dimensional (2-D) finite-difference time-domain (FDTD) algorithm is used to analyze ground wave propagation characteristics. Assuming an azimuthal symmetry, surface, and/or elevated ducts are represented via transverse and/or longitudinal refractivity and boundary perturbations in 2-D space. The 2-D FDTD space extends from x=0 (bottom) to x/spl rarr//spl infin/ (top), vertically and from z/spl rarr/-/spl infin/ (left) to z/spl rarr//spl infin/ (right), horizontally. Perfectly matched layer (PML) blocks on the left, right, and top terminate the FDTD computation space to simulate a semi-open propagation region. The ground at the bottom is simulated either as a perfectly electrical conductor (PEC) or as a lossy second medium. A desired, initial vertical field profile, which has a pulse character in time, is injected into the FDTD computation space. The PML blocks absorb field components that propagate towards left and top. The ground wave components (i.e., the direct, ground-reflected and surface waves) are traced longitudinally toward the right. The longitudinal propagation region is covered by a finite-sized FDTD computation space as if the space slides from left to right until the pulse propagates to a desired range. Transverse or longitudinal field profiles are obtained by accumulating the time-domain response at each altitude of range and by applying the discrete Fourier transformation (DFT) at various frequencies.

Wave propagation inside a two-dimensional perfectly conducting parallel-plate waveguide: hybrid ray-mode techniques and their visualizations

This work is intended as an educational aid, dealing with high-frequency (HF) electromagnetic wave propagation in guiding environments. It is aimed at advanced senior and first-year graduate students who are familiar with the usual engineering mathematics for wave equations, especially analytic functions, contour integrations in the complex plane, etc., and also with rudimentary saddle-point (HF) asymptotics. After an introductory overview of issues and physical interpretations pertaining to this broad subject area, detailed attention is given to the simplest canonical, thoroughly familiar, test environment: a (time harmonic) line-source-excited two-dimensional infinite waveguide with perfectly conducting (PEC) plane-parallel boundaries. After formulating the Greens function problem within the framework of Maxwells equations, alternative field representations are presented and interpreted in physical terms, highlighting two complementary phenomenologies: progressing (ray-type) and oscillatory (mode-type) phenomena, culminating in the self-consistent hybrid ray-mode scheme, which usually is not included in conventional treatments at this level. This provides the analytical background for two educational MATLAB packages, which explore the dynamics of ray fields, mode fields, and the ray-mode interplay. The first package, RAY-GUI, serves as a tool to compute and display eigenray trajectories between specified source/observer locations, and to analyze their individual contributions to wave fields. The second package, HYBRID-GUI, may be used to comparatively display range and/or height variations of the wave fields, calculated via ray summation, mode-field summation, and hybrid ray-mode synthesis.

A Novel MoM- and SSPE-based Groundwave-Propagation Field-Strength Prediction Simulator

Knowledge of the local groundwave-propagation characteristics is essential in wireless systems. Although Maxwells equations establish the theoretical background, only a limited number of highly idealized groundwave-propagation problems have mathematically exact and/or approximate solutions. Therefore, semi-analytical/numerical and pure numerical simulation methods are almost the only way to handle realistic groundwave-propagation problems. To a certain extent, numerical simulators should be capable of taking non-flat, penetrable terrain and inhomogeneous atmospheric effects into account. Unfortunately, a generally applicable simulator has not yet appeared; there are many methods that have been developed under different assumptions and approximations, valid in different parameter regimes. It is therefore a challenge to apply these methods to the same physical problems, to do comparisons, and to evaluate numerical results. With all these factors in mind, a new MATLAB-based package GrMoMPE is introduced. It is first validated and calibrated, and then applied to some characteristic groundwave-propagation problems. The introduction of GrMoMPE has made it possible to do direct and accurate comparisons and reliable physical interpretations.

A novel TLM-based time-domain wave propagator

In this letter, a novel time-domain wave propagator, based on the transmission line matrix (TLM) technique, is introduced. A two-dimensional (2-D) TLM algorithm is modified and the sliding window technique is applied to analyze ground wave propagation characteristics. The longitudinal propagation region over the Earths surface is covered by a finite-size TLM computation space, as if the space slides from source to observation point. A short pulse is injected into the TLM computation space as a vertical initial source distribution near the left end and is traced within an adjustable window while propagating towards the right. Perfectly matched layer (PML) blocks on the left, top and right terminate the TLM computation space to simulate the semi-open propagation region. The ground at the bottom is a perfect electrical conductor (PEC). The PML blocks absorb field components that scatter back and top. The ground wave components (i.e., the direct, ground-reflected and surface waves) are traced longitudinally towards the right. Transient propagation can be observed at any range/altitude by accumulating the time history of the desired field components and any steady-state vertical and/or horizontal field profile at a desired frequency can be extracted by applying the off-line discrete Fourier transformation (DFT).

Realistic surface modeling for a finite-difference time-domain wave propagator

A new time domain wave propagator (TDWP) based on the two-dimensional finite-difference time-domain (FDTD) technique (for original paper see ibid., vol. V-14, p. 302-307 (1966)) that was introduced in May 2000 issue) has been augmented in this paper so that it deals with impedance boundary condition or varying terrain heights and an example of each, with comparisons to other methods is presented.

Visualizations of Wave Dynamics in a Wedge Waveguide with Non-Penetrable Boundaries: Normal-, Adiabatic-, and Intrinsic-Mode Representations

Many natural or man-made guiding environments are characterized by physical parameters that render the wave equation non-separable in any of the standard coordinate systems. In particular, in the absence of transverse-longitudinal separability, it is not possible to define discrete or continuous normal modes (NM) that individually satisfy the transverse boundary conditions and that propagate longitudinally without coupling to other modes. When transverse-longitudinal separability is only weakly perturbed, one may define local (adiabatic) modes that adapt smoothly, without inter-mode coupling, to the slowly changing conditions. Adiabatic modes (AM) fail in cutoff regions, and can be made uniform there by intrinsic modes (IM), which are synthesized by a spectral continuum of adiabatic modes. These concepts have been elucidated and validated previously by investigating the wave dynamics in a simple test environment: a wedge waveguide with non-penetrable boundaries, viewed either in coordinate-separable cylindrical coordinates that yield exact field solutions in terms of normal mode, or in non-separable rectangular coordinates that yield approximate field solutions in terms of adiabatic modes and intrinsic modes. The present article is intended as a tutorial to enhance the utility and understanding of these analytical formulations through visualizations of the dynamic interaction between the various wave species, implemented through an educational MATLABtrade package. The visualizations for the full range of ray, mode, and hybrid options, parameterized in the spectral wavenumber domain, has been explored by us previously for the inherently separable canonical environment of a line-source-excited parallel-plate waveguide. In our present investigation of the wedge waveguide, we shall not attempt to mimic the variety of options because of the substantial complications and subtleties inherent in their rectilinearly weakly-non-separable implementation. For our purposes here, a single specific option suffices to address the normal-mode, adiabatic-mode, and intrinsic-mode phenomenologies. Throughout this article, the intended audience is expected to be familiar with asymptotic methods for the evaluation of integrals.

3-D Imaging of Inhomogeneous Materials Loaded in a Rectangular Waveguide

A Newton-type method for the reconstruction of inhomogeneous 3-D complex permittivity variation of arbitrary shaped materials loaded in a rectangular waveguide is presented. The problem is first formulated as a system of integral equations consist of the well-known data and object equations, which contain the dyadic Greens function of an empty rectangular waveguide. Two unknowns of this system are solved in an iterative fashion by linearizing one of them, i.e., the data equation in the sense of the Newton method, which corresponds to a first-order Taylor expansion of the related integral operator. Since the problem is severely ill posed by nature, a regularization in the sense of Tikhonov is applied to the data equation. A detailed numerical implementation of the method, together with some numerical examples are also given to show the capabilities and validation limits of the method.

A novel implementation of Berenger's PML for FDTD applications

In this letter, a new implementation of the three-dimensional (3-D) perfectly matched layer (PML) in finite-difference time-domain (FDTD) applications is introduced. This technique is based on doubling the cell dimensions in PML region where extra averaging of electrical field components are necessary at the edges and faces along the PML-FDTD interfaces. The presented numerical examples are for 3-D structures which exhibit complex wave phenomena. Significant improvement obtained after this implementation, especially at lower frequencies, is demonstrated.

Analysis of Direct and Inverse Problems Related to Circular Waveguides Loaded With Inhomogeneous Lossy Dielectric Objects

An integral-equation-based analysis for direct and inverse problems related to circular waveguides loaded with inhomogeneous and arbitrarily shaped lossy dielectric material is introduced. The problem is formulated as a system of integral equations composed of the well-known data and object equations, which contain the dyadic Greens function (DGF) of the empty circular waveguide. Both the direct and inverse algorithms are based on this 3-D system of equations. In the direct problem, the scattering parameters are calculated using the scattered electric fields caused by the inhomogeneous lossy dielectric objects located in circular waveguide, while in the inverse algorithm, the scattered fields are assumed to be known and used for the determination of the complex permittivity variation of the object loaded in the waveguide through a Newton-type iterative approach. In both algorithms, the integral equations are solved via a method-of-moments-based discretization, where the accurate integration of the DGF at each discrete 3-D cell is achieved by a special integration technique. The validity region and the reliability of the direct and inverse algorithms are examined analytically and numerically through elaborative examples.

Contrast source inversion technique for the reconstruction of 3D inhomogeneous materials loaded in a rectangular waveguide

An inverse scattering approach based on the contrast source inversion (CSI) algorithm is presented for the determination of the three-dimensional (3D) complex permittivity variation of arbitrarily shaped materials loaded in a rectangular waveguide. First the problem is introduced by the definition of the electric field integral equation based data and object equations, which contain the dyadic Green function of an empty rectangular waveguide. The resulting inverse scattering problem for the unknown complex permittivity of the loading is solved by the CSI technique, which is adapted by a modal expansion approach for the guiding structures. A detailed numerical implementation of the method together with some illustrative examples is given to show the effectiveness as well as the capabilities of the method.