Transient Electromagnetic Wave Propagation Research Articles

A Hybrid 3-D-ADI-TDPE/DGTD Method for Multiscale Target Echo Simulation in Large-Scale Complex Environments

In this article, we propose a novel hybrid method for multiscale target echo simulation in large-scale complex environments. The three-dimensional-alternating direction implicit-time domain parabolic equation (3-D-ADI-TDPE) method with refractive index terms and the discontinuous Galerkin time-domain (DGTD) method are combined to solve the propagation of transient electromagnetic waves in large-scale regions and backscattering in multiscale target regions, respectively. At the same time, to realize the connection of two regions and the prediction of target echo, the transfer functions of wave propagation and target backscattering are obtained by the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula> transform (ZT). In addition, the target echo process is transformed into a cascade of transfer functions to realize simulation modularization and parallel processing. We also discuss the performance of the proposed method in terms of accuracy, memory consumption, and CPU processing time. Results indicate that the processing time required by the 3-D-ADI-TDPE/DGTD hybrid method is more than 11 times less than that of DGTD alone. Moreover, the ZT improves the flexibility of the hybrid method and provides a new concept for the simulation technology of radio wave propagation.

3-D Forward Modeling of Transient EM Field in Rough Media Using Implicit Time-Domain Finite-Element Method

In a heterogeneous medium (usually called a rough medium) with fractured formations, the propagation of an electromagnetic (EM) field is a type of subdiffusion. Current mainstream geophysical EM data processing methods cannot be applied to data acquired on heterogeneous Earth, as they are not governed by the classic diffusion theory. To evaluate the influence of roughness on the transient EM (TEM) signal for a complex model and contribute to data inversion, we proposed a novel three-dimensional (3-D) forward modeling scheme for TEM in rough media. First, we derived the governing equation with a fractional-order time derivative for the subdiffusion of EM waves in rough media. Then, we proposed a novel time discretization using an unequal step length for the Caputo operator, which significantly reduces the total number of time steps. Finally, an implicit time-domain finite-element method using unstructured tetrahedron discretization was adopted to solve the 3-D forward problem. Furthermore, an efficient time segmentation strategy combined with parallel RHS construction was proposed to accelerate modeling. The numerical results prove that the proposed method is accurate and efficient, and will be a powerful numerical method for analyzing TEM wave propagation and processing TEM data in areas with multiscale fractures or porosity.

A new FDTD stencil for reduced numerical anisotropy in the computer modeling of wave phenomena

An isotropic finite difference scheme is utilized for the development of a new stencil for the finite-difference time-domain (FDTD) modeling of electromagnetic wave propagation. The key attribute of the new stencil is the improved isotropy of the numerical phase velocity at fairly moderate spatial sampling of the fields. More specifically, for a given phase velocity anisotropy error, the new stencil requires a much coarser grid than the one required by the standard, second-order accurate FDTD stencil. This, in turn, amounts to gains in computational resources when transient electromagnetic interactions in electrically-large domains are being modeled. The numerical attributes of the proposed stencil, namely, its dispersion, anisotropy and stability, are presented in the context of its application to the numerical simulation of two-dimensional transient electromagnetic wave propagation. Through a series of numerical studies, the enhanced isotropy provided by the proposed scheme is demonstrated and contrasted in a quantitative manner to that of the standard FDTD stencil. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.

Causality in the propagation of transient electromagnetic waves in a left-handed medium

Since the concept of left-handed medium (LHM) was proposed, the causality has been a big concern in the understanding of LHM. Through an exact analysis of a 1D transient current source radiating in a LHM, the causality in the propagation of electromagnetic waves is investigated where three cases are considered for different frequency dispersions in LHM. Numerical experiments have shown that the causality would be violated if the LHM were homogeneous and frequency nondispersive in the whole frequency range or in a certain frequency band. However, such a nondispersive LHM does not exist. For a realistic artificial LHM which is frequency dispersive [Science 292, 77 (2001)], we have shown that the causality is not violated at all.

Wavelet-based analysis of transient electromagnetic wave propagation in photonic crystals.

Photonic crystals and optical bandgap structures, which facilitate high-precision control of electromagnetic-field propagation, are gaining ever-increasing attention in both scientific and commercial applications. One common photonic device is the distributed Bragg reflector (DBR), which exhibits high reflectivity at certain frequencies. Analysis of the transient interaction of an electromagnetic pulse with such a device can be formulated in terms of the time-domain volume integral equation and, in turn, solved numerically with the method of moments. Owing to the frequency-dependent reflectivity of such devices, the extent of field penetration into deep layers of the device will be different depending on the frequency content of the impinging pulse. We show how this phenomenon can be exploited to reduce the number of basis functions needed for the solution. To this end, we use spatiotemporal wavelet basis functions, which possess the multiresolution property in both spatial and temporal domains. To select the dominant functions in the solution, we use an iterative impedance matrix compression (IMC) procedure, which gradually constructs and solves a compressed version of the matrix equation until the desired degree of accuracy has been achieved. Results show that when the electromagnetic pulse is reflected, the transient IMC omits basis functions defined over the last layers of the DBR, as anticipated.

Transient electromagnetic wave propagation in laterally discontinuous, dispersive media

This paper concerns propagation of transient electromagnetic waves in laterally discontinuous dispersive media. The approach, used here, employs a component decomposition of all fields. Specifically, the propagation operator that maps a transverse field on one plane to another plane is specified. Expansion of this mapping near the wave front determines the precursor or forerunner of the problem.

Propagation of transient electromagnetic waves in inhomogeneous and dispersive waveguides

Transient wave propagation in a waveguide filled with an inhomogeneous dispersive medium is analyzed. The waveguide is inhomogeneous in the longitudinal direction, but is homogeneously filled in the transverse directions. The analysis is performed in the time domain and is based upon a wave splitting technique and the method of propagators. The propagator maps the exciting field from one position in the waveguide to the field at another position. This mapping is represented as time convolution integrals. The theory is exemplified by numerical examples where it is shown how wave trains of different shapes are propagating in a waveguide filled with a homogeneous dispersive medium.

Wave propagators for transient waves in periodic media

One-dimensional propagation of transient electromagnetic waves in periodic media is studied. The media are periodic in the direction of propagation and can be of finite or infinite length. Wave propagators that map a transient field from one point in the medium to another are introduced. A number of useful relations for the propagators are presented. Some of these relations are used in the determination of explicit expressions for the short time behavior of a transient wave as it propagates in a periodic medium. The theory is exemplified by several numerical examples.

Propagation of transient electromagnetic waves in time-varying media-direct and inverse scattering problems

Wave propagation of transient electromagnetic waves in time-varying media is considered. The medium, which is assumed to be inhomogeneous and dispersive, lacks invariance under time translations. The spatial variation of the medium is assumed to be in the depth coordinate, i.e. it is stratified. The constitutive relations of the medium are a time integral of a generalized susceptibility kernel and the field. The generalized susceptibility kernel depends on one spatial and two time coordinates. The concept of wave splitting is introduced. The direct and inverse scattering problems are solved by the use of an imbedding or a Green function approach. The direct and the inverse scattering problems are solved for a homogeneous semi-infinite medium. Explicit algorithms are developed. In this inverse scattering problem, a function depending on two time coordinates is reconstructed. Several numerical computations illustrate the performance of the algorithms.

Transient electromagnetic wave propagation in waveguides

This paper focuses on propagation of transient electromagnetic waves in waveguides of general cross section with perfectly conducting walls. The solution of the transient wave propagation problem relies on a wave splitting technique, which has been frequently used in direct and inverse scattering problems during the last decade. The field in the waveguide is represented as a time convolution of a Green function and the excitation. Some numerical computations illustrate the method. A new way of calculating the first precursor in a Lorentz medium is presented. This method, which is not based upon the classical asymptotic methods, gives an expression of the first precursor at all depths in the medium. The excitation of the waveguide modes for time dependent sources is also addressed.

Transient electromagnetic wave propagation in anisotropic dispersive media

Transient electromagnetic wave propagation in a stratified, anisotropic, dispersive medium is considered. Specifically, the direct scattering problem is addressed. The dispersive, anisotropic medium is modeled by constitutive relations (a 3 × 3 matrix-valued susceptibility operator) containing time convolution integrals. In the general case, nine different susceptibility kernels characterize the medium. An incident plane wave impinges obliquely upon a finite slab consisting of a stratified anisotropic medium. The scattered fields are obtained as time convolutions of the incident field with the scattering kernels. The scattering (reflection and transmission) kernels are uniquely determined by the slab and are independent of the incident field. The scattering problem is solved by a wave-splitting technique. Two different methods for determining the scattering kernels are presented: an embedding and a Green’s function approach. Explicit analytic expressions of the wave front are given for a special class of media. Some numerical examples illustrate the analysis.

Scattering of Transient Electromagnetic Waves in Reciprocal Bi-Isotropic Media

In this paper propagation of transient electromagnetic waves in a reciprocal bi-isotropic medium is presented. The constitutive relations are convolution integrals with two susceptibility kernels that model the medium. The propagation problem is solved by the introduction of a wave-splitting technique. This wave-splitting is used to solve the propagation problem using either an imbedding approach or a Green's function technique. In particular, the scattering problem of an electromagnetic wave that impinges normally on a slab of finite or infinite extent is solved. The slab is assumed to be inhomogeneous with respect to depth. The scattering problem consists of finding the reflected and the transmitted fields and the generic quantities are the reflection and the transmission kernels of the medium. Explicit expressions for the rotation and the attenuation of the wave front is presented for the inhomogeneous slab. In the special case of a homogeneous infinite slab it is proved that the reflection kernel satisfies a nonlinear Volterra equation of the second kind, very suitable for numerical calculations. It is also proved that no cross polarization contribution appears for the homogeneous slab. Several numerical computations illustrate the analysis.

Scattering of Transient Electromagnetic Waves in Reciprocal Bi-Isotropic Media

In this paper propagation of transient electromagnetic waves in a reciprocal biisotropic medium is presented. The constitutive relations are convolution integrals with two susceptibility kernels that model the medium. The propagation problem is solved by the introduction of a wave-splitting technique. This wave-splitting is used to solve the propagation problem using either an imbedding approach or a Green's function technique. In particular, the scattering problem of an electromagnetic wave that impinges normally on a slab of finite or infinite extent is solved. The slab is assumed to be inhomogeneous with respect to depth. The scattering problem consists of finding the reflected and the transmitted fields and the generic quantities are the reflection and the transmission kernels of the medium. Explicit expressions for the rotation and the attenuation of the wave front is presented for the inhomogeneous slab. In the special case of a homogeneous infinite slab it is proved that the reflection kernel satisfies a nonlinear Volterra equation of the second kind, very suitable for numerical calculations. It is also proved that no cross polarization contribution appears for the homogeneous slab. Several numerical computations illustrate the analysis.

Transverse Propagation of Transient Electromagnetic Waves in a Non-homogeneous Half-space

The problem of a transient, transverse electromagnetic wave incident on a non-homogeneous half space is considered. Solutions are obtained by both the Laplace transform technique (LT) and the method of characteristics (MOC). The former method yields an infinite number of exact solutions in closed-form provided that the dielectric and permeability parameters are distributed as power laws in the spacial coordinate. A method for systematically generating these solutions is given. The method of characteristics, in numerical form, provides approximate solutions along the curved characteristics. Agreement between the two methods is excellent, except for a certain anomalous class of inhomogeneities. Finally, certain quasi-static solutions, involving a variety of inhomogeneities, are demonstrated.

Plane transient electromagnetic wave propagation in a generalized conducting medium

A technique first suggested by Knop ( 1) has been used to invert exactly a special contour integral arising in the study of space-time evolution of pulsed plane electro- magnetic signals in the presence of a class of generalized conducting media. The final expressions are given in terms of Lommel functions of two imaginary variables. These findings have been applied to the examination of plane transient wave propagation in uniformly moving conducting media, and materials described by a dissipative Klein-Gordon equation.

Transient Propagation of Electromagnetic Waves in a Stratified Plasma

The method of characteristics is applied to the study of transient electromagnetic wave propagation in a stratified plasma. The technique is applicable to lossy, anisotropic, time‐varying plasmas whose parameters may vary in the direction of wave propagation. Numerical results demonstrate good agreement with theory.

Experimental Observation of Sommerfeld and Brillouin Precursors in the Microwave Domain

An experimental investigation of transient electromagnetic wave propagation in the microwave frequency range related to the theoretical investigation of Sommerfeld and Brillouin is reported. Both the Sommerfeld and Brillouin precursors are shown experimentally.

Electromagnetic Pulse Propagation in Lossless, Inhomogeneous, Dispersive, Dielectric Media

This paper develops geometrical optics ray techniques for problems of transient electromagnetic wave propagation in inhomogeneous, lossless, dispersive, dielectric media. The method results in a series expansion of the fields about the wavefronts. The theory is applied to solve a few illustrative problems dealing with wave propagation in a cold isotropic plasma. Special attention is given to the fact that in all physical media the wavefronts must propagate at the speed of light in vacuum. This physical requirement does not seem to have been incorporated into the mathematical models used in previous works dealing with geometrical optics techniques for solving transient electromagnetic wave problems.

Discussions and Communications: Propagation of Transient Electromagnetic Waves in a Conducting Medium

Wait (1951) has calculated the transient electric fields for several types of step-function current sources placed inside a conducting medium. Now any generated pulse will require a finite build-up time to reach its final magnitude from its initial value of zero. In most cases, this type of pulse may be very well approximated by a ramp-function pulse (Figure 1). Expressions for the electric field of this type of pulse will be deduced in the following analysis.