General solutions of Maxwell's equations for signals in a lossymedium. II. Electric and magnetic field strengths due to magneticexponential ramp function excitation

For pt.I see ibid., vol.30, no.1, p.29-36 (1988). Solutions for the electric and magnetic field strengths in a lossy medium due to a magnetic exponential ramp function excitation are presented. The solutions are in integral form and are evaluated by numerical integration methods using a digital computer. Computer plots for the electric and magnetic field strengths at different locations in the propagation medium are given. The plots obtained for the transients can be used to represent solutions in lossy media for signals that can be represented in terms of a time-series expansion of the transients     

General solutions of Maxwell's equations for signals in a lossymedium. III. Electric and magnetic field strengths due to electric andmagnetic sinusoidal pulse excitation

For pt.II see ibid., vol.30, no.1, p.37-40 (1988). The representation of a function with a general time variation by a series expansion of time-shifted transients is discussed. On the basis of this representation, numerical solutions of Maxwell's equations are presented for the electric and magnetic field strengths in a lossy medium due to electric and magnetic excitation functions consisting of a finite number of sinusoidal cycles. The solutions are derived by means of a time-series expansion of the available solutions for the electric and magnetic exponential ramp function excitations     

Correction of Maxwell's Equations for Signals II

In the first of two companion papers it was shown that the addition of a magnetic current density to Maxwell's equations is a sufficient condition to obtain solutions in lossy propagation media for waves that are not infinitely extended periodic waves. The solutions obtained represented transients that may be used to represent signals having a beginning and an end. This second paper shows that the addition of a magnetic current density is also a necessary condition for the existence of transient solutions in lossy media. The modification of Maxwell's equations is thus necessary and sufficient for the study of the propagation of signals in lossy media.     

A comparison of transient solutions of Maxwell's equations to thatof the modified Maxwell's equations

In 1986 H.F. Harmuth introduced a modification of Maxwell's equations to study the propagation of transient electric and magnetic field strengths in lossy media. Opponents of this modification of Maxwell's equations have claimed and attempted to demonstrate that Maxwell's equations in their known forms can correctly be solved, for example by the Laplace transformation method, to obtain solutions of transient electric and associated magnetic field strengths in lossy media without encountering any difficulties. This work presents detailed computer plots of Harmuth's transient solutions of the modified Maxwell's equations and that of Maxwell's equations solved by the Laplace transformation characteristic for the two solutions, which indicate that they are not the same. It is shown that Harmuth's procedure results in physically more plausible solutions     

A set of integral equations for electromagnetic wave radiation from an arbitrary source in a linear, lossy, inhomogeneous, cold magnetoionic medium

By decomposing the permittivity tensor into its isotropic, longitudinal, and transverse parts (with respect to the static magnetic field), a set of simultaneous integral equations are derived for the electric field components in a linear, lossy, inhomogeneous, cold magneto-plasma. The developed integral equations are useful to obtain an approximate solution for electromagnetic radiation as well as scattering problems in such a medium.     

Solutions of Maxwell's equations for general nonperiodic waves inlossy media

Solutions of Maxwell's equations in lossy media for signals excited by a general applied source at the boundary plane are given. The excitation at the boundary plane can be through either electric or magnetic functions of any general time variation. No additional terms need be added to Maxwell's equations to obtain the solutions. Excitations by an electric step, exponential, and finite duration sinusoidal; functions of time are given as examples     

强非局域非线性介质中1+1维厄米高斯损耗光孤子

用变分法研究了强非局域非线性损耗介质中1+1维厄米高斯光束的传输特性，得到了损耗光束参量在介质中传输所遵循的规律及其形成损耗光孤子所需要的临界功率．当初始功率接近临界功率时，光束的束宽按准正弦或准余弦规律作准周期展宽变化．通过比较，利用变分法所得到的解析解与数值解在光束传输一段较长的距离内都符合的比较好．     

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.     

High-frequency scattering by objects buried in lossy media

The uniform geometrical theory of diffraction (UTD) is extended so that it can be used to calculate the scattering from an object buried in a lossy medium. First, the accuracy of this high frequency method is examined by comparing numerical results for the scattering by a polygonal cylinder in a lossy medium of infinite extent with calculations based on a method of moments (MoM) solution. Next, the more difficult scattering problem of a polygonal cylinder in a lossy half space is treated. The UTD solution for the unbounded region is employed together with the fields of rays introduced by the interface between air and the lossy medium to obtain expressions for the scattered field in air and in the lossy medium     

Scattering by a perfect electromagnetic conductor (PEMC) plate embedded in lossy medium

In this article, we develop an analytic theory for a perfect electromagnetic conductor (PEMC) plate embedded in lossy medium. The duality transformation introduced by Lindell and Sihvola is applied to study the electromagnetic wave scattering by a PEMC plate. Perfect electric conductor and perfect magnetic conductor are the limiting cases of PEMC media. Here, we study monoscattering by PEMC plate embedded in four different soil models. Numerical results are discussed and compared with the available literature.     

The surface impedance anomaly resulting from a subsurface,infinitely long conductive wire

The change in surface impedance caused by the fields generated by an infinitely long, subsurface wire located in a homogeneous lossy medium (e.g., the Earth) is investigated experimentally and numerically. Sets of curves illustrate the variation in the horizontal electric field, the horizontal magnetic field, and the surface impedance as a function of conductor depth. The half-width at half-amplitude (HWHA) can be used as a measure of the lateral dimensions of the anomaly. While the horizontal magnetic field HWHA is equal to the conductor depth, the horizontal electric field HWHA (and so the surface impedance HWHA) varies not only with depth but also with the conductivity of the medium     

Nonlinear differential equation for the reflection coefficient ofan 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     

Comments on `Some comments on Harmuth and his critics' by J.E. Grayand S.P. Bowen

J.E. Gray and S.P. Bowen (see ibid., vol.30, no.4, p.586-9, Nov. 1988) claim to have developed the formalism necessary to solve the propagation of pulses in a lossy medium for both the magnetic and electric fields using the Laplace transformation and generalized functions. They claim that Harmuth's introduction of the magnetic current s, is neither necessary nor a sufficient reason to insure consistency and that their method permits calculating both the electric and magnetic fields uniquely for a wide variety of pulses. The commenter claims, however, that Gray and Bowen introduce covert assumptions that deny their claim     

On Harmuth's `correction' of Maxwell's equations for pulsetransmission in lossy media

It is shown that H.F. Harmuth's magnetic conductivity term is not needed to predict the transient response for plane-wave transmission in a homogeneous lossy medium. Thus, his repeated harsh criticisms of S.A. Stratton's classic analysis using Laplace transforms are not justified     

Convergence of Numerical Solutions of Open-Ended Waveguide by Modal Analysis and Hybrid Modal- Spectral Techniques

Two different methods are considered to deal with open-ended waveguides with an infinite metallic flange. The first one, modal analysis, is valid only when the aperture is radiating into a Iossy medium. The second one is based on a hybrid modal-spectral technique, and it is valid for any medium, with or without losses. The rectangular aperture problem is solved by both methods, and the influence of different parameters on the convergence of numerical solutions is studied for each method. Finally, a comparison between both methods is presented for lossy and low-loss media.     

Remark on Harmuth's `Correction of Maxwell's equations for signals.I' [and response]

The commenter maintains that the claims made by H.F. Harmuth in the above-titled paper (ibid., vol.EMC-28, p.250-8, Nov. 1986) that a satisfactory condition for the existence of solutions for transients in lossy media is the modification of Maxwell's equations by the addition of a magnetic current density is not valid. In his reply, Harmuth states that if the commenter's claim holds true regardless of the method of solution, he will have contributed an important simplification to the problem of transient solutions of Maxwell's equations. He provides further discussion of the commenter's point     

Some comments on Harmuth and his critics [propagation of pulses ina lossy medium]

A series of controversial papers on the propagation of pulses in a lossy medium by H.F. Harmuth (1986) have appeared in Transactions on Electromagnetic Compatibility. Many negative comments have appeared subsequently that betray a limited understanding of the points Harmuth is trying to make. Part of this difficulty lies in the method Harmuth chooses to present his results, namely the Fourier transform instead of the Laplace transform. The authors develop the formalism necessary to solve the propagation of pulses in a lossy medium for both the magnetic and electric fields using the Laplace transformation and generalized functions in order to clarify the strengths and weaknesses of the points Harmuth is trying to make     

Electromagnetic coupling of coplanar waveguides and microstriplines to highly lossy dielectric media

The spectral-domain technique is utilized to analyze the coupling characteristics of coplanar waveguides and microstrip lines coupled with multilayer lossy dielectric media. Numerical results illustrating the dispersion characteristics of coplanar and microstrip lines, as well as the various electric field components coupled to highly lossy dielectric media, are presented. It is shown that the presence of a superstrate of lossless dielectric between the coplanar waveguide and the lossy medium plays a key role in setting up an axial electric field component that facilitates leaky-wave-type coupling to the lossy medium. The thickness of the superstrate relative to the gap width in the coplanar waveguide is important in controlling the magnitude of this axial electric field component. The coupling characteristics of the microstrip and coplanar lines are compared, and results generally show improved coupling if coplanar waveguides are utilized. Values of the attenuation constant α are higher for coplanar waveguide than for microstrip line, and for both structures α decreases with frequency     

Analysis of energy coupling into spheroidal ferritic implants forhyperthermia applications

The coupling of energy of RF power into lossy tissues using a needle-shaped ferromagnetic implant excited by an externally applied current loop is analyzed theoretically. The ferritic implant is assumed to be of prolate spheroidal shape, while the tissue medium is modeled as a lossy sphere. The electromagnetic fields inside the ferritic implant, the surrounding lossy tissue, and the free space are appropriately expressed in terms of spherical and spheroidal wave functions. Application of the boundary conditions results in an infinite system of equations for the unknown field expansion coefficients. This system is truncated and solved and the electromagnetic field is computed numerically. Absorbed power density inside the implant and the surrounding medium is computed, and the efficiency of the method in producing in-depth energy deposition is examined     

An efficient formulation to determine the scatteringcharacteristics of a conducting body with thin magnetic coatings

Two new and efficient surface integral equations, derived from corresponding volume integral equations, are developed to calculate the scattering of electromagnetic (EM) waveform from an arbitrarily shaped conducting body coated with thin lossy magnetic film. Their numerical solutions by the method of moments (MM) for two-dimensional structures with full or partial coatings are presented. It is shown that the radar cross-section of a conducting body can be significantly reduced by coating it with a lossy magnetic film. To verify the validity and accuracy of the proposed formulation, another method based on the expansion of cylindrical harmonic functions with real arguments is also developed to calculate the scattering of a plane EM wave from an electrically large coated circular cylinder. The same problem was also solved by the proposed formulation, and excellent agreement between the two approaches was achieved. In addition, numerical results of the scattering from a rectangular coated cylinder is shown to be consistent with that obtained by a modified finite-difference-time-domain (FDTD) method