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     

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     

Comments on `Riemann-Green function solution of transientelectromagnetic plane waves in lossy media'

In commenting on the above-named work by O.R. Asfar (see ibid., vol.EMC-32, no.3, p.228-31, Aug. 1990), the commenter notes that one can write infinitely many solutions for the associated magnetic field strength that will all satisfy Maxwell's equations, but Maxwell's equations cannot tell which one of these infinitely many solutions is the right one. It is further pointed out that the physical significance of the magnetic current density term used became clear when transients in lossy media were investigated with Lorentz's equations of electron theory, which allow for the fact that electric charges are always connected with particles having a mass, whereas Maxwell's original equations do not contain the concept of mass. A physical explanation for this is offered, and attention is given to the creation of the singularity in Maxwell's equations that make sit impossible to obtain the associated magnetic field strength without some limit process     

Propagation Velocity of Electromagnetic Signals

The propagation velocity of electromagnetic signals has been a vexing problem for about a century. The often-mentioned group velocity fails on two accounts, one being that it is generally larger than the velocity of light for waves in the atmosphere; the other that its derivation implies a transmission rate of information equal to zero. The reason why this problem has resisted a solution for so long is that Maxwell's equations fail for signals propagating in a lossy medium. The propagation velocity is of interest only in a lossy medium, since its value in a loss-free medium has been known since d'Alembert's solution of the wave equation. For infinite signal-to-noise ratios and ideal receivers, the propagation velocity of signals in media with ohmic losses equals the velocity of light; it decreases with decreasing signal-to-noise ratio and eventually approaches zero.     

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     

Correction of Maxwell's Equations for Signals I

Electromagnetic wave theory has been based on the concept of infinitely extended periodic sinusoidal waves ever since Maxwell published his theory a century ago. On the practical level this worked very well, but on the theoretical level we always had an indication that something was amiss. There was never a satisfactory concept of propagation velocity of signals within the framework of Maxwell's theory. The often-mentioned group velocity fails on two accounts, one being that it is almost always larger than the velocity of light in radio transmission through the atmosphere; the other being that its derivation implies a transmission rate of information equal to zero. A closer study shows that Maxwell's equations fail for waves with nonnegligible relative frequency bandwidth propagating in a medium with nonnegligible losses. The reason is singularities encountered in the course of calculation. The remedy is the addition of a magnetic current density which may be chosen zero after one has reached the last singularity but not before.     

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

Modification of Maxwell's equations to obtain general solutions for a lossy medium is reviewed. It is done by adding an extra term, referred to as the fictitious magnetic charge density. The solutions, which are in integral form, are solved numerically by computer for an exponential ramp function excitation. Computer plots for the electric and magnetic field strengths as functions of time at different locations in a lossy transmission medium are presented     

Hillion's proof of the nonexistence of certain solutions ofMaxwell's equations

The author notes that P. Hillion (see ibid., vol.33, no.2, p.144-5, 1991) has greatly simplified the author's proof that Maxwell's equations have generally no solution in the case of propagation of electromagnetic signals in lossy media. He clarifies some remarks on conservation of energy and causality law     

Signal solutions of Maxwell's equations for charge carriers withnon-negligible mass

Discusses signal solutions to Maxwell's equations for charge carriers with non-negligible mass. In order to find solutions the authors add information to Maxwell's equations by means of a physical assumption to obtain a defined solution. The authors' assumption is that magnetic dipoles and magnetic dipole currents should be represented by a magnetic (dipole) current density term just as electric dipoles and electric dipole currents-or electric polarization currents-have always been represented by an electric current density term. It is perfectly possible that other physical assumptions can be made that yield defined solutions and that will withstand public scrutiny     

Bidirectionality of Reciprocal, Lossy or Lossless, Uniform or Periodic Waveguides

Using the scattering-matrix equations for two antennas placed in the fields of a waveguide, it is proven that all reciprocal, lossy or lossless, uniform or periodic waveguides are bidirectional. Since Maxwell's equations imply directly that propagation constants on a lossless reciprocal waveguide come in pairs (beta,-beta*), "complex waves" on a lossless reciprocal, uniform or periodic waveguide come in quadruplets with propagation constants (beta,-beta, beta*,-beta*).     

旋光光纤的电磁场理论分析

本文求解张量介质电常数条件下的麦克斯韦方程，导出了纵向场作用下旋光材料的波动方程，由于电场与磁场是互相耦合不能单独存在，因而引入了孪生标量波的概念，并证明了该标量波满足亥姆霍兹方程，通过在圆柱座标系中求解该方程，得到了标量波的表达式、相位常数、特征方程、各个场分量的表达式，分析了光纤中的旋光特性。     

A 2×2 Matrix Algebra for Electromagnetic Wave Propagation in Stratified Biaxial Media

We present a new 2×2 matrix algebra for electromagnetic wave propagation in stratified biaxial media. Our method is based on Maxwell's equations and the continuity of the tangential components of the electric and magnetic field vectors and gives an exact complete solution. No restrictions are necessary for the orientations of the axes of the dielectric tensors of the stratified medium and the properties of the incident plane wave. A complete and systematic methodology is provided for calculating all wave parameters and all properties of the reflected and transmitted waves in terms of 2×2 Fresnel reflection and transmission matrices.     

Perturbed-TEM analysis of transmission lines with imperfectconductors

A perturbed-transverse electromagnetic (TEM) approach to studying the detailed current distribution and the propagation constant of a multiconductor transmission line system with imperfect conductors is discussed. The perturbed fields are derived assuming that the fields outside the conductors are TEM waves of the corresponding lossless system and those inside the conductors satisfy the transverse magnetic (TM) modal equations. These fields are then inserted into a perturbational formula to obtain the propagation constant of the lossy system. The current distribution and the propagation constant (which clearly illustrates the loss mechanism due to the skin effect and the proximity effect) of a lossy two-wire system are presented as an example     

A mathematical technique for an exact small-signal field analysis of multiple-stream interaction in a finite longitudinal magnetic field

A mathematical technique for solving Maxwell's equations and the Lorentz force equation with no approximations except the small-signal approximation is presented. A finite dc magnetic field parallel to the dc velocity of the charges is included. Polarization variables are used, and the boundary conditions include ac surface charge density and surface current density. The advantages of the method are that both fast waves and slow waves are included without a quasi-static approximation, and only the determinantal equation requires computer solution. The partial differential equations are solved directly and need not be solved by computer.     

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     

Time-domain electromagnetic plane waves in static and dynamicconducting media. I

Solutions are derived for the time-domain Maxwell equations for static (J=σE) and dynamic (τ∂/∂t+J= σ₀ E) conducting media where the field is assumed to vary with respect to only one spatial direction, i.e., plane-wave propagation. The plane wave is introduced into the media via the imposition of an electric field boundary condition at the plane boundary of a half-space and it is assumed that the fields inside the half-space are initially zero. Solutions are derived directly from the first-order system of partial differential equations and it is shown that once the electric field at the plane boundary is imposed, the magnetic field is automatically determined for causal solutions. It is shown that the form of the Maxwell equations, without a magnetic conductivity term added, is sufficient to allow well and uniquely defined solutions of this problem     

In defense of J.A. Stratton [pulse transmission in lossy media]

The author shows that Maxwell's equations can be employed to predict pulse transmission in lossy media. He concludes that Harmuth and company are wrong in stating that Stratton's classic treatise contains a `fundamental misunderstanding' in the application of the Laplace transform technique     

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     

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