Maxwell, Hertz, the Maxwellians, and the early history of electromagnetic waves

In 1864, Maxwell conjectured from his famous equations that light is a transverse electromagnetic wave. Maxwell's conjecture does not imply that he believed that light could be generated electromagnetically. In fact, he was silent about electromagnetic waves, and their generation and detection. It took almost a quarter of a century before Hertz discovered electromagnetic waves and his brilliant experiments confirmed Maxwell's theory. Maxwell's ideas and equations were expanded, modified, and made understandable by the efforts of Hertz, FitzGerald, Lodge, and Heaviside, the last three being referred to as the "Maxwellians." The early history of electromagnetic waves, up to the death of Hertz in 1894, is briefly discussed. The work of Hertz and the Maxwellians is briefly reviewed in the context of electromagnetic waves. It is found that historical facts do not support the views proposed by some, in the past, that Hertz's epoch-making findings and contributions were "significantly influenced by the Maxwellians.".     

The history of electromagnetics as Hertz would have known it

Highlights of the separate developments of the sciences of electrostatics and magnetostatics are traced through the end of the 18th century, climaxed by the work of Coulomb and Poisson. The linkage of these two sciences due to the discoveries of Oersted, Ampere, Biot and Savart, and Faraday are described, followed by the theoretical culmination embodied in the work of Maxwell. It is shown how Maxwell's prediction of the existence of electromagnetic waves set the stage for the epochal experiments of Hertz     

Mathematical apparatus for calculating radio-wave attenuation in the intermediate and diffraction zones

Methods for calculating the microwave-band diffraction-zone propagation factor are considered. A refinement of the simplified model of diffraction loss that makes it possible to reduce calculation errors for the over-the-horizon and near-the-horizon propagation paths is proposed.     

Influence of technological factors on dielectric permeability and radio-wave absorbing characteristics of nickel-zinc ferrites

The article discusses the results of efficiency improvement of wide-range nickel-zinc ferrites by increasing the role of the dielectric subsystem in the formation of radio-wave absorbing properties of material due to the action of technological factors. The influence of doping additives and gas conditions of furnace atmosphere within sintering on absorption of electromagnetic waves has been studied. The efficiency of sintering of nickel-zinc ferrites in the atmosphere with adjustable partial oxygen pressure aimed at increasing the dielectric permeability of material has been confirmed. A model is proposed, which explains the increase in losses within the sintering of ferrites in a reducing atmosphere.     

Ray-optical prediction of radio-wave propagation characteristics intunnel environments. 2. Analysis and measurements

For pt.I seeibid. vol.46, no.9, p.1328, (1998).The uniform theory of diffraction (UTD) developed in part 1 is used to predict narrow- and wide-band propagation characteristics in tunnels at 900- and 1800-MHz. Narrow-band propagation characteristics is shown in the spatial domain and wide-band propagation in the time domain. In empty straight-tunnel environments, propagation exhibits a break-point phenomenon and has very short time delay spread. In empty curved or branched tunnel environments, propagation suffers higher loss. Vehicles cause additional propagation loss and larger varying time delay spread in tunnels. The measured results have validated the accuracy of the theoretical model and provided important information on narrow-band and wide-band propagation characteristics in empty, branched and obstructed tunnels     

Maxwell Garnett formalism for weakly nonlinear,bianisotropic, dilute,particulate composite media

The homogenization of a composite medium formed by randomly dispersing electrically small, weakly nonlinear, bianisotropic, ellipsoidal inclusions in a linear bianisotropic host medium is considered. The effective constitutive properties of the homogenized composite medium (HCM) are estimated using the Maxwell Garnett formalism. The linear and nonlinear properties of the HCM are estimated separately because the nonlinearity of the inclusions is weak and the composite medium is dilute. Whereas previously available results were confined to simple dielectric media and spherical inclusions, the reach of the presented formalism is vast and can be significant for numerous technological applications.     

Logarithmic compression of Rayleigh and Maxwell distributions

The effect of logarithmic compression on a randomly fluctuating signal with either Rayleigh or Maxwell amplitude statistics is determined. A simple relationship between the logarithm of the average and the average of the logarithm is found for the large-signal situation.     

VOLMAX: a solid-model-based, transient volumetric Maxwell solverusing hybrid grids

This paper provides an overview of the finite-volume algorithm, the dissipative time-integration scheme, boundary condition implementation, grid generation, and a time-step definition suitable for sub-time cycling. To examine the accuracy of VOLMAX operating in either a purely unstructured or a hybrid-grid mode, the resonances of a rectangular cavity, the input admittance of a “thick” wire antenna, and three simple microstrip applications (microstrip line, patch antenna and low pass filter) with well-known FDTD solutions are examined. The latter three examples demonstrate the accuracy that can be obtained by launching microstrip-guided waves on cubical hexahedral (FDTD) grids and through a dense, unstructured linear tetrahedral region     

Three-dimensional finite, boundary, and hybrid element solutions ofthe Maxwell equations for lossy dielectric media

Finite, boundary, and hybrid element approaches are presented as numerical methods for computing electromagnetic (EM) fields inside lossy dielectric objects. These techniques are implemented as computer algorithms for solving the Maxwell equations in heterogeneous media in three dimensions. Algorithm verification takes the form of comparisons of test cases with analytic solutions. Computed results for each technique are in good agreement with exact solutions, especially in light of the coarse computational grid resolutions used. Implementation was in FORTRAN on a moderate-sized computer (MicroVax II). The basic problem formulation is quite general; however, it has direct application in hyperthermia as a cancer therapy where the EM fields produced inside the patient by external sources are of interest. An example of the application of these numerical methods in a three-dimensional clinical setting is shown     

Differential Forms, Galerkin Duality, and Sparse Inverse Approximations in Finite Element Solutions of Maxwell Equations

We identify primal and dual formulations in the finite element method (FEM) solution of the vector wave equation using a geometric discretization based on differential forms. These two formulations entail a mathematical duality denoted as Galerkin duality. Galerkin-dual FEM formulations yield identical nonzero (dynamical) eigenvalues (up to machine precision), but have static (zero eigenvalue) solution spaces of different dimensions. Algebraic relationships among the degrees of freedom of primal and dual formulations are explained using a deep-rooted connection between the Hodge-Helmholtz decomposition of differential forms and Descartes-Euler polyhedral formula, and verified numerically. In order to tackle the fullness of dual formulation, algebraic and topological thresholdings are proposed to approximate inverse mass matrices by sparse matrices     

Spectral purity and long-term stability of CO2 lasers atthe Hertz level

Ultra-high-resolution spectroscopy and metrology require very stable lasers with a high-spectral purity. For spectroscopy with a resolution in the range 10-100 Hz at 30 THz, we are developing a new stabilization scheme which acts separately on the long and short term stabilities. We present the results achieved with the first part of our new scheme, which is based upon the stabilization on a saturation signal detected in transmission of an active Fabry-Perot cavity. With a laser linewidth of 3.4 Hz (FWHM) and a flicker plateau of 0.7 Hz (Δν/ν=2.10^-14) obtained using a strong OsO₄ line as reference, this stabilization system already improves the both short and long-term stabilities obtained by our previous setup which involved an external cell instead of a Fabry-Perot cavity. We present also the results using a CO₂ laser line as frequency reference     

US and German analysts

Salomon Smith Barney recently started solar cell maker AstroPower Inc, with a ‘buy’ rating and a US$50 per share target price. Profitable since 1997, AstroPower expects to ship more than $100m in solar products in 2002, thanks to its new manufacturing facility.     

Asyntis supplies German PV maker,raises funds

In Germany, Munich-based Asyntis GmbH says that one of the country’s leading PV manufacturers — which was not named — has placed an order for its high-performance, high-throughput, silicon etch plasma system, the Pioneer No. 1, after a successful evaluation procedure in the production line.This is a short news story only. Visit www.re-focus.net for the latest renewable energy industry news.     

Comments, on `Three-dimensional finite, boundary, and hybridelement solutions of the Maxwell equations for lossy dielectric media'[and reply]

For the original article see ibid., vol.36, no.4, p.682-93 (1988). The commenters point out a potential source of error with the finite-element analysis of the vector wave equation in the paper of K.D. Paulsen, et al. Specifically, this error source is connected with the finding that, if spurious modes exist in the finite-element solution of the eigenvalue problem, the corresponding solution to the externally driven problem may consist of some linear combination of the nonphysical spurious modes in addition to the physical modes. In replying, the author acknowledges the importance of the question of spurious modes     

Current and Charge Integral Equation Formulations and Picard's Extended Maxwell System

Important connection between computational and mathematical electromagnetics is presented. The newly developed well-conditioned electromagnetic frequency domain surface integral equation formulations, the current and charge integral equations, are shown to be related to Picard's extended Maxwell system, an extended partial differential equation system that has the correct static behavior. Electromagnetic surface integral representations are derived in this paper for traditional surface integral equation formulations and for the Picard system using the fundamental solution approach, i.e., from the definition of Dirac's delta function. The surface integral representations are constructed with proper solid angle coefficients starting from the scalar Helmholtz equation. The traditional surface integral equation formulations are shown to be derived from Maxwell's curl equations and are thus lacking the contribution of the divergence equations at zero frequency. It is shown that the new current and charge formulations can be derived from the surface integral representation of the Picard system.     

On Improper Integrals in the Depolarization Dyadics of Lossless Gyrotropic Media, and the Maxwell Garnett Formalism

Improper integrals in the depolarization dyadic for the ellipsoidal-shaped inclusion embedded in an environment medium are considered and a method for obtaining their values in the lossless limit is suggested. The last is used to investigate the depolarization dyadics for a gyrotropic environment. Some key properties of mixtures with gyrotropic background are outlined.