Transients in dispersive media, part II: Excitation of space waves and surface waves in a bounded cold magnetoplasma

The present discussion is concerned with the study of transient phenomena due to localized sources in a bounded dispersive medium, with emphasis on the propagation of surface waves. To accommodate these features, the configuration of a magnetic line source parallel to the gyrotropic axis in a cold magnetoplasma has been chosen, with a perfectly conducting plane providing the bounding surface. After a formulation of the solution in integral form, the asymptotic considerations in Part I of this paper are applied for calculation of the transient behavior of the incident, reflected, and surface wave constituents. Properties of these source-excited waves are discussed and are compared with the corresponding response to plane wave excitation. By comparison with an exact solution, some observations are made concerning the accuracy of the asymptotic approximations.     

Weakly dispersive spectral theory of transients, part I: Formulation and interpretation

Dispersive effects in transient propagation and scattering are usually negligible over the high frequency portion of the signal spectrum, and for certain configurations, they may be neglected altogether. The source-excited field may then be expressed as a continuous spatial spectrum of nondispersive time-harmonic local plane waves, which can be inverted in closed form into the time domain to yield a fundamental field representation in terms of a spatial spectrum of transient local plane waves. By exploiting its analytic properties, one may evaluate the basic spectral integral in terms of its singularities-real and complex, time dependent and time independent-in the complex spectral plane. These singularities describe distinct features of the propagation and scattering process appropriate to a given environment. The theory is developed in detail for the generic local plane wave spectra representative of a broad class of two-dimensional propagation and diffraction problems, with emphasis on physical interpretation of the various spectral contributions. Moreover, the theory is compared with a similar approach that restricts all spectra to be real, thereby forcing certain wave processes into a spectral mold less natural than that admitting complex spectra. Finally, application of the theory is illustrated by specific examples. The presentation is divided into three parts. Part I, in this paper, deals with the formulation of the theory and the classification of the singularities. Parts II and III, to appear subsequently, contain the evaluation and interpretation of the spectral integral and the applications, respectively.     

The near field of dipole antennas, part I: Theory

The theoretical and experimental evaluation of the electromagnetic fields in the immediate vicinity of resonant dipole antennas is presented. This type of antenna is widely used with portable and mobile radio transmitters. The work presented herein has been motivated by the concern that future Radio Frequency Protection Guides with respect to human exposure to nonionizing electromagnetic radiation might be expressed strictly in terms of the intensity squared of the electric or magnetic fields. It is shown in the results that it is possible to detect relatively high intensity electromagnetic (EM) fields in close proximity to resonant dipoles even for very low levels of radiated power (1 mW and less). The paper is divided into a theoretical section and an experimental section because its goals are twofold. First, the formulas for the correct evaluation of the EM fields in the close proximity to dipole antennas are established. Second, it is shown that such EM fields, which can be theoretically predicted and experimentally verified with satisfactory accuracy, are indeed strong enough to violate proposed Radio Frequency Protection Guides even for very low levels of radiated power. Thus portable radios are rendered virtually useless, although the same guides permit exposures to much higher levels of power in the far field. Part I of the paper is essentially theoretical and expresses the fields near dipole antennas in terms of cylindrical waves, which lend themselves to closed form integration. The asymptotic expressions of some components of the field are particularly simple for close distances (in terms of wavelength) from the antenna. The correctness of the solution is checked by evaluating how closely boundary conditions are satisfied. Results have shown that previously used formulas for evaluating field intensity very near dipole antennas can give incorrect values.     

Weakly dispersive spectral theory of transients, part III: Applications

The spectral theory of transients (STT) formulated in Parts I and II of this paper is here applied to the evaluation of the source-excited pulsed response for a representative class of two-dimensional examples: 1) a dielectric half-space with planar interface, 2) a dielectric half-space with curved interface, and 3) an edge-terminated curved perfectly conducting sheet. These configurations give rise to a variety, of propagation and diffraction phenomena such as those caused by lateral waves, by caustic-forming multiple reflected fields, by edge diffraction with formation of shadow boundaries, and by combinations of these. The results are established by direct utilization of the general formulas in Parts I and II, with emphasis on the spectral features associated with the various wave types. Sketches of the corresponding waveforms elucidate the behavior of the observed signal response.     

The design of a slot array in nonradiating dielectric waveguide, part I: Theory

A set of theoretical design equations for a slot array fed by nonradiating dielectric (NRD) waveguide is developed. Mutual coupling between the slots cut into one of the metal walls of the waveguide is taken into consideration for a design that can have a predetermined radiation pattern. The theoretical development follows that of Elliott.     

On pulse compression in dispersive media

A comparison between three methods used for the synthesis of suitable signals which result in pulse compression, when transmitted through dispersive media, is presented. These are the equalization of group-time delay method, the space-time rays method, and the matched-signal method. The three methods are shown to be equivalent if the signals are restricted to be frequency-modulated with uniform envelopes. A generalized expression for the requited frequency modulation law for pulse compression in an inhomogeneous dispersive medium is obtained. Considerations for lossy dispersive media and additional optimization of the signal envelope are also discussed.     

在时域内计算色散媒质中光脉冲的传输

得到了时域内色散媒质中光脉冲传输的计算公式，并提出了时域内色散媒质中显式的光束传播法。计算了短脉冲在具有二阶色散效应的定向耦合器内的传输、计算结果同参考文献中的一致，但本文的计算方法简单、方便、实用。     

Wave packets in strongly dispersive media

An analytical study of the evolution of slowly varying wave pulses in strongly dispersive media which takes into account dispersive correction terms involving higher derivatives of the group velocity is given. A higher order differential equation for the envelope function is derived and solved recursively and by means of a procedure based on an analogy with the Schrödinger equation. The equation for the envelope function is used to obtain generalizations of the velocity of the pulse defined as the velocity of the center of inertia, and expressions are derived which determine the spreading of the pulse. Finally, we discuss how the presence of other wave modes affects the primary mode in the multimode case.     

Propagation in linear dispersive media: finite differencetime-domain methodologies

Finite difference time-domain (FDTD) methodologies are presented for electromagnetic wave propagation in two different kinds of linear dispersive media: an Nth order Lorentz and an Mth order Debye medium. The temporal discretization is accomplished by invoking the central difference approximation for the temporal derivatives that appear in the first-order differential equations. From this, the final equations are temporally advanced using the classical leapfrog method. One-dimensional scattering from a dielectric slab is chosen for a test case. Provided that the maximum operating frequency times the time step is small and that the wave is adequately resolved in space, as shown in the error analysis, the agreement between the computed and exact solutions will be excellent. The attached data, which are associated with the four pole Lorentz dielectric and the five pole Debye medium, verify this assertion     

Propagation of transients in dispersive dielectric media

The propagation of transient electromagnetic fields in dispersive dielectric media is studied. The dielectric medium is assumed to be linear, isotropic, and homogeneous, and is described by the Debye model. Incident fields are assumed to be transverse electromagnetic plane wave pulses. The dielectric body can assume the form of infinite half space or an infinite circular cylinder, either of which may be homogeneous or stratified. The electric fields induced in the dielectric are calculated from time-domain Maxwell's equations using the finite-difference time-domain method.<>     

Acoustic emission source location in dispersive media

In this paper, the acoustic emission source (AE) is located by a non-iterative method using the time-of-arrival (TOA) of several events, received in an array of sensors arbitrary positioning in the 3D space. If at least two event velocities are different, a common property in dispersive propagation, and the array of sensors is not lying in a plane, a close-form estimation of the source–sensors distances, AE time and material constant is derived. Moreover, a direct estimation of the source position is achieved using the multidimensional scaling approach. In simulation experiments, the proposed method detects accurately the location of AE sources, reducing also the ambiguity introduced by noisy arrival times.     

High-order compact schemes for dispersive media

Staggered high-order compact (HOC) finite difference schemes are developed for modelling electromagnetic wave propagation in dispersive media. The main advantage of HOC schemes is their very low dispersion error, which is dominant in low-order methods. The high accuracy of HOC schemes is demonstrated by examples of wave propagation through first-order Debye and Lorentz media in one dimension.     

Time-domain finite-element modeling of dispersive media

A general formulation is described for time-domain finite-element modeling of electromagnetic fields in a general dispersive medium. The formulation is based on the second-order vector wave equation and incorporates the dispersion effect of a medium via a recursively evaluated convolution integral. This evaluation is kept to second order in accuracy using linear interpolation within each time step. Numerical examples are given to validate the proposed formulation     

Energy relations for waves in strongly dispersive media

Expressions for the averaged stored energy, energy flow, and energy velocity of quasi-monochromatic waves in temporally and spatially dispersive media have been extended to take into account broad-band signals in strongly dispersive media.     

Tutorial 15: control theory, part I

Control theory is the branch of engineering that tries to answer questions like "given a system configured in a particular fashion, will the system behave reasonably?" That is, control theory deals with analyzing systems. Control theory also tries to answer the question "given a system with (negative) feedback, what can I add to my system to see to it that my system will meet its specifications?" That is, control theory deals with designing systems, too.     

Low frequency characteristics of a quasioptical Schottky diode detector part I: Theory

A theoretical study is made of saturation effects of FIR point contacts Schottky diodes when used in the envelope detection mode of operation. A model is described that fits experimental results for radiation wavelength ranging from microwaves down to FIR wavelengths. This model permits the prediction of saturation levels throughout this range.     

Theory of electromagnetic transmission structures part I: Relativistic foundation and network formalisms

A new theorem on a class of four-dimensional skew-symmetric tensors is demonstrated. Coupled with the relativistic covariant form of Maxwell's equations, this theorem consolidates the classifications of guided waves by combining the three types--TE, TM, TEM--under a uniform condition applied to the generating four-potential (A, i φ/c) which is Lorentz invariant. Each type corresponds to a potential of which a pair of the four components vanishes in a particular frame. Through appropriate normalization conditions, the resulting time-domain equations for the field amplitudes are readily reduced to modified telegraphist equations, which in turn lead to distributed network representations for each of the three types. The ambiguity of distributed network formalisms in general is elucidated and the concept of network parameter densities such as traditionally employed in TEM transmission line theory is questioned.     

Weakly dispersive spectral theory of transients, part II: Evaluation of the spectral integral

In the spectral theory of transients formulated in Part I of this paper, the transient response for weakly dispersive wave processes has been expressed in terms of canonical integrals in the complex spatial wavenumber domain. The real and complex singularities in the integrands, which dominate the behavior of the spectral integrals, have been categorized and associated with generic physical wave processes. The integrals are now evaluated by Contour deformation around the singularities. This yields general expressions for the transient Green's function that are applicable to a broad class of propagation and diffraction problems. The generic results, which can be grouped into contributions from real or complex singularities; express the transient field in terms of compact (and therefore physically incisive) wave spectra, in contrast to alternative procedures that always constrain the spectra to be real. These aspects, together with simplifying explicit wavefront approximations, are explored in the present paper, with the application to specific problems relegated to Part III.