Gerald M. Whitman

Wave propagation in time-varying media

This paper examines the propagation of waves in media which are spatially homogeneous but whose properties vary with time abruptly or continuously. Emphasis is placed on the excitation problem and on source-dependent phenomena which are not evident when attention is given only to the source-free case. After a presentation and interpretation of various exact closed-form solutions for simple nondispersive and dispersive media undergoing sudden or gradual temporal changes, attention is given to integral representations required under more general conditions. In the ensuing far-zone asymptotic analysis, dispersion surfaces and space-time rays are used extensively for identification of wave packets and other wave constituents descriptive of the field, and a comparison is made between the asymptotic results and the exact solutions noted above. Asymptotic field solutions are then derived by a direct ray procedure, without intervention of integral representations. The examples considered exhibit a variety of phenomena, among which the most interesting is the focusing of reflected waves when a dispersive medium undergoes a sudden change.

Scattering by periodic metal surfaces with sinusoidal height profiles--A theoretical approach

A theory of scattering by periodic metal surfaces is presented that utilizes the physical optics approximation to determine the current distribution in the metal surface to first order, but modifies this approximate distribution by multiplication with a Fourier series whose fundamental period is that of the surface profile (Floquets theorem). The coefficients of the Fourier series are determined from the condition that the field radiated by the current distribution into the lower (shielded) half-space must cancel the primary plane wave in this space range. The theory reduces the scatter problem to the familiar task of solving a linear system. For certain basic types of surface profiles, including the sinusoidal profile considered here, the coefficients of the linear system are obtained as closed form expressions in well-known functions (Bessel functions for sinusoidal profiles and exponential functions for piecewise linear profiles). The theory is thus amenable to efficient computer evaluation. Comparison of numerical results based on this theory with data obtained by recent numerical schemes shows that for depths of surface grooves less than a wavelength and for unrestricted groove widths, reliable and comparable, if not more accurate, data is obtained, in many cases at considerably cheaper computational cost.

A theoretical model for radio signal attenuation inside buildings

A theoretical model is proposed for predicting path loss inside buildings. The theory involves a waveguide model of the indoor environment which permits a rigorous modal solution similar to that developed by Mahmoud and Wait (1974) for propagation in tunnels. Comparisons of the theory with the measurements made by Arnold, Murray and Cox (1989) at the AT&T Laboratories building in Crawford Hill, NJ, show general agreement. >

A transport theory of pulse propagation in a strongly forward scattering random medium

The scalar time-dependent equation of radiative transfer is used to develop a theory of pulse propagation in a discrete random medium whose scatter function (phase function) consists of a strong, narrow forward lobe superimposed over an isotropic background. The situation analyzed is that of a periodic sequence of plane-wave pulses, incident from an air half-space, that impinges normally upon the planar boundary surface of a random medium half-space; the medium consists of a random distribution of particles that scatter (and absorb) radiation in accordance with the aforementioned phase function. After splitting the specific intensity into the reduced incident and diffuse intensities, the solution of the transport equation in the random medium half-space is obtained by expanding the angular dependence of both the scatter function and the diffuse intensity in terms of Legendre polynomials, and by using a point matching procedure to satisfy the boundary condition that the forward travelling diffuse intensity be zero at the interface. Curves of received power show that, at small penetration depths, the coherent (reduced incident) intensity dominates, whereas at large depths, the incoherent (diffuse) intensity is the strongest and causes the pulses to broaden and distort. The motivation for this study was to complement a test series, on mm-wave pulse propagation in vegetation, by a theory that provides understanding of overall trends and assistance in the interpretation of measured results. In the mm-wave region, all scatter objects in a forest have large dimensions compared to a wavelength and, therefore, produce strong forward scattering and a phase function of the type assumed in this paper.

Collimated Beam Wave Pulse Propagation and Scattering in Vegetation Using Scalar Transport Theory

This investigation develops a theoretical model for microwave and mm-wave propagation and scattering in vegetation that is based on radiative transfer theory (transport theory). The time-dependent, three dimensional, scalar radiative transport equation is solved (to a high degree analytically and then numerically) for strong forward scattering of a pulsed collimated beam wave in a strong forward scattering environment such as a forest at mm-wave frequencies. The problem analyzed is that of a periodic sequence of Gaussian pulses incident from free space onto a forest region. The forest is modeled as a half-space of randomly distributed particles that scatter and absorb electromagnetic energy. The incident pulse train is taken to be a collimated (cylindrical) beam wave. The theory allows for a comprehensive characterization of the influence of vegetation on the propagation of pulsed beam waves, which includes a description of the attenuation of these beams, their angular spread, their distortion due to pulse broadening, and the determination of out-of-the-beam scattering which was not previously available. The model should be useful for frequencies above 3 GHz.

An approximate but accurate analysis of the dielectric wedge antenna fed by a slab waveguide using the local mode theory and Schelkunoff equivalence principle

A computationally efficient method to obtain design parameters for tapered radiators is presented. The method uses a local mode theory in conjunction with the Schelkunoff equivalence principle. Radiation patterns of directive gain for dielectric wedge antennas of varying lengths and different dielectric constants are presented. Both the TE and TM cases are considered. The method is validated by comparison with data obtained from a recently developed more rigorous mode-matching method. Excellent agreement is obtained over the physically important angular range from endfire to broadside for the TE case and over the angular range spanned by the major lobe for the TM case.

Rigorous TE solution to the dielectric wedge antenna fed by a slab waveguide

A rigorous TE solution to the dielectric wedge antenna fed by a slab waveguide of the same material is presented. The method of solution involves modeling the wedge as a sequence of step discontinuities and uses an iterative procedure to track forward and backward partial wave fields, expressed as modal expansions, to obtain the rigorous field solution. Radiation patterns of directive gain are presented. All patterns smoothly decrease from a maximum in the endfire direction and exhibit extremely low side lobe levels. Longer length wedges or smaller dielectric constant materials are shown to produce higher directivity and smaller half-power beamwidths. For slender, gradually tapered wedges, the reflection coefficient of the guided (surface) wave at the input to the wedge is very small indicating a low VSWR for tapered dielectric antennas and there appears to be no gain limitation with antenna length for these antennas.

New full-wave theory for scattering from rough metal surfaces—the correction current method: the TE-polarization case

A new full-wave theory of scattering from metal surfaces with one-dimensional roughness profiles is presented. A primary field and a complete system of modal functions (radiation modes) are defined to be relatively simple in structure (plane-wave-type fields) and to satisfy the boundary conditions at the rough surface, individually and rigorously. These fields will not necessarily satisfy Maxwells equations. But compliance with these equations is enforced by the introduction of fictitious current distributions, associated with each of these fields, and chosen such that these ‘passive’ currents compensate for any field errors. In addition, each radiation mode is assumed to include an ‘active’ current distribution in the form of a current sheet which generates this mode. The composite field, formulated as a superposition of the primary field and the radiation modes, must be source free. It cannot involve any active or passive currents; and this zero-current requirement is then used to solve the scatter problem by an iterative procedure which, in a step-by-step fashion, eliminates the passive currents of the primary field and radiation modes by the active currents of the radiation modes. The result is a composite field that satisfies all requirements (Maxwells equations, boundary conditions and radiation condition) while all fictitious current distributions are eliminated by mutual compensation. This composite field is therefore the solution of the scatter problem. This new theory—involving fictitious current distributions—is unconventional. But after definition of the primary field and the radiation modes, it is straightforward and conceptually transparent. The first-order scatter pattern is reciprocal and bridges the gap between the small-perturbation method and the physical optics method. Since the passive currents quantify the field errors, the theory allows the establishment of an error criterion which indicates when field errors can be expected to be small. The results are compared with those of existing theories. The present paper presents the TE case; the TM case, which is more complex, will be described in a follow-on paper. (Some figures in this article are in colour only in the electronic version)

FM pulses in stratified isotropic plasma

A study of signals excited by FM pulses in an infinite inhomogeneous cold isotropic plasma is presented. The medium is assumed to vary arbitrarily with position, though sufficiently slowly with respect to all wavelengths contained in the source spectrum. For simplicity only one spatial dimension is considered, but the development may be extended to include more space variables. After deducing integral representations that are evaluated asymptotically, the theory is applied to a particular plasma inhomogeneity characterized by an exponential variation of plasma frequency. Space-time rays associated with an impulsive source are shown to justify the use of time-inversion in establishing the required phase of an FM pulse capable of producing an optimally compressed signal at a particular space-time point. Since ordinary asymptotic methods fail in the neighborhood of such a focal point, a theory that in a prior study described signals in the focal region of a homogeneous plasma is applied to signals in a plasma with exponentially varying plasma frequency. Computed results based on this theory display the character of optimally compressed signals in focal regions.

Frequency characterization of a thin linear antenna using diakoptic antenna theory

A frequency-dependent analytical expression for the input impedance of a thin wire antenna is obtained using diakoptic theory. The linear antenna is diakopted into electrically short segments, where each is treated as a component with two terminals (except for end pieces, which have only one terminal). An impedance matrix is found which characterizes coupling between all segments. By expanding the free-space Greens function in a power series in wavenumber k, each entry in the resultant impedance matrix is obtained as an explicit function of frequency. The input admittance is found as a ratio of two polynomials in wavenumber k. A more systematic approach for the solution of the input admittance is achieved by expanding both the unknown current vector and the Greens function in power series in k. Equating coefficients of like powers in k leads to a numerically efficient algorithm which is used to determine the input admittance as a function of frequency. Numerical results compare well with the input impedance obtained from a conventional integral equation solution. >