Fast Fourier Transform

A compact representation is given of the electric- and magnetic-type dyadic Green's functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the aids normal to the stratification. Furthermore, mixed-potential integral equations are derived within the framework of this transmission-line formalism for arbitrarily shaped, conducting or penetrable objects embedded in the multilayered medium. The development emphasizes laterally unbounded environments, but an extension to the case of a medium enclosed by a rectangular shield is also included.

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Multilayered media Green's functions in integral equation formulations

Resonance conditions for a substrate-superstrate printed antenna geometry which allow for large antenna gain are presented. Asymptotic formulas for gain, beamwidth, and bandwidth are given, and the bandwidth limitation of the method is discussed. The method is extended to produce narrow patterns about the horizon, and directive patterns at two different angles.

Gain enhancement methods for printed circuit antennas

Spatial-domain Green's functions for multilayer, planar geometries are cast into closed forms with two-level approximation of the spectral-domain representation of the Green's functions. This approach is very robust and much faster compared to the original one-level approximation. Moreover, it does not require the investigation of the spectral-domain behavior of the Green's functions in advance to decide on the parameters of the approximation technique, and it can be applied to any component of the dyadic Green's function with the same ease.

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A robust approach for the derivation of closed-form Green's functions

A new antenna, the planar inverted cone antenna (PICA), provides ultrawideband (UWB) performance with a radiation pattern similar to monopole disk antennas , but is smaller in size. Extensive simulations and experiments demonstrate that the PICA antenna provides more than a 10:1 impedance bandwidth (for VSWR<2) and supports a monopole type omnidirectional pattern over 4:1 bandwidth. A second version of the PICA with two circular holes changes the current flow on the metal disk and extends the high end of the operating frequency range, improving the pattern bandwidth to 7:1.

A new ultrawideband printed monopole antenna: the planar inverted cone antenna (PICA)

The problem of the diffraction of an arbitrary ray optical electromagnetic field by a smooth perfectly conducting convex surface is investigated. A pure ray optical solution to this problem has been developed by Keller within the framework of his geometrical theory of diffraction (GTD). However, the original GTD solution fails in the transition region adjacent to the shadow boundary where the diffracted field plays a significant role. A uniform GTD solution is developed which remains valid within the shadow boundary transition region, and which reduces to the GTD solution outside this transition region where the latter solution is valid. The construction of this uniform solution is based on an asymptotic solution obtained previously for a simpler canonical problem. The present uniform GTD solution can be conveniently and efficiently applied to many practical problems. Numerical results based on this uniform GTD solution are shown to agree very well with experiments.

A uniform GTD analysis of the diffraction of electromagnetic waves by a smooth convex surface

Techniques based on the method of modal expansions, the Rayleigh-Stevenson expansion in inverse powers of the wavelength, and also the method of moments solution of integral equations are essentially restricted to the analysis of electromagnetic radiating structures which are small in terms of the wavelength. It therefore becomes necessary to employ approximations based on “high-frequency techniques” for performing an efficient analysis of electromagnetic radiating systems that are large in terms of the wavelength.

Techniques for High-Frequency Problems

A compact approximate asymptotic solution is developed for the field radiated by an antenna on a perfectly conducting smooth convex surface. This high-frequency solution employs the ray coordinates of the geometrical theory of diffraction (GTD). In the shadow region the field radiated by the source propagates along Keller's surface diffracted ray path, whereas in the lit region the incident field propagates along the geometrical optics ray path directly from the source to the field point. These ray fields are expressed in terms of Fock functions which reduce to the geometrical optics field in the deep lit region and remain uniformly valid across the shadow boundary transition region into the deep shadow region. Surface ray torsion, which affects the radiated field in both the shadow and transition regions, appears explicitly in the solution as a torsion factor. The radiation patterns of slots and monopoles on cylinders, cones, and spheroids calculated from this solution agree very well with measured patterns and with patterns calculated from exact solutions.

A uniform GTD solution for the radiation from sources on a convex surface

An approximate asymptotic solution is presented for the electromagnetic fields which are induced on an electrically large perfectly conducting smooth convex surface by an infinitesimal magnetic or electric current moment on the same surface. This solution can be employed to calculate the mutual coupling between antennas on a convex surface in an efficient and accurate manner. In this solution, the surface fields propagate along Keller's surface ray paths, and their description remains uniformly valid within the shadow boundary transition region including the immediate vicinity of the source. Furthermore, the effect of surface ray torsion on the surface fields is indicated in the present solution, through a factor T/k , where T denotes the surface ray torsion and k is the surface curvature in the ray direction. This solution is deduced from the asymptotic solutions to simpler canonical problems. Numerical results for the mutual coupling between slots in cylinders and cones are presented, and are shown to compare very well with experiments.

Ray analysis of mutual coupling between antennas on a convex surface

A time-domain version of the uniform geometrical theory of diffraction (TD-UTD) is developed to describe, in closed form, the transient electromagnetic scattering from a perfectly conducting, arbitrarily curved wedge excited by a general time impulsive astigmatic wavefront. This TD-UTD impulse response is obtained by a Fourier inversion of the corresponding frequency domain UTD solution. An analytic signal representation of the transient fields is used because it provides a very simple procedure to avoid the difficulties that result when inverting frequency domain UTD fields associated with rays that traverse line or smooth caustics. The TD-UTD response to a more general transient wave excitation of the wedge may be found via convolution. A very useful representation for modeling a general pulsed astigmatic wave excitation is also developed which, in particular, allows its convolution with the TD-UTD impulse response to be done in closed form. Some numerical examples illustrating the utility of these developments are presented.

Prabhakar H. Pathak

Papers

A uniform GTD analysis of the diffraction of electromagnetic waves by a smooth convex surface

Techniques for High-Frequency Problems

A uniform GTD solution for the radiation from sources on a convex surface

Ray analysis of mutual coupling between antennas on a convex surface

Time-domain uniform geometrical theory of diffraction for a curved wedge