Prabhakar H. Pathak

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

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.

Techniques for High-Frequency Problems

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.

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

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 Kellers 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.

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

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.

Ray analysis of mutual coupling between antennas 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 Kellers 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.

Modal, ray, and beam techniques for analyzing the EM scattering by open-ended waveguide cavities

The problem of high-frequency electromagnetic scattering by open-ended waveguide cavities with an interior termination is analyzed via three different approaches. When cavities can be adequately modeled by joining together piecewise separable waveguide sections, a hybrid combination of asymptotic high-frequency and modal techniques is employed. In the case of more arbitrarily shaped waveguide cavities for which modes cannot even be defined in the conventional sense, the geometrical optics ray approach proves to be highly useful. However, at sufficiently high frequencies, both of these approaches tend to become inefficient; hence, a paraxial Gaussian beam technique, which retains much of the simplicity of the ray approximation but is potentially more efficient, is investigated. Typical numerical results based on the different approaches are discussed. >

High frequency techniques for antenna analysis

A summary of various high-frequency techniques is presented for analyzing the electromagnetic radiation from antennas in the presence of their host environment. These techniques provide physical insight into antenna radiation mechanisms and are found to be highly efficient and accurate for treating a variety of practical antenna configurations. Examples to which these techniques have been applied include open-ended waveguide antennas, horn and reflector antennas, and antennas on aircraft and spacecraft. The accuracy of these techniques is established via numerical results which are compared with those based on other independent methods or with measurements. These high frequency methods can be combined with other techniques, through a hybrid scheme, to solve an even greater class of problems than those which can be solved in an efficient and tractable manner by any one technique alone. >

Novel Gaussian beam method for the rapid analysis of large reflector antennas

A relatively fast and simple method utilizing Gaussian beams (GBs) is developed which requires only a few seconds on a workstation to compute the near/far fields of electrically large reflector antennas when they are illuminated by a feed with a known radiation pattern. This GB technique is fast, because it completely avoids any numerical integration on the large reflector surface which is required in the conventional physical optics (PO) analysis of such antennas and which could take several hours on a workstation. Specifically, the known feed radiation field is represented by a set of relatively few, rotationally symmetric GBs that are launched radially out from the feed plane and with almost identical interbeam angular spacing. These GBs strike the reflector surface from where they are reflected, and also diffracted by the reflector edge; the expressions for the fields reflected and diffracted by the reflector illuminated with a general astigmatic incident GB from an arbitrary direction (but not close to grazing on the reflector) have been developed in Chou and Pathak (1997) and utilized in this work. Numerical results are presented to illustrate the versatility, accuracy, and efficiency of this GB method when it is used for analyzing general offset parabolic reflectors with a single feed or an array feed, as well as for analyzing nonparabolic reflectors such as those described by ellipsoidal and even general shaped surfaces.

On the eigenfunction expansion of electromagnetic dyadic Green's functions

A relatively simple approach is described for developing the complete eigenfunction expansion of time-harmonic electric ( \bar{E} ) and magnetic ( \bar{H} ) fields within exterior or interior regions containing an arbitrarily oriented electric current point source. In particular, these results yield directly the complete eigenfunction expansion of the electric and magnetic dyadic Greens functions \bar\bar{G}_{e} and \bar\bar{G}_{m} that are associated with \bar{E} and \bar{H} , respectively. This expansion of \bar\bar{G}_{e} and \bar\bar{G}_{m} contains only the solenoidal type eigenfunctions. In addition, the expansion of \bar\bar{G}_{e} also contains an explicit dyadic delta function term which is required for making that expansion complete at the source point. The explicit dyadic delta function term in \bar\bar{G}_{e} is found readily from a simple condition governing the behavior of the eigenfunction expansion at the source point, provided one views that condition in the light of distribution theory. These general expressions for the eigenfunction expansion of \bar\bar{G}_{e} and \bar\bar{G}_{m} reduce properly to those obtained previously for special geometries by Tai.

An asymptotic closed-form microstrip surface Green's function for the efficient moment method analysis of mutual coupling in microstrip antennas

A relatively simple closed-form asymptotic representation for the single-layer microstrip dyadic surface Greens function is developed. The large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air-dielectric interface. This asymptotic solution remains surprisingly accurate even for very small (a few tenths of a free-space wavelength) lateral separation of the source and field points. Thus, using the present asymptotic approximation of the Greens function can lead to a very efficient moment method (MM) solution for the currents on an array of microstrip antenna patches and feed lines. Numerical results based on the efficient MM analysis using the present closed-form asymptotic approximation to the microstrip surface Greens function are given for the mutual coupling between a pair of printed dipoles on a single-layer grounded dielectric slab. The accuracy of the latter calculation is confirmed by comparison with numerical results based on a MM analysis which employs an exact integral representation for the microstrip Greens function. >