Two powerful techniques for the analysis of aperture antennas are now used. One is based on the convenient Fourier transform relationship between aperture field and far-field radiation pattern. Here this relationship is derived from the plane wave spectrum representation of the aperture fields. In the near field of the aperture, Fourier transforms become Fresnel transforms. Far-field patterns may be predicted from near-field measurements by treating the near field as the aperture plane. In its application this method is basically the Kirchhoff approximation of diffraction theory. It is accurate for the forward fields of large antennas but cannot provide the lateral and back radiation.
The other method is based on aperture edge diffraction and called the geometrical theory of diffraction. It is developed from an asymptotic approximation to rigorous diffraction theory. Inherently more accurate and more widely applicable, it is especially useful in the calculation of antenna radiation in the lateral and rear directions. However, at present it fails in some situations where the Kirchhoff method succeeds, for example the axial fields of paraboloidal reflectors. In this sense the two methods are complementary and often both are required in antenna analysis. Application of the two methods to the calculation of the pattern, gain and reflection coefficient of some common antenna types is shown and comparisons are made with experiment.
There have been significant developments in the field of numerical methods for diffraction problems in recent years, and as a result, it is now possible to perform computations with more than ten million unknowns. However, the importance of asymptotic methods should not be overlooked. Not only do they provide considerable physical insight into diffraction mechanisms, and can therefore aid the design of electromagnetic devices such as radar targets and antennas, some objects are still too large in terms of wavelengths to fall in the realm of numerical methods. Furthermore, very low Radar Cross Section objects are often difficult to compute using multiple methods. Finally, objects that are very large in terms of wavelength, but with complicated details, are still a challenge both for asymptotic and numerical methods. The best, but now widely explored, solution for these problems is to combine various methods in so called hybrid methods.
Asymptotic and Hybrid Methods in Electromagnetics is based on a short course, and presents recent developments in the field.
The geometrical theory of diffraction (GTD) is an efficient method of analysis and design of wave fields. It is widely used in antenna synthesis in microwave, millimetre and infra-red bands, in circuit engineering and laser system design. It is a convenient tool for tackling the problems of wave propagation and scattering at bodies of complex shape. The method combines the simplicity and physical transparency of geometrical optics with high computational accuracy over a wide dynamic range of quantities analysed. The advantage of GTD is particularly pronounced in applications where the wavelength is small compared with the typical size of scatterers, i.e. in situations where the known analytical techniques - variational calculus and numerical analysis - are no longer applicable.
This book painstakingly systematises the ideas underlying GTD, gives a detailed explanation of the modern state of the theory within the bounds of its validity, and elucidates its relationships with other popular asymptotic theories - the methods of physical optics and edge waves.
The book is designed for scientists, engineers and postgraduate students involved in electromagnetics, radio engineering and optical system design.
The continuous development of the Geometrical Theory of Diffraction (GTD), from its conception in the 1950s, has now established it as a leading analytical technique in the prediction of high-frequency electromagnetic radiation and scattering phenomena. Consequently, there is an increasing demand for research workers and students in electromagnetic waves to be familiar with this technique. In this book they will find a thorough and clear exposition of the GTD formulation for vector fields. It begins by describing the foundations of the theory in canonical problems and then proceeds to develop the method to treat a variety of circumstances. Where applicable, the relationship between GTD and other high-frequency methods, such as aperture field and the physical optics approximation, is stressed throughout the text. The purpose of the book, apart from expounding the GTD method, is to present useful formulations that can be readily applied to solve practical engineering problems. To this end, the final chapter supplies some fully worked examples to demonstrate the practical application of the GTD techniques developed in the earlier chapters.
This book describes new, highly effective, rigorous analysis methods for electromagnetic wave problems. Examples of their application to the mathematical modelling of micros trip lines, corrugated flexible waveguides, horn antennas, complex-shaped cavity resonators and periodic structures are considered.
Special attention is paid to energy dissipation effects. Various physical models and methods of analysis of dissipation are described and approximate formulas and computer-based calculation results for dissipation characteristics are given and compared with experimental data. Ways of decreasing dissipation in waveguides and resonators are discussed.
The book will be of interest to physicists and engineers working on the theory and design of microwave and millimetre-wave components and devices. Designers in microwave engineering will find here all the information they need for choosing the correct waveguide (resonator) for a stipulated dissipation characteristic. The numerical algorithms and formulas can be directly applied to CAD systems. The book is also relevant for students of electromagnetism and microwave circuits.
This book is an essential resource for researchers involved in designing antennas and RCS calculations. It is also useful for students studying high frequency diffraction techniques. It contains basic original ideas of the Physical Theory of Diffraction (PTD), examples of its practical application, and its validation by the mathematical theory of diffraction. The derived analytic expressions are convenient for numerical calculations and clearly illustrate the physical structure of the scattered field. The text's key topics include: Theory of diffraction at black bodies introduces the Shadow Radiation, a fundamental component of the scattered field; RCS of finite bodies of revolution-cones, paraboloids, etc.; models of construction elements for aircraft and missiles; scheme for measurement of that part of a scattered field which is radiated by the diffraction (so-called nonuniform) currents induced on scattering objects; development of the parabolic equation method for investigation of edge-diffraction; and a new exact and asymptotic solutions in the strip diffraction problems, including scattering at an open resonator.
This advanced research monograph is devoted to the Wiener-Hopf technique, a function-theoretic method that has found applications in a variety of fields, most notably in analytical studies of diffraction and scattering of waves. It provides a comprehensive treatment of the subject and covers the latest developments, illustrates the wide range of possible applications for this method, and includes an extensive outline of the most powerful analytical tool for the solution of diffraction problems.
This will be an invaluable compendium for scientists, engineers and applied mathematicians, and will serve as a benchmark reference in the field of theoretical electromagnetism for the foreseeable future.