This book is stated to be a revised translation of the French edition [Daniel Bouche and Frédéric Molinet, Méthodes asymptotiques en électromagnétisme, Springer, Paris (1994; Zbl 0817.35110)]. The work arises from calculations of radar cross sections and the associated asymptotic diffracted fields of plane waves, by perfectly conducting scatterers, some with dielectric coatings. There are eight chapters to the work.
The first chapter deals with ray optics. In this there is a discussion of topics such as caustics and creeping rays. The second chapter is concerned with the application of ideas of asymptotic expansions to diffraction problems. The Luneberg-Klein approach is referred to and the ideas of eikonals and boundary layer techniques are introduced. The third chapter is on the boundary layer. In this the usefulness of scaling coordinates is discussed together with the idea of expansions in terms of \(k^{1/3}\) when \(k\) is the separation constant. Also introduced is the idea of impedance conditions. There is a treatment of whispering gallery modes and the necessity for the matching of solutions for internal and exterior boundary layers is discussed. The fourth chapter introduces spectral theory – plane wave spectra, Sommerfeld contours, and Fock fields.
The fifth chapter on uniform solutions is a long one, of 140 pages. The idea of a uniform asymptotic expansion is introduced together with a comparison of the Pauli, Clemmov, and Van der Waerden techniques and others. Diffraction by wedges is discussed and there is a comparison between diffraction by two-dimensional and three-dimensional objects. Solutions valid in the region of the shadow boundary, and for imperfectly conducting objects are also discussed. The sixth chapter is entitled ‘Integral methods’. The subjects of this are Maslov’s use of Lagrangian manifolds, Arnold’s spectral reconstruction method, and the relation between caustics and catastrophe theory. The seventh chapter is entitled ‘Surface field and physical theory of diffraction’. Amongst the topics treated are transition zones, fringe waves, and the Ryan-Peters equivalent current method. The eighth chapter is concerned with surface impedance and an indication is given of the difficulties which can arise where there are edges and discontinuities. The body of the work is followed by six appendices, which supplement and expand various aspects of the mathematical treatments in the core of the work.
This is a solid work and the authors are to be thanked for it. It is a reference work rather than a textbook, much of it being statements of results (there are well over 200 references) although there is a certain amount of analysis. There is a limited amount of numerical work, and in some places reference is made to problems which have not yet been solved. Two minor criticisms are that there is very little on diffraction by concave surfaces and that an index of the references is needed. However, this is a well-written work and all those working on diffraction theory will need to have ready access to a copy.