ASYMPTOTIC EVALUATION OF RADIATION AND DIFFRACTION TYPE INTEGRALS FOR HIGH FREQUENCIES

This chapter develops asymptotic methods for evaluating radiation and diffraction type integrals so that they are valid for high frequencies. These asymptotic methods when applied to solve electrically large wave problems typically yield wave solutions in a form that directly provide a vivid physical picture in terms of rays for the mechanisms of wave radiation and scattering. The chapter focuses on the approximate evaluation of the radiation integrals primarily in the spectral domain. Integrals containing end points, but which do not contain any saddle point in their integrand, may be evaluated via an integration by parts technique. The method of steepest descent was developed for analyzing spectral wave integrals defined over a complex contour integration. Integrals containing a stationary point and end points which are far separated from each other may be evaluated via the nonuniform stationary phase method.