Rays aren't what they used to be

Abstract

Departing from the classical formulation of the propagation of light rays, modern ray theory has evolved by successive improvements and now provides one of the more effective methods for treating high‐frequency wave propagation in general—in various environments and disciplines—in terms of field contributions localized around ray trajectories. By asymptotic analysis of canonical problems in the geometrical theory of diffraction (GTD), the category of incident, reflected, and refracted rays has been enlarged through inclusion of diffracted rays accounting for edge scattering, critical angle phenomena, and creeping waves in shadow regions on smooth convex surfaces. By asymptotic uniformization, failures of GTD in transition regions near shadow boundaries, caustics, or foci have been repaired; by collective treatment, multiple reflected ray fields in guiding regions have been converted into ray congruences that represent the normal modes; and from partial conversion of poorly converging ray clusters, there have emerged self‐consistent and physically incisive hybrid ray‐mode combinations. By extending the notion of a ray into complex coordinate space, it has been possible to incorporate evanescent fields and highly collimated beam fields within the ray format. Very recent studies have shown that the common foundation for all of these ray phenomena is a local plane‐wave spectrum which is most severely shrunk around the ray paths when the ray fields are simple, but which must retain more “spectral flesh” in transitional and other critical domains. These concepts, which also extend to time‐dependent propagation, are explored in the presentation, with emphasis on the motion of generalized ray fields as spectral objects. [Work supported by ONR.]