On the theory of complex rays

The article surveys the application of complex-ray theory to the scaler Hel mholtz equation in two dimensions. The first objective is to motivate a framework within which complex rays ma y be used to make predictions about wavefields in a wide variety of geometr ical configurations. A crucial ingredient in this framework is the role pla yed by Stokes' phenomenon in determining the regions of existence of comple x rays. The identification of the Stokes surfaces emerges as a key step in the approximation procedure, and this leads to the consideration of the man y characteriaations of Stokes surfaces, including the adaptation and applic ation of recent developments in exponential asymptotics to the complex Went zel-Kramers-Brilbuin expansion of these wavefields. Examples are given for several cases of physical importance.