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Original Articles

The evanescent waves in geometrical optics and the mixed hyperbolic–elliptic type systems

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Pages 181-204 | Received 08 Jul 2004, Accepted 21 Sep 2004, Published online: 25 Jan 2007
 

Abstract

In this article we describe the generation of the evanescent waves which are present in the rarer medium at total reflection by using a mixed-type system, the Ludwig system, which leads naturally to consider a complex-valued phase. The Ludwig system is derived from the Helmholtz equation by using an appropriate modification of the stationary phase procedure: the Chester, Friedman and Ursell's method. The passage from the illuminated to the shadow region is described by means of the ray switching mechanism based on the Stokes phenomenon applied to the Airy function. Finally, the transport system connected to the Ludwig eikonal system is studied in the case of linear wavefronts and the existence of the Goos–Hänchen effect is proved.

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