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

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...

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Bibliographic Details
Published inApplicable analysis Vol. 85; no. 1-3; pp. 181 - 204
Main Authors De Micheli, Enrico, Alberto Viano, Giovanni
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.01.2006
Subjects
AMS Subject Classifications: 78A05
Evanescent waves
Geometrical optics
Goos-Hänchen effect
Mixed-type systems
Stokes phenomenon
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ISSN0003-6811
1563-504X
DOI10.1080/00036810500277173

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Summary: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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ISSN:0003-6811
1563-504X
DOI:10.1080/00036810500277173