Abstract
By utilizing a rigorous plane-wave representation, we investigate the basic wave mechanism that is responsible for both the lateral (Goos-Hänchen) shift of a gaussian light beam incident from a denser medium upon the interface to a rarer medium, and the weak radiance that accompanies the reflected beam. We thus find that the complete reflected field contains a geometric-optics component, whose domain is given by the mirror reflection of the incident beam, as well as a lateral-wave component which occupies a much larger domain. Our results show that the near field of the lateral-wave component interferes with the geometric-optics component and thereby produces the Goos-Hänchen shift of the reflected beam. The intermediate and far fields of the lateral-wave, on the other hand, are responsible for the weak radiance that trails the reflected beam. By demonstrating that both the beam shift and the trailing radiance represent two facets of the same wave process, the lateral-wave field is shown to provide a unified interpretation of two effects that have previously been regarded as separate phenomena. The dependence of these effects on beam width, angle of incidence, and polarization are also considered.
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L.M.Brekhovskikh:Waves in layered media (Academic Press, New York 1960) Sections 21 and 22, p. 270
T.Tamir: Optik36, 209 (1972)
F.Goos, H.Hänchen: Ann. Physik (6)1, 333 (1947)
H.K.V.Lotsch: J. Opt. Soc. Am.58, 551 (1968)
H.K.V.Lotsch: Die Strahlversetzung bei Totalreflexion: Der Goos-Hänchen-Effekt; Dr.-Ing. Dissertation. Technical University of Aachen, F.R. Germany (1970). Also, Optik32, 116, 189, 299 and 553 (1970–1971), in English
H.Wolter: Z. Naturforsch.5a, 139 and 143 (1950)
H.Wolter: Z. Naturforsch.5a, 276 (1950)
B.R.Horowitz, T.Tamir: J. Opt. Soc. Am.61, 586 (1971)
B.R.Horowitz: Critical angle effects for optical beams at a dielectric interface. Ph. D. Dissertation. Polytechnic Institute of Brooklyn, N. Y. 1972
L.M.Brekhovskikh:Waves in layered media, (Academic Press, New York 1960) Ref. [1], pp. 100–117
H.Maecker: Ann. Physik (6)4, 409 (1949)
H.Osterberg, L.W.Smith: J. Opt. Soc. Am.54, 1073 (1964)
T.Tamir, A.A.Oliner: J. Opt. Soc. Am.59, 942 (1969)
E.T.Whittaker, G.N.Watson:A course of modern analysis (Univ. Press, Cambridge 1963) Section 16. 52, p. 348
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Horowitz, B.R., Tamir, T. Unified theory of total reflection phenomena at a dielectric interface. Appl. Phys. 1, 31–38 (1973). https://doi.org/10.1007/BF00886802
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DOI: https://doi.org/10.1007/BF00886802