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2006 | 4 | 1 | 1-7
Article title

Divergence of geometrical optics series at the boundary of its applicability: An analytical example in elementary functions (2D Gaussian beam in free space)

Content
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Languages of publication
EN
Abstracts
EN
An analytical example in elementary functions is presented (2D Gaussian beam diffraction in free space), which demonstrates the divergence of the geometrical optics (GO) series when the conditions for its applicability are violated. This example shows that accounting for higher terms in GO power series leads to divergence and therefore becomes completely useless beyond the boundaries of GO applicability.
Publisher
Journal
Year
Volume
4
Issue
1
Pages
1-7
Physical description
Dates
published
1 - 3 - 2006
online
1 - 3 - 2006
References
  • [1] E.J. Weniger: “Mathematical properties of a new Levin-type sequence transformation introduced by Cizek, Zamastil and Skala - I. Algebraic theory”, J. Math. Phys., Vol. 45(3), (2004), pp. 1209–1246. http://dx.doi.org/10.1063/1.1643787[Crossref]
  • [2] M. Born and E. Wolf: Principles of optics, 6th ed., Pergamon Press, Oxford, England, 1985.
  • [3] L.D. Landau and E.M. Lifshits: Quantum Mechanics, Vol. III of Theoretical physics, Pergamon Press, Oxford, England, 1977.
  • [4] Yu.A. Kravtsov and Y.I. Orlov: Geometrical optics of inhomogeneous media, Springer Verlag, Berlin, Heidelberg, 1990.
  • [5] Yu.A. Kravtsov: Geometrical optics in Engineering Physics, Alpha Science International, Harrow, UK, 2005.
  • [6] Yu.A. Kravtsov and Y.I. Orlov: “Limits of applicability of the method of geometrical optics and related problems”, Soviet Physics-Uspekhi, (1980), 23(11), pp. 750–762; Reprinted: P.L. Marston (Ed.): Geometrical Aspects of Scattering, SPIE Milestone Series, Vol. MS89, SPIE Optical Engineering, Seattle, 1994, pp. 88-101. http://dx.doi.org/10.1070/PU1980v023n11ABEH005060[Crossref]
  • [7] Y.A. Kravtsov: “Rays and caustics as physical objects”, In: E. Wolf (Ed.): Progress in Optics, Vol. 26, Elsevier, Amsterdam, 1988, pp. 227–348.
  • [8] S. Buske and Yu.A. Kravtsov: “A study of the applicability and divergence of the ray series using a modified transport equation”, Geophys. J. Int., Vol. 160, (2005), pp. 1–4.
  • [9] H. Cartan: Elementary theory of analytic functions of one or several complex variables, Dover Books on Mathematics, New York, 1995.
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_1007_s11534-005-0001-y
Identifiers
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