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

• Authors: Yury Kravtsov , Stefan Buske
• 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.

Keywords

EN

Ray theory; geometrical optics; gaussian beam; 43.20.Dk; 43.20.Bi

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2006
• Volume: 4
• Issue: 1
• Pages: 1-7

Dates

published

1 - 3 - 2006

online

1 - 3 - 2006

Contributors

author

Yury Kravtsov

author

Stefan Buske

• Institute of Geological Sciences, Free University of Berlin, Malteserstr. 74-100, 12249, Berlin, Germany

References

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• [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.

Identifiers

DOI

10.1007/s11534-005-0001-y