Technical Physics Letters

, Volume 25, Issue 11, pp 891–893 | Cite as

Topological phase in a nonparaxial Gaussian beam

  • A. V. Volyar
  • T. A. Fadeeva
  • V. G. Shvedov


An analysis is made of the structure and evolution of the singularities of a nonparaxial Gaussian beam. It is shown that a Gaussian beam may be represented by a family of straight lines lying on the surface of a hyperboloid and that the wavefront of this beam is a function of a point source situated at a point on the z axis with the imaginary coordinate iz0. The argument of this complex function is the topological phase of the beam which characterizes the rotation of the wavefront. The singularities of a nonparaxial Gaussian beam are located in the focal plane and are annular edge dislocations. Dislocation processes near the constriction of the Gaussian beam only occur as a result of aperture diffraction.


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  1. 1.
    L. W. Davis, Phys. Rev. A 19, 1177 (1979).ADSGoogle Scholar
  2. 2.
    M. Lax, W. Louisell, and B. McKnight, Phys. Rev. A 11, 1365 (1975).CrossRefADSGoogle Scholar
  3. 3.
    G. P. Agrawal and D. N. Pattanayak, J. Opt. Soc. Am. 69, 575 (1979).ADSGoogle Scholar
  4. 4.
    C. J. R. Sheppard and S. Saghati, Phys. Rev. A 57, 2971 (1998).CrossRefADSGoogle Scholar
  5. 5.
    M. V. Berry, J. Mod. Opt. 45, 1845 (1998).ADSGoogle Scholar
  6. 6.
    M. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1968).Google Scholar
  7. 7.
    L. B. Felson, J. Opt. Soc. Am. 66, 751 (1976).ADSGoogle Scholar
  8. 8.
    G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge University Press, London, 1945).Google Scholar
  9. 9.
    A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Pis’ma Zh. Tekh. Fiz. 25(5), 87 (1999) [Tech. Phys. Lett. 25, 203 (1999)].Google Scholar
  10. 10.
    M. V. Berry, Proc. R. Soc. London A No. 392, 45 (1984).Google Scholar
  11. 11.
    J. E. Nye, J. Opt. Soc. Am. A 15, 1132 (1998).ADSGoogle Scholar

Copyright information

© American Institute of Physics 1999

Authors and Affiliations

  • A. V. Volyar
    • 1
  • T. A. Fadeeva
    • 1
  • V. G. Shvedov
    • 1
  1. 1.Simferopol State UniversitySimferopol

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