Gaussian beam diffraction in free space


  • Paweł Berczyński
  • Yury Kravtsov



In this paper complex geometrical optics (CGO) method is applied for Gaussian beam (GB) diffraction in free space. CGO reduces diffraction description to solving ordinary differential equations for the beam amplitude and for complex curvature of the wave front. We present analytical solutions for GB width, wave front curvature and complex amplitude. Moreover we discuss the influence of beam ellipticity on propagation in free space. Obtained CGO solutions are compared with solutions of diffraction theory, specifically from Kirchhoff-Fresnel integral.

Full Text: PDF

  1. Yu. A. Kravtsov, "Complex rays and complex caustics", Radiophys. Quantum Electronics 10, 719−730 (1967). CrossRef
  2. J. B. Keller and W. Streifer, "Complex rays with application to Gaussian beams", J. Opt. Soc. Am. 61, 40−43 (1971) CrossRef
  3. G. A. Deschamps, "Gaussian beam as a bundle of complex rays", Electron. Lett. 7(23), 684−685 (1971). CrossRef
  4. Yu. A. Kravtsov, G.W. Forbes, and A.A. Asatryan, "Theory and applications of complex rays", in Progress in Optics, edited by E.Wolf, 39, 1−62 (Elsevier, Amsterdam, 1999). CrossRef
  5. S. J. Chapman, J.M. Lawry, J.R. Ockendon, and R.H. Tew, "On the theory of complex rays", SIAM Review 41, 417−509 (1999). CrossRef
  6. Yu. A. Kravtsov, P. Berczynski, "Gaussian beams in inhomogeneous media: a review", Stud. Geophys. Geod. 51(1), 1-36 (2007). CrossRef
  7. Yu A. Kravtsov N. Y. Zhu, "Theory of diffraction: Heuristic Approaches", Alpha Science International, ISBN 1842653725, (2009).
  8. P. Berczynski, Yu.A. Kravtsov, "Theory for Gaussian beam diffraction in 2D inhomogeneous medium, based on the eikonal form of complex geometrical optics", Physics Letters A, 331(3-4), 265-268, (2004). CrossRef
  9. P. Berczynski, K. Yu. Bliokh, Yu. A. Kravtsov, A. Stateczny, "Diffraction of Gaussian beam in 3D smoothly inhomogeneous media: eikonal-based complex geometrical optics approach", J. Opt. Soc. Am. A, 23(6), 1442- 1451 (2006). CrossRef
  10. P. Berczyński, Yu. Kravtsov, "Gaussian beam evolution in nonlinear inhomogeneous fibres", Photonics Letters of Poland, Vol 4, No 1, 26-28 (2012). CrossRef
  11. P. Berczynski, Yu. A. Kravtsov, G. Zeglinski, "Gaussian beam diffraction in inhomogeneous media of cylindrical symmetry", Optica Applicata (Vol.40), No.3, pp. 705-718, (2010). DirectLink




How to Cite

P. Berczyński and Y. Kravtsov, “Gaussian beam diffraction in free space”, Photonics Lett. Pol., vol. 5, no. 1, pp. pp. 26–28, Mar. 2013.