Gaussian beam evolution in nonlinear media of Kerr type


  • Paweł Berczyński
  • Yury Kravtsov



The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. PCGO deals with ordinary differential equations for the beam amplitude and for complex curvature of the wave front which describe evolution of axially symmetric GB in Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in medium of Kerr type.

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  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, "Geometrical Optics in Engineering Physics", Alpha Science International, UK (2005)
  8. S. A. Akhmanov, A. P. Sukhorukov, R. V. Khokhlov, "Self-focusing and light diffraction in nonlinear medium", Soviet Phys. Uspekhi 10, 609-636 (1968). CrossRef
  9. S. A. Akhmanov, R.V. Khokhlov, and A. P. Sukhorukov, "Self-focusing, Self-defocusing and Self-modulation of Laser Beams", in Laser Handbook, F.T.Arecchi and E.O. Shulz-Dubois, Eds. (Elsevier, New York, 1972), Vol. 2, 1151-1228.6 S303 (2004).
  10. P. Berczyński, Yu. Kravtsov, "Gaussian beam evolution in nonlinear inhomogeneous fibres", Photonics Letters of Poland, Vol 4, No 1, 26-28 (2012). CrossRef




How to Cite

P. Berczyński and Y. Kravtsov, “Gaussian beam evolution in nonlinear media of Kerr type”, Photonics Lett. Pol., vol. 5, no. 1, pp. pp. 29–31, Mar. 2013.