Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On the statistical moments of the wave field in the presence of caustics

  • 16 Accesses

  • 1 Citations


The diffraction of a scalar wave field by a screen causing random and regular phase modulation is considered. The regular phase advance causes focusing of the field (i.e., the development of foci or caustic surfaces). It is shown that for strong phase fluctuations geometric optics is suitable for calculating the statistical moments of the field even in focusing regions if the singularity of the moment on the caustic is integrable. This is valid specifically for the average intensity. In calculating the higher moments it is necessary to take diffraction effects into account. Estimates are obtained of the intensity fluctuations in the region of the caustic shadow.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    L. D. Landau and E. M. Lifshits, Field Theory, GIFML, Moscow (1962).

  2. 2.

    V. A. Baranov and Yu. A. Kravtsov, Izv. VUZ., Radiofiz.,12, No. 10, 1500 (1969).

  3. 3.

    A. Ya. Usikov and P. V. Bliokh, Geomagnetizm i Aéronomiya,2, 293 (1962).

  4. 4.

    T. Golel and G. Silverso, Planet. and Space Sci.,16, 999 (1968).

  5. 5.

    P. V. Bliokh, V. G. Sinitsyn, and I. M. Fuks, Astron. Zh.,46, 348 (1969).

  6. 6.

    V. P. Maslov, Perturbation Theory and Asymptotic Methods [in Russian], Izd. MGU, Moscow (1965).

  7. 7.

    M. Born and E. Wolf, Foundations of Optics [Russian translation], Izd. Nauka, Moscow (1970).

  8. 8.

    G. B. Parrent, J. Opt. Soc. America,49, 787 (1959).

  9. 9.

    P. V. Bliokh and V. G. Sinitsyn, Report to International Symposium on Antennas and Wave Propagation (1971 ISAP, Japan), Sendai, Japan (Sept. 1–3, 1971).

  10. 10.

    E. E. Salpeter, Astrophys. J.,147, 433 (1967); M. H. Cohen, E. J. Gundermann, Astrophys. J.,155, 645 (1969).

  11. 11.

    T. D. Antonova, V. V. Vitkevich, and V. I. Vlasov, Dokl. Akad. Nauk SSSR,168, 55 (1966).

  12. 12.

    L. T. Little and A. Hewish, Monthly Not. Roy. Astron. Soc.,134, 222 (1969).

Download references

Author information

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 4, pp. 550–556, April, 1972.

In conclusion the author is pleased to thank P. V. Bliokh for his constant interest in the work and his help, and likewise F. G. Bass and I. M. Fuks for their helpful advice.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sinitsyn, V.G. On the statistical moments of the wave field in the presence of caustics. Radiophys Quantum Electron 15, 414–419 (1972). https://doi.org/10.1007/BF02210732

Download citation


  • Phase Modulation
  • Average Intensity
  • Quantum Electronics
  • Nonlinear Optic
  • Wave Field