The European Physical Journal Special Topics

, Volume 154, Issue 1, pp 77–83 | Cite as

Successive diffraction model based on Fourier optics as a tool for the studies of light interaction with arbitrary ultrasonic field

  • I. Grulkowski
  • P. Kwiek

Abstract.

In this paper we presented theoretical predictions of light diffraction by complex acoustic fields such as: two adjacent and superposed ultrasonic beams or ultrasound of cylindrical symmetry. The numerical calculations of light intensity of diffraction orders were performed by means of two methods: Nth Order Approximation (NOA) and Successive Diffraction Model (SDM) based on Fourier optics. The latter technique involves dividing the ultrasonic field into several adjacent sections provided that in each section the interaction of light and ultrasound is considered to fulfill Raman-Nath approximation. Propagation of light inside and behind the region with ultrasonic wave was described within the formalism of Fourier optics so that only both transfer and transmission functions had to be appropriately defined. It was revealed that SDM method based on Fourier optics might be applied in the studies of acousto-optic interaction in the cases of complex ultrasonic fields.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P.H. Van Cittert, Physica 4, 590 (1937) Google Scholar
  2. L.E. Hargrove, J. Acoust. Soc. Am. 34, 1547 (1962) Google Scholar
  3. V.N. Parygin, L.E. Chirkov, Radiotech. Electron. 18, 703 (1973) (in Russian) Google Scholar
  4. O. Nomoto, Y. Torikai, Acustica 24, 284 (1971) Google Scholar
  5. R.J. Pieper, A. Korpel, Appl. Opt. 22, 4073 (1983) Google Scholar
  6. A. Korpel, Acousto-Optics (Marcel Dekker, New York, 1988) Google Scholar
  7. V.I. Balakshy, V.N. Parygin, L.E. Chirkov, Physical Principles of Acousto-Optics (Radio i Sviaz, Moscow, 1985) Google Scholar
  8. P.P. Banerjee, C.-W. Tarn, Acustica 74, 181 (1991) Google Scholar
  9. Ch. Koch, R. Reibold, Fourier-optical Technique for the Investigation of Light Diffraction by Arbitrary Ultrasonic Fields (unpublished) Google Scholar
  10. Ch. Koch, R. Reibold, Acustica-Acta Acust. 82, S74 (1996) Google Scholar
  11. J.W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968) Google Scholar
  12. G. Gondek, T. Katkowski, P. Kwiek, Ultrasonics 38, 845 (2000) Google Scholar
  13. G. Gondek, P. Kwiek, R. Reibold, Diffraction of light by two superposed ultrasonic beams of frequency ratio 1:2, World Congress of Ultrasonics, Paris, 2003, in Proc. WCU 2003, pp. 357–360 (CDROM) Google Scholar
  14. G. Gondek, I. Grulkowski, P. Kwiek, R. Reibold, Ultrasonics (accepted) Google Scholar
  15. E.O. Brigham, The fast Fourier transform and its applications (Prentice Hall, Englewood Cliffs, 1988) Google Scholar
  16. I. Grulkowski, P. Kwiek, Opt. Commun. 267, 14 (2006) Google Scholar
  17. I. Grulkowski, D. Jankowski, P. Kwiek, Arch. Acoust. 31, 137 (2006) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Authors and Affiliations

  • I. Grulkowski
    • 1
  • P. Kwiek
    • 1
  1. 1.Division of Acousto-Optics and Laser PhysicsUniversity of Gdańsk, Institute of Experimental PhysicsGdańskPoland

Personalised recommendations