A. V. Kobyshev, E. V. Kurmyshev and I. N. Sisakyan

Computer programs developed for numerical evaluation of the Kirchhoff integral for the case of planar optical elements of arbitrary shape were thoroughly tested. The spatial distribution of diffracted wave fields was investigated as a function of shape of planar optical elements and Gaussian inhomogeneities in the irradiance of the illuminating beam. For the axially symmetric problem, analytical representations of the diffraction integral were obtained in the Fraunhofer and Fresnel approximations as a series in Bessel functions. These representations proved to be convenient in studying the asymptotic effect of inhomogeneities in the intensity of the incident beam. The wave field structure was investigated in the neighbourhood of a geometrical optics parabola, a point focus, and an axial segment with uniform distribution of irradiance.


  1. N. Sisakyan and V. A. Soifer. Computer-synthesized optics. Problems and advances. Kompyuternaya Optika No. 1, 5 (1987). [Computer Optics 1, 3 (1989).]
  2. A. E. Berezny, L. I. Brusilovsky, E. A. Otlivanchik et al. An automatic system for design, fabrication, and investigation of planar optical elements. Draft 1. Kompyuternaya Optika No. 2, 21 (1987). [Computer Optics 1, 163 (1989).]
  3. A. V. Goncharsky. Mathematical models in synthesis of planar optical elements. Kompyuternaya Optika No. 1, 19 (1987). [Computer Optics 1, 13 (1989).]
  4. M. A. Vorontsov, A. N. Matveyev and V. P. Sivokoni. Mode sensitive focuser of laser radiation: design in a diffraction approximation. Komputernaya Optika No. 1, 74-78 (1987). [Computer Optics 1, 57 (1989).]
  5. A. V. Goncharovsky, V. A. Danilov, V. V. Popov et al. Solution of inverse problem of focusing laser radiation into arbitrary curve. Dokl. Akad. Nauk SSSR 273 (3), 605 (1983).
  6. A. V. Goncharsky, V. A. Danilov, V. V. Popov, I. N. Sisakyan et al. Planar focusers of the visible range. Kvantovaya Elektron. (Moscow) 13 (3), 660 (1986).
  7. N. N. Rozanov and V. E. Semyonov. Formulation of specified profile of irradiation by phase control. Pisma Zh. Eksp. Teor. Fiz. 9 (24), 1531 (1983).
  8. V. I. Kxylov, V. V. Bobkov and P. I. Monastyrsky. Numerical Methods. Nauka, Moscow (1976).
  9. M. B. Vinogradova, O. V. Rudenko and A. P. Sukhoruchkov. Wave Theory. Nauka, Moscow (1979).
  10. V. Ya. Arsenin. Methods of Mathematical Physics and Higher Functions. Nauka, Moscow (1974).
  11. H. A. Lesson, W. V. T. Rusch and H. Schjar-Jacobsen. On numerical evaluation of two-dimensional phase integrals. IEEE Trans. A.P. AP-23 (3), 714 (1975).
  12. M. Born and E. Wolf. Principles of Optics, 5th edn. Pergamon Press, Oxford (1975).
  13. A. Erdelyi (ed.). Higher Transcendental Functions (California Institute of Technology, H. Bateman MS Project), 3 vols. McGraw Hill, New York (1953, 1955).
  14. V. A. Danilov, V. V. Popov, A. M. Prokhorov et al. Optical elements focusing coherent radiation into arbitrary focal curve. Preprint FIAN No. 69, Lebedev Physical Institute of the U.S.S.R. Academy of Sciences, Moscow (1983) (in Russian).
  15. A. G. Vasin, M. A. Golub, V. A. Danilov, et al. Evaluation and investigation of coherent wave field in the focal range of optical elements with rotational symmetry. Preprint FIAN No. 304, Moscow (1983) (in Russian).
  16. Yu. M. Klimov. Applied Laser Optics. Mashinostroyeniye, Moscow (1985).

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