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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 3 — Mar. 1, 2002
  • pp: 491–496

Design of diffractive axicons producing uniform line images in Gaussian Schell-model illumination

Anna Thaning, Ari T. Friberg, Sergei Yu. Popov, and Zbigniew Jaroszewicz  »View Author Affiliations

JOSA A, Vol. 19, Issue 3, pp. 491-496 (2002)

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We present a design method for diffractive axicons in spatially partially coherent Gaussian Schell-model illumination. The method of stationary phase applied to the Fresnel diffraction integral for on-axis intensity leads, on requiring a uniform axial image profile, to a second-order differential equation for the optimal axicon phase function. The first integral can be formally performed, and the phase function is subsequently obtained numerically. The correctness of the synthesized phase profiles is confirmed by numerical simulations using partially coherent Fresnel diffraction theory. The effects of input-beam spot size and coherence width are assessed, and influences of different forms of apodization, including asymmetric functions for narrow incident beams, in annular-aperture diffractive axicons are examined.

© 2002 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(050.1970) Diffraction and gratings : Diffractive optics

Anna Thaning, Ari T. Friberg, Sergei Yu. Popov, and Zbigniew Jaroszewicz, "Design of diffractive axicons producing uniform line images in Gaussian Schell-model illumination," J. Opt. Soc. Am. A 19, 491-496 (2002)

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  1. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954).
  2. L. M. Soroko, Meso-Optics—Foundations and Applications (World Scientific, Singapore, 1996), Chap. 2.
  3. Z. Jaroszewicz, Axicons: Design and Propagation Properties, Vol. 5 of Research & Development Treatises (SPIE Polish Chapter, Warsaw, 1997).
  4. J. Sochacki, A. Kołodziejczyk, Z. Jaroszewicz, and S. Bara, “Nonparaxial design of generalized axicons,” Appl. Opt. 31, 5326–5330 (1992).
  5. J. Pu, H. Zhang, S. Nemoto, W. Zhang, and W. Zhang, “Annular-aperture diffractive axicons illuminated by Gaussian beams,” J. Opt. A 1, 730–734 (1999).
  6. S. Yu. Popov and A. T. Friberg, “Design of diffractive axicons for partially coherent light,” Opt. Lett. 23, 1639–1641 (1998).
  7. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995), Secs. 4.3.2 and 5.6.4.
  8. F. Gori, “Collett–Wolf sources and multimode lasers,” Opt. Commun. 34, 301–305 (1980).
  9. S. Lavi, R. Prochaska, and E. Karen, “Generalized beam parameters and transformation laws for partially coherent light,” Appl. Opt. 27, 3696–3703 (1988).
  10. R. Gase, “The multimode laser radiation as a Gaussian Schell-model beam,” J. Mod. Opt. 38, 1107–1115 (1991).
  11. J. Sochacki, Z. Jaroszewicz, L. R. Staroński, and A. Kołodziejczyk, “Annular-aperture logarithmic axicon,” J. Opt. Soc. Am. A 10, 1765–1768 (1993).
  12. A. T. Friberg and S. Yu. Popov, “Effects of partial spatial coherence with uniform-intensity diffractive axicons,” J. Opt. Soc. Am. A 16, 1049–1058 (1999).
  13. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1965), Eq. (9.6.16).
  14. A. Erdelyi, Asymptotic Expansions (Dover, New York, 1956), Sec. 2.9, Eq. (2).
  15. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), Chap. 7, Eq. (3.10).
  16. R. M. Herman and T. A. Wiggins, “Apodization of diffractionless beams,” Appl. Opt. 31, 5913–5915 (1992).
  17. Z. Jaroszewicz, J. Sochacki, A. Kołodziejczyk, and L. R. Staroński, “Apodized annular-aperture logarithmic axicon: smoothness and uniformity of intensity distributions,” Opt. Lett. 18, 1893–1895 (1993).
  18. S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, and B. Schnabel, “Apodized annular-aperture diffractive axicons fabricated by continuous-path-control electron beam lithography,” Opt. Commun. 154, 359–367 (1998).
  19. A. T. Friberg, “Stationary-phase analysis of generalised axicons,” J. Opt. Soc. Am. A 13, 743–750 (1996).
  20. N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, and A. T. Friberg, “Asymptotic methods for evaluation of diffractive lenses,” J. Opt. A 1, 552–559 (1999).
  21. M. Hazewinkel, ed., Encyclopaedia of Mathematics (Reidel, Dordrecht, The Netherlands, 1998), Vol. 1 (A–B), p. 359.
  22. M. Braun, Differential Equations and Their Applications, 4th ed. (Springer, Berlin, 1993), Chap. 12, Eq. (11).
  23. J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Application (Akademie Verlag, Berlin, 1997).
  24. S. Yu. Popov and A. T. Friberg, “Apodization of generalized axicons to produce uniform axial line images,” Pure Appl. Opt. 7, 537–548 (1998).
  25. M. R. Perrone, A. Piegari, and S. Scaglione, “On the super-Gaussian unstable resonators for high-gain short-pulse laser media,” IEEE J. Quantum Electron. 29, 1423–1427 (1993).
  26. V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, D. Ambrosini, and G. Shirripa Spagnolo, “Propagation of axially symmetric flattened Gaussian beams,” J. Opt. Soc. Am. A 13, 1385–1394 (1996).

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