OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 39, Iss. 6 — Feb. 20, 2000
  • pp: 1059–1063

Diffraction of x rays in capillary optics

Sergei V. Kukhlevsky, Francesco Flora, Alessandro Marinai, Katalin Negrea, Libero Palladino, Armando Reale, Giuseppe Tomassetti, Antonio Ritucci, Gergely Nyitray, and Laszlo Kozma  »View Author Affiliations

Applied Optics, Vol. 39, Issue 6, pp. 1059-1063 (2000)

View Full Text Article

Acrobat PDF (140 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Propagation of x rays generated by a small-diameter incoherent source through the capillary waveguide that satisfies the multimode condition is studied with the Fresnel–Kirchhoff diffraction theory. The strong influence of diffraction on the propagation is demonstrated. The diffraction phenomenon is manifested by the appearance of diffraction fringes in both the guide channel and the far-field zone of the capillary output. Experimental data that confirm such behavior of the x-ray radiation is also presented. The results confirm the interference effects recently observed in some experiments on the grazing reflections of x rays in single- and multiple-capillary optics.

© 2000 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(340.0340) X-ray optics : X-ray optics

Sergei V. Kukhlevsky, Francesco Flora, Alessandro Marinai, Katalin Negrea, Libero Palladino, Armando Reale, Giuseppe Tomassetti, Antonio Ritucci, Gergely Nyitray, and Laszlo Kozma, "Diffraction of x rays in capillary optics," Appl. Opt. 39, 1059-1063 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. A. H. Compton, “The total reflection of x rays,” Philos. Mag. 45, 1121–1131 (1923).
  2. F. Jentzsch and E. Nähring, “Die Fortleitung von Licht- und Röntgen durch Röhren,” Z. Tech. Phys. 12, 185–189 (1931).
  3. J. A. Lely and T. W. Van Rijssel, “X-ray collimator producing a beam of very small divergence and large intensity,” Acta Crystallogr. 2, 337–338 (1949).
  4. P. B. Hirsch and J. N. Kellar, “An x-ray micro-beam technique: I. Collimation,” Proc. Phys. Soc. London 64, 369–374 (1951).
  5. P. Mallozzi, H. M. Epstein, R. G. Jung, D. C. Applebaum, B. P. Fairand, W. T. Gallagher, R. L. Uecker, and M. C. Muckerheide, “Laser-generated plasmas as a source of x rays for medical applications,” J. Appl. Phys. 45, 1891–1895 (1974).
  6. D. Mosher and S. J. Stephanakis, “X-ray light pipes,” Appl. Phys. Lett. 29, 105–107 (1976).
  7. A. Rindby, “Application of fiber technique in the x-ray region,” Nucl. Instrum. Methods Phys. Res. A 249, 536–540 (1986).
  8. E. A. Stern, Z. Kalman, A. Lewis, and K. Lieberman, “Simple method for focusing x rays using tapered capillaries,” Appl. Opt. 27, 5135–5139 (1988).
  9. M. A. Kumakhov and F. A. Komarov, “Multiple reflections from surface x-ray optics,” Phys. Rep. 191, 289–350 (1990).
  10. J. B. Hastings, S. L. Hulbert, and G. P. Williams, eds., Proceedings of the 5th International Conference on Synchrotron Radiation Instrumentation, Rev. Sci. Instrum. 66, 1271–2385 (1995).
  11. A. Kuczumow and S. Larsson, “Scheme for x-ray tracing in capillary optics,” Appl. Opt. 33, 7928–7932 (1994).
  12. C. M. Dozier, D. A. Newman, J. P. Gilfrich, R. K. Freitag, and J. P. Kirkland, “Capillary optics for x-ray analysis,” in Advances in X-Ray Analysis, Vol. 37, J. P. Gilfrich, ed. (Plenum, New York, 1994), pp. 507–514.
  13. L. Vincze, K. Janssens, F. Adams, and A. Rindby, “Detailed ray-tracing code for capillary optics,” X-Ray Spectrom. 24, 27–37 (1995).
  14. S. V. Kukhlevsky, L. Kozma, and K. Negrea, “Pulsed-mode analysis of soft-x-ray radiation passing through capillary waveguides,” J. Mod. Opt. 43, 2595–2604 (1996).
  15. S. B. Dabagov, S. V. Nikitina, M. A. Kumakhov, N. S. Ibraimov, G. A. Vartaniants, A. N. Nikitin, and L. Spielberger, “Focusing of x rays by capillary systems,” Nucl. Instrum. Methods Phys. Res. B 103, 99–105 (1995).
  16. Yu. M. Aleksandrov and M. N. Yakimenko, “Investigations on the S-60 SR source of the Lebedev Physical Institute,” Nucl. Instrum. Methods Phys. Res. A 359, 12–14 (1995).
  17. S. B. Dabagov, R. V. Fedorchuk, V. A. Murashova, S. V. Nikitina, and M. N. Yakimenko, “Interference phenomenon under focusing of synchrotron radiation by a Kumakhov lens,” Nucl. Instrum. Methods Phys. Res. B 108, 213–218 (1996).
  18. Yu. M. Alexandrov, S. B. Dabagov, M. A. Kumakhov, V. A. Murashova, D. A. Fedin, R. V. Fedorchuk, and M. N. Yakimenko, “Peculiarities of photon transmission through capillary systems,” Nucl. Instrum. Methods Phys. Res. B 134, 174–180 (1998).
  19. J. C. Jans, Philips Research Laboratories Eindhoven, Netherlandse Philips Bedrijven B. V., Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands (personal communication, 1997).
  20. S. V. Kukhlevsky, L. Kozma, L. Palladino, A. Reale, F. Flora, L. Mezi, and G. Giordano, “Double-pulse excitation of x-ray capillary lasers,” Soft X-ray Lasers and Applications II, J. J. Rocca and L. B. Da Silva, eds., Proc. SPIE. 3156, 180–187 (1997).
  21. S. B. Dabagov, M. A. Kumakhov, and S. V. Nikitina, “On the interference of x rays in multiple reflection optics,” Phys. Lett. A 203, 279–282 (1995).
  22. L. I. Ognev, “On the structure of x-ray glass capillary lens focal spots,” Nucl. Instrum. Methods Phys. Res. B 124, 624–626 (1997).
  23. E. E. Spiller and A. Segmuller, “Propagation of x rays in waveguides,” Appl. Phys. Lett. 24, 60–61 (1974).
  24. T. Hidaka, “Extremely low-loss hollow core waveguide for VUV light,” Opt. Commun. 44, 90–93 (1982).
  25. S. P. Pogossian and H. Le Gall, “Neutron and x-ray propagation laws in thin film waveguides,” Opt. Commun. 114, 235–241 (1995).
  26. B. L. Henke, E. M. Gullikson, and J. C. Davis, “Low-energy x-ray interaction coefficients: photoabsorption, scattering and reflection, E = 30 − 3000 eV, Z = 1 − 92,” At. Data Nucl. Data Tables 53, 340–388 (1993).
  27. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980)
  28. S. V. Kukhlevsky and L. Kozma, “Guiding of light by short-length multimode waveguides. I,” Nuovo Cimento D 20, 783–789 (1998).
  29. S. V. Kukhlevsky and L. Kozma, “Modal and focusing properties of the plasma based waveguides for x-ray beams,” Contrib. Plasma Phys. 38, 583–597 (1998).
  30. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  31. S. Bollanti, P. Albertano, M. Belli, P. Di Lazzaro, A. Yu. Faenov, F. Flora, G. Giordano, A. Grilli, F. Ianzini, S. V. Kukhlevsky, T. Letardi, A. Nottola, L. Palladino, T. Pikuz, A. Reale, L. Reale, A. Scafati, M. A. Tabocchini, I. C. Edmond Turcu, K. Vigli-Papadaki, and G. Schina, “Soft x-ray plasma source for atmospheric pressure microscopy, radiobiology and other applications,” Nuovo Cimento D 20, 1685–1696 (1998).
  32. R. H. Pantell and P. S. Chung, “Influence of surface roughness on the propagation of x rays through capillaries,” Appl. Opt. 18, 897–899 (1979).
  33. T. A. Bobrova and L. Ognev, “On the ‘supercollimation’ of x-ray beams in rough interfacial channels,” JETP Lett. 69, 734–738 (1999).
  34. V. L. Kantsyrev, R. Bruch, R. Phaneuf, and N. G. Publicover, “New concepts for x-ray, soft x-ray, and EUV optical instrumentation including applications in spectroscopy, plasma diagnostics, and biomedical microscopy: a status report,” J. X-Ray Sci. Technol. 7, 139–158 (1997).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article

OSA is a member of CrossRef.

CrossCheck Deposited