OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 3 — Feb. 11, 2013
  • pp: 3225–3234

Speckle statistics and transverse coherence of an x-ray laser with fluctuations in its active medium

K. A. Janulewicz, C. M. Kim, and H. Stiel  »View Author Affiliations

Optics Express, Vol. 21, Issue 3, pp. 3225-3234 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (3445 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



It is shown that the statistics of the intensity distribution in the output beam of a collisional X-ray laser, analysed in terms of the degree of freedom or equivalently the number of the coherence modes in the beam cross-section, has non-Gaussian character. The non-Gaussian character seems to be caused by the small-scale plasma/medium fluctuations. It was assumed that these overlap the modal structure imposed by the geometry of the medium and considered as equivalent to a large-scale inhomogeneity. Thus, the fluctuations decide about the character of the output beam transverse coherence. It is also shown that the relevant to this model compound statistics of the intensity fluctuations in the output beam is well described by the m-m-distribution, a specific form of the K-distribution. The deviation from the Gaussian statistics was confirmed by the field correlation function at the laser exit plane, retrieved from the experimental data.

© 2013 OSA

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(140.7240) Lasers and laser optics : UV, EUV, and X-ray lasers

ToC Category:
Coherence and Statistical Optics

Original Manuscript: November 6, 2012
Revised Manuscript: January 18, 2013
Manuscript Accepted: January 20, 2013
Published: February 1, 2013

K. A. Janulewicz, C. M. Kim, and H. Stiel, "Speckle statistics and transverse coherence of an x-ray laser with fluctuations in its active medium," Opt. Express 21, 3225-3234 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. P. D. Drummond and J. H. Eberly, “Transverse coherence and scaling in four dimensional simulations of superfluorescence,” Phys. Rev. A25, 3446 (1982) [CrossRef]
  2. G. Hazak and A. Bar-Shalom, “Mode-selecting effects and coherence in hot-plasma x-ray lasers,” Phys. Rev. A40, 7055 (1989) [CrossRef] [PubMed]
  3. R. A. London, M. Strauss, and M. D. Rosen, “Modal analysis of x-ray laser coherence,” Phys. Rev. Lett.65, 563 (1990) [CrossRef] [PubMed]
  4. P. Amendt, R. London, and M. Strauss, “Optimization of single-stage- x-ray laser coherence,” Phys. Rev. A47, 4348 (1993) [CrossRef] [PubMed]
  5. R. P. Ratowsky and R. A. London, “Propagation of mutual coherence in refratctive x-ray lasers using a WKB method,” Phys. Rev. A51, 2361 (1995) [CrossRef] [PubMed]
  6. G. J. Pert, “Output characteristics of amplified-stimulated-emission lasers,” J. Opt. Soc. Am. B11, 1425 (1994) [CrossRef]
  7. J. E. Trebes, K. A. Nugent, S. Mrowka, R. A. London, T. W. Barbee, M. R. Carter, J. A. Koch, B. J. MacGowan, D. L. Matthews, L. B. Da Silva, G. F. Stone, and M. D. Feit, “Measurement of the spatial coherence of a soft-x-ray laser,” Phys. Rev. Lett.68, 588 (1992) [CrossRef] [PubMed]
  8. Y. Liu, Y. Wang, M. A. Larotonda, B. M. Luther, J. J. Rocca, and D. T. Attwood, “Spatial coherence measurements of a 13.2 nm transient nickel-like cadmium soft X-ray laser pumped at grazing incidence,” Opt. Express14, 12872–9 (2006) [CrossRef] [PubMed]
  9. O. Gilbaud, A. Klisnick, K. Cassou, S. Kazamias, D. Ros, G. Jamelot, D. Joyeux, and D. Phalippou, “Origin of microstructures in picosecond X-ray laser beam,” Europhys. Lett.74, 823–829 (2006) [CrossRef]
  10. J. W. Goodman, Statistical Optics, chapt.9.1, (A Wiley-Interscience Publication, John Wiley and Sons, Inc., 1985)
  11. P. Amendt, M. Strauss, and R. A. London, “Plasma fluctuations and X-ray laser transverse coherence,” Phys. Rev. A53, R23 (1996) [CrossRef] [PubMed]
  12. G. J. Pert, “Two-dimensional hydrodynamic models of laser-produced plasmas,” J. Plasma Physics41 (part 2), 263 (1989) [CrossRef]
  13. R. G. Evans, A.J. Bennett, and G.J. Pert, “Rayleigh-Taylor instabilities in laser accelerated targets,” Phys. Rev. Lett.49, 1639 (1982) [CrossRef]
  14. B. Crosignani and A. Yariv, “Statistical properties of modal noise in fiber-laser systems,” J. Opt. Soc. Am.73, 1022 (1983) [CrossRef]
  15. L. Casperson and A. Yariv, “Pulse propagation in a high-gain medium,” Phys. Rev. Lett.26, 293 (1971) [CrossRef]
  16. G. J. Pert, “Optimizing the performance of nickel-like collisionally pumped x-ray lasers,” Phys. Rev. A73, 033809 (2006) [CrossRef]
  17. K. A. Janulewicz and C. M. Kim, “Role of the precursor in a triple-pulse pumping scheme of a nickel-like silver soft-x-ray laser in the grazing-incidence-pumping geometry,” Phys. Rev. E82, 056405 (2010) [CrossRef]
  18. E. Jakeman and P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett.40, 546 (1978) [CrossRef]
  19. V. S. Rao Gudimetla and J. Fred Holmes, “Probability density function of the intensity for a laser-generated speckle field after propagation through the turbulent atmosphere,” J. Opt. Soc. Am.72, 1213 (1982) [CrossRef]
  20. M. A. Al-Habash, L. C. Andrews, and R. L. Phillips, “Mathematical model for the irradiance probability density function of a laser bem propagating through turbulent media,” Opt. Eng.40, 1554 (2001) [CrossRef]
  21. H. T. Kim, C.-M Kim, I. W. Choi, H. C. Kang, N Hafz, S. G. Lee, J. H. Sung, T. J. Yu, K.-H. Hong, T. M. Jeong, Y.-C. Noh, D.-K. Ko, J. Tümmler, P. V. Nickles, W. Sandner, K. A. Janulewicz, and J. Lee, “Characteristics of Ni-like silver x-ray laser pumped by single profiled laser pulse,” J. Opt. Soc. Am B25, B76–B84 (2008) [CrossRef]
  22. J. W. Goodman, “Statistical properties of laser speckle patterns” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed., (Springer Verlag, 2nd. edition, 1984)
  23. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, (Roberts & Company Publishers, Englewood, Colorado2006)
  24. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995)
  25. R. Barakat, “The brightness distribution of the sum of two coherent speckle patterns,” Opt. Commun.8, 14–16 (1973) [CrossRef]
  26. E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng.23, 453 (1984) [CrossRef]
  27. L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, “Theory of optical scintillation,” J. Opt. Soc. Am16, 1417 (1999) [CrossRef]
  28. M. Nakagami, “The m-distribution - a general formula of intensity distribution of rapid fading,” in Statistical Methods in Radio Wave Propagation, W. C. Hoffman, ed. (Pergamon, 1960), p.6–36

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.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited