OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 22, Iss. 3 — Mar. 1, 2005
  • pp: 547–555

Coherency saturation in periodic structures with randomization

Alexander E. Kaplan and Sergey G. Zykov  »View Author Affiliations

JOSA B, Vol. 22, Issue 3, pp. 547-555 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (192 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We study the effect of coherency saturation in spatially or temporally periodical structures with randomization, applicable to a very broad class of systems. We derive a simple analytical formula in the case of uncorrelated deviations of periods with Gaussian probability distribution. Using Monte Carlo simulations, we also demonstrate that many other distributions show statistical properties that closely coincide with the Gaussian, although some of them are drastically different from it. We observed that the characteristic number of elements necessary for the saturation of the coherency (the “coherency range”) depends only on the normalized standard deviation of the size of the elements and not on their probability distribution function. A greatly simplified heuristic formula found by us also fits all of these results with very reasonable precision. In the specific case of x ray transition radiation of low-to-medium relativistic electron beams in multilayer solid-state nanostructures, we show that a structure of a few hundred layers can generate resonantly enhanced radiation in the hard x ray domain with almost unhampered coherency gain.

© 2005 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(230.1950) Optical devices : Diffraction gratings
(230.4170) Optical devices : Multilayers
(260.3160) Physical optics : Interference

Alexander E. Kaplan and Sergey G. Zykov, "Coherency saturation in periodic structures with randomization," J. Opt. Soc. Am. B 22, 547-555 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. Ya. S. Shifrin, Statistical Antenna Theory (Golem, Boulder, Co., 1971).
  2. M. Kominami and K. Rokushima, "Analysis of an antenna composed of arbitrarily located slots and wires," IEEE Trans. Antennas Propag. 32, 154-158 (1984). [CrossRef]
  3. W. J. Hendricks, "The totally random versus the bin approach for random arrays," IEEE Trans. Antennas Propag. 39, 1757-1762 (1991). [CrossRef]
  4. T. Lyman, "False spectra from the Rowland concave grating," Phys. Rev. 12, 1 (1901).
  5. R. Wood, "Anomalous diffraction gratings," Astrophys. J. 48, 928 (1935).
  6. J. Rossi and D. Maystre, "Light scattering by diffraction gratings, false gratings and random rough surfaces: numerical comparison," J. Opt. Soc. Am. A 17, 165-173 (1986).
  7. D. Photiadis, "The effect of irregularity on the scattering of acoustic waves from a ribbed plate," J. Acoust. Soc. Am. 91, 1897-1903 (1992). [CrossRef]
  8. B. Cray, "Acoustic radiation from periodic and sectionally aperiodic rib-stiffened plates," J. Acoust. Soc. Am. 95, 256-264 (1994). [CrossRef]
  9. D. Hughes, C. Gaumond, L. Dragonette, and B. Houston, "Synthesized wave-packet basis for monostatic scatteringfrom a randomly ribbed, finite cylindrical-shell," J. Acoust. Soc. Am. 97, 1399-1408 (1995). [CrossRef]
  10. J. Albert, S. Theriault, F. Bilodeau, D. C. Johnson, K. O. Hill, P. Sixt, and M. J. Rooks, "Minimization of phase errors in long fiber Bragg grating phase masks made using electron beam lithography," IEEE Photonics Technol. Lett. 8, 1334-1336 (1996). [CrossRef]
  11. E. Spiller, "Coherence effects from visible light to X-rays," Nucl. Instrum. Methods 347, 161-169 (1994). [CrossRef]
  12. E. Spiller, D. Stearns, and M. Krumrey, "Multilayer X-ray mirrors - interfacial roughness, scattering, and image quality," J. Appl. Phys. 74, 107-118 (1993). [CrossRef]
  13. T. W. Barbee, "Multilayer optics for the soft-X-ray and extreme ultra-violet," Phys. Scr. 31, 147-153 (1990). [CrossRef]
  14. E. Esarey, C. Tang, and W. Marable, "The effects of field errors on low-gain free-electron lasers," IEEE J. Quantum Electron. 27, 2682-2692 (1991). [CrossRef]
  15. M. Takao, S. Hashimoto, S. Sasaki, and Y. Miyahara, "Analytical formulation of a quasi-periodic ondulator," in Proceedings of the Particle Accelerator Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995), Vol. 3, pp. 1438-1440.
  16. P. Emma, "Phase slip in an ondulator with pole and BPM errors," in Proceedings of the Particle Accelerator Conference , (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), Vol. 4, pp. 2742-2744.
  17. G. Garibian, L. Gevorgian, and C. Yang, "Calculation of X-ray transition radiation generated in regular-layered and irregular-layered media," Nucl. Instrum. Methods 125, 133-137 (1975). [CrossRef]
  18. C. Fabjan, "Transition radiation spectra from randomly spaced interfaces," Nucl. Instrum. Methods 146, 343-346 (1977). [CrossRef]
  19. Z. Gevorkian, C. Chen, and C. Hu, "New mechanism of x-ray radiation from a relativistic charged particle in a dielectric random medium," Phys. Rev. Lett. 86, 3324-3327 (2001). [CrossRef] [PubMed]
  20. K. Platonov and G. Fleishman, "Transition radiation in media with random inhomogeneities," Phys. Usp. 45, 235-291 (2002). [CrossRef]
  21. Y. Yamakoshi, K. Muto, and Z. Yoshida, "Numerical analysis of quasi-periodic perturbations for the Alfvén-wave," Phys. Rev. E 50, 1437-1444 (1994). [CrossRef]
  22. R. Grisenti, W. Schöllkopf, J. Toennies, J. R. Manson, T. A. Savas, and H. I. Smith, "He-atom diffraction from nano-structure transmission gratings: the role of imperfections," Phys. Rev. A 61, 33608-33612 (2000). [CrossRef]
  23. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  24. E. Yablonovitch and T. G. Gmitter, "Photonics band-structure," Phys. Rev. Lett. 63, 1950-1953 (1989). [CrossRef] [PubMed]
  25. S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Theoretical investigation of fabrication-related disorder on the properties of photonic crystals," J. Appl. Phys. 78, 1415-1418 (1995). [CrossRef]
  26. A. Siegman, Lasers (University Science, 1986).
  27. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge', Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a train of attosecond pulses from high harmonic generation," Science 292, 1689-1692 (2001). [CrossRef] [PubMed]
  28. M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, "Attosecond metrology," Nature (London) 414, 509-513 (2001). [CrossRef]
  29. A. E. Kaplan, "Subfemtosecond pulses in mode-locked 2pi solitons of the cascade stimulated Raman scattering," Phys. Rev. Lett. 73, 1243-1246 (1994). [CrossRef] [PubMed]
  30. A. E. Kaplan and P. L. Shkolnikov, "Subfemtosecond pulses in the multi-cascade stimulated Raman Scattering," J. Opt. Soc. Am. B 13, 347-354 (1996). [CrossRef]
  31. S. E. Harris and A. V. Sokolov, "Subfemtosecond pulse generation by molecular modulation," Phys. Rev. Lett. 81, 2894-2897 (1998). [CrossRef]
  32. M. Sebastian and P. Krishna, Random, Non-Random and Periodic Faulting in Crystals (Gordon and Breach, New York, 1994).
  33. J. Sasaki, L. Cardoso, C. Campos, K. Roberts, G. Clark, E. Pantos, and M. Sacilotti, "Using synchrotron radiation x-ray multiple diffraction to examine the lattice coherency of semiconductor surfaces and epitaxial layers," J. Appl. Phys. 79, 34923498 (1996). [CrossRef]
  34. T. Valla, P. Johnson, Z. Yusof, B. Wells, Q. Li, S. Loureiro, R. Cava, M. Mikami, Y. Mori, M. Yoshimura, and T. Sasaki, "Coherence-incoherence and dimensional crossover in layered strongly correlated metals," Nature 417, 627-630 (2002). [CrossRef] [PubMed]
  35. S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics , "Elements of random fields" (Springer-Verlag, Berlin, 1989), Vol. 3.
  36. M. L. Ter-Mikaelian, High Energy Electromagnetic Processes in Condensed Media (Wiley Interscience, New York, 1972).
  37. M. L. Ter-Mikhaelyan, "Electromagnetic radiative pro-cesses in periodic media at high energies," Phys. Usp. 44, 571-596 (2001). [CrossRef]
  38. A. E. Kaplan and S. Datta, "Extreme-ultraviolet and x-ray emission and amplification by non-relativistic beams traversing a superlattice," Appl. Phys. Lett. 44, 661-663 (1984). [CrossRef]
  39. S. Datta and A. E. Kaplan, "Quantum theory of spontaneous and stimulated resonant transition radiation," Phys. Rev. A 31, 790-796 (1985). [CrossRef] [PubMed]
  40. C. T. Law and A. E. Kaplan, "X-ray transition radiation in a solid-state superlattice: photon-absorption, electron scattering, and radiation optimization," Opt. Lett. 12, 900-902 (1987). [CrossRef] [PubMed]
  41. A. E. Kaplan, C. T. Law, and P. L. Shkolnikov, "X-ray narrow-line transition radiation source based on low-energy electron beams traversing a multilayer nano-structure," Phys. Rev. E 52, 6795-6808 (1995). [CrossRef]

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