Abstract

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

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    [CrossRef]

2002 (2)

K. Platonov and G. Fleishman, "Transition radiation in media with random inhomogeneities," Phys. Usp. 45, 235-291 (2002).
[CrossRef]

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]

2001 (4)

M. L. Ter-Mikhaelyan, "Electromagnetic radiative pro-cesses in periodic media at high energies," Phys. Usp. 44, 571-596 (2001).
[CrossRef]

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]

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]

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]

2000 (1)

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]

1998 (1)

S. E. Harris and A. V. Sokolov, "Subfemtosecond pulse generation by molecular modulation," Phys. Rev. Lett. 81, 2894-2897 (1998).
[CrossRef]

1996 (3)

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]

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]

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]

1995 (3)

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]

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]

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]

1994 (4)

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]

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]

B. Cray, "Acoustic radiation from periodic and sectionally aperiodic rib-stiffened plates," J. Acoust. Soc. Am. 95, 256-264 (1994).
[CrossRef]

E. Spiller, "Coherence effects from visible light to X-rays," Nucl. Instrum. Methods 347, 161-169 (1994).
[CrossRef]

1993 (1)

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]

1992 (1)

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]

1991 (2)

W. J. Hendricks, "The totally random versus the bin approach for random arrays," IEEE Trans. Antennas Propag. 39, 1757-1762 (1991).
[CrossRef]

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]

1990 (1)

T. W. Barbee, "Multilayer optics for the soft-X-ray and extreme ultra-violet," Phys. Scr. 31, 147-153 (1990).
[CrossRef]

1989 (1)

E. Yablonovitch and T. G. Gmitter, "Photonics band-structure," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

1987 (2)

1986 (1)

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).

1985 (1)

S. Datta and A. E. Kaplan, "Quantum theory of spontaneous and stimulated resonant transition radiation," Phys. Rev. A 31, 790-796 (1985).
[CrossRef] [PubMed]

1984 (2)

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]

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]

1977 (1)

C. Fabjan, "Transition radiation spectra from randomly spaced interfaces," Nucl. Instrum. Methods 146, 343-346 (1977).
[CrossRef]

1975 (1)

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]

1935 (1)

R. Wood, "Anomalous diffraction gratings," Astrophys. J. 48, 928 (1935).

1901 (1)

T. Lyman, "False spectra from the Rowland concave grating," Phys. Rev. 12, 1 (1901).

Agostini, P.

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]

Albert, J.

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]

Auge', F.

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]

Balcou, Ph.

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]

Barbee, T. W.

T. W. Barbee, "Multilayer optics for the soft-X-ray and extreme ultra-violet," Phys. Scr. 31, 147-153 (1990).
[CrossRef]

Bilodeau, F.

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]

Brabec, T.

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]

Breger, P.

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]

Campos, C.

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]

Cardoso, L.

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]

Cava, R.

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]

Chen, C.

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]

Clark, G.

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]

Corkum, P.

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]

Cray, B.

B. Cray, "Acoustic radiation from periodic and sectionally aperiodic rib-stiffened plates," J. Acoust. Soc. Am. 95, 256-264 (1994).
[CrossRef]

Datta , S.

S. Datta and A. E. Kaplan, "Quantum theory of spontaneous and stimulated resonant transition radiation," Phys. Rev. A 31, 790-796 (1985).
[CrossRef] [PubMed]

Datta, S.

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]

Dragonette, L.

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]

Drescher, M.

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]

Esarey, E.

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]

Fabjan, C.

C. Fabjan, "Transition radiation spectra from randomly spaced interfaces," Nucl. Instrum. Methods 146, 343-346 (1977).
[CrossRef]

Fan, S. H.

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]

Fleishman, G.

K. Platonov and G. Fleishman, "Transition radiation in media with random inhomogeneities," Phys. Usp. 45, 235-291 (2002).
[CrossRef]

Garibian, G.

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]

Gaumond, C.

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]

Gevorgian, L.

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]

Gevorkian, Z.

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]

Gmitter, T. G.

E. Yablonovitch and T. G. Gmitter, "Photonics band-structure," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

Grisenti, R.

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]

Harris , S. E.

S. E. Harris and A. V. Sokolov, "Subfemtosecond pulse generation by molecular modulation," Phys. Rev. Lett. 81, 2894-2897 (1998).
[CrossRef]

Heinzmann, U.

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]

Hendricks, W. J.

W. J. Hendricks, "The totally random versus the bin approach for random arrays," IEEE Trans. Antennas Propag. 39, 1757-1762 (1991).
[CrossRef]

Hentschel, M.

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]

Hill, K. O.

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]

Houston, B.

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]

Hu, C.

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]

Hughes, D.

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]

Joannopoulos, J. D.

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]

Johnson, D. C.

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]

Johnson, P.

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]

Kaplan , A. E.

Kaplan, A. E.

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]

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]

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]

S. Datta and A. E. Kaplan, "Quantum theory of spontaneous and stimulated resonant transition radiation," Phys. Rev. A 31, 790-796 (1985).
[CrossRef] [PubMed]

Kaplan , A. E.

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]

Kienberger, R.

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]

Kominami , M.

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]

Krausz, F.

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]

Krumrey, M.

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]

Law, C. T.

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]

Law , C. T.

Li, Q.

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]

Loureiro, S.

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]

Lyman, T.

T. Lyman, "False spectra from the Rowland concave grating," Phys. Rev. 12, 1 (1901).

Manson, J. R.

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]

Marable, W.

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]

Maystre, D.

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).

Mikami, M.

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]

Milosevic, N.

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]

Mori, Y.

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]

Muller, H. G.

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]

Mullot, G.

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]

Muto, K.

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]

Pantos, E.

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]

Paul, P. M.

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]

Photiadis, D.

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]

Platonov , K.

K. Platonov and G. Fleishman, "Transition radiation in media with random inhomogeneities," Phys. Usp. 45, 235-291 (2002).
[CrossRef]

Reider, G. A.

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]

Roberts, K.

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]

Rokushima, K.

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]

Rooks, M. J.

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]

Rossi , J.

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).

Sacilotti, M.

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]

Sasaki, J.

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]

Sasaki, T.

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]

Savas, T. A.

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]

Schöllkopf, W.

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]

Shkolnikov, P. L.

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]

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]

Sixt, P.

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]

Smith, H. I.

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]

Sokolov, A. V.

S. E. Harris and A. V. Sokolov, "Subfemtosecond pulse generation by molecular modulation," Phys. Rev. Lett. 81, 2894-2897 (1998).
[CrossRef]

Spielmann, C.

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]

Spiller, E.

E. Spiller, "Coherence effects from visible light to X-rays," Nucl. Instrum. Methods 347, 161-169 (1994).
[CrossRef]

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]

Stearns, D.

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]

Tang, C.

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]

Ter-Mikhaelyan, M. L.

M. L. Ter-Mikhaelyan, "Electromagnetic radiative pro-cesses in periodic media at high energies," Phys. Usp. 44, 571-596 (2001).
[CrossRef]

Theriault, S.

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]

Toennies, J.

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]

Toma, E. S.

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]

Valla, T.

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]

Villeneuve, P. R.

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]

Wells, B.

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]

Wood, R.

R. Wood, "Anomalous diffraction gratings," Astrophys. J. 48, 928 (1935).

Yablonovitch , E.

E. Yablonovitch and T. G. Gmitter, "Photonics band-structure," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yamakoshi, Y.

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]

Yang, C.

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]

Yoshida, Z.

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]

Yoshimura, M.

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]

Yusof, Z.

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]

Appl. Phys. Lett. (1)

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]

Astrophys. J. (1)

R. Wood, "Anomalous diffraction gratings," Astrophys. J. 48, 928 (1935).

IEEE J. Quantum Electron. (1)

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]

IEEE Photonics Technol. Lett. (1)

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]

IEEE Trans. Antennas Propag. (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]

W. J. Hendricks, "The totally random versus the bin approach for random arrays," IEEE Trans. Antennas Propag. 39, 1757-1762 (1991).
[CrossRef]

J. Acoust. Soc. Am. (3)

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]

B. Cray, "Acoustic radiation from periodic and sectionally aperiodic rib-stiffened plates," J. Acoust. Soc. Am. 95, 256-264 (1994).
[CrossRef]

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]

J. Appl. Phys. (3)

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]

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]

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]

J. Opt. Soc. Am. A (1)

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).

J. Opt. Soc. Am. B (1)

Nature (1)

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]

Nature (London) (1)

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]

Nucl. Instrum. Methods (3)

E. Spiller, "Coherence effects from visible light to X-rays," Nucl. Instrum. Methods 347, 161-169 (1994).
[CrossRef]

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]

C. Fabjan, "Transition radiation spectra from randomly spaced interfaces," Nucl. Instrum. Methods 146, 343-346 (1977).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

T. Lyman, "False spectra from the Rowland concave grating," Phys. Rev. 12, 1 (1901).

Phys. Rev. A (2)

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]

S. Datta and A. E. Kaplan, "Quantum theory of spontaneous and stimulated resonant transition radiation," Phys. Rev. A 31, 790-796 (1985).
[CrossRef] [PubMed]

Phys. Rev. E (2)

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]

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]

Phys. Rev. Lett. (5)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

E. Yablonovitch and T. G. Gmitter, "Photonics band-structure," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

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]

S. E. Harris and A. V. Sokolov, "Subfemtosecond pulse generation by molecular modulation," Phys. Rev. Lett. 81, 2894-2897 (1998).
[CrossRef]

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).
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K. Platonov and G. Fleishman, "Transition radiation in media with random inhomogeneities," Phys. Usp. 45, 235-291 (2002).
[CrossRef]

M. L. Ter-Mikhaelyan, "Electromagnetic radiative pro-cesses in periodic media at high energies," Phys. Usp. 44, 571-596 (2001).
[CrossRef]

Science (1)

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).
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S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics , "Elements of random fields" (Springer-Verlag, Berlin, 1989), Vol. 3.

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M. Sebastian and P. Krishna, Random, Non-Random and Periodic Faulting in Crystals (Gordon and Breach, New York, 1994).

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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.

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Figures (3)

Fig. 1
Fig. 1

Coherency enhancement E=GM/M versus the number M of elements in the structure for various models of probability distributions, and various standard deviations, σ0. The upper straight line E=M is due to the fully coherent structure (σ0=0), whereas E=1 is due to the fully randomized (σ0=) structure. The rest of the lines correspond to σ0=1%, 7%, 15%, and 23% from top to bottom, respectively. Each group of curves corresponding to each specific σ0 consists of a solid curve due to the exact analytical result [Eq. (13)] for a Gaussian statistical distribution of the spacings and four others due to the models [Eqs. (20)–(23)] and was obtained by Monte Carlo simulations. The dotted curve in the group that corresponds to σ0=7% is due to heuristic model, Eq. (18).

Fig. 2
Fig. 2

Various probability distribution models used for calculation in Fig. 1. The solid curve corresponds to a normal (Gaussian) distribution, Eq. (10), the “polinom” corresponds to the model described by Eq. (23), the “cos2” corresponds to Eq. (22), the “cos” corresponds to Eq. (21), and “rectangular” corresponds to Eq. (20).

Fig. 3
Fig. 3

The coherency gain GM versus the detuning/angle θ for various standard deviations σ0 in the case M=1000. The solid curve corresponds to the ideally coherent grating σ0=0.

Equations (47)

Equations on this page are rendered with MathJax. Learn more.

Gcoh(M)=M2.
Grand(M)=M,
ϕn=2Sπln/λ=2π(1+θ+xn),
xn=0,xn2=σ02=σl2/l02,
fn=exp[2πi(Xn+nθ)],
FM=n=1Mfn,
GM=|FM|2=n=1M exp[2πi(Xn+θn)]2,
GM=n,k=1M exp{2iπ[Xn-Xk+(n-k)θ]}=12n,k=1M(exp{2iπ[Xn-Xk+(n-k)θ]}+c.c.)=n,k=1M{cos[2π(Xn-Xk)]cos[2π(n-k)θ]-sin[2π(Xn-Xk)]sin[2π(n-k)θ]}.
GM=n,k=1M cos[2π(n-k)θ]cos[2π(Xn-Xk)],
P(x)=(σ02π)-1 exp(-x2/2σ02),
Pnk(y)=1σnk2π exp-y22σnk2,
σnk2Ynk2-Ynk2=|n-k|σ02,
cos(2πYnk)=- cos(2πy)Pnk(y)dy=exp(-2π2σ02|n-k|).
r=(πσ0)2,Ncoh=r-1,
GM(θ=0)=n,k=1M exp(-2r|n-k|)=(M/2)sinh(2r)-exp(-rM)sinh(rM)sinh2(r).
GM(θ=0)=Ncoh2[μ-exp(-μ)sinh(μ)],
μ=Mr=M/Ncoh.
E(M)M(1-2µ/3),μ1,
E(M)Ncoh[1-(2µ)-1],μ1,
GM=NblGbl=MNcoh,E(M)Ncoh,
EH(M)MNcohM+Ncoh-1=M(M-1)r+1.
P(x)>0for|x|<δ-10otherwise,
P(x)=const=1/2δ,withδ=σ03,
P(x)=(π/4δ)cos(πx/2δ),withδ=σ0/(1-8/π2)1/2
P(x)=δ-1 cos2(πx/2δ),withδ=σ0/(1/3-2/π2)1/2
P(x)=158δ1-|x|δ21-251-|x|δ3,withδ=4σ07131/2.
W(x)=-δxδP(ξ)dξ
rrnd=-δxδP(ξ)dξforx,
rrnd=W(x)-xP(ξ)dξ
P(x)=1/(2δ)cosh2(x/δ),W(x)=12+tanh(x/δ)2,
δσ0=1Ich1.102658,
Ich0ξ2dξcosh2(ξ)0.822467,
P(x)=12δ1+|x|δexp-(1+|x|/δ)2-12,
W(x)=12+sign(x)2×1-exp-(1+|x|/δ)2-12,
δσ0=1IqG1.2050459,
IqG1ξ(ξ-1)2dξexp[-(ξ2-1)/2]0.6886409.
d=πθ,
EM(r, d)GMM=rd2+r2-exp(-rM)M(d2+r2)2×{(r2-d2)[sinh(rM)-exp(-rM)sin2(dM)]+rdexp(-rM)sin(2dM)}.
GM=sin2(dM)/d2,
d1/22/M.
EMr(1+Δ)d2+r2,
Δ=μ-1O(1)=d2-r2μ(d2+r2).
EMr/(d2+r2),d1/2r=Ncoh-1=(πσ0)2.
d1/2=πθ1/21M1+exp-2MNcoh1/2+1Ncoh=[1+exp(-2Mr)]1/2M+r.
ϕπ(γ-2+θ2)(l0/λ),
l0=λ×γ2,S=1/γ2,
σL=Mσl,orσL/L=σ0/M.

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