Abstract

We study the propagation of ultrashort pulses in x-ray waveguides (WGs) by addressing the problem of the temporal dispersion. Starting from basic equations, by means of numerical calculation we demonstrate that far from the absorption edges of the WGs the cladding's material dispersion is negligible. However, close to the absorption edge significant dispersion can take place. This behavior could in principle be exploited to manipulate incoming chirped beams. Moreover, using the two coherent beams produced by the WG in the second (and higher) order of resonance suggests the use of the WC as a dispersion-free beam splitter, which can facilitate x-ray pump–probe experiments in the femtosecond temporal range without the need for external sources.

© 2006 Optical Society of America

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  1. J. J. Macklin, J. D. Kmetec, and C. L. Gordon III, " High-order harmonic generation using intense femtosecond pulses," Phys. Rev. Lett. 70, 766- 769 ( 1993).
    [CrossRef] [PubMed]
  2. J. Zhou, J. Peatross, M. M. Mumane, H. C. Kapteyn, and I. P. Christov, " Enhanced high-harmonic generation using 25 fs laser pulses," Phys. Rev. Lett. 76, 752- 755 ( 1996).
    [CrossRef] [PubMed]
  3. S. Kiselev, A Pukhov, and I. Kostyukov, " X-ray generation in strongly nonlinear plasma waves," Phys. Rev. Lett. 93, 135004 ( 2004).
    [CrossRef] [PubMed]
  4. H. P. Freund and T. M. Antonsen, Jr., Principles of Free-Electron Lasers (Chapman & Hall, 1996).
  5. G. Dattoli and A. Renieri, " Overview of proposed VUV and soft x-ray projects in the world," Nucl. Instrum. Methods A 507, 464- 469 ( 2003).
    [CrossRef]
  6. T. Tschentscher, " Investigation of ultrafast processes using x-ray free-electron laser radiation," Chem. Phys. 299, 271- 276 ( 2004).
    [CrossRef]
  7. G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
    [CrossRef]
  8. I. P. Christov, " Propagation of an attosecond pulse in an atomic-scale waveguide," Appl. Phys. B 80, 405- 408 ( 2005).
    [CrossRef]
  9. B. L. Henke, E. M. Gullikson, and J. C. Davis, " X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181- 342 ( 1993).
    [CrossRef]
  10. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).
  11. J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, " Propagation of partially coherent focused x-ray beam within a planar x-ray waveguide," J. Synchrotron Radiat. 9, 383- 393 ( 2002).
    [CrossRef]
  12. C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tocoulou, " Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide," Appl. Phys. Lett. 85, 1907- 1909 ( 2004).
    [CrossRef]
  13. W. Jark and S. Di Fonzo, " Prediction of the transmission through thin-film waveguides for x-ray microscopy," J. Synchrotron Radiat. 11, 386- 392 ( 2004).
    [CrossRef] [PubMed]
  14. A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tocoulou, and T. Salditt, " Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 ( 2005).
    [CrossRef] [PubMed]
  15. W. Jark, S. Di Fonzo, S. Lagomarsino, A. Cedola, E. Di Fabrizio, A. Bram, and C. Riekel, " Properties of a submicrometer x-ray beam at the exit of a waveguide," J. Appl. Phys. 80, 4831- 4836 ( 1996).
    [CrossRef]
  16. A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, and V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).
  17. J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996).
  18. BESSY FEL, " Technical Design Report" (BESSY m.b.H., Berlin, 2004), p. 56.
  19. L. Giannessi, " Preliminary simulations of the SPARX FEL," Tech. Note SPARC-FEL 05/001; http://efrosf.frascati.enea.it/SPARC/noteslowbarfel.htm (2005).
  20. C. Fuhse and T. Salditt, " Finite-difference field calculations for one-dimensionally confined x-ray waveguides," Physica B 357, 57- 60 ( 2005).
    [CrossRef]

2005

I. P. Christov, " Propagation of an attosecond pulse in an atomic-scale waveguide," Appl. Phys. B 80, 405- 408 ( 2005).
[CrossRef]

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tocoulou, and T. Salditt, " Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 ( 2005).
[CrossRef] [PubMed]

C. Fuhse and T. Salditt, " Finite-difference field calculations for one-dimensionally confined x-ray waveguides," Physica B 357, 57- 60 ( 2005).
[CrossRef]

2004

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tocoulou, " Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide," Appl. Phys. Lett. 85, 1907- 1909 ( 2004).
[CrossRef]

W. Jark and S. Di Fonzo, " Prediction of the transmission through thin-film waveguides for x-ray microscopy," J. Synchrotron Radiat. 11, 386- 392 ( 2004).
[CrossRef] [PubMed]

T. Tschentscher, " Investigation of ultrafast processes using x-ray free-electron laser radiation," Chem. Phys. 299, 271- 276 ( 2004).
[CrossRef]

S. Kiselev, A Pukhov, and I. Kostyukov, " X-ray generation in strongly nonlinear plasma waves," Phys. Rev. Lett. 93, 135004 ( 2004).
[CrossRef] [PubMed]

2003

G. Dattoli and A. Renieri, " Overview of proposed VUV and soft x-ray projects in the world," Nucl. Instrum. Methods A 507, 464- 469 ( 2003).
[CrossRef]

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

2002

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, " Propagation of partially coherent focused x-ray beam within a planar x-ray waveguide," J. Synchrotron Radiat. 9, 383- 393 ( 2002).
[CrossRef]

1996

W. Jark, S. Di Fonzo, S. Lagomarsino, A. Cedola, E. Di Fabrizio, A. Bram, and C. Riekel, " Properties of a submicrometer x-ray beam at the exit of a waveguide," J. Appl. Phys. 80, 4831- 4836 ( 1996).
[CrossRef]

J. Zhou, J. Peatross, M. M. Mumane, H. C. Kapteyn, and I. P. Christov, " Enhanced high-harmonic generation using 25 fs laser pulses," Phys. Rev. Lett. 76, 752- 755 ( 1996).
[CrossRef] [PubMed]

1993

J. J. Macklin, J. D. Kmetec, and C. L. Gordon III, " High-order harmonic generation using intense femtosecond pulses," Phys. Rev. Lett. 70, 766- 769 ( 1993).
[CrossRef] [PubMed]

B. L. Henke, E. M. Gullikson, and J. C. Davis, " X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181- 342 ( 1993).
[CrossRef]

Antonsen, T. M.

H. P. Freund and T. M. Antonsen, Jr., Principles of Free-Electron Lasers (Chapman & Hall, 1996).

Austin, R. H.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Bongaerts, J. H. H.

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, " Propagation of partially coherent focused x-ray beam within a planar x-ray waveguide," J. Synchrotron Radiat. 9, 383- 393 ( 2002).
[CrossRef]

Bram, A.

W. Jark, S. Di Fonzo, S. Lagomarsino, A. Cedola, E. Di Fabrizio, A. Bram, and C. Riekel, " Properties of a submicrometer x-ray beam at the exit of a waveguide," J. Appl. Phys. 80, 4831- 4836 ( 1996).
[CrossRef]

Brytov, I. A.

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, and V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Carroll, F. E.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Cedola, A.

W. Jark, S. Di Fonzo, S. Lagomarsino, A. Cedola, E. Di Fabrizio, A. Bram, and C. Riekel, " Properties of a submicrometer x-ray beam at the exit of a waveguide," J. Appl. Phys. 80, 4831- 4836 ( 1996).
[CrossRef]

Christov, I. P.

I. P. Christov, " Propagation of an attosecond pulse in an atomic-scale waveguide," Appl. Phys. B 80, 405- 408 ( 2005).
[CrossRef]

J. Zhou, J. Peatross, M. M. Mumane, H. C. Kapteyn, and I. P. Christov, " Enhanced high-harmonic generation using 25 fs laser pulses," Phys. Rev. Lett. 76, 752- 755 ( 1996).
[CrossRef] [PubMed]

Copeland, M. L.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Couprie, M. E.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Dattoli, G.

G. Dattoli and A. Renieri, " Overview of proposed VUV and soft x-ray projects in the world," Nucl. Instrum. Methods A 507, 464- 469 ( 2003).
[CrossRef]

David, C.

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, " Propagation of partially coherent focused x-ray beam within a planar x-ray waveguide," J. Synchrotron Radiat. 9, 383- 393 ( 2002).
[CrossRef]

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, " X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181- 342 ( 1993).
[CrossRef]

Di Fabrizio, E.

W. Jark, S. Di Fonzo, S. Lagomarsino, A. Cedola, E. Di Fabrizio, A. Bram, and C. Riekel, " Properties of a submicrometer x-ray beam at the exit of a waveguide," J. Appl. Phys. 80, 4831- 4836 ( 1996).
[CrossRef]

Di Fonzo, S.

W. Jark and S. Di Fonzo, " Prediction of the transmission through thin-film waveguides for x-ray microscopy," J. Synchrotron Radiat. 11, 386- 392 ( 2004).
[CrossRef] [PubMed]

W. Jark, S. Di Fonzo, S. Lagomarsino, A. Cedola, E. Di Fabrizio, A. Bram, and C. Riekel, " Properties of a submicrometer x-ray beam at the exit of a waveguide," J. Appl. Phys. 80, 4831- 4836 ( 1996).
[CrossRef]

Diels, J. C.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996).

Drakopoulos, M.

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, " Propagation of partially coherent focused x-ray beam within a planar x-ray waveguide," J. Synchrotron Radiat. 9, 383- 393 ( 2002).
[CrossRef]

Edwards, G. S.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

FEL, BESSY

BESSY FEL, " Technical Design Report" (BESSY m.b.H., Berlin, 2004), p. 56.

Freund, H. P.

H. P. Freund and T. M. Antonsen, Jr., Principles of Free-Electron Lasers (Chapman & Hall, 1996).

Fuhse, C.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tocoulou, and T. Salditt, " Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 ( 2005).
[CrossRef] [PubMed]

C. Fuhse and T. Salditt, " Finite-difference field calculations for one-dimensionally confined x-ray waveguides," Physica B 357, 57- 60 ( 2005).
[CrossRef]

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tocoulou, " Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide," Appl. Phys. Lett. 85, 1907- 1909 ( 2004).
[CrossRef]

Gabella, W. E.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Giannessi, L.

L. Giannessi, " Preliminary simulations of the SPARX FEL," Tech. Note SPARC-FEL 05/001; http://efrosf.frascati.enea.it/SPARC/noteslowbarfel.htm (2005).

Gordon, C. L.

J. J. Macklin, J. D. Kmetec, and C. L. Gordon III, " High-order harmonic generation using intense femtosecond pulses," Phys. Rev. Lett. 70, 766- 769 ( 1993).
[CrossRef] [PubMed]

Grudski, A. Ya.

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, and V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Gullikson, E. M.

B. L. Henke, E. M. Gullikson, and J. C. Davis, " X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181- 342 ( 1993).
[CrossRef]

Haglund, R. F.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Henke, B. L.

B. L. Henke, E. M. Gullikson, and J. C. Davis, " X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181- 342 ( 1993).
[CrossRef]

Hooper, B. A.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Hutson, M. S.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Jansen, E. D.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Jark, W.

W. Jark and S. Di Fonzo, " Prediction of the transmission through thin-film waveguides for x-ray microscopy," J. Synchrotron Radiat. 11, 386- 392 ( 2004).
[CrossRef] [PubMed]

W. Jark, S. Di Fonzo, S. Lagomarsino, A. Cedola, E. Di Fabrizio, A. Bram, and C. Riekel, " Properties of a submicrometer x-ray beam at the exit of a waveguide," J. Appl. Phys. 80, 4831- 4836 ( 1996).
[CrossRef]

Jarre, A.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tocoulou, and T. Salditt, " Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 ( 2005).
[CrossRef] [PubMed]

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tocoulou, " Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide," Appl. Phys. Lett. 85, 1907- 1909 ( 2004).
[CrossRef]

Joos, K. M.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Kapteyn, H. C.

J. Zhou, J. Peatross, M. M. Mumane, H. C. Kapteyn, and I. P. Christov, " Enhanced high-harmonic generation using 25 fs laser pulses," Phys. Rev. Lett. 76, 752- 755 ( 1996).
[CrossRef] [PubMed]

Keymeulen, H.

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, " Propagation of partially coherent focused x-ray beam within a planar x-ray waveguide," J. Synchrotron Radiat. 9, 383- 393 ( 2002).
[CrossRef]

Kiehart, D. P.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Kiselev, S.

S. Kiselev, A Pukhov, and I. Kostyukov, " X-ray generation in strongly nonlinear plasma waves," Phys. Rev. Lett. 93, 135004 ( 2004).
[CrossRef] [PubMed]

Kmetec, J. D.

J. J. Macklin, J. D. Kmetec, and C. L. Gordon III, " High-order harmonic generation using intense femtosecond pulses," Phys. Rev. Lett. 70, 766- 769 ( 1993).
[CrossRef] [PubMed]

Kogan, M. N.

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, and V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Kostyukov, I.

S. Kiselev, A Pukhov, and I. Kostyukov, " X-ray generation in strongly nonlinear plasma waves," Phys. Rev. Lett. 93, 135004 ( 2004).
[CrossRef] [PubMed]

Kozhevnikov, I. V.

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, and V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Lackner, T.

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, " Propagation of partially coherent focused x-ray beam within a planar x-ray waveguide," J. Synchrotron Radiat. 9, 383- 393 ( 2002).
[CrossRef]

Lagomarsino, S.

W. Jark, S. Di Fonzo, S. Lagomarsino, A. Cedola, E. Di Fabrizio, A. Bram, and C. Riekel, " Properties of a submicrometer x-ray beam at the exit of a waveguide," J. Appl. Phys. 80, 4831- 4836 ( 1996).
[CrossRef]

Lindau, I.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Macklin, J. J.

J. J. Macklin, J. D. Kmetec, and C. L. Gordon III, " High-order harmonic generation using intense femtosecond pulses," Phys. Rev. Lett. 70, 766- 769 ( 1993).
[CrossRef] [PubMed]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).

Miao, J.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Mumane, M. M.

J. Zhou, J. Peatross, M. M. Mumane, H. C. Kapteyn, and I. P. Christov, " Enhanced high-harmonic generation using 25 fs laser pulses," Phys. Rev. Lett. 76, 752- 755 ( 1996).
[CrossRef] [PubMed]

Ollinger, C.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tocoulou, and T. Salditt, " Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 ( 2005).
[CrossRef] [PubMed]

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tocoulou, " Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide," Appl. Phys. Lett. 85, 1907- 1909 ( 2004).
[CrossRef]

Peatross, J.

J. Zhou, J. Peatross, M. M. Mumane, H. C. Kapteyn, and I. P. Christov, " Enhanced high-harmonic generation using 25 fs laser pulses," Phys. Rev. Lett. 76, 752- 755 ( 1996).
[CrossRef] [PubMed]

Pratisto, H. S.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Pukhov, A

S. Kiselev, A Pukhov, and I. Kostyukov, " X-ray generation in strongly nonlinear plasma waves," Phys. Rev. Lett. 93, 135004 ( 2004).
[CrossRef] [PubMed]

Renieri, A.

G. Dattoli and A. Renieri, " Overview of proposed VUV and soft x-ray projects in the world," Nucl. Instrum. Methods A 507, 464- 469 ( 2003).
[CrossRef]

Riekel, C.

W. Jark, S. Di Fonzo, S. Lagomarsino, A. Cedola, E. Di Fabrizio, A. Bram, and C. Riekel, " Properties of a submicrometer x-ray beam at the exit of a waveguide," J. Appl. Phys. 80, 4831- 4836 ( 1996).
[CrossRef]

Rudolph, W.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996).

Salditt, T.

C. Fuhse and T. Salditt, " Finite-difference field calculations for one-dimensionally confined x-ray waveguides," Physica B 357, 57- 60 ( 2005).
[CrossRef]

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tocoulou, and T. Salditt, " Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 ( 2005).
[CrossRef] [PubMed]

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tocoulou, " Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide," Appl. Phys. Lett. 85, 1907- 1909 ( 2004).
[CrossRef]

Seeger, J.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tocoulou, and T. Salditt, " Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 ( 2005).
[CrossRef] [PubMed]

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tocoulou, " Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide," Appl. Phys. Lett. 85, 1907- 1909 ( 2004).
[CrossRef]

Shen, J. H.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Slemzin, V. A.

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, and V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Tocoulou, R.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tocoulou, and T. Salditt, " Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 ( 2005).
[CrossRef] [PubMed]

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tocoulou, " Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide," Appl. Phys. Lett. 85, 1907- 1909 ( 2004).
[CrossRef]

Tokutake, Y.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Tschentscher, T.

T. Tschentscher, " Investigation of ultrafast processes using x-ray free-electron laser radiation," Chem. Phys. 299, 271- 276 ( 2004).
[CrossRef]

van der Meer, A. F. G.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

van der Veen, J. F.

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, " Propagation of partially coherent focused x-ray beam within a planar x-ray waveguide," J. Synchrotron Radiat. 9, 383- 393 ( 2002).
[CrossRef]

Vinogradov, A. V.

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, and V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

Wegdam, G. H.

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, " Propagation of partially coherent focused x-ray beam within a planar x-ray waveguide," J. Synchrotron Radiat. 9, 383- 393 ( 2002).
[CrossRef]

Xie, A.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Zhou, J.

J. Zhou, J. Peatross, M. M. Mumane, H. C. Kapteyn, and I. P. Christov, " Enhanced high-harmonic generation using 25 fs laser pulses," Phys. Rev. Lett. 76, 752- 755 ( 1996).
[CrossRef] [PubMed]

Zwanenburg, M. J.

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, " Propagation of partially coherent focused x-ray beam within a planar x-ray waveguide," J. Synchrotron Radiat. 9, 383- 393 ( 2002).
[CrossRef]

Appl. Phys. B

I. P. Christov, " Propagation of an attosecond pulse in an atomic-scale waveguide," Appl. Phys. B 80, 405- 408 ( 2005).
[CrossRef]

Appl. Phys. Lett.

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tocoulou, " Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide," Appl. Phys. Lett. 85, 1907- 1909 ( 2004).
[CrossRef]

At. Data Nucl. Data Tables

B. L. Henke, E. M. Gullikson, and J. C. Davis, " X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, Z = 1-92," At. Data Nucl. Data Tables 54, 181- 342 ( 1993).
[CrossRef]

Chem. Phys.

T. Tschentscher, " Investigation of ultrafast processes using x-ray free-electron laser radiation," Chem. Phys. 299, 271- 276 ( 2004).
[CrossRef]

J. Appl. Phys.

W. Jark, S. Di Fonzo, S. Lagomarsino, A. Cedola, E. Di Fabrizio, A. Bram, and C. Riekel, " Properties of a submicrometer x-ray beam at the exit of a waveguide," J. Appl. Phys. 80, 4831- 4836 ( 1996).
[CrossRef]

J. Synchrotron Radiat.

W. Jark and S. Di Fonzo, " Prediction of the transmission through thin-film waveguides for x-ray microscopy," J. Synchrotron Radiat. 11, 386- 392 ( 2004).
[CrossRef] [PubMed]

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, " Propagation of partially coherent focused x-ray beam within a planar x-ray waveguide," J. Synchrotron Radiat. 9, 383- 393 ( 2002).
[CrossRef]

Nucl. Instrum. Methods A

G. Dattoli and A. Renieri, " Overview of proposed VUV and soft x-ray projects in the world," Nucl. Instrum. Methods A 507, 464- 469 ( 2003).
[CrossRef]

Phys. Rev. Lett.

A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tocoulou, and T. Salditt, " Two-dimensional hard x-ray beam compression by combined focusing and waveguide optics," Phys. Rev. Lett. 94, 074801 ( 2005).
[CrossRef] [PubMed]

J. J. Macklin, J. D. Kmetec, and C. L. Gordon III, " High-order harmonic generation using intense femtosecond pulses," Phys. Rev. Lett. 70, 766- 769 ( 1993).
[CrossRef] [PubMed]

J. Zhou, J. Peatross, M. M. Mumane, H. C. Kapteyn, and I. P. Christov, " Enhanced high-harmonic generation using 25 fs laser pulses," Phys. Rev. Lett. 76, 752- 755 ( 1996).
[CrossRef] [PubMed]

S. Kiselev, A Pukhov, and I. Kostyukov, " X-ray generation in strongly nonlinear plasma waves," Phys. Rev. Lett. 93, 135004 ( 2004).
[CrossRef] [PubMed]

Physica B

C. Fuhse and T. Salditt, " Finite-difference field calculations for one-dimensionally confined x-ray waveguides," Physica B 357, 57- 60 ( 2005).
[CrossRef]

Rev. Sci. Instrum.

G. S. Edwards, R. H. Austin, F. E. Carroll, M. L. Copeland, M. E. Couprie, W. E. Gabella, R. F. Haglund, B. A. Hooper, M. S. Hutson, E. D. Jansen, K. M. Joos, D. P. Kiehart, I. Lindau, J. Miao, H. S. Pratisto, J. H. Shen, Y. Tokutake, A. F. G. van der Meer, and A. Xie, " Free-electron-laser-based biophysical and biomedical instrumentation," Rev. Sci. Instrum. 74, 3207- 3245 ( 2003)
[CrossRef]

Tech. Note SPARC-FEL 05/001; http://efrosf.frascati.enea.it/SPARC/noteslowbarfel.htm (2005).

L. Giannessi, " Preliminary simulations of the SPARX FEL," Tech. Note SPARC-FEL 05/001; http://efrosf.frascati.enea.it/SPARC/noteslowbarfel.htm (2005).

Other

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).

H. P. Freund and T. M. Antonsen, Jr., Principles of Free-Electron Lasers (Chapman & Hall, 1996).

A. V. Vinogradov, I. A. Brytov, A. Ya. Grudski, M. N. Kogan, I. V. Kozhevnikov, and V. A. Slemzin, Reflective X-Ray Optics (Mashinostroenie, Leningrad, 1989).

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996).

BESSY FEL, " Technical Design Report" (BESSY m.b.H., Berlin, 2004), p. 56.

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Figures (5)

Fig. 1
Fig. 1

Schematics of (a) of resonant beam coupling, (b) front coupling, and (c) front coupling with the formations of a standing-wave pattern that permit mode selection.

Fig. 2
Fig. 2

Example of propagating modes for (a) first order (a) and (b) second order. In the latter case beam splitting is accomplished. (c) A magnified image of the exit of the WG in the case of a second mode is shown at the right. The intensity is in arbitrary units.

Fig. 3
Fig. 3

Dispersion versus wavelength in the hard-x-ray region for a WG with a vacuum core layer and a Si cladding material: (a) mode orders for a fixed square gap of 200   nm × 200   nm , (b) several values of the gap for the first resonance order.

Fig. 4
Fig. 4

Dispersion and attenuation lengths for Si and C for a WG with a vacuum gap of 400   nm × 400   nm : (a) dispersion D for Si, (b) attenuation length for Si, (c) dispersion for C, (d) attenuation length for C. Inset, magnified part of (c).

Fig. 5
Fig. 5

WG as a beam splitter and a delay line in the second (or higher) resonance mode. In (b), with two mirrors a zero delay between the two beams can be obtained.

Equations (18)

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

2 E + k 2 E = 0 ,
φ m = k m d x ( m 1 ) π .
φ m = 2 arctan [ ( cos 2 θ m cos 2 θ c ) 1 / 2 sin θ m ] .
E m n ( x , y , z ) = E m ( x ) E n ( y ) exp ( i k z     m n z ) ,
k z     m n = ( ω / c ) ( 1 sin 2 θ m sin 2 θ n ) 1 / 2 .
v g = ( k z ω | ω 0 ) 1 1 k x ( ω 0 ) ,
G V D = 2 k z ω 2 | ω 0 k z ( ω 0 ) .
D = 2 π c λ 2 G V D .
Δ t D L Δ λ,
GVD = 1 k z [ ( ω / c 2 k x k x k y k y ) 2 2 k z 2 + 1 / c 2 k x 2 k x k x k y 2 k y k y ] .
k x = 1 c ( sin θ m + ω θ m ω ) ;
k x = 1 c [ 2 cos θ m θ m ω ω sin θ m ( θ m ω ) 2 + ω cos θ m 2 θ m ω 2 ] .
M sin θ c λ / 2 d .
T = L ( 1 v g 1 1 v g M ) .
L ( δ / 2 ) 3 / 2 2 β θ m         2 d .
E ( t ) = E 0 exp ( Γ 0 t 2 ) exp ( i ω 0 t ) .
θ m ω = 2 cot ( φ m / 2 ) cot θ c sin θ c δ ω d x c sin θ m ω c cos θ m + 2 cot ( φ m / 2 ) cot θ m ,
2 θ m ω 2 = 1 ( ω c d cos θ m φ m θ m ) 2 { [ 2 φ m θ m       2 ( θ c ω ) 2 + φ m θ c 2 θ c ω 2 d c cos θ m θ m ω ] ( ω c d cos θ m φ m θ m ) ( φ m θ c θ c ω d c sin θ m ) ( d c cos θ m ω c d sin θ m θ m ω 2 φ m θ m         2 θ m ω ) } .

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