Abstract

Single-mode propagation conditions of X-ray waveguides are investigated by numerical calculations in order to understand the importance of waveguide design parameters, such as core thickness and the optical constants of waveguide materials, on the transmission and coherence properties of the waveguide. The simulation code for mode analyzing is developed based on a numerical solution of the parabolic wave equation. The initial boundary value problem is solved numerically using a finite-difference scheme based on the Crank-Nicolson scheme. The E-field intensities in a core layer are calculated at an X-ray energy of 8.0 keV for air and beryllium(Be) core waveguides with different cladding layers such as Pt, Au, W, Ni and Si to determine the dependence on waveguide materials. The highest E-field intensity radiated at the exit of the waveguide is obtained from the Pt cladded beryllium core with a thickness of 20 nm. However, the intensity from the air core waveguide with Pt cladding reaches 64% of the Be-Pt waveguide. The dependence on the core thickness, which is the major parameter used to generate a single mode in the waveguide, is investigated for the air-Pt, and Be-Pt waveguides at an X-ray energy of 8.0 keV. The mode profiles at the exit are shown for the single mode at a thickness of up to 20 nm for the air-Pt and the Be-Pt waveguides.

© 2008 Optical Society of Korea

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2007 (1)

J. Buschbeck,1,2 I. Lindemann,1,2 L. Schultz,1,2 and S. Fahler1,“Growth, structure, and texture of epitaxial Fe100.xPdx films deposited on MgO(100) at room temperature: An x-ray diffraction study,” Phys. Rev., vol.B76, pp. 205421-205428, 2007

2006 (5)

Christian G. Schroer, “Focusing hard x rays to nanometer dimensions using Fresnel zone plates,” Phys. Rev., B74, pp.033405-033408, 2006
[Crossref]

Gung-Chian Yin, Yen-Fang Song, Mau-Tsu Tang, Fu-Rong Chen, Keng S. Liang, Frederick W. Duewer, Michael Feser, Wenbing Yun, and Han-Ping D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett., vol. 89, pp. 221-122, 2006
[Crossref]

H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander, and S. Vogt, “Nanometer Linear Focusing of Hard X Rays by a Multilayer Laue Lens,” Phys. Rev. Lett., vol. 96, pp. 127401- 127404, 2006
[Crossref]

F. Pfeiffer, C. David, J. F. van der Veen, C. Bergemann, “Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory,” Phys. Rev., vol. B73, pp. 245331-245340, 2006

Christian Fuhse, X-ray Waveguides and Waveguidebased Lensless Imaging, (Dissertation, Georg-August University, Germany, 2006.)

2005 (4)

Weilun Chao, Bruce D. Harteneck, J. Alexander Liddle, Erik H. Anderson and David T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature, vol. 435, pp. 1210-1213, 2005
[Crossref]

G. G. Schroer, and B. Lengeler, “Focusing Hard X-ray to Nanometers Dimensions by Adiabatically Focusing Lenses,” Phys. Rev. Lett., vol. 94, pp.1-4, 2005
[Crossref]

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, and B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, ”Hard x-ray nanoprobe based on refractive x-ray lenses,” Appl. Phys. Lett., vol. 87, pp. 124103-12410, 2005
[Crossref]

A. G. Michette. S. J. Pfauntsch, A. Erko, A, and A. Svintsov,” Nanometer Focusing of X-ray with Modified Reflection Zone Plates,” Opt., vol. 245, pp. 349-253, 2005
[Crossref]

2003 (1)

C. Brgemann, H. Keymeulen, and J. F. Van der Veen, “Focusing X-ray Beams to Nanometer Dimensions,” Phys. Rev. Lett., vol. 91, pp. 204801-204805, 2003
[Crossref]

2002 (1)

F. Pfeiffer, C. David, M. Burghammer, C. Rickel, and T. Salditt, “Two-Dimensional X-ray Waveguides and Point Sources,” Science, vol. 297, pp. 230-234, 2002
[Crossref]

2000 (1)

F. Pfeitter, T. Salditt, P. Hoghoj, I. Anderson, and N. Schell, “X-ray Waveguides with Multiple Guiding Layers,” Phys. Rev., vol. B62, pp. 16939-16943, 2000

1999 (1)

Jianwei Miao, Pambos Charalambous, Janos Kirz and David Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre- sized non-crystalline specimens,” Nature, vol. 400, pp. 342-344, 1999
[Crossref]

1997 (2)

Y. Suzuki, N. Kamijo, S. Tamura, K. Honda, A. Takeuchi, S. Yamamoto, H. Sugiyama, K. Ohsumi, and M. Ando, ”Hard X-ray Micro-beam Experiment at the Tristan Main Ring Test Beam-line of the KEK,” J. Synchrotron Radiat., vol. 4, pp. 60-63, 1997
[Crossref]

J. W. Thomas, Numerical Partial Differential Equations, (Springer-Verlag, New York, 1997.)

1995 (1)

Y. P. Feng, S.K. Sinha, E. E. Fullerton, G. Grubel, D. Abemathy, D. P. Siddons, and J. B. Hastings, “X-ray Fraunhofer Diffraction Patterns from a Thin-Film Waveguide,” Appl. phys. Lett., vol. 67, pp. 3647-3649, 1995
[Crossref]

1994 (1)

D. H. Bilderback, S. A. Hottman, and D. J. Thiel, “Nanometer Spatial Resolution Achieved in Hard X-ray Imaging and Lave Diffraction Experiments.” Science, vol. 263, pp. 201-203, 1994
[Crossref]

1992 (1)

J. Wang, M. J. Beyk and M. Caffrey, “Resonance- Enhanced X-rays in Thin-films,” Science, vol. 258, pp. 775-778, 1992
[Crossref]

1989 (1)

M. J. Bedzyk, G. M. Bommarito and J. S. Schildkraut “X-ray Standing Waves at a Reflecting Mirror Surface,” phys. Rev. Lett., vol. 62, pp. 1376-1379, 1989
[Crossref]

Appl. Phys. Lett. (3)

C. G. Schroer, O. Kurapova, J. Patommel, P. Boye, J. Feldkamp, and B. Lengeler, M. Burghammer, C. Riekel, L. Vincze, A. van der Hart, and M. Kuchler, ”Hard x-ray nanoprobe based on refractive x-ray lenses,” Appl. Phys. Lett., vol. 87, pp. 124103-12410, 2005
[Crossref]

Y. P. Feng, S.K. Sinha, E. E. Fullerton, G. Grubel, D. Abemathy, D. P. Siddons, and J. B. Hastings, “X-ray Fraunhofer Diffraction Patterns from a Thin-Film Waveguide,” Appl. phys. Lett., vol. 67, pp. 3647-3649, 1995
[Crossref]

Gung-Chian Yin, Yen-Fang Song, Mau-Tsu Tang, Fu-Rong Chen, Keng S. Liang, Frederick W. Duewer, Michael Feser, Wenbing Yun, and Han-Ping D. Shieh, “30 nm resolution x-ray imaging at 8 keV using third order diffraction of a zone plate lens objective in a transmission microscope,” Appl. Phys. Lett., vol. 89, pp. 221-122, 2006
[Crossref]

J. Synchrotron Rad. (1)

Y. Suzuki, N. Kamijo, S. Tamura, K. Honda, A. Takeuchi, S. Yamamoto, H. Sugiyama, K. Ohsumi, and M. Ando, ”Hard X-ray Micro-beam Experiment at the Tristan Main Ring Test Beam-line of the KEK,” J. Synchrotron Radiat., vol. 4, pp. 60-63, 1997
[Crossref]

Letter Nature (1)

Weilun Chao, Bruce D. Harteneck, J. Alexander Liddle, Erik H. Anderson and David T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature, vol. 435, pp. 1210-1213, 2005
[Crossref]

Nature (1)

Jianwei Miao, Pambos Charalambous, Janos Kirz and David Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre- sized non-crystalline specimens,” Nature, vol. 400, pp. 342-344, 1999
[Crossref]

Optics Communications (1)

A. G. Michette. S. J. Pfauntsch, A. Erko, A, and A. Svintsov,” Nanometer Focusing of X-ray with Modified Reflection Zone Plates,” Opt., vol. 245, pp. 349-253, 2005
[Crossref]

Phys. Rev. (3)

F. Pfeiffer, C. David, J. F. van der Veen, C. Bergemann, “Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory,” Phys. Rev., vol. B73, pp. 245331-245340, 2006

J. Buschbeck,1,2 I. Lindemann,1,2 L. Schultz,1,2 and S. Fahler1,“Growth, structure, and texture of epitaxial Fe100.xPdx films deposited on MgO(100) at room temperature: An x-ray diffraction study,” Phys. Rev., vol.B76, pp. 205421-205428, 2007

F. Pfeitter, T. Salditt, P. Hoghoj, I. Anderson, and N. Schell, “X-ray Waveguides with Multiple Guiding Layers,” Phys. Rev., vol. B62, pp. 16939-16943, 2000

Phys. Rev. B (1)

Christian G. Schroer, “Focusing hard x rays to nanometer dimensions using Fresnel zone plates,” Phys. Rev., B74, pp.033405-033408, 2006
[Crossref]

Phys. Rev. Lett. (4)

G. G. Schroer, and B. Lengeler, “Focusing Hard X-ray to Nanometers Dimensions by Adiabatically Focusing Lenses,” Phys. Rev. Lett., vol. 94, pp.1-4, 2005
[Crossref]

C. Brgemann, H. Keymeulen, and J. F. Van der Veen, “Focusing X-ray Beams to Nanometer Dimensions,” Phys. Rev. Lett., vol. 91, pp. 204801-204805, 2003
[Crossref]

H. C. Kang, J. Maser, G. B. Stephenson, C. Liu, R. Conley, A. T. Macrander, and S. Vogt, “Nanometer Linear Focusing of Hard X Rays by a Multilayer Laue Lens,” Phys. Rev. Lett., vol. 96, pp. 127401- 127404, 2006
[Crossref]

M. J. Bedzyk, G. M. Bommarito and J. S. Schildkraut “X-ray Standing Waves at a Reflecting Mirror Surface,” phys. Rev. Lett., vol. 62, pp. 1376-1379, 1989
[Crossref]

Science (3)

J. Wang, M. J. Beyk and M. Caffrey, “Resonance- Enhanced X-rays in Thin-films,” Science, vol. 258, pp. 775-778, 1992
[Crossref]

F. Pfeiffer, C. David, M. Burghammer, C. Rickel, and T. Salditt, “Two-Dimensional X-ray Waveguides and Point Sources,” Science, vol. 297, pp. 230-234, 2002
[Crossref]

D. H. Bilderback, S. A. Hottman, and D. J. Thiel, “Nanometer Spatial Resolution Achieved in Hard X-ray Imaging and Lave Diffraction Experiments.” Science, vol. 263, pp. 201-203, 1994
[Crossref]

Other (2)

Christian Fuhse, X-ray Waveguides and Waveguidebased Lensless Imaging, (Dissertation, Georg-August University, Germany, 2006.)

J. W. Thomas, Numerical Partial Differential Equations, (Springer-Verlag, New York, 1997.)

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