Abstract

We have coupled a nano-focused synchrotron beam into a planar x-ray waveguide structure through a thinned cladding, using the resonant beam coupling (RBC) geometry, which is well established for coupling of macroscopic x-ray beams into x-ray waveguides. By reducing the beam size and using specially designed waveguide structures with multiple guiding layers, we can observe two reflected beams of similar amplitudes upon resonant mode excitation. At the same time, the second reflected beam is shifted along the surface by several millimeters, constituting a exceptionally large Goos-Hänchen effect. We evidence this effect based on its characteristic far-field patterns resulting from interference of the multiple reflected beams. The experimental results are in perfect agreement with finite-difference simulations.

© 2017 Optical Society of America

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References

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  1. E. Spiller and A. Segmüller, “Propagation of x rays in waveguides,” Appl. Phys. Lett. 24(2), 60–61 (1974).
    [Crossref]
  2. Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, and D. P. Siddons, “X-ray flux enhancement in thin-film waveguides using resonant beam couplers,” Phys. Rev. Lett. 71(4), 537–540 (1993).
    [Crossref] [PubMed]
  3. S. Lagomarsino, A. Cedola, P. Cloetens, S. Di Fonzo, W. Jark, G. Soullie, and C. Riekel, “Phase contrast hard x-ray microscopy with submicron resolution,” Appl. Phys. Lett. 71(18), 2557–2559 (1997).
    [Crossref]
  4. M. J. Zwanenburg, J. F. Peters, J. H. H. Bongaerts, S. A. de Vries, D. L. Abernathy, and J. F. van der Veen, “Coherent Propagation of X Rays in a Planar Waveguide with a Tunable Air Gap,” Phys. Rev. Lett. 82(8), 1696–1699 (1999).
    [Crossref]
  5. W. Jark and S. Di Fonzo, “Prediction of the transmission through thin-film waveguides for X-ray microscopy,” J. Synchrotron Radiat. 11(5), 386–392 (2004).
  6. V. K. Egorov and E. V. Egorov, “Physics of planar x-ray waveguide,” Proc. SPIE 4502, 148–172 (2001).
    [Crossref]
  7. M. Osterhoff and T. Salditt, “Coherence filtering of x-ray waveguides: analytical and numerical approach,” Phys. Rev. Lett. 13(10), 103026 (2011).
  8. M. Bartels, M. Krenkel, J. Haber, R. N. Wilke, and T. Salditt, “X-Ray Holographic Imaging of Hydrated Biological Cells in Solution,” Phys. Rev. Lett. 114(4), 048103 (2015).
    [Crossref] [PubMed]
  9. F. Pfeiffer, T. Salditt, P. Høghøj, I. Anderson, and N. Schell, “X-ray waveguides with multiple guiding layers,” Phys. Rev. B 62(24), 16939–16943 (2000).
    [Crossref]
  10. Q. Zhong, M. Osterhoff, M. W. Wen, Z. S. Wang, and T. Salditt, “X-ray waveguide arrays: tailored near fields by multi-beam interference,” X-ray Spectrom. 46(2), 107–115 (2017).
  11. C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tucoulou, “Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide,” Appl. Phys. Lett. 85(11), 1907–1909 (2004).
    [Crossref]
  12. S. P. Krüger, K. Giewekemeyer, S. Kalbfleisch, M. Bartels, H. Neubauer, and T. Salditt, “Sub-15 nm beam confinement by twocrossed x-ray waveguides,” Opt. Express 18(13), 13492–13501 (2010).
    [Crossref] [PubMed]
  13. A. Jarre, T. Salditt, T. Panzner, U. Pietsch, and F. Pfeiffer, “White beam x-ray waveguide optics,” Appl. Phys. Lett. 85(2), 161–163 (2004).
    [Crossref]
  14. T. Salditt, F. Pfeiffer, H. Perzl, A. Vix, U. Mennicke, A. Jarre, A. Mazuelas, and T. Metzger, “X-ray waveguides and thin macromolecular films,” Physica B: Phys. Condens. Mat. 336(1), 181–192 (2003).
  15. Z. Jiang, D. R. Lee, S. Narayanan, J. Wang, and S. K. Sinha, “Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films,” Phys. Rev. B 84(7), 075440 (2011).
    [Crossref]
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  19. F. Goos and H. Lindberg-Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” J. Opt. Soc. Am. A 440(5), 251–252 (1949).
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    [Crossref]
  21. T. Tamir and H. L. Bertoni, “Lateral Displacement of Optical Beams at Multilayered and Periodic Structures,” J. Opt. Soc. Am. 61(10), 1397–1413 (1971).
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    [Crossref]
  24. M. Delgado and E. Delgado, “Evaluation of a total reflection set-up by an interface geometric model,” Phys. Rev. E 113(12), 520–526 (2003).
  25. X. M. Liu, Z. Q. Cao, P. F. Zhu, and Q. S. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73(1), 016615 (2006).
    [Crossref]
  26. A. Sharon, D. Rosenblatt, and A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14(11), 2985–2993 (1997).
    [Crossref]
  27. C. Kappel, A. Selle, M. A. Bader, and G. Marowsky, “Resonant double-grating waveguide structures as inverted Fabry-Perot interferometers,” J. Opt. Soc. Am. B 21(6), 1127–1136 (2004).
    [Crossref]
  28. L. G. Parratt, “Surface studies of solids by total reflection of X rays,” Photon. Res. 95(12), 359–369 (1954).
  29. D. L. Windt, “IMD – Software for modeling the optical properties of multilayer films,” Comp. Phys. 12(4), 360–370 (1998).
  30. C. Fuhse and T. Salditt, “Finite-difference field calculations for one-dimensionally confined X-ray waveguides,” Physica B: Phys. Condens. Mat. 357(1–2), 57–60 (2005).
  31. M. J. Bedzyk, G. M. Bommarito, M. Caffrey, and T. L. Penner, “Diffuse-Double Layer at a Membrane-Aqueous Interface Measured with X-ray Standing Waves,” Science 248(4951), 52–56 (1990).
  32. Q. Zhong, W. B. Li, Z. Zhang, J. T. Zhu, Q. S. Huang, H. C. Li, Z. S. Wang, P. Jonnard, K. L. Guen, J. M. André, H. J. Zhou, and T. L. Huo, “Optical and structural performance of the Al(1%wtSi)/Zr reflection multilayers in the 17–19nm region,” Opt. Express 20(10), 10692–10700 (2012).
    [Crossref] [PubMed]
  33. Q. Zhong, Z. Zhang, R. Z. Qi, J. Li, Z. S. Wang, K. L. Guen, J. M. André, and P. Jonnard, “Enhancement of the reflectivity of Al/Zr multilayers by a novel structure,” Opt. Express 21(12), 14399–14408 (2013).
    [Crossref] [PubMed]
  34. T. Salditt, M. Osterhoff, M. Krenkel, R. N. Wilke, M. Priebe, M. Bartels, S. Kalbfleisch, and M. Sprung, “Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction,” J. Synchrotron Radiat. 22(4), 867–878 (2015).
  35. C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
    [Crossref]
  36. A. Barty, “Time-resolved imaging using x-ray free electron lasers,” J. Phys. B: Atom. Molec. Opt. Phys. 43(19), 194014 (2010).
  37. R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science 328(5983), 1248–1251 (2010).
  38. S. Aeffner, T. Reusch, B. Weinhausen, and T. Salditt, “Energetics of stalk intermediates in membrane fusion are controlled by lipid composition,”. Nat. Acad. Sci. 109(25), E1609–E1618 (2012).
    [Crossref]

2017 (1)

Q. Zhong, M. Osterhoff, M. W. Wen, Z. S. Wang, and T. Salditt, “X-ray waveguide arrays: tailored near fields by multi-beam interference,” X-ray Spectrom. 46(2), 107–115 (2017).

2015 (2)

M. Bartels, M. Krenkel, J. Haber, R. N. Wilke, and T. Salditt, “X-Ray Holographic Imaging of Hydrated Biological Cells in Solution,” Phys. Rev. Lett. 114(4), 048103 (2015).
[Crossref] [PubMed]

T. Salditt, M. Osterhoff, M. Krenkel, R. N. Wilke, M. Priebe, M. Bartels, S. Kalbfleisch, and M. Sprung, “Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction,” J. Synchrotron Radiat. 22(4), 867–878 (2015).

2014 (1)

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

2013 (2)

D. Pelliccia, S. Kandasamy, and M. James, “Characterization of thin films for X-ray and neutron waveguiding by X-ray reflectivity and atomic force microscopy,” Physica Stat. Sol. A 210(11), 2416–2422 (2013).

Q. Zhong, Z. Zhang, R. Z. Qi, J. Li, Z. S. Wang, K. L. Guen, J. M. André, and P. Jonnard, “Enhancement of the reflectivity of Al/Zr multilayers by a novel structure,” Opt. Express 21(12), 14399–14408 (2013).
[Crossref] [PubMed]

2012 (2)

2011 (2)

M. Osterhoff and T. Salditt, “Coherence filtering of x-ray waveguides: analytical and numerical approach,” Phys. Rev. Lett. 13(10), 103026 (2011).

Z. Jiang, D. R. Lee, S. Narayanan, J. Wang, and S. K. Sinha, “Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films,” Phys. Rev. B 84(7), 075440 (2011).
[Crossref]

2010 (3)

S. P. Krüger, K. Giewekemeyer, S. Kalbfleisch, M. Bartels, H. Neubauer, and T. Salditt, “Sub-15 nm beam confinement by twocrossed x-ray waveguides,” Opt. Express 18(13), 13492–13501 (2010).
[Crossref] [PubMed]

A. Barty, “Time-resolved imaging using x-ray free electron lasers,” J. Phys. B: Atom. Molec. Opt. Phys. 43(19), 194014 (2010).

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science 328(5983), 1248–1251 (2010).

2006 (1)

X. M. Liu, Z. Q. Cao, P. F. Zhu, and Q. S. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73(1), 016615 (2006).
[Crossref]

2005 (2)

F. Pillon, H. Gilles, S. Girard, M. Laroche, R. Kaiser, and A. Gazibegovic, “Goos-Hänchen and Imbert-Fedorov shifts for leaky guided modes,” J. Opt. Soc. Am. B 22(6), 1290–1299 (2005).
[Crossref]

C. Fuhse and T. Salditt, “Finite-difference field calculations for one-dimensionally confined X-ray waveguides,” Physica B: Phys. Condens. Mat. 357(1–2), 57–60 (2005).

2004 (4)

C. Kappel, A. Selle, M. A. Bader, and G. Marowsky, “Resonant double-grating waveguide structures as inverted Fabry-Perot interferometers,” J. Opt. Soc. Am. B 21(6), 1127–1136 (2004).
[Crossref]

A. Jarre, T. Salditt, T. Panzner, U. Pietsch, and F. Pfeiffer, “White beam x-ray waveguide optics,” Appl. Phys. Lett. 85(2), 161–163 (2004).
[Crossref]

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tucoulou, “Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide,” Appl. Phys. Lett. 85(11), 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(5), 386–392 (2004).

2003 (2)

T. Salditt, F. Pfeiffer, H. Perzl, A. Vix, U. Mennicke, A. Jarre, A. Mazuelas, and T. Metzger, “X-ray waveguides and thin macromolecular films,” Physica B: Phys. Condens. Mat. 336(1), 181–192 (2003).

M. Delgado and E. Delgado, “Evaluation of a total reflection set-up by an interface geometric model,” Phys. Rev. E 113(12), 520–526 (2003).

2001 (1)

V. K. Egorov and E. V. Egorov, “Physics of planar x-ray waveguide,” Proc. SPIE 4502, 148–172 (2001).
[Crossref]

2000 (1)

F. Pfeiffer, T. Salditt, P. Høghøj, I. Anderson, and N. Schell, “X-ray waveguides with multiple guiding layers,” Phys. Rev. B 62(24), 16939–16943 (2000).
[Crossref]

1999 (1)

M. J. Zwanenburg, J. F. Peters, J. H. H. Bongaerts, S. A. de Vries, D. L. Abernathy, and J. F. van der Veen, “Coherent Propagation of X Rays in a Planar Waveguide with a Tunable Air Gap,” Phys. Rev. Lett. 82(8), 1696–1699 (1999).
[Crossref]

1998 (1)

D. L. Windt, “IMD – Software for modeling the optical properties of multilayer films,” Comp. Phys. 12(4), 360–370 (1998).

1997 (2)

S. Lagomarsino, A. Cedola, P. Cloetens, S. Di Fonzo, W. Jark, G. Soullie, and C. Riekel, “Phase contrast hard x-ray microscopy with submicron resolution,” Appl. Phys. Lett. 71(18), 2557–2559 (1997).
[Crossref]

A. Sharon, D. Rosenblatt, and A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14(11), 2985–2993 (1997).
[Crossref]

1993 (1)

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, and D. P. Siddons, “X-ray flux enhancement in thin-film waveguides using resonant beam couplers,” Phys. Rev. Lett. 71(4), 537–540 (1993).
[Crossref] [PubMed]

1992 (1)

J. Wang, M. J. Bedzyk, and M. Caffrey, “Resonance-enhanced x-rays in thin films: a structure probe for membranes and surface layers,” Science 258(258), 775–778 (1992).

1990 (1)

M. J. Bedzyk, G. M. Bommarito, M. Caffrey, and T. L. Penner, “Diffuse-Double Layer at a Membrane-Aqueous Interface Measured with X-ray Standing Waves,” Science 248(4951), 52–56 (1990).

1976 (1)

1974 (1)

E. Spiller and A. Segmüller, “Propagation of x rays in waveguides,” Appl. Phys. Lett. 24(2), 60–61 (1974).
[Crossref]

1971 (1)

1964 (1)

1954 (1)

L. G. Parratt, “Surface studies of solids by total reflection of X rays,” Photon. Res. 95(12), 359–369 (1954).

1949 (1)

F. Goos and H. Lindberg-Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” J. Opt. Soc. Am. A 440(5), 251–252 (1949).

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Annalen der Physik 436(7), 333–346 (1947).

Abernathy, D. L.

M. J. Zwanenburg, J. F. Peters, J. H. H. Bongaerts, S. A. de Vries, D. L. Abernathy, and J. F. van der Veen, “Coherent Propagation of X Rays in a Planar Waveguide with a Tunable Air Gap,” Phys. Rev. Lett. 82(8), 1696–1699 (1999).
[Crossref]

Aeffner, S.

S. Aeffner, T. Reusch, B. Weinhausen, and T. Salditt, “Energetics of stalk intermediates in membrane fusion are controlled by lipid composition,”. Nat. Acad. Sci. 109(25), E1609–E1618 (2012).
[Crossref]

Anderson, I.

F. Pfeiffer, T. Salditt, P. Høghøj, I. Anderson, and N. Schell, “X-ray waveguides with multiple guiding layers,” Phys. Rev. B 62(24), 16939–16943 (2000).
[Crossref]

André, J. M.

Bader, M. A.

Bartels, M.

T. Salditt, M. Osterhoff, M. Krenkel, R. N. Wilke, M. Priebe, M. Bartels, S. Kalbfleisch, and M. Sprung, “Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction,” J. Synchrotron Radiat. 22(4), 867–878 (2015).

M. Bartels, M. Krenkel, J. Haber, R. N. Wilke, and T. Salditt, “X-Ray Holographic Imaging of Hydrated Biological Cells in Solution,” Phys. Rev. Lett. 114(4), 048103 (2015).
[Crossref] [PubMed]

S. P. Krüger, K. Giewekemeyer, S. Kalbfleisch, M. Bartels, H. Neubauer, and T. Salditt, “Sub-15 nm beam confinement by twocrossed x-ray waveguides,” Opt. Express 18(13), 13492–13501 (2010).
[Crossref] [PubMed]

Barty, A.

A. Barty, “Time-resolved imaging using x-ray free electron lasers,” J. Phys. B: Atom. Molec. Opt. Phys. 43(19), 194014 (2010).

Bedzyk, M. J.

J. Wang, M. J. Bedzyk, and M. Caffrey, “Resonance-enhanced x-rays in thin films: a structure probe for membranes and surface layers,” Science 258(258), 775–778 (1992).

M. J. Bedzyk, G. M. Bommarito, M. Caffrey, and T. L. Penner, “Diffuse-Double Layer at a Membrane-Aqueous Interface Measured with X-ray Standing Waves,” Science 248(4951), 52–56 (1990).

Bertoni, H. L.

Bommarito, G. M.

M. J. Bedzyk, G. M. Bommarito, M. Caffrey, and T. L. Penner, “Diffuse-Double Layer at a Membrane-Aqueous Interface Measured with X-ray Standing Waves,” Science 248(4951), 52–56 (1990).

Bongaerts, J. H. H.

M. J. Zwanenburg, J. F. Peters, J. H. H. Bongaerts, S. A. de Vries, D. L. Abernathy, and J. F. van der Veen, “Coherent Propagation of X Rays in a Planar Waveguide with a Tunable Air Gap,” Phys. Rev. Lett. 82(8), 1696–1699 (1999).
[Crossref]

Caffrey, M.

J. Wang, M. J. Bedzyk, and M. Caffrey, “Resonance-enhanced x-rays in thin films: a structure probe for membranes and surface layers,” Science 258(258), 775–778 (1992).

M. J. Bedzyk, G. M. Bommarito, M. Caffrey, and T. L. Penner, “Diffuse-Double Layer at a Membrane-Aqueous Interface Measured with X-ray Standing Waves,” Science 248(4951), 52–56 (1990).

Cao, Z. Q.

X. M. Liu, Z. Q. Cao, P. F. Zhu, and Q. S. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73(1), 016615 (2006).
[Crossref]

Capotondi, F.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Cedola, A.

S. Lagomarsino, A. Cedola, P. Cloetens, S. Di Fonzo, W. Jark, G. Soullie, and C. Riekel, “Phase contrast hard x-ray microscopy with submicron resolution,” Appl. Phys. Lett. 71(18), 2557–2559 (1997).
[Crossref]

Cloetens, P.

S. Lagomarsino, A. Cedola, P. Cloetens, S. Di Fonzo, W. Jark, G. Soullie, and C. Riekel, “Phase contrast hard x-ray microscopy with submicron resolution,” Appl. Phys. Lett. 71(18), 2557–2559 (1997).
[Crossref]

Couet, S.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science 328(5983), 1248–1251 (2010).

de Vries, S. A.

M. J. Zwanenburg, J. F. Peters, J. H. H. Bongaerts, S. A. de Vries, D. L. Abernathy, and J. F. van der Veen, “Coherent Propagation of X Rays in a Planar Waveguide with a Tunable Air Gap,” Phys. Rev. Lett. 82(8), 1696–1699 (1999).
[Crossref]

Deckman, H. W.

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, and D. P. Siddons, “X-ray flux enhancement in thin-film waveguides using resonant beam couplers,” Phys. Rev. Lett. 71(4), 537–540 (1993).
[Crossref] [PubMed]

Delgado, E.

M. Delgado and E. Delgado, “Evaluation of a total reflection set-up by an interface geometric model,” Phys. Rev. E 113(12), 520–526 (2003).

Delgado, M.

M. Delgado and E. Delgado, “Evaluation of a total reflection set-up by an interface geometric model,” Phys. Rev. E 113(12), 520–526 (2003).

Egorov, E. V.

V. K. Egorov and E. V. Egorov, “Physics of planar x-ray waveguide,” Proc. SPIE 4502, 148–172 (2001).
[Crossref]

Egorov, V. K.

V. K. Egorov and E. V. Egorov, “Physics of planar x-ray waveguide,” Proc. SPIE 4502, 148–172 (2001).
[Crossref]

Eisebitt, S.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Feng, Y. P.

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, and D. P. Siddons, “X-ray flux enhancement in thin-film waveguides using resonant beam couplers,” Phys. Rev. Lett. 71(4), 537–540 (1993).
[Crossref] [PubMed]

Fonzo, S. Di

W. Jark and S. Di Fonzo, “Prediction of the transmission through thin-film waveguides for X-ray microscopy,” J. Synchrotron Radiat. 11(5), 386–392 (2004).

S. Lagomarsino, A. Cedola, P. Cloetens, S. Di Fonzo, W. Jark, G. Soullie, and C. Riekel, “Phase contrast hard x-ray microscopy with submicron resolution,” Appl. Phys. Lett. 71(18), 2557–2559 (1997).
[Crossref]

Friesem, A. A.

Fuhse, C.

C. Fuhse and T. Salditt, “Finite-difference field calculations for one-dimensionally confined X-ray waveguides,” Physica B: Phys. Condens. Mat. 357(1–2), 57–60 (2005).

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tucoulou, “Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide,” Appl. Phys. Lett. 85(11), 1907–1909 (2004).
[Crossref]

Gazibegovic, A.

Giewekemeyer, K.

Gilles, H.

Giovannella, M.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Girard, S.

Goos, F.

F. Goos and H. Lindberg-Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” J. Opt. Soc. Am. A 440(5), 251–252 (1949).

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Annalen der Physik 436(7), 333–346 (1947).

Guen, K. L.

Günther, C. M.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Haber, J.

M. Bartels, M. Krenkel, J. Haber, R. N. Wilke, and T. Salditt, “X-Ray Holographic Imaging of Hydrated Biological Cells in Solution,” Phys. Rev. Lett. 114(4), 048103 (2015).
[Crossref] [PubMed]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Annalen der Physik 436(7), 333–346 (1947).

Hastings, J. B.

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, and D. P. Siddons, “X-ray flux enhancement in thin-film waveguides using resonant beam couplers,” Phys. Rev. Lett. 71(4), 537–540 (1993).
[Crossref] [PubMed]

Høghøj, P.

F. Pfeiffer, T. Salditt, P. Høghøj, I. Anderson, and N. Schell, “X-ray waveguides with multiple guiding layers,” Phys. Rev. B 62(24), 16939–16943 (2000).
[Crossref]

Huang, Q. S.

Huo, T. L.

James, M.

D. Pelliccia, S. Kandasamy, and M. James, “Characterization of thin films for X-ray and neutron waveguiding by X-ray reflectivity and atomic force microscopy,” Physica Stat. Sol. A 210(11), 2416–2422 (2013).

Jark, W.

W. Jark and S. Di Fonzo, “Prediction of the transmission through thin-film waveguides for X-ray microscopy,” J. Synchrotron Radiat. 11(5), 386–392 (2004).

S. Lagomarsino, A. Cedola, P. Cloetens, S. Di Fonzo, W. Jark, G. Soullie, and C. Riekel, “Phase contrast hard x-ray microscopy with submicron resolution,” Appl. Phys. Lett. 71(18), 2557–2559 (1997).
[Crossref]

Jarre, A.

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tucoulou, “Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide,” Appl. Phys. Lett. 85(11), 1907–1909 (2004).
[Crossref]

A. Jarre, T. Salditt, T. Panzner, U. Pietsch, and F. Pfeiffer, “White beam x-ray waveguide optics,” Appl. Phys. Lett. 85(2), 161–163 (2004).
[Crossref]

T. Salditt, F. Pfeiffer, H. Perzl, A. Vix, U. Mennicke, A. Jarre, A. Mazuelas, and T. Metzger, “X-ray waveguides and thin macromolecular films,” Physica B: Phys. Condens. Mat. 336(1), 181–192 (2003).

Jiang, Z.

Z. Jiang, D. R. Lee, S. Narayanan, J. Wang, and S. K. Sinha, “Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films,” Phys. Rev. B 84(7), 075440 (2011).
[Crossref]

Jonnard, P.

Kaiser, R.

Kalbfleisch, S.

T. Salditt, M. Osterhoff, M. Krenkel, R. N. Wilke, M. Priebe, M. Bartels, S. Kalbfleisch, and M. Sprung, “Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction,” J. Synchrotron Radiat. 22(4), 867–878 (2015).

S. P. Krüger, K. Giewekemeyer, S. Kalbfleisch, M. Bartels, H. Neubauer, and T. Salditt, “Sub-15 nm beam confinement by twocrossed x-ray waveguides,” Opt. Express 18(13), 13492–13501 (2010).
[Crossref] [PubMed]

Kandasamy, S.

D. Pelliccia, S. Kandasamy, and M. James, “Characterization of thin films for X-ray and neutron waveguiding by X-ray reflectivity and atomic force microscopy,” Physica Stat. Sol. A 210(11), 2416–2422 (2013).

Kappel, C.

Krenkel, M.

T. Salditt, M. Osterhoff, M. Krenkel, R. N. Wilke, M. Priebe, M. Bartels, S. Kalbfleisch, and M. Sprung, “Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction,” J. Synchrotron Radiat. 22(4), 867–878 (2015).

M. Bartels, M. Krenkel, J. Haber, R. N. Wilke, and T. Salditt, “X-Ray Holographic Imaging of Hydrated Biological Cells in Solution,” Phys. Rev. Lett. 114(4), 048103 (2015).
[Crossref] [PubMed]

Krüger, S. P.

Lagomarsino, S.

S. Lagomarsino, A. Cedola, P. Cloetens, S. Di Fonzo, W. Jark, G. Soullie, and C. Riekel, “Phase contrast hard x-ray microscopy with submicron resolution,” Appl. Phys. Lett. 71(18), 2557–2559 (1997).
[Crossref]

Laroche, M.

Lee, D. R.

Z. Jiang, D. R. Lee, S. Narayanan, J. Wang, and S. K. Sinha, “Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films,” Phys. Rev. B 84(7), 075440 (2011).
[Crossref]

Li, H. C.

Li, J.

Li, W. B.

Lindberg-Hänchen, H.

F. Goos and H. Lindberg-Hänchen, “Neumessung des Strahlversetzungseffektes bei Totalreflexion,” J. Opt. Soc. Am. A 440(5), 251–252 (1949).

Liu, X. M.

X. M. Liu, Z. Q. Cao, P. F. Zhu, and Q. S. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73(1), 016615 (2006).
[Crossref]

Love, J. D.

Lüning, J.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Mahne, N.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Marowsky, G.

Mazuelas, A.

T. Salditt, F. Pfeiffer, H. Perzl, A. Vix, U. Mennicke, A. Jarre, A. Mazuelas, and T. Metzger, “X-ray waveguides and thin macromolecular films,” Physica B: Phys. Condens. Mat. 336(1), 181–192 (2003).

Mennicke, U.

T. Salditt, F. Pfeiffer, H. Perzl, A. Vix, U. Mennicke, A. Jarre, A. Mazuelas, and T. Metzger, “X-ray waveguides and thin macromolecular films,” Physica B: Phys. Condens. Mat. 336(1), 181–192 (2003).

Metzger, T.

T. Salditt, F. Pfeiffer, H. Perzl, A. Vix, U. Mennicke, A. Jarre, A. Mazuelas, and T. Metzger, “X-ray waveguides and thin macromolecular films,” Physica B: Phys. Condens. Mat. 336(1), 181–192 (2003).

Müller, L.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Narayanan, S.

Z. Jiang, D. R. Lee, S. Narayanan, J. Wang, and S. K. Sinha, “Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films,” Phys. Rev. B 84(7), 075440 (2011).
[Crossref]

Neubauer, H.

Ollinger, C.

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tucoulou, “Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide,” Appl. Phys. Lett. 85(11), 1907–1909 (2004).
[Crossref]

Osterhoff, M.

Q. Zhong, M. Osterhoff, M. W. Wen, Z. S. Wang, and T. Salditt, “X-ray waveguide arrays: tailored near fields by multi-beam interference,” X-ray Spectrom. 46(2), 107–115 (2017).

T. Salditt, M. Osterhoff, M. Krenkel, R. N. Wilke, M. Priebe, M. Bartels, S. Kalbfleisch, and M. Sprung, “Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction,” J. Synchrotron Radiat. 22(4), 867–878 (2015).

M. Osterhoff and T. Salditt, “Coherence filtering of x-ray waveguides: analytical and numerical approach,” Phys. Rev. Lett. 13(10), 103026 (2011).

Panzner, T.

A. Jarre, T. Salditt, T. Panzner, U. Pietsch, and F. Pfeiffer, “White beam x-ray waveguide optics,” Appl. Phys. Lett. 85(2), 161–163 (2004).
[Crossref]

Parratt, L. G.

L. G. Parratt, “Surface studies of solids by total reflection of X rays,” Photon. Res. 95(12), 359–369 (1954).

Pedersoli, E.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Pelliccia, D.

D. Pelliccia, S. Kandasamy, and M. James, “Characterization of thin films for X-ray and neutron waveguiding by X-ray reflectivity and atomic force microscopy,” Physica Stat. Sol. A 210(11), 2416–2422 (2013).

Penner, T. L.

M. J. Bedzyk, G. M. Bommarito, M. Caffrey, and T. L. Penner, “Diffuse-Double Layer at a Membrane-Aqueous Interface Measured with X-ray Standing Waves,” Science 248(4951), 52–56 (1990).

Perron, J.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Perzl, H.

T. Salditt, F. Pfeiffer, H. Perzl, A. Vix, U. Mennicke, A. Jarre, A. Mazuelas, and T. Metzger, “X-ray waveguides and thin macromolecular films,” Physica B: Phys. Condens. Mat. 336(1), 181–192 (2003).

Peters, J. F.

M. J. Zwanenburg, J. F. Peters, J. H. H. Bongaerts, S. A. de Vries, D. L. Abernathy, and J. F. van der Veen, “Coherent Propagation of X Rays in a Planar Waveguide with a Tunable Air Gap,” Phys. Rev. Lett. 82(8), 1696–1699 (1999).
[Crossref]

Pfau, B.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Pfeiffer, F.

A. Jarre, T. Salditt, T. Panzner, U. Pietsch, and F. Pfeiffer, “White beam x-ray waveguide optics,” Appl. Phys. Lett. 85(2), 161–163 (2004).
[Crossref]

T. Salditt, F. Pfeiffer, H. Perzl, A. Vix, U. Mennicke, A. Jarre, A. Mazuelas, and T. Metzger, “X-ray waveguides and thin macromolecular films,” Physica B: Phys. Condens. Mat. 336(1), 181–192 (2003).

F. Pfeiffer, T. Salditt, P. Høghøj, I. Anderson, and N. Schell, “X-ray waveguides with multiple guiding layers,” Phys. Rev. B 62(24), 16939–16943 (2000).
[Crossref]

Pietsch, U.

A. Jarre, T. Salditt, T. Panzner, U. Pietsch, and F. Pfeiffer, “White beam x-ray waveguide optics,” Appl. Phys. Lett. 85(2), 161–163 (2004).
[Crossref]

Pillon, F.

Priebe, M.

T. Salditt, M. Osterhoff, M. Krenkel, R. N. Wilke, M. Priebe, M. Bartels, S. Kalbfleisch, and M. Sprung, “Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction,” J. Synchrotron Radiat. 22(4), 867–878 (2015).

Qi, R. Z.

Renard, R. H.

Reusch, T.

S. Aeffner, T. Reusch, B. Weinhausen, and T. Salditt, “Energetics of stalk intermediates in membrane fusion are controlled by lipid composition,”. Nat. Acad. Sci. 109(25), E1609–E1618 (2012).
[Crossref]

Riekel, C.

S. Lagomarsino, A. Cedola, P. Cloetens, S. Di Fonzo, W. Jark, G. Soullie, and C. Riekel, “Phase contrast hard x-ray microscopy with submicron resolution,” Appl. Phys. Lett. 71(18), 2557–2559 (1997).
[Crossref]

Röhlsberger, R.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science 328(5983), 1248–1251 (2010).

Rosenblatt, D.

Rüffer, R.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science 328(5983), 1248–1251 (2010).

Sahoo, B.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science 328(5983), 1248–1251 (2010).

Salditt, T.

Q. Zhong, M. Osterhoff, M. W. Wen, Z. S. Wang, and T. Salditt, “X-ray waveguide arrays: tailored near fields by multi-beam interference,” X-ray Spectrom. 46(2), 107–115 (2017).

M. Bartels, M. Krenkel, J. Haber, R. N. Wilke, and T. Salditt, “X-Ray Holographic Imaging of Hydrated Biological Cells in Solution,” Phys. Rev. Lett. 114(4), 048103 (2015).
[Crossref] [PubMed]

T. Salditt, M. Osterhoff, M. Krenkel, R. N. Wilke, M. Priebe, M. Bartels, S. Kalbfleisch, and M. Sprung, “Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction,” J. Synchrotron Radiat. 22(4), 867–878 (2015).

S. Aeffner, T. Reusch, B. Weinhausen, and T. Salditt, “Energetics of stalk intermediates in membrane fusion are controlled by lipid composition,”. Nat. Acad. Sci. 109(25), E1609–E1618 (2012).
[Crossref]

M. Osterhoff and T. Salditt, “Coherence filtering of x-ray waveguides: analytical and numerical approach,” Phys. Rev. Lett. 13(10), 103026 (2011).

S. P. Krüger, K. Giewekemeyer, S. Kalbfleisch, M. Bartels, H. Neubauer, and T. Salditt, “Sub-15 nm beam confinement by twocrossed x-ray waveguides,” Opt. Express 18(13), 13492–13501 (2010).
[Crossref] [PubMed]

C. Fuhse and T. Salditt, “Finite-difference field calculations for one-dimensionally confined X-ray waveguides,” Physica B: Phys. Condens. Mat. 357(1–2), 57–60 (2005).

A. Jarre, T. Salditt, T. Panzner, U. Pietsch, and F. Pfeiffer, “White beam x-ray waveguide optics,” Appl. Phys. Lett. 85(2), 161–163 (2004).
[Crossref]

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tucoulou, “Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide,” Appl. Phys. Lett. 85(11), 1907–1909 (2004).
[Crossref]

T. Salditt, F. Pfeiffer, H. Perzl, A. Vix, U. Mennicke, A. Jarre, A. Mazuelas, and T. Metzger, “X-ray waveguides and thin macromolecular films,” Physica B: Phys. Condens. Mat. 336(1), 181–192 (2003).

F. Pfeiffer, T. Salditt, P. Høghøj, I. Anderson, and N. Schell, “X-ray waveguides with multiple guiding layers,” Phys. Rev. B 62(24), 16939–16943 (2000).
[Crossref]

Schell, N.

F. Pfeiffer, T. Salditt, P. Høghøj, I. Anderson, and N. Schell, “X-ray waveguides with multiple guiding layers,” Phys. Rev. B 62(24), 16939–16943 (2000).
[Crossref]

Schlage, K.

R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, and R. Rüffer, “Collective Lamb Shift in Single-Photon Superradiance,” Science 328(5983), 1248–1251 (2010).

Schmising, C. K.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Schneider, M.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Seeger, J.

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tucoulou, “Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide,” Appl. Phys. Lett. 85(11), 1907–1909 (2004).
[Crossref]

Segmüller, A.

E. Spiller and A. Segmüller, “Propagation of x rays in waveguides,” Appl. Phys. Lett. 24(2), 60–61 (1974).
[Crossref]

Selle, A.

Sharon, A.

Shen, Q. S.

X. M. Liu, Z. Q. Cao, P. F. Zhu, and Q. S. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73(1), 016615 (2006).
[Crossref]

Siddons, D. P.

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, and D. P. Siddons, “X-ray flux enhancement in thin-film waveguides using resonant beam couplers,” Phys. Rev. Lett. 71(4), 537–540 (1993).
[Crossref] [PubMed]

Sinha, S. K.

Z. Jiang, D. R. Lee, S. Narayanan, J. Wang, and S. K. Sinha, “Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films,” Phys. Rev. B 84(7), 075440 (2011).
[Crossref]

Y. P. Feng, S. K. Sinha, H. W. Deckman, J. B. Hastings, and D. P. Siddons, “X-ray flux enhancement in thin-film waveguides using resonant beam couplers,” Phys. Rev. Lett. 71(4), 537–540 (1993).
[Crossref] [PubMed]

Snyder, A. W.

Soullie, G.

S. Lagomarsino, A. Cedola, P. Cloetens, S. Di Fonzo, W. Jark, G. Soullie, and C. Riekel, “Phase contrast hard x-ray microscopy with submicron resolution,” Appl. Phys. Lett. 71(18), 2557–2559 (1997).
[Crossref]

Spiller, E.

E. Spiller and A. Segmüller, “Propagation of x rays in waveguides,” Appl. Phys. Lett. 24(2), 60–61 (1974).
[Crossref]

Sprung, M.

T. Salditt, M. Osterhoff, M. Krenkel, R. N. Wilke, M. Priebe, M. Bartels, S. Kalbfleisch, and M. Sprung, “Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction,” J. Synchrotron Radiat. 22(4), 867–878 (2015).

Tamir, T.

Tucoulou, R.

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tucoulou, “Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide,” Appl. Phys. Lett. 85(11), 1907–1909 (2004).
[Crossref]

van der Veen, J. F.

M. J. Zwanenburg, J. F. Peters, J. H. H. Bongaerts, S. A. de Vries, D. L. Abernathy, and J. F. van der Veen, “Coherent Propagation of X Rays in a Planar Waveguide with a Tunable Air Gap,” Phys. Rev. Lett. 82(8), 1696–1699 (1999).
[Crossref]

Vix, A.

T. Salditt, F. Pfeiffer, H. Perzl, A. Vix, U. Mennicke, A. Jarre, A. Mazuelas, and T. Metzger, “X-ray waveguides and thin macromolecular films,” Physica B: Phys. Condens. Mat. 336(1), 181–192 (2003).

Vodungbo, B.

C. K. Schmising, B. Pfau, M. Schneider, C. M. Günther, M. Giovannella, J. Perron, B. Vodungbo, L. Müller, F. Capotondi, E. Pedersoli, N. Mahne, J. Lüning, and S. Eisebitt, “Imaging Ultrafast Demagnetization Dynamics after a Spatially Localized Optical Excitation,” Phys. Rev. Lett. 112(21), 217203 (2014).
[Crossref]

Wang, J.

Z. Jiang, D. R. Lee, S. Narayanan, J. Wang, and S. K. Sinha, “Waveguide-enhanced grazing-incidence small-angle x-ray scattering of buried nanostructures in thin films,” Phys. Rev. B 84(7), 075440 (2011).
[Crossref]

J. Wang, M. J. Bedzyk, and M. Caffrey, “Resonance-enhanced x-rays in thin films: a structure probe for membranes and surface layers,” Science 258(258), 775–778 (1992).

Wang, Z. S.

Weinhausen, B.

S. Aeffner, T. Reusch, B. Weinhausen, and T. Salditt, “Energetics of stalk intermediates in membrane fusion are controlled by lipid composition,”. Nat. Acad. Sci. 109(25), E1609–E1618 (2012).
[Crossref]

Wen, M. W.

Q. Zhong, M. Osterhoff, M. W. Wen, Z. S. Wang, and T. Salditt, “X-ray waveguide arrays: tailored near fields by multi-beam interference,” X-ray Spectrom. 46(2), 107–115 (2017).

Wilke, R. N.

M. Bartels, M. Krenkel, J. Haber, R. N. Wilke, and T. Salditt, “X-Ray Holographic Imaging of Hydrated Biological Cells in Solution,” Phys. Rev. Lett. 114(4), 048103 (2015).
[Crossref] [PubMed]

T. Salditt, M. Osterhoff, M. Krenkel, R. N. Wilke, M. Priebe, M. Bartels, S. Kalbfleisch, and M. Sprung, “Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction,” J. Synchrotron Radiat. 22(4), 867–878 (2015).

Windt, D. L.

D. L. Windt, “IMD – Software for modeling the optical properties of multilayer films,” Comp. Phys. 12(4), 360–370 (1998).

Zhang, Z.

Zhong, Q.

Zhou, H. J.

Zhu, J. T.

Zhu, P. F.

X. M. Liu, Z. Q. Cao, P. F. Zhu, and Q. S. Shen, “Solution to causality paradox upon total reflection in optical planar waveguide,” Phys. Rev. E 73(1), 016615 (2006).
[Crossref]

Zwanenburg, M. J.

M. J. Zwanenburg, J. F. Peters, J. H. H. Bongaerts, S. A. de Vries, D. L. Abernathy, and J. F. van der Veen, “Coherent Propagation of X Rays in a Planar Waveguide with a Tunable Air Gap,” Phys. Rev. Lett. 82(8), 1696–1699 (1999).
[Crossref]

Annalen der Physik (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Annalen der Physik 436(7), 333–346 (1947).

Appl. Opt. (1)

Appl. Phys. Lett. (4)

C. Fuhse, A. Jarre, C. Ollinger, J. Seeger, T. Salditt, and R. Tucoulou, “Front-coupling of a prefocused x-ray beam into a monomodal planar waveguide,” Appl. Phys. Lett. 85(11), 1907–1909 (2004).
[Crossref]

A. Jarre, T. Salditt, T. Panzner, U. Pietsch, and F. Pfeiffer, “White beam x-ray waveguide optics,” Appl. Phys. Lett. 85(2), 161–163 (2004).
[Crossref]

E. Spiller and A. Segmüller, “Propagation of x rays in waveguides,” Appl. Phys. Lett. 24(2), 60–61 (1974).
[Crossref]

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Comp. Phys. (1)

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J. Opt. Soc. Am. (2)

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A. Barty, “Time-resolved imaging using x-ray free electron lasers,” J. Phys. B: Atom. Molec. Opt. Phys. 43(19), 194014 (2010).

J. Synchrotron Radiat. (2)

T. Salditt, M. Osterhoff, M. Krenkel, R. N. Wilke, M. Priebe, M. Bartels, S. Kalbfleisch, and M. Sprung, “Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction,” J. Synchrotron Radiat. 22(4), 867–878 (2015).

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Nat. Acad. Sci. (1)

S. Aeffner, T. Reusch, B. Weinhausen, and T. Salditt, “Energetics of stalk intermediates in membrane fusion are controlled by lipid composition,”. Nat. Acad. Sci. 109(25), E1609–E1618 (2012).
[Crossref]

Opt. Express (3)

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F. Pfeiffer, T. Salditt, P. Høghøj, I. Anderson, and N. Schell, “X-ray waveguides with multiple guiding layers,” Phys. Rev. B 62(24), 16939–16943 (2000).
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Phys. Rev. E (2)

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Phys. Rev. Lett. (5)

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Physica B: Phys. Condens. Mat. (2)

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D. Pelliccia, S. Kandasamy, and M. James, “Characterization of thin films for X-ray and neutron waveguiding by X-ray reflectivity and atomic force microscopy,” Physica Stat. Sol. A 210(11), 2416–2422 (2013).

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Q. Zhong, M. Osterhoff, M. W. Wen, Z. S. Wang, and T. Salditt, “X-ray waveguide arrays: tailored near fields by multi-beam interference,” X-ray Spectrom. 46(2), 107–115 (2017).

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Figures (10)

Fig. 1
Fig. 1 (a) A simple sketch of a RBC, consisting of one C layer (red) and two Ni layers (purple), deposited on the GaAs substrate. (b) Reflectivity as a function of αi for 13.8 keV photon energy. The critical angles of C ( α c C ) and N i ( a c N i ) are shown as black dotted lines. (c) Calculated field intensity in the RBC in logarithmic scaling. The modes TEm observed at different αi are labeled. (d–f) The corresponding plots for a multi-guide RBCs structure with three C guiding layers and four Ni cladding layers. In the schematic (d) the incoming beam with a beam size FWHM is coupled into the multi-guide RBCs structure, illuminating the surface over a size s = FWHM/sin(αi). If FWHM and s are sufficiently small, the RBCs structure can exhibit several reflected beams, which is the central phenomenon studied in this work. Important parameters characterizing the 1st and 2nd reflected beams are the path length of 1st reflected beam l1 (red dash line), the path length of 2nd reflected beam l2 (black dash line), the beam offsets on the surface o (green dash lines), and the distance between two beams p (blue dash lines). Note that the simulation shown in (e,f) assume an infinite beam and structure.
Fig. 2
Fig. 2 Simulation of mode excitation with finite (sub-μm) beams. The near-field distributions for (a, b, c, d) on-mode conditions at αi = 0.133°, and (e, g, h, f) off-mode conditions at αi = 0.145°, simulated for the theoretical RBCs parameters tabulated in Tab. 1, and (the experimental) photon energy 13.8 keV. For the incoming beam a Gaussian profile with beam size FWHM = 600 nm was assumed. (c, g) The 1-D profiles in the near-field, and (d, h) the corresponding normalized far-field patterns.
Fig. 3
Fig. 3 Under excitation of the TE2 mode, simulated for the theoretical design parameters, the two reflected beams (1st and 2nd) are almost equal amplitude. This is true for a range of beam sizes, here demonstrated for (a) FWHM= 600 nm, and (b) FWHM= 300 nm. Note the small offset in αi appears when changing the beam size.
Fig. 4
Fig. 4 (a) Schematic of the GINIX experimental setup. The RBCs is positioned in the focal plane at distance f behind the Kirkpatrick-Baez (KB) mirror system. The reflection plane is horizontal. By closing the slits in front of the KB mirror, the focus is made fully coherent (in the relevant horizontal plane). The diffraction limited spot size is then adjusted by the gap of the horizontal slits hg. The far-field intensity patterns at 13.8 keV photon energy (selected by the Si(111) monochromator) is then recorded as a function of exit angle αf for each finely tuned incidence angle αi, using a Eiger 4 M pixel detector (Dectris) at distance D = 5.4 m. The lineshape of the reflected beam is then analyzed as a function of αfαi. (b) An exemplary two-dimensional (2-D) far-field pattern with primary and reflected beams for αi = 0.187° and hg = 0.05 mm. (c, d) Zoom of the reflected beam, for (c) αi = 0.170°, and (d) αi = 0.187°, corresponding to off-mode and on-mode (TE2) conditions, respectively. (e, f) The corresponding integrated 1-D far-field curves, obtained after integration along y. (g) The intensity distribution as a function of αi and x, integrated over y. The integration domain is indicated by the red dash rectangles in (b). The relevant region α c C α i α c N i containing the characteristic reflectivity cusps of the TEm mode is marked by orange lines.
Fig. 5
Fig. 5 Comparison of experimental and simulation results. (a) Experimental results: Closeup of the experimental lineshape in the relevant αi range, for the data shown in Fig. 4(g), after transformation xαfαi. (b) FD near-field distribution (amplitude) of the RBCs structure with tabulated XMR fitting parameters, for αi = 0.133°. (c) Simulated near-field amplitude in the plane indicated by the red line in (b) for all αi in the relevant range. (d) Simulation results, corresponding to (a), obtained by transforming the FD data shown in (b, c) to the far-field pattern.
Fig. 6
Fig. 6 The extended comparison of the measured far-field patterns and the simulated far-field patterns, presented for different beam sizes, as controlled by the entrance slits. The results are presented for (a, e) hg = 0.1 mm, (b, f) hg =0.2 mm, (c, g) hg = 0.3 mm, and (d, h) hg = 0.4 mm, respectively.
Fig. 7
Fig. 7 (a) The near-field distributions for the multi-guide RBCs structure at αi = 0.187°, as computed by FD simulation for the theoretical RBCs parameters tabulated in Tab. 1, and for the experimental photon energy 13.8 keV, and beam size FWHM = 600 nm. (b) The 1-D near-field profile, with (c) the corresponding far-field profile calculated by a FFT. (d, e) Analogous simulations for the RBCs parameters as refined by XMR fitting structure, for αi = 0.187° and FWHM=300 nm. (f) Comparison between the simulated (red) and experimental (black) far-field profiles. The cusps along the detector coordinate αf are ’fingerprints’ for the presence of two reflected beams. By comparison, we can further infer that both reflected beams in the experiment are of similar amplitude, around ≃ 0.29.
Fig. 8
Fig. 8 Measured reflectivity (black line) and fitting curve (red line) as a function of incident angle αi for the RBCs sample.
Fig. 9
Fig. 9 (a) Schematic of the experimental setup, and field distribution calculated by free space propagation between the KB mirror and focal plane. The incoming beam, with primary intensity I0 and photon energy 13.8 keV is coupled into the RBCs, which is positioned at f = 200 mm in the focal plane of KB mirror system. (b) Close-up of the focal intensity for hg = 0.4 mm, resulting in FWHM = 40 nm. (c) Simulated beam profiles (normalized) in the focal plane (hg = 0.4 mm in red line, hg = 0.3 mm in light blue line, hg = 0.2 mm in green line, hg = 0.1 mm in dark blue line, hg = 0.05 mm in purple line). (d) The corresponding 1-D profiles from Fig. 5(a) and Fig. 6 are compared to the reflectivity calculated for infinite beams by IMD (black line), plotted for an angular range of αi from 0.1 to 0.25 degrees.
Fig. 10
Fig. 10 Using similar simulations as shown in Fig. 7, Figures 10(a, c, e, g, i) near-field and 10(b, d, f, h, j) far-field profiles, calculated for increasing FWHM, from 130 nm to 1800 nm.

Tables (2)

Tables Icon

Table 1 The theoretical designed parameters and XMR fitting structure are compared.

Tables Icon

Table 2 Comparison of beam size FWHM, between the free propagation simulated results and FD simulated data.

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