Abstract

Diffraction gratings are ubiquitous wavelength dispersive elements for photons as well as for subatomic particles, atoms, and large molecules. They serve as enabling devices for spectroscopy, microscopy, and interferometry in numerous applications across the physical sciences. Transmission gratings are required in applications that demand high alignment and figure error tolerances, low weight and size, or a straight-through zero-order beam. However, photons or particles are often strongly absorbed upon transmission, e.g., in the increasingly important extreme ultraviolet (EUV) and soft x-ray band, leading to low diffraction efficiency. We demonstrate the performance of a critical-angle transmission (CAT) grating in the EUV and soft x-ray band that for the first time combines the advantages of transmission gratings with the superior broadband efficiency of blazed reflection gratings via reflection from nanofabricated periodic arrays of atomically smooth nanometer-thin silicon mirrors at angles below the critical angle for total external reflection. The efficiency of the CAT grating design is not limited to photons, but also opens the door to new, sensitive, and compact experiments and applications in atom and neutron optics, as well as for the efficient diffraction of electrons, ions, or molecules.

© 2008 Optical Society of America

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    [Crossref] [PubMed]
  3. M. Arndt, et al., “Wave-particle duality of C-60 molecules,” Nature 401, 680–682 (1999).
    [Crossref]
  4. P. R. Berman, Atom Interferometry (Academic Press, 1997).
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    [Crossref]
  6. M. L. Schattenburg, “From nanometers to gigaparsecs: The role of nanostructures in unraveling the mysteries of the cosmos,” J. Vac. Sci. Technol. B 19, 2319–2328 (2001).
    [Crossref]
  7. T. Wilheinet al., “A slit grating spectrograph for quantitative soft x-ray spectroscopy,” Rev. Sci. Instrum. 70, 1694–1699 (1999).
    [Crossref]
  8. B. Blagojevicet al., “Imaging transmission grating spectrometer for magnetic fusion experiments,” Rev. Sci. Instrum. 74, 1988–1992 (2003).
    [Crossref]
  9. D. Stutmanet al., “Spectroscopic imaging diagnostics for burning plasma experiments,” Rev. Sci. Instrum. 76, 023505 (2005).
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  13. A. I. Ioffe, V. S. Zabiyakin, and G. M. Drabkin, “Test of a diffraction grating neutron interferometer,” Phys. Lett. A 111, 373–375 (1985).
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  14. H. H. Solak, “Nanolithography with coherent extreme ultraviolet light,” J. Phys. D Appl. Phys. 39, R171–R188 (2006).
    [Crossref]
  15. P. P. Naulleau, C. H. Cho, E. M. Gullikson, and J. Bokor, “Transmission phase gratings for EUV interferometry,” J. Synch. Rad. 7, 405–410 (2000).
    [Crossref]
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  24. R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometer-scale science and engineering: Towards sub-nanometer accurate encoders,” Nanotechnology 15, S504–S511 (2004).
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    [Crossref]
  26. D. Hambach, G. Schneider, and E. M. Gullikson, “Efficient high-order diffraction of extreme-ultraviolet light and soft x-rays by nanostructured volume gratings,” Opt. Lett. 26, 1200–1202 (2001).
    [Crossref]
  27. H. L. Marshall, “A soft x-ray polarimeter designed for broadband x-ray telescopes,” Proc. SPIE 6688, 66880Z (2007).
    [Crossref]
  28. A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
    [Crossref]
  29. M. Engelhardtet al., “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
    [Crossref]
  30. C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
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    [Crossref] [PubMed]
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    [Crossref]
  33. H. Takenaka, S. Ichimaru, and E. M. Gullikson, “EUV beam splitter for use in the wavelength region around 6 nm,” J. Electron Spectrosc. Relat. Phenom. 144, 1043–1045 (2005).
    [Crossref]
  34. J. W. Elam, D. Routkevitch, P. P. Mardilovich, and S. M. George, “Conformal coating on ultrahigh-aspect-ratio nanopores of anodic alumina by atomic layer deposition,” Chem. Mat. 15, 3507–3517 (2003).
    [Crossref]
  35. A. Andersonet al., “Reflection of thermal Cs atoms grazing a polished glass surface,” Phys. Rev. A 34, 3513–3516 (1986).
    [Crossref] [PubMed]
  36. H. Oberst, Y. Tashiro, K. Shimizu, and F. Shimizu, “Quantum reflection of He* on silicon,” Phys. Rev. A 71, 052901 (2005).
    [Crossref]
  37. A. D. Cronin and B. McMorran, “Electron interferometry with nanogratings,” Phys. Rev. A 74, 061602 (2006).
    [Crossref]
  38. B. Barwicket al., “A measurement of electron-wall interactions using transmission diffraction from nanofabricated gratings,” J. Appl. Phys. 100, 074322 (2006).
    [Crossref]
  39. A. Kalinin, O. Kornilov, W. Schöllkopf, and J. P. Toennies, “Observation of mixed fermionic-bosonic helium clusters by transmission grating diffraction,” Phys. Rev. Lett. 95, 113402 (2005).
    [Crossref] [PubMed]
  40. J. D. Perreault and A. D. Cronin, “Using atomic diffraction of Na from material gratings to measure atom-surface interactions,” Phys. Rev. A 71, 053612 (2005).
    [Crossref]
  41. S. Wethekam and H. Winter, “Excitation of fullerene ions during grazing scattering from a metal surface,” Phys. Rev. A 76, 032901 (2007).
    [Crossref]

2007 (4)

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of ultrahigh aspect ratio freestanding gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 25, 2593–2597 (2007).
[Crossref]

H. L. Marshall, “A soft x-ray polarimeter designed for broadband x-ray telescopes,” Proc. SPIE 6688, 66880Z (2007).
[Crossref]

M. Engelhardtet al., “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[Crossref]

S. Wethekam and H. Winter, “Excitation of fullerene ions during grazing scattering from a metal surface,” Phys. Rev. A 76, 032901 (2007).
[Crossref]

2006 (5)

J. F. Seelyet al., “Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region,” Appl. Opt. 45, 1680–1687 (2006).
[Crossref] [PubMed]

H. C. Kanget al., “Nanometer linear focusing of hard x rays by a multilayer Laue lens,” Phys. Rev. Lett. 96, 127401 (2006).
[Crossref] [PubMed]

A. D. Cronin and B. McMorran, “Electron interferometry with nanogratings,” Phys. Rev. A 74, 061602 (2006).
[Crossref]

B. Barwicket al., “A measurement of electron-wall interactions using transmission diffraction from nanofabricated gratings,” J. Appl. Phys. 100, 074322 (2006).
[Crossref]

H. H. Solak, “Nanolithography with coherent extreme ultraviolet light,” J. Phys. D Appl. Phys. 39, R171–R188 (2006).
[Crossref]

2005 (7)

A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
[Crossref]

C. R. Canizares, et al., “The Chandra high-energy transmission grating: Design, fabrication, ground calibration, and 5 years in flight,” PASP 117, 1144–1171 (2005).
[Crossref]

D. Stutmanet al., “Spectroscopic imaging diagnostics for burning plasma experiments,” Rev. Sci. Instrum. 76, 023505 (2005).
[Crossref]

A. Kalinin, O. Kornilov, W. Schöllkopf, and J. P. Toennies, “Observation of mixed fermionic-bosonic helium clusters by transmission grating diffraction,” Phys. Rev. Lett. 95, 113402 (2005).
[Crossref] [PubMed]

J. D. Perreault and A. D. Cronin, “Using atomic diffraction of Na from material gratings to measure atom-surface interactions,” Phys. Rev. A 71, 053612 (2005).
[Crossref]

H. Takenaka, S. Ichimaru, and E. M. Gullikson, “EUV beam splitter for use in the wavelength region around 6 nm,” J. Electron Spectrosc. Relat. Phenom. 144, 1043–1045 (2005).
[Crossref]

H. Oberst, Y. Tashiro, K. Shimizu, and F. Shimizu, “Quantum reflection of He* on silicon,” Phys. Rev. A 71, 052901 (2005).
[Crossref]

2004 (1)

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometer-scale science and engineering: Towards sub-nanometer accurate encoders,” Nanotechnology 15, S504–S511 (2004).
[Crossref]

2003 (2)

B. Blagojevicet al., “Imaging transmission grating spectrometer for magnetic fusion experiments,” Rev. Sci. Instrum. 74, 1988–1992 (2003).
[Crossref]

J. W. Elam, D. Routkevitch, P. P. Mardilovich, and S. M. George, “Conformal coating on ultrahigh-aspect-ratio nanopores of anodic alumina by atomic layer deposition,” Chem. Mat. 15, 3507–3517 (2003).
[Crossref]

2002 (2)

A. N. Kurokhtin and A. V. Popov, “Simulation of high-resolution x-ray zone plates,” J. Opt. Soc. Am. A 19, 315–324 (2002).
[Crossref]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

2001 (2)

D. Hambach, G. Schneider, and E. M. Gullikson, “Efficient high-order diffraction of extreme-ultraviolet light and soft x-rays by nanostructured volume gratings,” Opt. Lett. 26, 1200–1202 (2001).
[Crossref]

M. L. Schattenburg, “From nanometers to gigaparsecs: The role of nanostructures in unraveling the mysteries of the cosmos,” J. Vac. Sci. Technol. B 19, 2319–2328 (2001).
[Crossref]

2000 (1)

P. P. Naulleau, C. H. Cho, E. M. Gullikson, and J. Bokor, “Transmission phase gratings for EUV interferometry,” J. Synch. Rad. 7, 405–410 (2000).
[Crossref]

1999 (2)

T. Wilheinet al., “A slit grating spectrograph for quantitative soft x-ray spectroscopy,” Rev. Sci. Instrum. 70, 1694–1699 (1999).
[Crossref]

M. Arndt, et al., “Wave-particle duality of C-60 molecules,” Nature 401, 680–682 (1999).
[Crossref]

1997 (1)

A. E. Frankeet al., “Super-smooth x-ray reflection grating fabrication,” J. Vac. Sci. Technol. B 15, 2940–2945 (1997).
[Crossref]

1995 (3)

J. Kirz, C. Jacobsen, and M. Howells, “Soft x-ray microscopes and their biological applications,” Q. Rev. Biophys. 28, 33–130 (1995).
[Crossref] [PubMed]

G. Schmahlet al., “Phase-contrast studies of biological specimens with the x-ray microscope at BESSY,” Rev. Sci. Instrum. 66, 1282–1286 (1995).
[Crossref]

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupledwave analysis for surface-relief gratings - enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
[Crossref]

1993 (1)

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,” Atomic Data and Nuclear Data Tables 54, 181–342 (1993).
[Crossref]

1988 (1)

D. W. Keith, M. L. Schattenburg, H. I. Smith, and D. E. Pritchard, “Diffraction of atoms by a transmission grating,” Phys. Rev. Lett. 61, 1580–1583 (1988).
[Crossref] [PubMed]

1986 (1)

A. Andersonet al., “Reflection of thermal Cs atoms grazing a polished glass surface,” Phys. Rev. A 34, 3513–3516 (1986).
[Crossref] [PubMed]

1985 (1)

A. I. Ioffe, V. S. Zabiyakin, and G. M. Drabkin, “Test of a diffraction grating neutron interferometer,” Phys. Lett. A 111, 373–375 (1985).
[Crossref]

1983 (1)

A. G. Klein and S. A. Werner, “Neutron Optics,” Rep. Prog. Phys. 46, 259–335 (1983).
[Crossref]

Ahn, M.

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of ultrahigh aspect ratio freestanding gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 25, 2593–2597 (2007).
[Crossref]

Anderson, A.

A. Andersonet al., “Reflection of thermal Cs atoms grazing a polished glass surface,” Phys. Rev. A 34, 3513–3516 (1986).
[Crossref] [PubMed]

Arndt, M.

M. Arndt, et al., “Wave-particle duality of C-60 molecules,” Nature 401, 680–682 (1999).
[Crossref]

Attwood, D. T.

D. T. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge University Press, 1999).

Barwick, B.

B. Barwicket al., “A measurement of electron-wall interactions using transmission diffraction from nanofabricated gratings,” J. Appl. Phys. 100, 074322 (2006).
[Crossref]

Berman, P. R.

P. R. Berman, Atom Interferometry (Academic Press, 1997).

Blagojevic, B.

B. Blagojevicet al., “Imaging transmission grating spectrometer for magnetic fusion experiments,” Rev. Sci. Instrum. 74, 1988–1992 (2003).
[Crossref]

Bokor, J.

P. P. Naulleau, C. H. Cho, E. M. Gullikson, and J. Bokor, “Transmission phase gratings for EUV interferometry,” J. Synch. Rad. 7, 405–410 (2000).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1998).

Buckley, C. J.

A. G. Michette and C. J. Buckley, X-ray Science and Technology (Institute of Physics Publishing, 1993).

Canizares, C. R.

C. R. Canizares, et al., “The Chandra high-energy transmission grating: Design, fabrication, ground calibration, and 5 years in flight,” PASP 117, 1144–1171 (2005).
[Crossref]

Chen, C. G.

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometer-scale science and engineering: Towards sub-nanometer accurate encoders,” Nanotechnology 15, S504–S511 (2004).
[Crossref]

Cho, C. H.

P. P. Naulleau, C. H. Cho, E. M. Gullikson, and J. Bokor, “Transmission phase gratings for EUV interferometry,” J. Synch. Rad. 7, 405–410 (2000).
[Crossref]

Cronin, A. D.

A. D. Cronin and B. McMorran, “Electron interferometry with nanogratings,” Phys. Rev. A 74, 061602 (2006).
[Crossref]

J. D. Perreault and A. D. Cronin, “Using atomic diffraction of Na from material gratings to measure atom-surface interactions,” Phys. Rev. A 71, 053612 (2005).
[Crossref]

David, C.

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (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,” Atomic Data and Nuclear Data Tables 54, 181–342 (1993).
[Crossref]

Drabkin, G. M.

A. I. Ioffe, V. S. Zabiyakin, and G. M. Drabkin, “Test of a diffraction grating neutron interferometer,” Phys. Lett. A 111, 373–375 (1985).
[Crossref]

Elam, J. W.

J. W. Elam, D. Routkevitch, P. P. Mardilovich, and S. M. George, “Conformal coating on ultrahigh-aspect-ratio nanopores of anodic alumina by atomic layer deposition,” Chem. Mat. 15, 3507–3517 (2003).
[Crossref]

Engelhardt, M.

M. Engelhardtet al., “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[Crossref]

Flanagan, K.

K. Flanaganet al., “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE6688, 66880Y (2007).
[Crossref]

Franke, A. E.

A. E. Frankeet al., “Super-smooth x-ray reflection grating fabrication,” J. Vac. Sci. Technol. B 15, 2940–2945 (1997).
[Crossref]

Gaylord, T. K.

George, S. M.

J. W. Elam, D. Routkevitch, P. P. Mardilovich, and S. M. George, “Conformal coating on ultrahigh-aspect-ratio nanopores of anodic alumina by atomic layer deposition,” Chem. Mat. 15, 3507–3517 (2003).
[Crossref]

Grann, E. B.

Gullikson, E. M.

H. Takenaka, S. Ichimaru, and E. M. Gullikson, “EUV beam splitter for use in the wavelength region around 6 nm,” J. Electron Spectrosc. Relat. Phenom. 144, 1043–1045 (2005).
[Crossref]

D. Hambach, G. Schneider, and E. M. Gullikson, “Efficient high-order diffraction of extreme-ultraviolet light and soft x-rays by nanostructured volume gratings,” Opt. Lett. 26, 1200–1202 (2001).
[Crossref]

P. P. Naulleau, C. H. Cho, E. M. Gullikson, and J. Bokor, “Transmission phase gratings for EUV interferometry,” J. Synch. Rad. 7, 405–410 (2000).
[Crossref]

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,” Atomic Data and Nuclear Data Tables 54, 181–342 (1993).
[Crossref]

Hambach, D.

Heilmann, R. K.

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of ultrahigh aspect ratio freestanding gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 25, 2593–2597 (2007).
[Crossref]

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometer-scale science and engineering: Towards sub-nanometer accurate encoders,” Nanotechnology 15, S504–S511 (2004).
[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,” Atomic Data and Nuclear Data Tables 54, 181–342 (1993).
[Crossref]

Howells, M.

J. Kirz, C. Jacobsen, and M. Howells, “Soft x-ray microscopes and their biological applications,” Q. Rev. Biophys. 28, 33–130 (1995).
[Crossref] [PubMed]

Ichimaru, S.

H. Takenaka, S. Ichimaru, and E. M. Gullikson, “EUV beam splitter for use in the wavelength region around 6 nm,” J. Electron Spectrosc. Relat. Phenom. 144, 1043–1045 (2005).
[Crossref]

Ioffe, A. I.

A. I. Ioffe, V. S. Zabiyakin, and G. M. Drabkin, “Test of a diffraction grating neutron interferometer,” Phys. Lett. A 111, 373–375 (1985).
[Crossref]

Jacobsen, C.

J. Kirz, C. Jacobsen, and M. Howells, “Soft x-ray microscopes and their biological applications,” Q. Rev. Biophys. 28, 33–130 (1995).
[Crossref] [PubMed]

Kalinin, A.

A. Kalinin, O. Kornilov, W. Schöllkopf, and J. P. Toennies, “Observation of mixed fermionic-bosonic helium clusters by transmission grating diffraction,” Phys. Rev. Lett. 95, 113402 (2005).
[Crossref] [PubMed]

Kang, H. C.

H. C. Kanget al., “Nanometer linear focusing of hard x rays by a multilayer Laue lens,” Phys. Rev. Lett. 96, 127401 (2006).
[Crossref] [PubMed]

Keith, D. W.

D. W. Keith, M. L. Schattenburg, H. I. Smith, and D. E. Pritchard, “Diffraction of atoms by a transmission grating,” Phys. Rev. Lett. 61, 1580–1583 (1988).
[Crossref] [PubMed]

Kirz, J.

J. Kirz, C. Jacobsen, and M. Howells, “Soft x-ray microscopes and their biological applications,” Q. Rev. Biophys. 28, 33–130 (1995).
[Crossref] [PubMed]

Klein, A. G.

A. G. Klein and S. A. Werner, “Neutron Optics,” Rep. Prog. Phys. 46, 259–335 (1983).
[Crossref]

Konkola, P. T.

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometer-scale science and engineering: Towards sub-nanometer accurate encoders,” Nanotechnology 15, S504–S511 (2004).
[Crossref]

Kornilov, O.

A. Kalinin, O. Kornilov, W. Schöllkopf, and J. P. Toennies, “Observation of mixed fermionic-bosonic helium clusters by transmission grating diffraction,” Phys. Rev. Lett. 95, 113402 (2005).
[Crossref] [PubMed]

Kurokhtin, A. N.

Mardilovich, P. P.

J. W. Elam, D. Routkevitch, P. P. Mardilovich, and S. M. George, “Conformal coating on ultrahigh-aspect-ratio nanopores of anodic alumina by atomic layer deposition,” Chem. Mat. 15, 3507–3517 (2003).
[Crossref]

Marshall, H. L.

H. L. Marshall, “A soft x-ray polarimeter designed for broadband x-ray telescopes,” Proc. SPIE 6688, 66880Z (2007).
[Crossref]

McMorran, B.

A. D. Cronin and B. McMorran, “Electron interferometry with nanogratings,” Phys. Rev. A 74, 061602 (2006).
[Crossref]

Michette, A. G.

A. G. Michette and C. J. Buckley, X-ray Science and Technology (Institute of Physics Publishing, 1993).

Moharam, M. G.

Momose, A.

A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
[Crossref]

Naulleau, P. P.

P. P. Naulleau, C. H. Cho, E. M. Gullikson, and J. Bokor, “Transmission phase gratings for EUV interferometry,” J. Synch. Rad. 7, 405–410 (2000).
[Crossref]

Nöhammer, B.

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

Oberst, H.

H. Oberst, Y. Tashiro, K. Shimizu, and F. Shimizu, “Quantum reflection of He* on silicon,” Phys. Rev. A 71, 052901 (2005).
[Crossref]

Perreault, J. D.

J. D. Perreault and A. D. Cronin, “Using atomic diffraction of Na from material gratings to measure atom-surface interactions,” Phys. Rev. A 71, 053612 (2005).
[Crossref]

Pommet, D. A.

Popov, A. V.

Pritchard, D. E.

D. W. Keith, M. L. Schattenburg, H. I. Smith, and D. E. Pritchard, “Diffraction of atoms by a transmission grating,” Phys. Rev. Lett. 61, 1580–1583 (1988).
[Crossref] [PubMed]

Rasmussen, A.

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Figures (6)

Fig. 1.
Fig. 1.

Comparison of traditional gratings and CAT grating. (a) Schematic of a traditional phase-shifting transmission grating. Reflection gratings utilize diffraction orders on the same side of the grating as the incident beam, and transmission gratings utilize orders on the opposite side of the grating. (b) CAT grating schematic. The path length difference acquired between paths AA’ and BB’ (in green) determines the condition for the directions where diffraction peaks occur. The special case βm =α is shown. (All photons that exit the grating on the bottom are considered as transmitted, even if they underwent reflection on the grating bar sidewalls.) (c) Schematic of the variable-ratio beam splitter concept. Here rotation of the CAT grating changes the intensity ratio between 0th and -1st order.

Fig. 2.
Fig. 2.

Structure of the CAT grating sample. (a) Schematic of the grating frame (top) and of the monolithic Si CAT grating structure with the integrated support mesh (dark grey) and the CAT grating bars (white). Only the area above the 5µm open gap (light grey) contributes significantly to transmission. The open area fraction is ≈5µm/(40+30)µm≈7%. (b)–(c) Scanning electron micrographs of the tested CAT grating sample. (b) Top view of the 10µm thick silicon membrane, showing the 40µm long grating bars. Only the central 5µm are open all the way through the membrane. The blow-up shows the narrow grating bar width. (c) Bottom view of the same structure, showing the open gaps. (The blow-ups are not necessarily from the indicated spots.) (d) Schematic cross section of two adjacent grating bars, drawn to scale. The dashed arrows indicate the path of a photon reflecting off a sidewall.

Fig. 3.
Fig. 3.

Schematic of the diffraction efficiency measurements (see text for details).

Fig. 4.
Fig. 4.

Detector angle scan data. (a) Transmitted diffraction peaks at α=0° and λ=4.0 nm (unnormalized). (b) Logarithmic plot of the normalized intensity for the -2nd order transmitted peak at α=0° (filled circles) and at α=2.8° (open circles) at λ=27 nm. Blazing increases the peak intensity more than twenty-fold at this wavelength.

Fig. 5.
Fig. 5.

Comparison of normalized detector angle scan data and the simple model from Eqns. (2)–(4). The results for different wavelengths are shifted for clarity. The peaks under the blaze envelope are labeled according to their diffraction order. The dashed line at zero degrees defines the direction of the direct beam from the synchrotron. The model used k=2000, α=2.8°, ε=0.17°, p=574 nm, b/p=0.176, and a=473 nm, corresponding to the narrowest part of the grating slits.

Fig. 6.
Fig. 6.

Normalized diffraction efficiency. (a) 10–50 nm wavelengths. (b) 2.5–10 nm wavelengths. Data are shown with error bars. We fit diffraction peaks to Gaussians and obtain error bars from estimates of standard errors. Data points corresponding to a fixed diffraction order are connected by dashed or dotted lines to guide the eye. Theoretical RCWA results for each order are drawn with solid lines. The sum of diffracted intensities close to the blaze condition is shown at the measured wavelengths with black diamonds. The solid line above shows the predicted sum of the same orders at the same wavelengths. The wavelengths that fulfill the blazing condition are labeled according to diffraction order m above each graph. The dip in diffraction efficiency around λ=13 nm is due to the silicon L absorption edges.

Equations (4)

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m λ p = sin α sin β m ,
I g r a t ( λ , p , α , β , k ) = sin k g k sin g 2 ,
I s l i t ( λ , α , β , a , ε ) = sin f f 2 ,
I ( λ , p , α , β , k , a , ε , R ) = I g r a t I s l i t R ( α + ε , n 2 ( λ ) ) ( a p ) ,

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