Abstract

We report on measurements of the diffraction efficiency of 200-nm-period freestanding blazed transmission gratings for wavelengths in the 0.96 to 19.4nm range. These critical-angle transmission (CAT) gratings achieve highly efficient blazing over a broad band via total external reflection off the sidewalls of smooth, tens of nanometer thin ultrahigh aspect-ratio silicon grating bars and thus combine the advantages of blazed x-ray reflection gratings with those of more conventional x-ray transmission gratings. Prototype gratings with maximum depths of 3.2 and 6μm were investigated at two different blaze angles. In these initial CAT gratings the grating bars are monolithically connected to a cross support mesh that only leaves less than half of the grating area unobstructed. Because of our initial fabrication approach, the support mesh bars feature a strongly trapezoidal cross section that leads to varying CAT grating depths and partial absorption of diffracted orders. While theory predicts broadband absolute diffraction efficiencies as high as 60% for ideal CAT gratings without a support mesh, experimental results show efficiencies in the range of 50100% of theoretical predictions when taking the effects of the support mesh into account. Future minimization of the support mesh therefore promises broadband CAT grating absolute diffraction efficiencies of 50% or higher.

© 2011 Optical Society of America

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  1. Lord Rayleigh, “On the manufacture and theory of diffraction gratings,” Philos. Mag. , Series 4, 47, 193–205 (1874).
  2. R. Wood, “The echelette grating for the infra-red,” Philos. Mag. , Series 6, 20, 770–778 (1910).
  3. C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
    [CrossRef]
  4. C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
    [CrossRef]
  5. A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
    [CrossRef]
  6. J. F. Seely, L. I. Goray, B. Kjornrattanawanich, J. M. Laming, G. E. Holland, K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen, “Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region,” Appl. Opt. 45, 1680–1687 (2006).
    [CrossRef] [PubMed]
  7. D. L. Voronov, M. Ahn, E. H. Anderson, R. Cambie, C.-H. Chang, E. M. Gullikson, R. K. Heilmann, F. Salmassi, M. L. Schattenburg, T. Warwick, V. V. Yashchuk, L. Zipp, and H. A. Padmore, “High efficiency 5000 lines/mm multilayer-coated blazed grating for extreme ultraviolet wavelengths,” Opt. Lett. 35, 2615–2617 (2010).
    [CrossRef] [PubMed]
  8. C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
    [CrossRef]
  9. R. K. Heilmann, M. Ahn, E. M. Gullikson, and M. L. Schattenburg, “Blazed high-efficiency x-ray diffraction via transmission through arrays of nanometer-scale mirrors,” Opt. Express 16, 8658–8669 (2008).
    [CrossRef] [PubMed]
  10. See for example http://ixo.gsfc.nasa.gov/.
  11. K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
    [CrossRef]
  12. R. K. Heilmann, M. Ahn, and M. L. Schattenburg, “Fabrication and performance of blazed transmission gratings for x-ray astronomy,” Proc. SPIE 7011, 701106 (2008).
    [CrossRef]
  13. R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
    [CrossRef]
  14. R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
    [CrossRef]
  15. M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of 200 nm-period blazed transmission gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 26, 2179–2182(2008).
    [CrossRef]
  16. M. Ahn, “Fabrication of critical-angle transmission gratings for high efficiency x-ray spectroscopy,” Ph.D. thesis (Department of Mechanical Engineering, Massachusetts Institute of Technology, 2009).
  17. 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]
  18. C. G. Chen, P. T. Konkola, R. K. Heilmann, G. S. Pati, and M. L. Schattenburg, “Image metrology and system controls for scanning beam interference lithography,” J. Vac. Sci. Technol. B 19, 2335–2341 (2001).
    [CrossRef]
  19. 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]
  20. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1998).
  21. The term a/p in Eq. (4) of Ref.  and Eq. (2) of Ref.  should have been replaced with (a/p)2.
  22. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings—enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
    [CrossRef]
  23. 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]
  24. See for example J. E. Davis, H. L. Marshall, D. Dewey, and M. L. Schattenburg, “Analysis and modeling of anomalous scattering in the AXAF HETGS,” Proc. SPIE 3444, 76 (1998).
    [CrossRef]
  25. P. Mukherjee, A. Bruccoleri, R. K. Heilmann, M. L. Schattenburg, A. F. Kaplan, and L. J. Guo, “Plasma etch fabrication of 60∶1 aspect ratio silicon nanogratings on 200 nm pitch,” J. Vac. Sci. Technol. B 28, C6P70 (2010).
    [CrossRef]

2010

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

P. Mukherjee, A. Bruccoleri, R. K. Heilmann, M. L. Schattenburg, A. F. Kaplan, and L. J. Guo, “Plasma etch fabrication of 60∶1 aspect ratio silicon nanogratings on 200 nm pitch,” J. Vac. Sci. Technol. B 28, C6P70 (2010).
[CrossRef]

D. L. Voronov, M. Ahn, E. H. Anderson, R. Cambie, C.-H. Chang, E. M. Gullikson, R. K. Heilmann, F. Salmassi, M. L. Schattenburg, T. Warwick, V. V. Yashchuk, L. Zipp, and H. A. Padmore, “High efficiency 5000 lines/mm multilayer-coated blazed grating for extreme ultraviolet wavelengths,” Opt. Lett. 35, 2615–2617 (2010).
[CrossRef] [PubMed]

2009

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

2008

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of 200 nm-period blazed transmission gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 26, 2179–2182(2008).
[CrossRef]

R. K. Heilmann, M. Ahn, and M. L. Schattenburg, “Fabrication and performance of blazed transmission gratings for x-ray astronomy,” Proc. SPIE 7011, 701106 (2008).
[CrossRef]

R. K. Heilmann, M. Ahn, E. M. Gullikson, and M. L. Schattenburg, “Blazed high-efficiency x-ray diffraction via transmission through arrays of nanometer-scale mirrors,” Opt. Express 16, 8658–8669 (2008).
[CrossRef] [PubMed]

2007

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

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]

2006

2005

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

2004

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
[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]

2003

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[CrossRef]

2001

C. G. Chen, P. T. Konkola, R. K. Heilmann, G. S. Pati, and M. L. Schattenburg, “Image metrology and system controls for scanning beam interference lithography,” J. Vac. Sci. Technol. B 19, 2335–2341 (2001).
[CrossRef]

1998

See for example J. E. Davis, H. L. Marshall, D. Dewey, and M. L. Schattenburg, “Analysis and modeling of anomalous scattering in the AXAF HETGS,” Proc. SPIE 3444, 76 (1998).
[CrossRef]

1995

1993

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]

1910

R. Wood, “The echelette grating for the infra-red,” Philos. Mag. , Series 6, 20, 770–778 (1910).

1874

Lord Rayleigh, “On the manufacture and theory of diffraction gratings,” Philos. Mag. , Series 4, 47, 193–205 (1874).

Ahn, M.

D. L. Voronov, M. Ahn, E. H. Anderson, R. Cambie, C.-H. Chang, E. M. Gullikson, R. K. Heilmann, F. Salmassi, M. L. Schattenburg, T. Warwick, V. V. Yashchuk, L. Zipp, and H. A. Padmore, “High efficiency 5000 lines/mm multilayer-coated blazed grating for extreme ultraviolet wavelengths,” Opt. Lett. 35, 2615–2617 (2010).
[CrossRef] [PubMed]

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of 200 nm-period blazed transmission gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 26, 2179–2182(2008).
[CrossRef]

R. K. Heilmann, M. Ahn, and M. L. Schattenburg, “Fabrication and performance of blazed transmission gratings for x-ray astronomy,” Proc. SPIE 7011, 701106 (2008).
[CrossRef]

R. K. Heilmann, M. Ahn, E. M. Gullikson, and M. L. Schattenburg, “Blazed high-efficiency x-ray diffraction via transmission through arrays of nanometer-scale mirrors,” Opt. Express 16, 8658–8669 (2008).
[CrossRef] [PubMed]

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]

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

M. Ahn, “Fabrication of critical-angle transmission gratings for high efficiency x-ray spectroscopy,” Ph.D. thesis (Department of Mechanical Engineering, Massachusetts Institute of Technology, 2009).

Akilian, M.

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

Anderson, E. H.

Aquila, A.

A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
[CrossRef]

Bailey, T. C.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[CrossRef]

Bautz, M. W.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

Bookbinder, J.

A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
[CrossRef]

Born, M.

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

Bruccoleri, A.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

P. Mukherjee, A. Bruccoleri, R. K. Heilmann, M. L. Schattenburg, A. F. Kaplan, and L. J. Guo, “Plasma etch fabrication of 60∶1 aspect ratio silicon nanogratings on 200 nm pitch,” J. Vac. Sci. Technol. B 28, C6P70 (2010).
[CrossRef]

Cambie, R.

Canizares, C. R.

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

Carter, J.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[CrossRef]

Chang, C.-H.

D. L. Voronov, M. Ahn, E. H. Anderson, R. Cambie, C.-H. Chang, E. M. Gullikson, R. K. Heilmann, F. Salmassi, M. L. Schattenburg, T. Warwick, V. V. Yashchuk, L. Zipp, and H. A. Padmore, “High efficiency 5000 lines/mm multilayer-coated blazed grating for extreme ultraviolet wavelengths,” Opt. Lett. 35, 2615–2617 (2010).
[CrossRef] [PubMed]

J. F. Seely, L. I. Goray, B. Kjornrattanawanich, J. M. Laming, G. E. Holland, K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen, “Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region,” Appl. Opt. 45, 1680–1687 (2006).
[CrossRef] [PubMed]

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
[CrossRef]

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[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]

C. G. Chen, P. T. Konkola, R. K. Heilmann, G. S. Pati, and M. L. Schattenburg, “Image metrology and system controls for scanning beam interference lithography,” J. Vac. Sci. Technol. B 19, 2335–2341 (2001).
[CrossRef]

Davis, J.

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[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]

Davis, J. E.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

See for example J. E. Davis, H. L. Marshall, D. Dewey, and M. L. Schattenburg, “Analysis and modeling of anomalous scattering in the AXAF HETGS,” Proc. SPIE 3444, 76 (1998).
[CrossRef]

Dewey, D.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

See for example J. E. Davis, H. L. Marshall, D. Dewey, and M. L. Schattenburg, “Analysis and modeling of anomalous scattering in the AXAF HETGS,” Proc. SPIE 3444, 76 (1998).
[CrossRef]

Ekerdt, J. G.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[CrossRef]

Flanagan, K.

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

Flanagan, K. A.

J. F. Seely, L. I. Goray, B. Kjornrattanawanich, J. M. Laming, G. E. Holland, K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen, “Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region,” Appl. Opt. 45, 1680–1687 (2006).
[CrossRef] [PubMed]

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

Fleming, R. C.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[CrossRef]

Foster, R.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

Frankel, R. D.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[CrossRef]

Galton, E. B.

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

Gaylord, T. K.

Goray, L. I.

J. F. Seely, L. I. Goray, B. Kjornrattanawanich, J. M. Laming, G. E. Holland, K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen, “Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region,” Appl. Opt. 45, 1680–1687 (2006).
[CrossRef] [PubMed]

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

Grann, E. B.

Gullikson, E.

A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
[CrossRef]

Gullikson, E. M.

Guo, L. J.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

P. Mukherjee, A. Bruccoleri, R. K. Heilmann, M. L. Schattenburg, A. F. Kaplan, and L. J. Guo, “Plasma etch fabrication of 60∶1 aspect ratio silicon nanogratings on 200 nm pitch,” J. Vac. Sci. Technol. B 28, C6P70 (2010).
[CrossRef]

Heilmann, R. K.

P. Mukherjee, A. Bruccoleri, R. K. Heilmann, M. L. Schattenburg, A. F. Kaplan, and L. J. Guo, “Plasma etch fabrication of 60∶1 aspect ratio silicon nanogratings on 200 nm pitch,” J. Vac. Sci. Technol. B 28, C6P70 (2010).
[CrossRef]

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

D. L. Voronov, M. Ahn, E. H. Anderson, R. Cambie, C.-H. Chang, E. M. Gullikson, R. K. Heilmann, F. Salmassi, M. L. Schattenburg, T. Warwick, V. V. Yashchuk, L. Zipp, and H. A. Padmore, “High efficiency 5000 lines/mm multilayer-coated blazed grating for extreme ultraviolet wavelengths,” Opt. Lett. 35, 2615–2617 (2010).
[CrossRef] [PubMed]

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of 200 nm-period blazed transmission gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 26, 2179–2182(2008).
[CrossRef]

R. K. Heilmann, M. Ahn, and M. L. Schattenburg, “Fabrication and performance of blazed transmission gratings for x-ray astronomy,” Proc. SPIE 7011, 701106 (2008).
[CrossRef]

R. K. Heilmann, M. Ahn, E. M. Gullikson, and M. L. Schattenburg, “Blazed high-efficiency x-ray diffraction via transmission through arrays of nanometer-scale mirrors,” Opt. Express 16, 8658–8669 (2008).
[CrossRef] [PubMed]

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]

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

J. F. Seely, L. I. Goray, B. Kjornrattanawanich, J. M. Laming, G. E. Holland, K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen, “Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region,” Appl. Opt. 45, 1680–1687 (2006).
[CrossRef] [PubMed]

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[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]

A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
[CrossRef]

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[CrossRef]

C. G. Chen, P. T. Konkola, R. K. Heilmann, G. S. Pati, and M. L. Schattenburg, “Image metrology and system controls for scanning beam interference lithography,” J. Vac. Sci. Technol. B 19, 2335–2341 (2001).
[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]

Holland, G. E.

Huenemoerder, D.

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

Huenemoerder, D. P.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

Ishibashi, K.

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

Kahn, S. M.

A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
[CrossRef]

Kaplan, A. F.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

P. Mukherjee, A. Bruccoleri, R. K. Heilmann, M. L. Schattenburg, A. F. Kaplan, and L. J. Guo, “Plasma etch fabrication of 60∶1 aspect ratio silicon nanogratings on 200 nm pitch,” J. Vac. Sci. Technol. B 28, C6P70 (2010).
[CrossRef]

Kjornrattanawanich, B.

J. F. Seely, L. I. Goray, B. Kjornrattanawanich, J. M. Laming, G. E. Holland, K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen, “Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region,” Appl. Opt. 45, 1680–1687 (2006).
[CrossRef] [PubMed]

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[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]

C. G. Chen, P. T. Konkola, R. K. Heilmann, G. S. Pati, and M. L. Schattenburg, “Image metrology and system controls for scanning beam interference lithography,” J. Vac. Sci. Technol. B 19, 2335–2341 (2001).
[CrossRef]

Laming, J. M.

J. F. Seely, L. I. Goray, B. Kjornrattanawanich, J. M. Laming, G. E. Holland, K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen, “Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region,” Appl. Opt. 45, 1680–1687 (2006).
[CrossRef] [PubMed]

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

Lapsa, A.

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

Levine, A.

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

Li, M.

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

Markert, T. H.

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

Marshall, H.

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

Marshall, H. L.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

See for example J. E. Davis, H. L. Marshall, D. Dewey, and M. L. Schattenburg, “Analysis and modeling of anomalous scattering in the AXAF HETGS,” Proc. SPIE 3444, 76 (1998).
[CrossRef]

McGuirk, M.

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

Moharam, M. G.

Montoya, J. C.

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

Mukherjee, P.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

P. Mukherjee, A. Bruccoleri, R. K. Heilmann, M. L. Schattenburg, A. F. Kaplan, and L. J. Guo, “Plasma etch fabrication of 60∶1 aspect ratio silicon nanogratings on 200 nm pitch,” J. Vac. Sci. Technol. B 28, C6P70 (2010).
[CrossRef]

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

Murphy, E.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[CrossRef]

Padmore, H. A.

Paerels, F.

A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
[CrossRef]

Pati, G. S.

C. G. Chen, P. T. Konkola, R. K. Heilmann, G. S. Pati, and M. L. Schattenburg, “Image metrology and system controls for scanning beam interference lithography,” J. Vac. Sci. Technol. B 19, 2335–2341 (2001).
[CrossRef]

Pommet, D. A.

Prigozhin, G.

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

Rasmussen, A.

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
[CrossRef]

Rasmussen, A. P.

J. F. Seely, L. I. Goray, B. Kjornrattanawanich, J. M. Laming, G. E. Holland, K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen, “Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region,” Appl. Opt. 45, 1680–1687 (2006).
[CrossRef] [PubMed]

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, “On the manufacture and theory of diffraction gratings,” Philos. Mag. , Series 4, 47, 193–205 (1874).

Ricker, G.

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

Robinson, D.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

Salmassi, F.

Schattenburg, M. L.

D. L. Voronov, M. Ahn, E. H. Anderson, R. Cambie, C.-H. Chang, E. M. Gullikson, R. K. Heilmann, F. Salmassi, M. L. Schattenburg, T. Warwick, V. V. Yashchuk, L. Zipp, and H. A. Padmore, “High efficiency 5000 lines/mm multilayer-coated blazed grating for extreme ultraviolet wavelengths,” Opt. Lett. 35, 2615–2617 (2010).
[CrossRef] [PubMed]

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

P. Mukherjee, A. Bruccoleri, R. K. Heilmann, M. L. Schattenburg, A. F. Kaplan, and L. J. Guo, “Plasma etch fabrication of 60∶1 aspect ratio silicon nanogratings on 200 nm pitch,” J. Vac. Sci. Technol. B 28, C6P70 (2010).
[CrossRef]

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of 200 nm-period blazed transmission gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 26, 2179–2182(2008).
[CrossRef]

R. K. Heilmann, M. Ahn, and M. L. Schattenburg, “Fabrication and performance of blazed transmission gratings for x-ray astronomy,” Proc. SPIE 7011, 701106 (2008).
[CrossRef]

R. K. Heilmann, M. Ahn, E. M. Gullikson, and M. L. Schattenburg, “Blazed high-efficiency x-ray diffraction via transmission through arrays of nanometer-scale mirrors,” Opt. Express 16, 8658–8669 (2008).
[CrossRef] [PubMed]

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]

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

J. F. Seely, L. I. Goray, B. Kjornrattanawanich, J. M. Laming, G. E. Holland, K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen, “Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region,” Appl. Opt. 45, 1680–1687 (2006).
[CrossRef] [PubMed]

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
[CrossRef]

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[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]

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[CrossRef]

C. G. Chen, P. T. Konkola, R. K. Heilmann, G. S. Pati, and M. L. Schattenburg, “Image metrology and system controls for scanning beam interference lithography,” J. Vac. Sci. Technol. B 19, 2335–2341 (2001).
[CrossRef]

See for example J. E. Davis, H. L. Marshall, D. Dewey, and M. L. Schattenburg, “Analysis and modeling of anomalous scattering in the AXAF HETGS,” Proc. SPIE 3444, 76 (1998).
[CrossRef]

Schulz, N.

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

Schulz, N. S.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

Schweikart, R. B.

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

Seely, J. F.

J. F. Seely, L. I. Goray, B. Kjornrattanawanich, J. M. Laming, G. E. Holland, K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen, “Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region,” Appl. Opt. 45, 1680–1687 (2006).
[CrossRef] [PubMed]

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

Smith, H. I.

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

Smith, M.

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

Voisin, R.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[CrossRef]

Voronov, D. L.

Warwick, T.

Wise, M.

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

Wolf, E.

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

Wood, R.

R. Wood, “The echelette grating for the infra-red,” Philos. Mag. , Series 6, 20, 770–778 (1910).

Yashchuk, V. V.

Zhao, Y.

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

Zipp, L.

Appl. Opt.

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]

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

P. Mukherjee, A. Bruccoleri, R. K. Heilmann, M. L. Schattenburg, A. F. Kaplan, and L. J. Guo, “Plasma etch fabrication of 60∶1 aspect ratio silicon nanogratings on 200 nm pitch,” J. Vac. Sci. Technol. B 28, C6P70 (2010).
[CrossRef]

M. Ahn, R. K. Heilmann, and M. L. Schattenburg, “Fabrication of 200 nm-period blazed transmission gratings on silicon-on-insulator wafers,” J. Vac. Sci. Technol. B 26, 2179–2182(2008).
[CrossRef]

C. G. Chen, P. T. Konkola, R. K. Heilmann, G. S. Pati, and M. L. Schattenburg, “Image metrology and system controls for scanning beam interference lithography,” J. Vac. Sci. Technol. B 19, 2335–2341 (2001).
[CrossRef]

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]

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of saw-tooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755–2759 (2003).
[CrossRef]

C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, R. K. Heilmann, M. L. Schattenburg, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B 22, 3260–3264 (2004).
[CrossRef]

Nanotechnology

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]

Opt. Express

Opt. Lett.

Philos. Mag.

Lord Rayleigh, “On the manufacture and theory of diffraction gratings,” Philos. Mag. , Series 4, 47, 193–205 (1874).

R. Wood, “The echelette grating for the infra-red,” Philos. Mag. , Series 6, 20, 770–778 (1910).

Proc. SPIE

See for example J. E. Davis, H. L. Marshall, D. Dewey, and M. L. Schattenburg, “Analysis and modeling of anomalous scattering in the AXAF HETGS,” Proc. SPIE 3444, 76 (1998).
[CrossRef]

K. Flanagan, M. Ahn, J. Davis, R. K. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. L. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for x-ray astronomy using a blazed transmission grating,” Proc. SPIE 6688, 66880Y(2007).
[CrossRef]

R. K. Heilmann, M. Ahn, and M. L. Schattenburg, “Fabrication and performance of blazed transmission gratings for x-ray astronomy,” Proc. SPIE 7011, 701106 (2008).
[CrossRef]

R. K. Heilmann, M. Ahn, M. W. Bautz, R. Foster, D. P. Huenemoerder, H. L. Marshall, P. Mukherjee, M. L. Schattenburg, N. S. Schulz, and M. Smith, “Development of a critical-angle transmission grating spectrometer for the International X-Ray Observatory,” Proc. SPIE 7437, 74370G(2009).
[CrossRef]

R. K. Heilmann, J. E. Davis, D. Dewey, M. W. Bautz, R. Foster, A. Bruccoleri, P. Mukherjee, D. Robinson, D. P. Huenemoerder, H. L. Marshall, M. L. Schattenburg, N. S. Schulz, L. J. Guo, A. F. Kaplan, and R. B. Schweikart, “Critical-angle transmission grating spectrometer for high-resolution soft x-ray spectroscopy on the International X-Ray Observatory,” Proc. SPIE 7732, 77321J (2010).
[CrossRef]

A. Rasmussen, A. Aquila, J. Bookbinder, C.-H. Chang, E. Gullikson, R. K. Heilmann, S. M. Kahn, F. Paerels, and M. L. Schattenburg, “Grating arrays for high-throughput soft x-ray spectrometers,” Proc. SPIE 5168, 248 (2004).
[CrossRef]

Publ. Astron. Soc. Pac.

C. R. Canizares, J. E. Davis, D. Dewey, K. A. Flanagan, E. B. Galton, D. P. Huenemoerder, K. Ishibashi, T. H. Markert, H. L. Marshall, M. McGuirk, M. L. Schattenburg, N. S. Schulz, H. I. Smith, and M. Wise, “The Chandra high-energy transmission grating: design, fabrication, ground calibration, and 5 years in flight,” Publ. Astron. Soc. Pac. 117, 1144–1171(2005).
[CrossRef]

Other

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

The term a/p in Eq. (4) of Ref.  and Eq. (2) of Ref.  should have been replaced with (a/p)2.

See for example http://ixo.gsfc.nasa.gov/.

M. Ahn, “Fabrication of critical-angle transmission gratings for high efficiency x-ray spectroscopy,” Ph.D. thesis (Department of Mechanical Engineering, Massachusetts Institute of Technology, 2009).

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Figures (12)

Fig. 1
Fig. 1

Schematic cross section through a CAT grating. The mth diffraction order occurs at an angle β m where the path length difference between AA and BB is m λ . Shown is the case where β m coincides with the direction of specular reflection from the grating bar sidewalls ( β m = α ), i.e., blazing in the mth order.

Fig. 2
Fig. 2

(a) Top view SEM images from sample S6 at increasing magnifications from left to right, showing the support grid consisting of support mesh SM2 and support mesh SM1, with the CAT grating bars suspended from SM1 bars. Only in the leftmost image can the gap at the bottom of the SM1 mesh be seen from above. (b) Schematic of a sample, viewed from the handle layer side (not to scale). (c) SEM of a cleaved cross section parallel to mesh SM1, showing the high aspect ratio and the low duty cycle of the CAT grating bars. X rays enter from the top.

Fig. 3
Fig. 3

Schematic of CAT grating bars with support mesh SM1 (not to scale). Top, perspective view. Support mesh bars are dark gray and CAT grating bars are light gray. Bottom, cross section through the plane of a CAT grating bar. In our model we divide the support mesh period p SM 1 into N slabs of width Δ y each. Grating depth is defined to be zero on top of the mesas and d at the bottom of the gap between support mesh bars.

Fig. 4
Fig. 4

Transmission as a function of wavelength through a bulk silicon film of thickness 6 μm (solid line) and 3.2 μm (dashed line), respectively. Curves are based on data from [23].

Fig. 5
Fig. 5

Sample scans in the plane normal to the x-ray beam. Solid lines are scans perpendicular to support mesh SM2, dashed lines parallel to SM2. (a) S4 at λ = 3.5 nm , α = 2.6 ° , blazed in 5 th order. (b) S6 at λ = 3.0 nm , α = 1.18 ° , blazed in 3 rd order.

Fig. 6
Fig. 6

Example normalized detector scans for sample S4 at α = 2.6 ° . Circles represent experimental data, the dashed line is the blaze envelope, the solid line represents the simple model, and bar heights show diffraction peak intensities predicted via RCWA (coherent model). Data and theory are shifted vertically for clarity for the different wavelengths.

Fig. 7
Fig. 7

Example normalized detector scans for sample S6 at α = 1.18 ° . Legend is the same as in Fig. 6.

Fig. 8
Fig. 8

Absolute diffraction peak intensity for sample S4 as a function of wavelength for orders 0, 1 , and 6 through 11 . Circles are measured data, and solid lines are predictions from the coherent model. Dashed lines connect data points for a given diffraction order and serve as guides for the eye. Vertical bars show range of predicted efficiencies taking uncertainties in SEM-derived parameters into account.

Fig. 9
Fig. 9

Absolute diffraction peak intensity for sample S4 as a function of wavelength for orders 0 through 5 (continued from Fig. 8 for longer wavelengths). Circles are measured data, and solid lines are predictions from the coherent model. Dashed lines connect data points for a given diffraction order and serve as guides for the eye. Vertical bars show range of predicted efficiencies taking uncertainties in SEM-derived parameters into account. The squares show predictions for 1 st order from the incoherent model at four wavelengths. The jump in zeroth order efficiency around 13 nm is due to the silicon L absorption edges.

Fig. 10
Fig. 10

Absolute diffraction peak intensity for sample S6 as a function of wavelength for orders 0, 1 , and 3 through 10 . Circles are measured data, and solid lines are predictions from the coherent model. Dashed lines connect data points for a given diffraction order and serve as guides for the eye. Vertical bars show range of predicted efficiencies taking uncertainties in SEM-derived parameters into account.

Fig. 11
Fig. 11

Absolute diffraction peak intensity for sample S6 as a function of wavelength for orders 0 through 3 (continued from Fig. 10 for longer wavelengths). Circles are measured data, and solid lines are predictions from the coherent model. Dashed lines connect data points for a given diffraction order and serve as guides for the eye. Vertical bars show range of predicted efficiencies taking uncertainties in SEM-derived parameters into account.

Fig. 12
Fig. 12

Predicted absolute diffraction efficiencies (solid lines, orders 0 through 10 ) according to the incoherent model for a CAT grating with a 1D support mesh and the following parameters: p = 200 nm , α = 1.5 ° , d = 6186 nm , p SM 1 = 5 μm , s = 100 nm , g = 4.5 μm , and d.c. = 0.19 . The dashed line shows the sum of diffraction efficiencies for orders 1 through 10 .

Tables (1)

Tables Icon

Table 1 Geometrical Parameters for Samples S4 and S6

Equations (7)

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

m λ p = sin α sin β ( λ ) m ,
I ( λ , p , α , β , k , a , ϵ , R ) = I grat I slit R ( α + ϵ , n ( λ ) ) ( a / p ) 2 .
I grat ( λ , p , α , β , k ) = | sin k g k sin g | 2 ,
I slit ( λ , α , β , a , ϵ ) = | sin f f | 2 ,
I ( m , k ) = 1 N 2 | j = 1 N A j ( m ) exp [ i ( Φ j ( m ) + 2 π k j Δ y p SM 1 ) ] | 2 .
I ( m ) = k = 0 ± I ( m , k ) = 1 N 2 k = 0 ± l = 1 N q = 1 N A l ( m ) A q * ( m ) exp [ i ( Φ l ( m ) Φ q ( m ) + 2 π k ( l q ) Δ y p SM 1 ) ] .
I ( m ) = 1 N j = 1 N A j ( m ) A j * ( m ) = 1 N j = 1 N | A j ( m ) e i Φ j ( m ) | 2 .

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