Abstract

Laminar-type gratings as soft x-ray beam splitters for interferometry are presented. Gold-coated grating beam splitters with 1000 lines/mm are designed for grazing incidence operation at 13.9nm. They are routinely fabricated using electron beam lithography and ion etching techniques. The laminar grating is measured to have almost equal absolute efficiencies of about 20% in the zeroth and 1st orders, which enables a fringe visibility up to 0.99 in the interferometer. The discrepancy of the grating profiles between the optimized theoretical and the experimental results is analyzed according to the comparison of the optimized simulation results and the measurement realization of the grating efficiencies. By a precise control of the grating profile, the grating efficiency in the 1st order and the fringe visibility could be improved to 25% and 1, respectively.

© 2010 Optical Society of America

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  1. J. Filevich, K. Kanizay, M. C. Marconi, J. L. A. Chilla, and J. J. Rocca, “Dense plasma diagnostics with an amplitude-division soft-x-ray laser interferometer based on diffraction gratings,” Opt. Lett. 25, 356–358 (2000).
    [CrossRef]
  2. R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
    [CrossRef] [PubMed]
  3. J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V. N. Shlyaptsev, “Picosecond-resolution soft-x-ray laser plasma interferometry,” Appl. Opt. 43, 3938–3946 (2004).
    [CrossRef] [PubMed]
  4. E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi, and J. J. Rocca, “Soft x-ray laser diagnostics of exploding aluminum wire plasmas,” Appl. Phys. B 78, 933–937 (2004).
    [CrossRef]
  5. J. Filevich, J. Grava, M. Purvis, M. C. Marconi, and J. J. Rocca, “Prediction and observation of tin and silver plasmas with index of refraction greater than one in the soft x-ray range,” Phys. Rev. E 74, 016404 (2006).
    [CrossRef]
  6. M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
    [CrossRef]
  7. J. Grava, M. A. Purvis, J. Filevich, M. C. Marconi, J. J. Rocca, J. Dunn, S. J. Moon, and V. N. Shlyaptsev, “Dynamics of a dense laboratory plasma jet investigated using soft x-ray laser interferometry,” Phys. Rev. E 78, 016403 (2008).
    [CrossRef]
  8. Y. Liu, X. Tan, Z. Liu, X. Xu, Y. Hong, and S. Fu, “Soft x-ray holographic grating beam splitter including a double frequency grating for interferometer pre-alignment,” Opt. Express 16, 14761–14770 (2008).
    [CrossRef] [PubMed]
  9. U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
    [CrossRef]
  10. Y. Kitajima, K. Amemiya, Y. Yonamoto, T. Ohta, T. Kikuchi, T. Kosuge, A. Toyoshimaa, and K. Itoa, “A soft x-ray (80–1500eV) grazing incidence monochromator with varied-line-spacing plane gratings at PF-BL-11A,” J. Synchrotron Radiat. 5, 729–731(1998).
    [CrossRef]
  11. S. Ishikawa, T. Imazono, T. Hatano, M. Yanagihara, and M. Watanabe, “Efficiency and polarization performance of a multilayer-coated laminar grating in the 6.5–6.9nm wavelength region,” Appl. Opt. 41, 763–767 (2002).
    [CrossRef] [PubMed]
  12. M. Ishino, P. A. Heimann, H. Sasai, M. Hatayama, H. Takenaka, K. Sano, E. M. Gullikson, and M. Koike, “Development of multilayer laminar-type diffraction gratings to achieve high diffraction efficiencies in the 1–8keV energy region,” Appl. Opt. 45, 6741–6745 (2006).
    [CrossRef] [PubMed]
  13. M. P. Kowalski, R. G. Cruddace, J. F. Seely, and J. C. Rife, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, and D. Menke, W. R. Hunter, “Efficiency of a multilayer-coated, ion-etched laminar holographic grating in the 14.5–16.0nm wavelength region,” Opt. Lett. 22, 834–836 (1997).
    [CrossRef] [PubMed]
  14. W. R. Hunter, M. P. Kowalski, J. C. Rife, and R. G. Cruddace, “Investigation of the properties of an ion-etched plane laminar holographic grating,” Appl. Opt. 40, 6157–6165 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
  16. S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
    [CrossRef]
  17. L. I. Goray, “Grazing incidence off-plane lamellar grating as a beam splitter for a 1Å free electron laser,” J. Synch. Investig. 2, 796–800 (2008).
    [CrossRef]
  18. X. Tan, Y. Liu, X. Xu, Y. Hong, and S. Fu, “13.9nm laminar grating as beam splitter,” Opt. Precision Eng. 17, 33–37 (2009) (in Chinese).
  19. If we set the normal of grating G2 parallel to that of grating G1, we would obtain another configuration of the grating interferometer, as shown in Fig. . The main difference between the two configurations is that, in the second configuration, the zeroth order of G1 and the −1st order of G2 are used as one arm of the interferometer. The other arm of the interferometer is constructed by the −1st order of G1 and the zeroth order of G2. Accordingly, the throughput of the system changes to η0η−1 if G1 and G2 have the same profile. This configuration would be favorable with respect to the fringe visibility because fringe visibility V will approach 1, even if the efficiencies of the zeroth and −1st orders are different. Considering the spatial arrangement of the grating interferometer, we restrict use to the first configuration in this paper.
  20. E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1998).
  21. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  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=50–30000eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
    [CrossRef]
  24. http://henke.lbl.gov/optical_constants/layer2.html (1995–2008).

2009 (1)

X. Tan, Y. Liu, X. Xu, Y. Hong, and S. Fu, “13.9nm laminar grating as beam splitter,” Opt. Precision Eng. 17, 33–37 (2009) (in Chinese).

2008 (3)

J. Grava, M. A. Purvis, J. Filevich, M. C. Marconi, J. J. Rocca, J. Dunn, S. J. Moon, and V. N. Shlyaptsev, “Dynamics of a dense laboratory plasma jet investigated using soft x-ray laser interferometry,” Phys. Rev. E 78, 016403 (2008).
[CrossRef]

Y. Liu, X. Tan, Z. Liu, X. Xu, Y. Hong, and S. Fu, “Soft x-ray holographic grating beam splitter including a double frequency grating for interferometer pre-alignment,” Opt. Express 16, 14761–14770 (2008).
[CrossRef] [PubMed]

L. I. Goray, “Grazing incidence off-plane lamellar grating as a beam splitter for a 1Å free electron laser,” J. Synch. Investig. 2, 796–800 (2008).
[CrossRef]

2007 (1)

M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
[CrossRef]

2006 (2)

J. Filevich, J. Grava, M. Purvis, M. C. Marconi, and J. J. Rocca, “Prediction and observation of tin and silver plasmas with index of refraction greater than one in the soft x-ray range,” Phys. Rev. E 74, 016404 (2006).
[CrossRef]

M. Ishino, P. A. Heimann, H. Sasai, M. Hatayama, H. Takenaka, K. Sano, E. M. Gullikson, and M. Koike, “Development of multilayer laminar-type diffraction gratings to achieve high diffraction efficiencies in the 1–8keV energy region,” Appl. Opt. 45, 6741–6745 (2006).
[CrossRef] [PubMed]

2005 (1)

S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
[CrossRef]

2004 (3)

2002 (2)

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

S. Ishikawa, T. Imazono, T. Hatano, M. Yanagihara, and M. Watanabe, “Efficiency and polarization performance of a multilayer-coated laminar grating in the 6.5–6.9nm wavelength region,” Appl. Opt. 41, 763–767 (2002).
[CrossRef] [PubMed]

2001 (1)

2000 (1)

1998 (2)

Y. Kitajima, K. Amemiya, Y. Yonamoto, T. Ohta, T. Kikuchi, T. Kosuge, A. Toyoshimaa, and K. Itoa, “A soft x-ray (80–1500eV) grazing incidence monochromator with varied-line-spacing plane gratings at PF-BL-11A,” J. Synchrotron Radiat. 5, 729–731(1998).
[CrossRef]

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1998).

1997 (1)

1996 (1)

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

1995 (2)

1993 (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Amemiya, K.

Y. Kitajima, K. Amemiya, Y. Yonamoto, T. Ohta, T. Kikuchi, T. Kosuge, A. Toyoshimaa, and K. Itoa, “A soft x-ray (80–1500eV) grazing incidence monochromator with varied-line-spacing plane gratings at PF-BL-11A,” J. Synchrotron Radiat. 5, 729–731(1998).
[CrossRef]

Barbee, T. W.

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

Brown, C. M.

Chilla, J. L. A.

Cruddace, R. G.

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Donguy, S.

Dunn, J.

J. Grava, M. A. Purvis, J. Filevich, M. C. Marconi, J. J. Rocca, J. Dunn, S. J. Moon, and V. N. Shlyaptsev, “Dynamics of a dense laboratory plasma jet investigated using soft x-ray laser interferometry,” Phys. Rev. E 78, 016403 (2008).
[CrossRef]

M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
[CrossRef]

J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V. N. Shlyaptsev, “Picosecond-resolution soft-x-ray laser plasma interferometry,” Appl. Opt. 43, 3938–3946 (2004).
[CrossRef] [PubMed]

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

Dvorak, J.

S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
[CrossRef]

Filevich, J.

J. Grava, M. A. Purvis, J. Filevich, M. C. Marconi, J. J. Rocca, J. Dunn, S. J. Moon, and V. N. Shlyaptsev, “Dynamics of a dense laboratory plasma jet investigated using soft x-ray laser interferometry,” Phys. Rev. E 78, 016403 (2008).
[CrossRef]

M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
[CrossRef]

J. Filevich, J. Grava, M. Purvis, M. C. Marconi, and J. J. Rocca, “Prediction and observation of tin and silver plasmas with index of refraction greater than one in the soft x-ray range,” Phys. Rev. E 74, 016404 (2006).
[CrossRef]

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi, and J. J. Rocca, “Soft x-ray laser diagnostics of exploding aluminum wire plasmas,” Appl. Phys. B 78, 933–937 (2004).
[CrossRef]

J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V. N. Shlyaptsev, “Picosecond-resolution soft-x-ray laser plasma interferometry,” Appl. Opt. 43, 3938–3946 (2004).
[CrossRef] [PubMed]

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

J. Filevich, K. Kanizay, M. C. Marconi, J. L. A. Chilla, and J. J. Rocca, “Dense plasma diagnostics with an amplitude-division soft-x-ray laser interferometer based on diffraction gratings,” Opt. Lett. 25, 356–358 (2000).
[CrossRef]

Fu, S.

Fuchs, D.

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

Gaylord, T. K.

Goray, L. I.

L. I. Goray, “Grazing incidence off-plane lamellar grating as a beam splitter for a 1Å free electron laser,” J. Synch. Investig. 2, 796–800 (2008).
[CrossRef]

Grann, E. B.

Grantham, S.

S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
[CrossRef]

Grava, J.

J. Grava, M. A. Purvis, J. Filevich, M. C. Marconi, J. J. Rocca, J. Dunn, S. J. Moon, and V. N. Shlyaptsev, “Dynamics of a dense laboratory plasma jet investigated using soft x-ray laser interferometry,” Phys. Rev. E 78, 016403 (2008).
[CrossRef]

M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
[CrossRef]

J. Filevich, J. Grava, M. Purvis, M. C. Marconi, and J. J. Rocca, “Prediction and observation of tin and silver plasmas with index of refraction greater than one in the soft x-ray range,” Phys. Rev. E 74, 016404 (2006).
[CrossRef]

Gullikson, E. M.

M. Ishino, P. A. Heimann, H. Sasai, M. Hatayama, H. Takenaka, K. Sano, E. M. Gullikson, and M. Koike, “Development of multilayer laminar-type diffraction gratings to achieve high diffraction efficiencies in the 1–8keV energy region,” Appl. Opt. 45, 6741–6745 (2006).
[CrossRef] [PubMed]

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Gum, J. S.

S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
[CrossRef]

Hammarsten, E. C.

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi, and J. J. Rocca, “Soft x-ray laser diagnostics of exploding aluminum wire plasmas,” Appl. Phys. B 78, 933–937 (2004).
[CrossRef]

Hatano, T.

Hatayama, M.

Heidemann, K. F.

Heimann, P. A.

Heinzmann, U.

M. P. Kowalski, R. G. Cruddace, J. F. Seely, and J. C. Rife, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, and D. Menke, W. R. Hunter, “Efficiency of a multilayer-coated, ion-etched laminar holographic grating in the 14.5–16.0nm wavelength region,” Opt. Lett. 22, 834–836 (1997).
[CrossRef] [PubMed]

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

Henke, B. L.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Hong, Y.

Hunter, J. R.

J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V. N. Shlyaptsev, “Picosecond-resolution soft-x-ray laser plasma interferometry,” Appl. Opt. 43, 3938–3946 (2004).
[CrossRef] [PubMed]

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

Hunter, W. R.

Imazono, T.

Ishikawa, S.

Ishino, M.

Itoa, K.

Y. Kitajima, K. Amemiya, Y. Yonamoto, T. Ohta, T. Kikuchi, T. Kosuge, A. Toyoshimaa, and K. Itoa, “A soft x-ray (80–1500eV) grazing incidence monochromator with varied-line-spacing plane gratings at PF-BL-11A,” J. Synchrotron Radiat. 5, 729–731(1998).
[CrossRef]

Jankowska, E.

M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
[CrossRef]

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi, and J. J. Rocca, “Soft x-ray laser diagnostics of exploding aluminum wire plasmas,” Appl. Phys. B 78, 933–937 (2004).
[CrossRef]

Kanizay, K.

Kankelborg, C. C.

S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
[CrossRef]

Keenan, R.

Keski-Kuha, R.

S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
[CrossRef]

Kikuchi, T.

Y. Kitajima, K. Amemiya, Y. Yonamoto, T. Ohta, T. Kikuchi, T. Kosuge, A. Toyoshimaa, and K. Itoa, “A soft x-ray (80–1500eV) grazing incidence monochromator with varied-line-spacing plane gratings at PF-BL-11A,” J. Synchrotron Radiat. 5, 729–731(1998).
[CrossRef]

Kitajima, Y.

Y. Kitajima, K. Amemiya, Y. Yonamoto, T. Ohta, T. Kikuchi, T. Kosuge, A. Toyoshimaa, and K. Itoa, “A soft x-ray (80–1500eV) grazing incidence monochromator with varied-line-spacing plane gratings at PF-BL-11A,” J. Synchrotron Radiat. 5, 729–731(1998).
[CrossRef]

Kjornrattanawanich, B.

S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
[CrossRef]

J. F. Seely, C. M. Brown, D. L. Windt, S. Donguy, and B. Kjornrattanawanich, “Normal-incidence efficiencies of multilayer-coated laminar gratings for the Extreme-Ultraviolet Imaging Spectrometer on the Solar-B mission,” Appl. Opt. 43, 1463–1471 (2004).
[CrossRef] [PubMed]

Kleineberg, U.

M. P. Kowalski, R. G. Cruddace, J. F. Seely, and J. C. Rife, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, and D. Menke, W. R. Hunter, “Efficiency of a multilayer-coated, ion-etched laminar holographic grating in the 14.5–16.0nm wavelength region,” Opt. Lett. 22, 834–836 (1997).
[CrossRef] [PubMed]

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

Kloidt, A.

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

Koike, M.

Kosuge, T.

Y. Kitajima, K. Amemiya, Y. Yonamoto, T. Ohta, T. Kikuchi, T. Kosuge, A. Toyoshimaa, and K. Itoa, “A soft x-ray (80–1500eV) grazing incidence monochromator with varied-line-spacing plane gratings at PF-BL-11A,” J. Synchrotron Radiat. 5, 729–731(1998).
[CrossRef]

Kowalski, M. P.

Liu, Y.

Liu, Z.

Marconi, M. C.

J. Grava, M. A. Purvis, J. Filevich, M. C. Marconi, J. J. Rocca, J. Dunn, S. J. Moon, and V. N. Shlyaptsev, “Dynamics of a dense laboratory plasma jet investigated using soft x-ray laser interferometry,” Phys. Rev. E 78, 016403 (2008).
[CrossRef]

M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
[CrossRef]

J. Filevich, J. Grava, M. Purvis, M. C. Marconi, and J. J. Rocca, “Prediction and observation of tin and silver plasmas with index of refraction greater than one in the soft x-ray range,” Phys. Rev. E 74, 016404 (2006).
[CrossRef]

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi, and J. J. Rocca, “Soft x-ray laser diagnostics of exploding aluminum wire plasmas,” Appl. Phys. B 78, 933–937 (2004).
[CrossRef]

J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V. N. Shlyaptsev, “Picosecond-resolution soft-x-ray laser plasma interferometry,” Appl. Opt. 43, 3938–3946 (2004).
[CrossRef] [PubMed]

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

J. Filevich, K. Kanizay, M. C. Marconi, J. L. A. Chilla, and J. J. Rocca, “Dense plasma diagnostics with an amplitude-division soft-x-ray laser interferometer based on diffraction gratings,” Opt. Lett. 25, 356–358 (2000).
[CrossRef]

Menke, D.

M. P. Kowalski, R. G. Cruddace, J. F. Seely, and J. C. Rife, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, and D. Menke, W. R. Hunter, “Efficiency of a multilayer-coated, ion-etched laminar holographic grating in the 14.5–16.0nm wavelength region,” Opt. Lett. 22, 834–836 (1997).
[CrossRef] [PubMed]

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

Miiller, P.

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

Moharam, M. G.

Moon, S.

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

Moon, S. J.

J. Grava, M. A. Purvis, J. Filevich, M. C. Marconi, J. J. Rocca, J. Dunn, S. J. Moon, and V. N. Shlyaptsev, “Dynamics of a dense laboratory plasma jet investigated using soft x-ray laser interferometry,” Phys. Rev. E 78, 016403 (2008).
[CrossRef]

M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
[CrossRef]

J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V. N. Shlyaptsev, “Picosecond-resolution soft-x-ray laser plasma interferometry,” Appl. Opt. 43, 3938–3946 (2004).
[CrossRef] [PubMed]

Ng, A.

Nilsen, J.

J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V. N. Shlyaptsev, “Picosecond-resolution soft-x-ray laser plasma interferometry,” Appl. Opt. 43, 3938–3946 (2004).
[CrossRef] [PubMed]

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

Ohta, T.

Y. Kitajima, K. Amemiya, Y. Yonamoto, T. Ohta, T. Kikuchi, T. Kosuge, A. Toyoshimaa, and K. Itoa, “A soft x-ray (80–1500eV) grazing incidence monochromator with varied-line-spacing plane gratings at PF-BL-11A,” J. Synchrotron Radiat. 5, 729–731(1998).
[CrossRef]

Osterried, K.

M. P. Kowalski, R. G. Cruddace, J. F. Seely, and J. C. Rife, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, and D. Menke, W. R. Hunter, “Efficiency of a multilayer-coated, ion-etched laminar holographic grating in the 14.5–16.0nm wavelength region,” Opt. Lett. 22, 834–836 (1997).
[CrossRef] [PubMed]

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

Owens, S. M.

S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1998).

Pommet, D. A.

Purvis, M.

M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
[CrossRef]

J. Filevich, J. Grava, M. Purvis, M. C. Marconi, and J. J. Rocca, “Prediction and observation of tin and silver plasmas with index of refraction greater than one in the soft x-ray range,” Phys. Rev. E 74, 016404 (2006).
[CrossRef]

Purvis, M. A.

J. Grava, M. A. Purvis, J. Filevich, M. C. Marconi, J. J. Rocca, J. Dunn, S. J. Moon, and V. N. Shlyaptsev, “Dynamics of a dense laboratory plasma jet investigated using soft x-ray laser interferometry,” Phys. Rev. E 78, 016403 (2008).
[CrossRef]

Rife, J. C.

Rocca, J. J.

J. Grava, M. A. Purvis, J. Filevich, M. C. Marconi, J. J. Rocca, J. Dunn, S. J. Moon, and V. N. Shlyaptsev, “Dynamics of a dense laboratory plasma jet investigated using soft x-ray laser interferometry,” Phys. Rev. E 78, 016403 (2008).
[CrossRef]

M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
[CrossRef]

J. Filevich, J. Grava, M. Purvis, M. C. Marconi, and J. J. Rocca, “Prediction and observation of tin and silver plasmas with index of refraction greater than one in the soft x-ray range,” Phys. Rev. E 74, 016404 (2006).
[CrossRef]

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi, and J. J. Rocca, “Soft x-ray laser diagnostics of exploding aluminum wire plasmas,” Appl. Phys. B 78, 933–937 (2004).
[CrossRef]

J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V. N. Shlyaptsev, “Picosecond-resolution soft-x-ray laser plasma interferometry,” Appl. Opt. 43, 3938–3946 (2004).
[CrossRef] [PubMed]

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

J. Filevich, K. Kanizay, M. C. Marconi, J. L. A. Chilla, and J. J. Rocca, “Dense plasma diagnostics with an amplitude-division soft-x-ray laser interferometer based on diffraction gratings,” Opt. Lett. 25, 356–358 (2000).
[CrossRef]

Sano, K.

Sasai, H.

Schmiedeskamp, B.

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

Scholze, F.

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

Seely, J. F.

Shlyaptsev, V. N.

J. Grava, M. A. Purvis, J. Filevich, M. C. Marconi, J. J. Rocca, J. Dunn, S. J. Moon, and V. N. Shlyaptsev, “Dynamics of a dense laboratory plasma jet investigated using soft x-ray laser interferometry,” Phys. Rev. E 78, 016403 (2008).
[CrossRef]

M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
[CrossRef]

J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V. N. Shlyaptsev, “Picosecond-resolution soft-x-ray laser plasma interferometry,” Appl. Opt. 43, 3938–3946 (2004).
[CrossRef] [PubMed]

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

Smith, R. F.

J. Filevich, J. J. Rocca, M. C. Marconi, R. F. Smith, J. Dunn, R. Keenan, J. R. Hunter, S. J. Moon, J. Nilsen, A. Ng, and V. N. Shlyaptsev, “Picosecond-resolution soft-x-ray laser plasma interferometry,” Appl. Opt. 43, 3938–3946 (2004).
[CrossRef] [PubMed]

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

Stock, H.-J.

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

Szapiro, B.

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi, and J. J. Rocca, “Soft x-ray laser diagnostics of exploding aluminum wire plasmas,” Appl. Phys. B 78, 933–937 (2004).
[CrossRef]

Takenaka, H.

Tan, X.

Tarrio, C.

S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
[CrossRef]

Thomas, R. J.

S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
[CrossRef]

Toyoshimaa, A.

Y. Kitajima, K. Amemiya, Y. Yonamoto, T. Ohta, T. Kikuchi, T. Kosuge, A. Toyoshimaa, and K. Itoa, “A soft x-ray (80–1500eV) grazing incidence monochromator with varied-line-spacing plane gratings at PF-BL-11A,” J. Synchrotron Radiat. 5, 729–731(1998).
[CrossRef]

Ulm, G.

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

Watanabe, M.

Windt, D. L.

Xu, X.

Yanagihara, M.

Yonamoto, Y.

Y. Kitajima, K. Amemiya, Y. Yonamoto, T. Ohta, T. Kikuchi, T. Kosuge, A. Toyoshimaa, and K. Itoa, “A soft x-ray (80–1500eV) grazing incidence monochromator with varied-line-spacing plane gratings at PF-BL-11A,” J. Synchrotron Radiat. 5, 729–731(1998).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. B (1)

E. C. Hammarsten, B. Szapiro, E. Jankowska, J. Filevich, M. C. Marconi, and J. J. Rocca, “Soft x-ray laser diagnostics of exploding aluminum wire plasmas,” Appl. Phys. B 78, 933–937 (2004).
[CrossRef]

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

J. Electron Spectrosc. Relat. Phenom. (1)

U. Kleineberg, H.-J. Stock, A. Kloidt, K. Osterried, D. Menke, B. Schmiedeskamp, U. Heinzmann, D. Fuchs, P. Miiller, F. Scholze, and G. Ulm, “Mo/Si multilayer coated laminar phase and ruled blaze gratings for the soft x-ray region,” J. Electron Spectrosc. Relat. Phenom. 80, 389–392 (1996).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Synch. Investig. (1)

L. I. Goray, “Grazing incidence off-plane lamellar grating as a beam splitter for a 1Å free electron laser,” J. Synch. Investig. 2, 796–800 (2008).
[CrossRef]

J. Synchrotron Radiat. (1)

Y. Kitajima, K. Amemiya, Y. Yonamoto, T. Ohta, T. Kikuchi, T. Kosuge, A. Toyoshimaa, and K. Itoa, “A soft x-ray (80–1500eV) grazing incidence monochromator with varied-line-spacing plane gratings at PF-BL-11A,” J. Synchrotron Radiat. 5, 729–731(1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Precision Eng. (1)

X. Tan, Y. Liu, X. Xu, Y. Hong, and S. Fu, “13.9nm laminar grating as beam splitter,” Opt. Precision Eng. 17, 33–37 (2009) (in Chinese).

Phys. Rev. E (3)

J. Filevich, J. Grava, M. Purvis, M. C. Marconi, and J. J. Rocca, “Prediction and observation of tin and silver plasmas with index of refraction greater than one in the soft x-ray range,” Phys. Rev. E 74, 016404 (2006).
[CrossRef]

M. Purvis, J. Grava, J. Filevich, M. C. Marconi, J. Dunn, S. J. Moon, V. N. Shlyaptsev, E. Jankowska, and J. J. Rocca, “Dynamics of converging laser-created plasmas in semicylindrical cavities studied using soft x-ray laser interferometry,” Phys. Rev. E 76, 046402 (2007).
[CrossRef]

J. Grava, M. A. Purvis, J. Filevich, M. C. Marconi, J. J. Rocca, J. Dunn, S. J. Moon, and V. N. Shlyaptsev, “Dynamics of a dense laboratory plasma jet investigated using soft x-ray laser interferometry,” Phys. Rev. E 78, 016403 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

R. F. Smith, J. Dunn, J. Nilsen, V. N. Shlyaptsev, S. Moon, J. Filevich, J. J. Rocca, M. C. Marconi, J. R. Hunter, and T. W. Barbee, Jr., “Picosecond x-ray laser interferometry of dense plasmas,” Phys. Rev. Lett. 89, 065004 (2002).
[CrossRef] [PubMed]

Proc. SPIE (1)

S. M. Owens, J. S. Gum, C. Tarrio, S. Grantham, J. Dvorak, B. Kjornrattanawanich, R. Keski-Kuha, R. J. Thomas, and C. C. Kankelborg, “Narrow-band EUV multilayer coating for the MOSES sounding rocket,” Proc. SPIE 5900, 590003 (2005).
[CrossRef]

Other (3)

If we set the normal of grating G2 parallel to that of grating G1, we would obtain another configuration of the grating interferometer, as shown in Fig. . The main difference between the two configurations is that, in the second configuration, the zeroth order of G1 and the −1st order of G2 are used as one arm of the interferometer. The other arm of the interferometer is constructed by the −1st order of G1 and the zeroth order of G2. Accordingly, the throughput of the system changes to η0η−1 if G1 and G2 have the same profile. This configuration would be favorable with respect to the fringe visibility because fringe visibility V will approach 1, even if the efficiencies of the zeroth and −1st orders are different. Considering the spatial arrangement of the grating interferometer, we restrict use to the first configuration in this paper.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1998).

http://henke.lbl.gov/optical_constants/layer2.html (1995–2008).

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Figures (18)

Fig. 1
Fig. 1

Principle diagram of a soft x-ray laser interferometer based on diffraction gratings.

Fig. 2
Fig. 2

Geometry for a gold-coated laminar grating analyzed herein. Let a grating structure with a period d and a fill factor of f be periodic in the x direction and independent of the y direction.

Fig. 3
Fig. 3

Calculated (a) TE and (b) TM efficiencies in the zeroth order as a function of the laminar grating profile (fill factor and depth) at a wavelength of 13.9 nm and an incidence angle of 84 ° . Figures 3, 4 only show the simulation results in a small range around the parameter V = 1 .

Fig. 4
Fig. 4

Calculated nonpolarized efficiencies in the (a) zeroth and (b) 1 st orders as a function of the laminar grating profile at a wavelength of 13.9 nm and an incidence angle of 84 ° .

Fig. 5
Fig. 5

Calculated fringe visibility as a function of the laminar grating profile at a wavelength of 13.9 nm and an incidence angle of 84 ° .

Fig. 6
Fig. 6

SEM images of sample A 1 (before etching) and sample B 1 (after coated with gold layer).

Fig. 7
Fig. 7

Typical TE efficiency measurement of sample A 1 , performed at 13.9 nm as a function of the diffraction angle.

Fig. 8
Fig. 8

Calculated TE efficiency ratio of the 1 st to the zeroth order as a function of the profile parameters at a wavelength of 13.9 nm and an incidence angle of 83.5 ° .

Fig. 9
Fig. 9

Measured and simulated grating efficiencies of sample A 1 for TE polarization in the (a) zeroth and (b) 1 st order as a function of the incidence angle. The symbols show the measured diffraction efficiencies and the curves show the simulated diffraction efficiencies with a fill factor of 0.39 and variable depths.

Fig. 10
Fig. 10

Calculated and measured TE efficiency ratio of sample A 1 as a function of the incidence angle.

Fig. 11
Fig. 11

Calculated TE efficiency ratio of the 1 st to the zeroth order for sample B 1 at a wavelength of 13.9 nm and an incidence angle of 84 ° .

Fig. 12
Fig. 12

Calculated and measured TE efficiency ratio of sample B 1 as a function of the incidence angle at a wavelength of 13.9 nm .

Fig. 13
Fig. 13

Measured and simulated grating efficiencies of sample B 1 for TE polarization in the (a) zeroth and (b) 1 st order as a function of the incidence angle. The symbols show the measured diffraction efficiencies and the curves show the simulated diffraction efficiencies with a fill factor of 0.43 and variable depths.

Fig. 14
Fig. 14

Calculated and measured reflectivity of the gold layer as a function of the incidence angle in parametric dependence on the surface roughness.

Fig. 15
Fig. 15

Geometry of trapezoidal profile.

Fig. 16
Fig. 16

Comparison of the calculated and measured efficiencies of sample A 1 for TE polarization in the (a) zeroth and (b) 1 st order as a function of the incidence angle. The grating efficiencies are simulated with a fill factor of 0.39 as well as a depth of 27 nm . The curves show the simulated diffraction efficiencies of trapezoidal profiles with variable slope angles. The symbols show the measured diffraction efficiencies.

Fig. 17
Fig. 17

Comparison of the calculated and measured efficiencies of sample B 1 for TE polarization in the (a) zeroth and (b) 1 st order as a function of the incidence angle. The grating efficiencies are simulated with a fill factor of 0.43 as well as a depth of 31 nm . The curves show the simulated diffraction efficiencies of trapezoidal profiles with variable slope angles. The symbols show the measured diffraction efficiencies.

Fig. 18
Fig. 18

Optimized and fabricated profiles of the grating beam splitter. It implies that grating efficiencies of in the 1 st order and fringe visibility would be improved if both the depth and the fill factor of sample A 1 and B 1 are decreased.

Tables (2)

Tables Icon

Table 1 Optimized Grating Parameters and Fabrication Tolerance

Tables Icon

Table 2 Characteristics of the Two Gratings

Equations (11)

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

V = 2 η 0 η 1 ( η 0 2 + η 1 2 ) .
E I , y = exp [ j k 0 n I ( sin θ · x + cos θ · z ) ] + i R i exp [ j ( k x i x k I , z i z ) ] ,
E I I , y = i T i exp { j [ k x i x + k I I , z i ( z H ) ] } ,
k x i = k 0 [ n I sin θ i ( λ 0 / d ) ] ,
k ξ , z i = { + k 0 [ n 2 ( k x i / k 0 ) 2 ] 1 / 2 k 0 n > k x i j k 0 [ ( k x i / k 0 ) 2 n 2 ] 1 / 2 k x i > k 0 n , = I , I I .
ε ( x ) = m ε m exp ( j 2 π m x d ) ,
E g y = i S y i ( z ) exp ( j k x i x ) ,
D E r i = R i R i * Re [ k I , z i / ( k 0 n I cos θ ) ] , D E t i = T i T i * Re [ k I I , z i / ( k 0 n I cos θ ) ] .
D E r i = R i R i * Re [ k I , z i / ( k 0 n I cos θ ) ] , D E t i = T i T i * Re ( k I I , z i n I I 2 ) / ( k 0 cos θ n I ) .
ε l ( x ) = m ε l , m exp ( j 2 π m x d ) ,
E l , g y = i S l , y i ( z ) exp ( j k x i x ) ,

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