Abstract

To the best of our knowledge, the first direct measurement of the dispersive part of the refractive index is performed at extreme-ultraviolet (EUV) wavelengths, where absorption is higher as compared with hard-x-ray and visible wavelengths. A novel diffractive optical element that combines the functions of a grating and a zone plate is fabricated with Fourier optical techniques and employed here for the first time at EUV/soft-x-ray wavelengths. Both the real and the imaginary parts of the complex refractive indices are measured directly by this technique without recourse to Kramers–Kronig transformations. Data for Al and Ni in the vicinity of their L and M edges, respectively, are presented as first examples of this technique.

© 2002 Optical Society of America

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References

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  1. D. T. Attwood, Soft X-Rays and Extreme Ultraviolet Radiation: Principles and Applications (Cambridge U. Press, Cambridge, 1999).
    [CrossRef]
  2. D. Joyeux, F. Polack, and D. Phalippou, Rev. Sci. Instrum. 70, 2921 (1999).
    [CrossRef]
  3. U. Bonse and M. Hart, Appl. Phys. Lett. 6, 155 (1965).
    [CrossRef]
  4. H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
    [CrossRef]
  5. H.-J. Hagemann, W. Gudat, and C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).
  6. E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612 (1980).
    [CrossRef]
  7. R. Soufli, “Optical constants of materials in the EUV/soft x-ray region for multilayer mirror applications,” Ph.D. dissertation (University of California, Berkeley, Berkeley, Calif., 1997).
  8. W. R. Hunter, Appl. Opt. 21, 2103 (1982).
    [CrossRef] [PubMed]
  9. C. Chang, P. Naulleau, E. Anderson, and D. Attwood, Opt. Commun. 182, 25 (2000).
    [CrossRef]
  10. M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. 72, 156 (1982).
  11. The xor pattern is obtained first by pixelization of the binary grating and the zone plate. Each pixel is 1 for transmission and 0 for absorption. The two pixelized patterns are then overlapped and compared pixel by pixel, producing the resulting xor pattern; i.e., at each pixel position, if the pixel values of the grating and the zone plate are the same (both 0’s or both 1’s), the value of the corresponding pixel on the xor pattern is 0. Otherwise, the value of the corresponding pixel on the xor pattern is 1.
  12. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  13. D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
    [CrossRef]
  14. E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
    [CrossRef]
  15. E. Gullikson, http://www-cxro.lbl.gov/optical_constants/ .

2000 (2)

C. Chang, P. Naulleau, E. Anderson, and D. Attwood, Opt. Commun. 182, 25 (2000).
[CrossRef]

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
[CrossRef]

1999 (2)

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

D. Joyeux, F. Polack, and D. Phalippou, Rev. Sci. Instrum. 70, 2921 (1999).
[CrossRef]

1982 (2)

1980 (1)

E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612 (1980).
[CrossRef]

1975 (1)

1965 (1)

U. Bonse and M. Hart, Appl. Phys. Lett. 6, 155 (1965).
[CrossRef]

1962 (1)

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

Anderson, E.

C. Chang, P. Naulleau, E. Anderson, and D. Attwood, Opt. Commun. 182, 25 (2000).
[CrossRef]

Anderson, E. H.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
[CrossRef]

Attwood, D.

C. Chang, P. Naulleau, E. Anderson, and D. Attwood, Opt. Commun. 182, 25 (2000).
[CrossRef]

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
[CrossRef]

Attwood, D. T.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

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

Batson, P.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

Beguiristain, R.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

Bokor, J.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

Bonse, U.

U. Bonse and M. Hart, Appl. Phys. Lett. 6, 155 (1965).
[CrossRef]

Chang, C.

C. Chang, P. Naulleau, E. Anderson, and D. Attwood, Opt. Commun. 182, 25 (2000).
[CrossRef]

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

Chao, W.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
[CrossRef]

Denbeaux, G.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
[CrossRef]

Ehrenreich, H.

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

Goldberg, K. A.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Gudat, W.

Gullikson, E. M.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

Hagemann, H.-J.

Hart, M.

U. Bonse and M. Hart, Appl. Phys. Lett. 6, 155 (1965).
[CrossRef]

Harteneck, B.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
[CrossRef]

Hunter, W. R.

Ina, H.

Inokuti, M.

E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Johnson, L.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
[CrossRef]

Joyeux, D.

D. Joyeux, F. Polack, and D. Phalippou, Rev. Sci. Instrum. 70, 2921 (1999).
[CrossRef]

Kobayashi, S.

Koike, M.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

Kunz, C.

Lucero, A.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
[CrossRef]

Medecki, H.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

Naulleau, P.

C. Chang, P. Naulleau, E. Anderson, and D. Attwood, Opt. Commun. 182, 25 (2000).
[CrossRef]

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

Olynick, D. L.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
[CrossRef]

Phalippou, D.

D. Joyeux, F. Polack, and D. Phalippou, Rev. Sci. Instrum. 70, 2921 (1999).
[CrossRef]

Philipp, H. R.

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

Polack, F.

D. Joyeux, F. Polack, and D. Phalippou, Rev. Sci. Instrum. 70, 2921 (1999).
[CrossRef]

Sasaki, T.

E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Shiles, E.

E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Smith, D. Y.

E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Soufli, R.

R. Soufli, “Optical constants of materials in the EUV/soft x-ray region for multilayer mirror applications,” Ph.D. dissertation (University of California, Berkeley, Berkeley, Calif., 1997).

Takeda, M.

Tejnil, E.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

Underwood, J. H.

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

Veklerov, E.

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

U. Bonse and M. Hart, Appl. Phys. Lett. 6, 155 (1965).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. T. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, and J. H. Underwood, IEEE J. Quantum Electron. 35, 709 (1999).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Vac. Sci. Technol. B (1)

E. H. Anderson, D. L. Olynick, B. Harteneck, E. Veklerov, G. Denbeaux, W. Chao, A. Lucero, L. Johnson, and D. Attwood, J. Vac. Sci. Technol. B 18, 2970 (2000).
[CrossRef]

Opt. Commun. (1)

C. Chang, P. Naulleau, E. Anderson, and D. Attwood, Opt. Commun. 182, 25 (2000).
[CrossRef]

Phys. Rev. (1)

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

Phys. Rev. B (1)

E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612 (1980).
[CrossRef]

Rev. Sci. Instrum. (1)

D. Joyeux, F. Polack, and D. Phalippou, Rev. Sci. Instrum. 70, 2921 (1999).
[CrossRef]

Other (5)

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

R. Soufli, “Optical constants of materials in the EUV/soft x-ray region for multilayer mirror applications,” Ph.D. dissertation (University of California, Berkeley, Berkeley, Calif., 1997).

E. Gullikson, http://www-cxro.lbl.gov/optical_constants/ .

The xor pattern is obtained first by pixelization of the binary grating and the zone plate. Each pixel is 1 for transmission and 0 for absorption. The two pixelized patterns are then overlapped and compared pixel by pixel, producing the resulting xor pattern; i.e., at each pixel position, if the pixel values of the grating and the zone plate are the same (both 0’s or both 1’s), the value of the corresponding pixel on the xor pattern is 0. Otherwise, the value of the corresponding pixel on the xor pattern is 1.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

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Figures (3)

Fig. 1
Fig. 1

EUV interferometer for direct nω measurement.

Fig. 2
Fig. 2

Al data (with error bars) are shown with the current standard.

Fig. 3
Fig. 3

Ni data (with error bars) shown with the current standard.

Equations (1)

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XORx,y=12-2m=-m0sinmπ/2mπexp-i2mπxd×n=-n0sinnπ/2nπexp-inπx2+y2ΔrD-Δr.

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