Abstract

The chemical reaction of a sample with atmospheric gases causes a significant error in the determinantion of the complex refractive index n=1-δ+iβ in the extreme-ultraviolet region. The protection of samples removes this effect but hampers the interpretation of measurements. To overcome this difficulty, we derive the exact dependences on film thickness of the reflectivity and transmissivity of a protected film. These dependences greatly simplify the determination of δ and β when the spectra of several films with different thickness and identical protection are measured. They also allow the verification of the δ(ω) obtained from the Kramers–Kronig relation and even make the Kramers–Kronig method unnecessary in many cases. As a practical application, the optical constants of Sc and Ti are determined at ω=1870 eV and 18–99 eV, respectively. The essential feature of our experimental technique is deposition of a film sample directly on a silicon photodiode that allows easy operation with both thin (∼10-nm) and thick (∼100-nm) films. The comparison of calculated reflectivities of Si–Sc multilayers with the measured values shows the high accuracy of the determined δ(ω) and β(ω).

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Tarrio, R. N. Watts, T. B. Lucatorto, J. M. Slaughter, M. Falce, “Optical constants of in situ-deposited films of important extreme-ultraviolet multilayer mirror materials,” Appl. Opt. 37, 4100–4104 (1998).
    [CrossRef]
  2. R. M. Fechtchenko, A. V. Vinogradov, “Reflection from surfaces with a thin overlayer,” Opt. Lett. 25, 998–1000 (2000).
    [CrossRef]
  3. R. M. Fechtchenko, A. V. Popov, A. V. Vinogradov, “On reflection from surfaces with a thin overlayer,” J. Russ. Laser Res. 22, 139–148 (2001).
    [CrossRef]
  4. R. Soufli, E. M. Gullikson, “Reflectance measurements on clean surfaces for the determination of optical constants of silicon in the extreme ultraviolet–soft-x-ray region,” Appl. Opt. 36, 5499–5507 (1997).
    [CrossRef] [PubMed]
  5. I. A. Artioukov, B. R. Benware, J. J. Rocca, M. Forsythe, Yu. A. Uspenskii, A. V. Vinogradov, “Determination of XUV optical constants by reflectometry using a high-repetition rate 46.9-nm laser,” IEEE J. Sel. Top. Quantum Electron. 5, 1495–1501 (1999).
    [CrossRef]
  6. E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
    [CrossRef]
  7. R. Soufli, E. M. Gullikson, “Absolute photoabsorption measurements of molybdenum in the range 60–930 eV for optical constant determination,” Appl. Opt. 37, 1713–1719 (1998).
    [CrossRef]
  8. Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, V. Yu. Fedotov, “High-reflectivity multilayer mirrors for a vacuum-ultraviolet interval of 35–50 nm,” Opt. Lett. 23, 771–773 (1998).
    [CrossRef]
  9. Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, S. Mrowka, F. Schäfers, “Sc–Si normal incidence mirrors for a VUV interval of 35–50 nm,” Nucl. Instrum. Methods Phys. Res. A 448, 147–151 (2000).
    [CrossRef]
  10. J. F. Seely, Yu. A. Uspenskii, Yu. P. Pershin, V. V. Kondratenko, A. V. Vinogradov, “Skylab 3600 groove/mm replica grating with a scandium–silicon multilayer coating and high normal-incidence efficiency at 38-nm wavelength,” Appl. Opt. 41, 1846–1851 (2002).
    [CrossRef] [PubMed]
  11. Yu. A. Uspenskii, S. V. Antonov, V. Yu. Fedotov, A. V. Vinogradov, “Optical properties of 3D transition metals in the spectral interval of interest for discharge-pumped XUV lasers,” in Soft X-Ray Lasers and Applications II, J. J. Rocca, L. B. Da Silva, eds., Proc. SPIE3156, 288–294 (1997).
    [CrossRef]
  12. Yu. A. Uspenskii, B. N. Harmon, “Large selective magneto-optic response from magnetic semiconducting layered structures,” Phys. Rev. B 61, R10571–R10574 (2000).
    [CrossRef]
  13. Yu. A. Uspenskii, A. V. Vinogradov (data available from the authors).
  14. B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interaction: photoabsorption, scattering, transmission and reflection at E=10–30,000 eV,Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
    [CrossRef]
  15. J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).
  16. A. G. Nargizyan, S. N. Rashkeev, Yu. A. Uspenskii, “Microscopic calculations of the optical properties of 4d-transition metals in the vacuum UV,” Sov. Phys. Solid State 34, 626–632 (1992).
  17. E. Spiller, Soft X-Ray Optics (SPIE Optical Engineering Press, Bellingham, Wash., 1994).
  18. Y. Hotta, N. Furudate, M. Yamamoto, N. Watanabe, “Design and fabrication of multilayer mirrors for He-II radiation,” Surf. Rev. Lett. 9, 571–576 (2002).
    [CrossRef]
  19. C. Chang, E. Anderson, P. Naulleau, E. Gullikson, K. Goldberg, D. Attwood, “Direct measurement of index of refraction in the extreme-ultraviolet wavelength region with a novel interferometer,” Opt. Lett. 27, 1028–1030 (2002).
    [CrossRef]

2002 (3)

2001 (1)

R. M. Fechtchenko, A. V. Popov, A. V. Vinogradov, “On reflection from surfaces with a thin overlayer,” J. Russ. Laser Res. 22, 139–148 (2001).
[CrossRef]

2000 (4)

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, S. Mrowka, F. Schäfers, “Sc–Si normal incidence mirrors for a VUV interval of 35–50 nm,” Nucl. Instrum. Methods Phys. Res. A 448, 147–151 (2000).
[CrossRef]

Yu. A. Uspenskii, B. N. Harmon, “Large selective magneto-optic response from magnetic semiconducting layered structures,” Phys. Rev. B 61, R10571–R10574 (2000).
[CrossRef]

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

R. M. Fechtchenko, A. V. Vinogradov, “Reflection from surfaces with a thin overlayer,” Opt. Lett. 25, 998–1000 (2000).
[CrossRef]

1999 (1)

I. A. Artioukov, B. R. Benware, J. J. Rocca, M. Forsythe, Yu. A. Uspenskii, A. V. Vinogradov, “Determination of XUV optical constants by reflectometry using a high-repetition rate 46.9-nm laser,” IEEE J. Sel. Top. Quantum Electron. 5, 1495–1501 (1999).
[CrossRef]

1998 (3)

1997 (1)

1994 (1)

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

1993 (1)

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interaction: photoabsorption, scattering, transmission and reflection at E=10–30,000 eV,Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

1992 (1)

A. G. Nargizyan, S. N. Rashkeev, Yu. A. Uspenskii, “Microscopic calculations of the optical properties of 4d-transition metals in the vacuum UV,” Sov. Phys. Solid State 34, 626–632 (1992).

Anderson, E.

Antonov, S. V.

Yu. A. Uspenskii, S. V. Antonov, V. Yu. Fedotov, A. V. Vinogradov, “Optical properties of 3D transition metals in the spectral interval of interest for discharge-pumped XUV lasers,” in Soft X-Ray Lasers and Applications II, J. J. Rocca, L. B. Da Silva, eds., Proc. SPIE3156, 288–294 (1997).
[CrossRef]

Artioukov, I. A.

I. A. Artioukov, B. R. Benware, J. J. Rocca, M. Forsythe, Yu. A. Uspenskii, A. V. Vinogradov, “Determination of XUV optical constants by reflectometry using a high-repetition rate 46.9-nm laser,” IEEE J. Sel. Top. Quantum Electron. 5, 1495–1501 (1999).
[CrossRef]

Artukov, I. A.

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

Attwood, D.

Benware, B.

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

Benware, B. R.

I. A. Artioukov, B. R. Benware, J. J. Rocca, M. Forsythe, Yu. A. Uspenskii, A. V. Vinogradov, “Determination of XUV optical constants by reflectometry using a high-repetition rate 46.9-nm laser,” IEEE J. Sel. Top. Quantum Electron. 5, 1495–1501 (1999).
[CrossRef]

Chang, C.

Davis, J. C.

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interaction: photoabsorption, scattering, transmission and reflection at E=10–30,000 eV,Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Denham, P.

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

Falce, M.

Fechtchenko, R. M.

R. M. Fechtchenko, A. V. Popov, A. V. Vinogradov, “On reflection from surfaces with a thin overlayer,” J. Russ. Laser Res. 22, 139–148 (2001).
[CrossRef]

R. M. Fechtchenko, A. V. Vinogradov, “Reflection from surfaces with a thin overlayer,” Opt. Lett. 25, 998–1000 (2000).
[CrossRef]

Fedorenko, A. I.

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, S. Mrowka, F. Schäfers, “Sc–Si normal incidence mirrors for a VUV interval of 35–50 nm,” Nucl. Instrum. Methods Phys. Res. A 448, 147–151 (2000).
[CrossRef]

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, V. Yu. Fedotov, “High-reflectivity multilayer mirrors for a vacuum-ultraviolet interval of 35–50 nm,” Opt. Lett. 23, 771–773 (1998).
[CrossRef]

Fedotov, V. Yu.

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, V. Yu. Fedotov, “High-reflectivity multilayer mirrors for a vacuum-ultraviolet interval of 35–50 nm,” Opt. Lett. 23, 771–773 (1998).
[CrossRef]

Yu. A. Uspenskii, S. V. Antonov, V. Yu. Fedotov, A. V. Vinogradov, “Optical properties of 3D transition metals in the spectral interval of interest for discharge-pumped XUV lasers,” in Soft X-Ray Lasers and Applications II, J. J. Rocca, L. B. Da Silva, eds., Proc. SPIE3156, 288–294 (1997).
[CrossRef]

Filevich, J.

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

Forsythe, M.

I. A. Artioukov, B. R. Benware, J. J. Rocca, M. Forsythe, Yu. A. Uspenskii, A. V. Vinogradov, “Determination of XUV optical constants by reflectometry using a high-repetition rate 46.9-nm laser,” IEEE J. Sel. Top. Quantum Electron. 5, 1495–1501 (1999).
[CrossRef]

Frati, M.

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

Furudate, N.

Y. Hotta, N. Furudate, M. Yamamoto, N. Watanabe, “Design and fabrication of multilayer mirrors for He-II radiation,” Surf. Rev. Lett. 9, 571–576 (2002).
[CrossRef]

Goldberg, K.

Gullikson, E.

Gullikson, E. M.

R. Soufli, E. M. Gullikson, “Absolute photoabsorption measurements of molybdenum in the range 60–930 eV for optical constant determination,” Appl. Opt. 37, 1713–1719 (1998).
[CrossRef]

R. Soufli, E. M. Gullikson, “Reflectance measurements on clean surfaces for the determination of optical constants of silicon in the extreme ultraviolet–soft-x-ray region,” Appl. Opt. 36, 5499–5507 (1997).
[CrossRef] [PubMed]

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interaction: photoabsorption, scattering, transmission and reflection at E=10–30,000 eV,Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Harmon, B. N.

Yu. A. Uspenskii, B. N. Harmon, “Large selective magneto-optic response from magnetic semiconducting layered structures,” Phys. Rev. B 61, R10571–R10574 (2000).
[CrossRef]

Henke, B. L.

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interaction: photoabsorption, scattering, transmission and reflection at E=10–30,000 eV,Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Hotta, Y.

Y. Hotta, N. Furudate, M. Yamamoto, N. Watanabe, “Design and fabrication of multilayer mirrors for He-II radiation,” Surf. Rev. Lett. 9, 571–576 (2002).
[CrossRef]

Kanizay, K.

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

Kondratenko, V. V.

Levashov, V. E.

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, S. Mrowka, F. Schäfers, “Sc–Si normal incidence mirrors for a VUV interval of 35–50 nm,” Nucl. Instrum. Methods Phys. Res. A 448, 147–151 (2000).
[CrossRef]

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, V. Yu. Fedotov, “High-reflectivity multilayer mirrors for a vacuum-ultraviolet interval of 35–50 nm,” Opt. Lett. 23, 771–773 (1998).
[CrossRef]

Lucatorto, T. B.

Marconi, M.

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

Mrowka, S.

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, S. Mrowka, F. Schäfers, “Sc–Si normal incidence mirrors for a VUV interval of 35–50 nm,” Nucl. Instrum. Methods Phys. Res. A 448, 147–151 (2000).
[CrossRef]

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

Nargizyan, A. G.

A. G. Nargizyan, S. N. Rashkeev, Yu. A. Uspenskii, “Microscopic calculations of the optical properties of 4d-transition metals in the vacuum UV,” Sov. Phys. Solid State 34, 626–632 (1992).

Naulleau, P.

Ozols, A.

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

Pershin, Yu. P.

Popov, A. V.

R. M. Fechtchenko, A. V. Popov, A. V. Vinogradov, “On reflection from surfaces with a thin overlayer,” J. Russ. Laser Res. 22, 139–148 (2001).
[CrossRef]

Rashkeev, S. N.

A. G. Nargizyan, S. N. Rashkeev, Yu. A. Uspenskii, “Microscopic calculations of the optical properties of 4d-transition metals in the vacuum UV,” Sov. Phys. Solid State 34, 626–632 (1992).

Rocca, J. J.

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

I. A. Artioukov, B. R. Benware, J. J. Rocca, M. Forsythe, Yu. A. Uspenskii, A. V. Vinogradov, “Determination of XUV optical constants by reflectometry using a high-repetition rate 46.9-nm laser,” IEEE J. Sel. Top. Quantum Electron. 5, 1495–1501 (1999).
[CrossRef]

Schäfers, F.

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, S. Mrowka, F. Schäfers, “Sc–Si normal incidence mirrors for a VUV interval of 35–50 nm,” Nucl. Instrum. Methods Phys. Res. A 448, 147–151 (2000).
[CrossRef]

Seely, J. F.

Seminario, M.

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

Slaughter, J. M.

Soufli, R.

Spiller, E.

E. Spiller, Soft X-Ray Optics (SPIE Optical Engineering Press, Bellingham, Wash., 1994).

Tarrio, C.

Underwood, J. H.

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

Uspenskii, Yu. A.

J. F. Seely, Yu. A. Uspenskii, Yu. P. Pershin, V. V. Kondratenko, A. V. Vinogradov, “Skylab 3600 groove/mm replica grating with a scandium–silicon multilayer coating and high normal-incidence efficiency at 38-nm wavelength,” Appl. Opt. 41, 1846–1851 (2002).
[CrossRef] [PubMed]

Yu. A. Uspenskii, B. N. Harmon, “Large selective magneto-optic response from magnetic semiconducting layered structures,” Phys. Rev. B 61, R10571–R10574 (2000).
[CrossRef]

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, S. Mrowka, F. Schäfers, “Sc–Si normal incidence mirrors for a VUV interval of 35–50 nm,” Nucl. Instrum. Methods Phys. Res. A 448, 147–151 (2000).
[CrossRef]

I. A. Artioukov, B. R. Benware, J. J. Rocca, M. Forsythe, Yu. A. Uspenskii, A. V. Vinogradov, “Determination of XUV optical constants by reflectometry using a high-repetition rate 46.9-nm laser,” IEEE J. Sel. Top. Quantum Electron. 5, 1495–1501 (1999).
[CrossRef]

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, V. Yu. Fedotov, “High-reflectivity multilayer mirrors for a vacuum-ultraviolet interval of 35–50 nm,” Opt. Lett. 23, 771–773 (1998).
[CrossRef]

A. G. Nargizyan, S. N. Rashkeev, Yu. A. Uspenskii, “Microscopic calculations of the optical properties of 4d-transition metals in the vacuum UV,” Sov. Phys. Solid State 34, 626–632 (1992).

Yu. A. Uspenskii, S. V. Antonov, V. Yu. Fedotov, A. V. Vinogradov, “Optical properties of 3D transition metals in the spectral interval of interest for discharge-pumped XUV lasers,” in Soft X-Ray Lasers and Applications II, J. J. Rocca, L. B. Da Silva, eds., Proc. SPIE3156, 288–294 (1997).
[CrossRef]

Vinogradov, A.

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

Vinogradov, A. V.

J. F. Seely, Yu. A. Uspenskii, Yu. P. Pershin, V. V. Kondratenko, A. V. Vinogradov, “Skylab 3600 groove/mm replica grating with a scandium–silicon multilayer coating and high normal-incidence efficiency at 38-nm wavelength,” Appl. Opt. 41, 1846–1851 (2002).
[CrossRef] [PubMed]

R. M. Fechtchenko, A. V. Popov, A. V. Vinogradov, “On reflection from surfaces with a thin overlayer,” J. Russ. Laser Res. 22, 139–148 (2001).
[CrossRef]

R. M. Fechtchenko, A. V. Vinogradov, “Reflection from surfaces with a thin overlayer,” Opt. Lett. 25, 998–1000 (2000).
[CrossRef]

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, S. Mrowka, F. Schäfers, “Sc–Si normal incidence mirrors for a VUV interval of 35–50 nm,” Nucl. Instrum. Methods Phys. Res. A 448, 147–151 (2000).
[CrossRef]

I. A. Artioukov, B. R. Benware, J. J. Rocca, M. Forsythe, Yu. A. Uspenskii, A. V. Vinogradov, “Determination of XUV optical constants by reflectometry using a high-repetition rate 46.9-nm laser,” IEEE J. Sel. Top. Quantum Electron. 5, 1495–1501 (1999).
[CrossRef]

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, V. Yu. Fedotov, “High-reflectivity multilayer mirrors for a vacuum-ultraviolet interval of 35–50 nm,” Opt. Lett. 23, 771–773 (1998).
[CrossRef]

Yu. A. Uspenskii, S. V. Antonov, V. Yu. Fedotov, A. V. Vinogradov, “Optical properties of 3D transition metals in the spectral interval of interest for discharge-pumped XUV lasers,” in Soft X-Ray Lasers and Applications II, J. J. Rocca, L. B. Da Silva, eds., Proc. SPIE3156, 288–294 (1997).
[CrossRef]

Watanabe, N.

Y. Hotta, N. Furudate, M. Yamamoto, N. Watanabe, “Design and fabrication of multilayer mirrors for He-II radiation,” Surf. Rev. Lett. 9, 571–576 (2002).
[CrossRef]

Watts, R. N.

Yamamoto, M.

Y. Hotta, N. Furudate, M. Yamamoto, N. Watanabe, “Design and fabrication of multilayer mirrors for He-II radiation,” Surf. Rev. Lett. 9, 571–576 (2002).
[CrossRef]

Zubarev, E. N.

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, S. Mrowka, F. Schäfers, “Sc–Si normal incidence mirrors for a VUV interval of 35–50 nm,” Nucl. Instrum. Methods Phys. Res. A 448, 147–151 (2000).
[CrossRef]

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, V. Yu. Fedotov, “High-reflectivity multilayer mirrors for a vacuum-ultraviolet interval of 35–50 nm,” Opt. Lett. 23, 771–773 (1998).
[CrossRef]

Appl. Opt. (4)

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullikson, J. C. Davis, “X-ray interaction: photoabsorption, scattering, transmission and reflection at E=10–30,000 eV,Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

C. R. Acad. Sci. Paris Ser. IV (1)

J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, Yu. A. Uspenskii, “Capillary discharge tabletop soft X-ray lasers reach new wavelengths and applications,” C. R. Acad. Sci. Paris Ser. IV 1, 1063–1072 (2000).

IEEE J. Sel. Top. Quantum Electron. (1)

I. A. Artioukov, B. R. Benware, J. J. Rocca, M. Forsythe, Yu. A. Uspenskii, A. V. Vinogradov, “Determination of XUV optical constants by reflectometry using a high-repetition rate 46.9-nm laser,” IEEE J. Sel. Top. Quantum Electron. 5, 1495–1501 (1999).
[CrossRef]

J. Russ. Laser Res. (1)

R. M. Fechtchenko, A. V. Popov, A. V. Vinogradov, “On reflection from surfaces with a thin overlayer,” J. Russ. Laser Res. 22, 139–148 (2001).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, S. Mrowka, F. Schäfers, “Sc–Si normal incidence mirrors for a VUV interval of 35–50 nm,” Nucl. Instrum. Methods Phys. Res. A 448, 147–151 (2000).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. B (2)

E. M. Gullikson, P. Denham, S. Mrowka, J. H. Underwood, “Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges,” Phys. Rev. B 49, 16283–16288 (1994).
[CrossRef]

Yu. A. Uspenskii, B. N. Harmon, “Large selective magneto-optic response from magnetic semiconducting layered structures,” Phys. Rev. B 61, R10571–R10574 (2000).
[CrossRef]

Sov. Phys. Solid State (1)

A. G. Nargizyan, S. N. Rashkeev, Yu. A. Uspenskii, “Microscopic calculations of the optical properties of 4d-transition metals in the vacuum UV,” Sov. Phys. Solid State 34, 626–632 (1992).

Surf. Rev. Lett. (1)

Y. Hotta, N. Furudate, M. Yamamoto, N. Watanabe, “Design and fabrication of multilayer mirrors for He-II radiation,” Surf. Rev. Lett. 9, 571–576 (2002).
[CrossRef]

Other (3)

E. Spiller, Soft X-Ray Optics (SPIE Optical Engineering Press, Bellingham, Wash., 1994).

Yu. A. Uspenskii, A. V. Vinogradov (data available from the authors).

Yu. A. Uspenskii, S. V. Antonov, V. Yu. Fedotov, A. V. Vinogradov, “Optical properties of 3D transition metals in the spectral interval of interest for discharge-pumped XUV lasers,” in Soft X-Ray Lasers and Applications II, J. J. Rocca, L. B. Da Silva, eds., Proc. SPIE3156, 288–294 (1997).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Schematic representation of the refractive-index profile n(z) in the protected layered structure under consideration. Vacuum and substrate regions are labeled V and S, a material under study is marked as M, and capping and buffer structures are symbolized by C and B.

Fig. 2
Fig. 2

Transmissivity spectra of Sc and Ti (a) for Sc films with thickness d=7.5, 10, 12.5, 70, 100, and 130 nm (going from the top down) and (b) for Ti films with d=10, 14, 18, 40, 70, and 100 nm.

Fig. 3
Fig. 3

Net β(ω) of Sc found from Eq. (15). Insert (a) shows agreement between this β(ω) (solid curve) and the values obtained from the films pairs of 7.5–130, 10–100, and 12.5–100 nm (symbols) in the low-absorption region of 18–24 eV. Insert (b) demonstrates the agreement of the β(ω) with the results found for the film pairs 7.5–10, 7.5–12.5, and 10–12.5 nm in the high-absorption region of 35–45 eV.

Fig. 4
Fig. 4

Reflectivity spectra for Sc films of different thickness.

Fig. 5
Fig. 5

Calculated optical constants δ(ω) and β(ω) (curves) in comparison with the atomic tables data (symbols): (a) Sc and (b) Ti.

Fig. 6
Fig. 6

Calculated and experimental reflectivity ratios Ri(ω)/Rj(ω) for di=100 nm and dj=7.5 nm.

Fig. 7
Fig. 7

Calculated and experimental angle-dependent reflectivity of the Si (15-nm)/Sc (12-nm) multilayer at λ=46.9 nm.

Fig. 8
Fig. 8

Calculated (solid curve) and experimental (curve with symbols) normal-incidence reflectivity spectra of (a) the Si (10.9-nm) and Sc (8.6-nm) multilayer (the dashed curve shows the result of calculation with optical constants of Sc from Ref. 14) and (b) the Si (14.8-nm) and Sc (11.6-nm) multilayer.

Fig. 9
Fig. 9

Calculated (solid curve) and measured (symbols) normal-incidence reflectivity of the Si (7.3-nm), W (0.6-nm), Sc (10.9-nm), and W (0.6-nm) multilayer.

Equations (19)

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

U+(z)=exp[ik0(z-z1)pV]+r+ exp[-ik0(z-z1)pV],z<z1t+ exp[ik0(z-z2)p],z>z2,
U-(z)=t- exp[-ik0(z-z1)pV],z<z1exp[-ik0(z-z2)p]+r- exp[ik0(z-z2)p],z>z2
V+(z)=exp[ik0(z-z3)p]+ρ+ exp[-ik0(z-z3)p],z<z3τ+ exp[ik0(z-z4)pS],z>z4,
V-(z)=τ- exp[-ik0(z-z3)p],z<z3exp[-ik0(z-z4)pS]+ρ- exp[ik0(z-z4)pS],z>z4
E(z)=A+U+(z)+A-U-(z),z<z1A+U+(z)+A-U-(z)=B+V+(z)+B-V-(z),z2<z<z3B+V+(z)+B-V-(z),z>z4
E(z)=exp[ik0(z-z1)pV]A++exp[-ik0(z-z1)pV](r+A++t-A-),z<z1exp[ik0(z-z2)p]W++exp[-ik0(z-z2)p]W-,z2<z<z3exp[ik0(z-z4)pS](B+τ++B-ρ-)+exp[-ik0(z-z4)pS]B-,z>z4
W+=A+t++A-r-=B+ exp(-ik0pd),
W-=A-=(B+ρ++B-τ-)exp(ik0pd).
A-/A+=t+ρ+ exp(2iD)1-r-ρ+ exp(2iD),
B+/A+=t+ exp(iD)1-r-ρ+ exp(2iD),
r=r++t+t- exp(2iD)ρ+1-r-ρ+ exp(2iD),
t=t+τ+ exp(iD)1-r-ρ+ exp(2iD).
R=Rc|1+ξf exp(2iD)|2,
T=TcTb|f exp(iD)|2,
R=Rc[1+2 cos(2D+χ)|ξ|exp(-2D)+|ξ|2 exp(-4D)],
T=TcTb exp(-2D),
β(ω)=12k0(dj-di)ln[Ti(ω)/Tj(ω)],
Ri(ω)/Rj(ω)=1+2 cos(2Di+χ)|ξ|exp(-2Di)+|ξ|2 exp(-4Di)1+2 cos(2Dj+χ)|ξ|exp(-2Dj)+|ξ|2 exp(-4Dj),
Δδ(ω)=0ωmin2ωΔβ(ω)ω2-ω2dω+ωmax2ωΔβ(ω)ω2-ω2dω-1ω20ωmin2ωΔβ(ω)dω+ωmin2Δβ(ω)/ωdω-δf/ω2+Δ,

Metrics