OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 2 — Feb. 1, 2004
  • pp: 298–305

Efficient method for the determination of extreme-ultraviolet optical constants in reactive materials: application to scandium and titanium

Yu. A. Uspenskii, John F. Seely, N. L. Popov, A. V. Vinogradov, Yu. P. Pershin, and V. V. Kondratenko  »View Author Affiliations

JOSA A, Vol. 21, Issue 2, pp. 298-305 (2004)

View Full Text Article

Acrobat PDF (204 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The chemical reaction of a sample with atmospheric gases causes a significant error in the determinantion of the complex refractive index n = 1 − δ + <i>i</i>β 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 ħω = 18–70 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

OCIS Codes
(160.3900) Materials : Metals
(260.7200) Physical optics : Ultraviolet, extreme
(300.6560) Spectroscopy : Spectroscopy, x-ray
(340.6720) X-ray optics : Synchrotron radiation
(340.7480) X-ray optics : X-rays, soft x-rays, extreme ultraviolet (EUV)

Yu. A. Uspenskii, John F. Seely, N. L. Popov, A. V. Vinogradov, Yu. P. Pershin, and V. V. Kondratenko, "Efficient method for the determination of extreme-ultraviolet optical constants in reactive materials: application to scandium and titanium," J. Opt. Soc. Am. A 21, 298-305 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. C. Tarrio, R. N. Watts, T. B. Lucatorto, J. M. Slaughter, and M. Falce, “Optical constants of in situ-deposited films of important extreme-ultraviolet multilayer mirror materials,” Appl. Opt. 37, 4100–4104 (1998).
  2. R. M. Fechtchenko and A. V. Vinogradov, “Reflection from surfaces with a thin overlayer,” Opt. Lett. 25, 998–1000 (2000).
  3. R. M. Fechtchenko, A. V. Popov, and A. V. Vinogradov, “On reflection from surfaces with a thin overlayer,” J. Russ. Laser Res. 22, 139–148 (2001).
  4. R. Soufli and 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).
  5. I. A. Artioukov, B. R. Benware, J. J. Rocca, M. Forsythe, Yu. A. Uspenskii, and 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).
  6. E. M. Gullikson, P. Denham, S. Mrowka, and 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).
  7. R. Soufli and E. M. Gullikson, “Absolute photoabsorption measurements of molybdenum in the range 60–930 eV for optical constant determination,” Appl. Opt. 37, 1713–1719 (1998).
  8. Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, and V. Yu. Fedotov, “High-reflectivity multilayer mirrors for a vacuum-ultraviolet interval of 35–50 nm,” Opt. Lett. 23, 771–773 (1998).
  9. Yu. A. Uspenskii, V. E. Levashov, A. V. Vinogradov, A. I. Fedorenko, V. V. Kondratenko, Yu. P. Pershin, E. N. Zubarev, S. Mrowka, and 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).
  10. J. F. Seely, Yu. A. Uspenskii, Yu. P. Pershin, V. V. Kondratenko, and 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).
  11. Yu. A. Uspenskii, S. V. Antonov, V. Yu. Fedotov, and 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 and L. B. Da Silva, eds., Proc. SPIE 3156, 288–294 (1997).
  12. Yu. A. Uspenskii and B. N. Harmon, “Large selective magneto-optic response from magnetic semiconducting layered structures,” Phys. Rev. B 61, R10571–R10574 (2000).
  13. Yu. A. Uspenskii and A. V. Vinogradov (data available from the authors).
  14. B. L. Henke, E. M. Gullikson, and 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).
  15. J. J. Rocca, M. Frati, B. Benware, M. Seminario, J. Filevich, M. Marconi, K. Kanizay, A. Ozols, I. A. Artukov, A. Vinogradov, and 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, and 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, and N. Watanabe, “Design and fabrication of multilayer mirrors for He-II radiation,” Surf. Rev. Lett. 9, 571–576 (2002).
  19. C. Chang, E. Anderson, P. Naulleau, E. Gullikson, K. Goldberg, and D. Attwood, “Direct measurement of index of refraction in the extreme-ultraviolet wavelength region with a novel interferometer,” Opt. Lett. 27, 1028–1030 (2002).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited