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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 7 — Mar. 1, 2002
  • pp: 1434–1445

Efficiencies of Master, Replica, and Multilayer Gratings for the Soft-X-Ray-Extreme-Ultraviolet Range: Modeling Based on the Modified Integral Method and Comparisons with Measurements

Leonid I. Goray and John F. Seely  »View Author Affiliations


Applied Optics, Vol. 41, Issue 7, pp. 1434-1445 (2002)
http://dx.doi.org/10.1364/AO.41.001434


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Abstract

The near-normal-incidence efficiencies of a 2400-groove/mm holographic master grating, a replica grating, and a multilayer grating are modeled in the soft-x-ray-extreme-ultraviolet (EUV) regions and are compared with efficiencies that are measured with synchrotron radiation. The efficiencies are calculated by the computer program PCGrate, which is based on a rigorous modified integral method. The theory of our integral method is described both for monolayer and multilayer gratings designated for the soft-x-ray-EUV-wavelength range. The calculations account for the groove profile as determined from atomic force microscopy with a depth scaling in the case of the multilayer grating and an average random microroughness (0.7 nm) for the short wavelengths. The refractive indices of the grating substrate and coatings have been taken from different sources because of the wide range of the wavelengths (4.5–50 nm). The measured peak absolute efficiency of 10.4% in the second diffraction order at a wavelength of 11.4 nm is achieved for the multilayer grating and is in good agreement with a computed value of ~11.5%. Rigorous modeling of the efficiencies of three similar gratings is in good overall agreement with the measured efficiency over a wide wavelength region. Additional calculations have indicated that relatively high normal incidence efficiency (of at least several percent) and large angular dispersion in the higher orders can be achieved in the 4.5–10.5-nm range by application of various multilayer coatings.

© 2002 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(260.7200) Physical optics : Ultraviolet, extreme
(310.6860) Thin films : Thin films, optical properties
(340.7470) X-ray optics : X-ray mirrors

Citation
Leonid I. Goray and John F. Seely, "Efficiencies of Master, Replica, and Multilayer Gratings for the Soft-X-Ray-Extreme-Ultraviolet Range: Modeling Based on the Modified Integral Method and Comparisons with Measurements," Appl. Opt. 41, 1434-1445 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-7-1434


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References

  1. J. F. Seely, R. G. Cruddace, M. P. Kowalski, W. R. Hunter, T. W. Barbee, J. C. Rife, R. Ely, and K. G. Stilt, “Polarization and efficiency of a concave multilayer grating in the 135–250-Å region and in normal-incidence and Seya-Namioka mounts,” Appl. Opt. 34, 7347–7354 (1995).
  2. J. F. Seely, M. P. Kowalski, R. G. Cruddace, K. F. Heidemann, U. Heinzmann, U. Kleineberg, K. Osterried, D. Menke, J. C. Rife, and W. R. Hunter, “Multilayer-coated laminar grating with 16% normal-incidence efficiency in the 150-Å region,” Appl. Opt. 36, 8206–8213 (1997).
  3. C. Montcalm, S. Bajt, and J. F. Seely, “MoRu-Be multilayer-coated grating with 10.4% normal-incidence efficiency near the 11.4-nm wavelength,” Opt. Lett. 26, 125–127 (2001).
  4. V. V. Martynov, H. A. Padmore, Yu. Agafonov, and A. Yuakshin, “X-ray multilayer gratings with very high diffraction efficiency,” in Gratings and Grating Monochromators for Synchrotron Radiation, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3150, 2–8 (1997).
  5. M. P. Kowalski, J. F. Seely, L. I. Goray, W. R. Hunter, and J. C. Rife, “Comparison of the calculated and the measured efficiencies of a normal-incidence grating in the 125–225-Å wavelength range,” Appl. Opt. 36, 8939–8943 (1997).
  6. J. F. Seely, L. I. Goray, W. R. Hunter, and J. C. Rife, “Thin-film interference effects of a normal-incidence grating in the 100–350-Å wavelength region,” Appl. Opt. 38, 1251–1258 (1999).
  7. J. F. Seely, C. Montcalm, and S. Bajt, “High-efficiency MoRu-Be multilayer-coated gratings operating near normal incidence in the 11.1–12.0-nm wavelength range,” Appl. Opt. 40, 5565–5574 (2001).
  8. A. I. Erko, B. Vidal, P. Vincent, Yu. A. Agafonov, V. V. Martynov, D. V. Roschupkin, and M. Brunel, “Multilayer grating efficiency: numerical and physical experiments,” Nucl. Instrum. Methods A 333, 599–606 (1993).
  9. V. Martynov, B. Vidal, P. Vincent, M. Brunel, D. V. Roschupkin, Yu. Agafonov, A. Erko, and A. Yuakshin, “Comparison of modal and diffirential methods for multilayer gratings,” Nucl. Instrum. Methods A 339, 617–625 (1994).
  10. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
  11. L. I. Goray, “Nonscalar properties of high groove frequency gratings for soft-x-ray and XUV regions: the integral equation method,” in X-Ray and UV Detectors, R. B. Hoover and M. W. Tate, eds., Proc. SPIE 2278, 173–177 (1994).
  12. M. Nevière and J. Flamand, “Electromagnetic theory as it applies to x-ray and XUV gratings,” Nucl. Instrum. Methods 172, 273–279 (1980).
  13. H. A. Podmore, V. Martynov, and K. Holis, “The use of diffraction efficiency theory in the design of soft-x-ray monochromators,” Nucl. Instrum. Methods A 347, 206–215 (1994).
  14. L. I. Goray, “Numerical analysis for relief gratings working in the soft-x-ray and XUV region by the integral equation method,” in X-Ray and UV Detectors, R. B. Hoover and M. W. Tate, eds., Proc. SPIE 2278, 168–172 (1994).
  15. L. I. Goray, “Rigorous integral method in application to computing diffraction on relief gratings working in wavelength range from microwaves to x ray,” in Application and Theory of Periodic Structures, T. Jannson and N. C. Gallagher, eds., Proc. SPIE 2532, 427–433 (1995).
  16. L. I. Goray and B. C. Chernov, “Comparison of rigorous methods for x-ray and XUV grating diffraction analysis,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover and A. B. Walker, eds., Proc. SPIE 2515, 240–245 (1995).
  17. B. Vidal, P. Vincent, P. Dhez, and M. Nevière, “Thin films and gratings: theories used to optimize the high reflectivity of mirrors and gratings for x-ray optics,” in Applications of Thin-Film Multilayered Structures to Figured X-Ray Optics, G. F. Marshall, ed., Proc. SPIE 563, 142–149 (1985).
  18. M. Nevière, “Multilayer coated gratings for x-ray diffraction: differential theory,” J. Opt. Soc. Am. A 8, 1468–1473 (1991).
  19. A. Sammar, J.-M. André, and B. Pardo, “Diffraction and scattering by lamellar amplitude multilayer gratings in the XUV region,” Opt. Commun. 86, 245–254 (1991).
  20. V. I. Erofeev and N. V. Kovalenko, “Method of eigenvectors for numerical studies of multilayer gratings,” X-Ray Sci. Technol. 7, 75 (1997).
  21. M. Nevière, “Bragg-Fresnel multilayer gratings electromagnetic theory,” J. Opt. Soc. Am. A 11, 1835–1845 (1994).
  22. A. Sammar and J.-M. André, “Diffraction of multilayer gratings and zone plates in the x-ray region using the Born approximation,” J. Opt. Soc. Am. A 10, 600–613 (1993).
  23. L. I. Goray, “Modified integral method for weak convergence problems of light scattering on relief grating,” in Diffractive and Holographic Technologies for Integrated Photonic Systems, R. I. Sutherland, D. W. Prather, and I. Cindrich, eds., Proc. SPIE 4291, 1–12 (2001).
  24. Internet site, http://www.pcgrate.com.
  25. J. F. Seely and L. I. Goray, “Normal incidence multilayer gratings for the extreme ultraviolet region: experimental measurements and computational modeling,” in X-Ray Optics, Instruments, and Missions II, R. B. Hoover and A. B. Walker, eds., Proc. SPIE 3766, 364–370 (1999).
  26. J. F. Seely, “Multilayer grating for the extreme ultraviolet spectrometer (EIS),” in X-Ray Optics, Instruments, and Missions IV, R. B. Hoover and A. B. C. Walker, eds., Proc. SPIE 4138, 174–181 (2000).
  27. D. A. Content, “Diffraction grating groove analysis used to predict efficiency and scatter performance,” in Conference on Gradient Index, Miniature, and Diffractive Optical Systems, A. D. Kathman, ed., Proc. SPIE 3778, 19–30 (1999).
  28. D. A. Content, “Grating groove metrology and efficiency predictions from the soft-x-ray to the far infrared,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research IV, A. M. Larar and M. G. Mlynczak, eds., Proc. SPIE 4485 (to be published).
  29. L. I. Goray, “Modified integral method and real electromagnetic properties of echelles,” in Diffractive and Holographic Technologies for Integrated Photonic Systems, R. I. Sutherland, D. W. Prather, and I. Cindrich, eds., Proc. SPIE 4291, 13–24 (2001).
  30. M. Nevière and F. Montiel, “Soft-x-ray multilayer coated echelle gratings: electromagnetic and phenomenological study,” J. Opt. Soc. Am. A 13, 811–818 (1996).
  31. A. Pomp, “The integral method for coated gratings: computational cost,” J. Mod. Opt. 38, 109–120 (1991).
  32. S. Yu. Sadov and L. I. Goray are preparing a manuscript to be called “The modified integral method for gratings covered with thin or thick layers of arbitrary shape.”
  33. A. Spiller and A. E. Rosenbluth, “Determination of thickness errors and boundary roughness from the measured performance of a multilayer coating,” in Applications of Thin-Film Multilayered Structures to Figured X-Ray Optics, G. F. Marshall, ed., Proc. SPIE 563, 221–236 (1985).
  34. W. Jark, “Enhancement of diffraction grating efficiencies in soft-x-ray region by multilayer coating,” Opt. Commun. 60, 201–205 (1986).
  35. S. Bajt, “Molybdenum-ruthenium/beryllium multilayer coatings,” J. Vac. Sci. Technol. A 18, 557–559 (2000).
  36. A. 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). Updated optical constants were obtained from the Internet site, http://cindy.lbl.gov/optical_constants.
  37. A. T. Arakawa, T. A. Callcott, and Y. C. Chang, “Beryllium (Be),” in Handbook of Optical Constants of Solids II, E. D. Palik, ed. (Academic, New York, 1991), pp. 421–433.
  38. A. W. Lynch and W. R. Hunter, “Molybdenum (Mo),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 303–313.

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