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

Applied Optics

Volumn 41, Issue 7, 2002, Pages 1434-1445

  Goray, Leonid I ^a   Seely, John F ^b  

^a Intl Intellectual Group Inc   (United States)

^b NAVAL RESEARCH LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISPERSION (WAVES); HOLOGRAPHY; INTEGRAL EQUATIONS; MONOLAYERS; MULTILAYERS; SYNCHROTRON RADIATION; ULTRAVIOLET RADIATION; X RAY OPTICS;

SOFT X-RAYS;

DIFFRACTION GRATINGS;

EID: 0036507807     PISSN: 1559128X     EISSN: 21553165     Source Type: Journal    
DOI: 10.1364/AO.41.001434     Document Type: Article

References (37)

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-Â 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-Â 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. Yuak-shin, “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-Â 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-Â 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. Roschup-kin, 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 (SpringerVerlag, 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. Neviere 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. Neviere, “Thin films and gratings: theories used to optimize the high reflectivity of mirrors and gratings for x-ray optics, ” in Applications ofThin-Film Multilayered Structures to Figured X-Ray Optics, G. F. Marshall, ed., Proc. SPIE 563, 142-149 (1985).
18. M. Neviere, “Multilayer coated gratings for x-ray diffraction: differential theory, ” J. Opt. Soc. Am. A 8, 1468-1473 (1991).
19. A. Sammar, J.-M. Andre, 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. Andre, “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). Internet site, http://www.pcgrate.com.
24. J. F. Seely and L. I. Goray, “Normal incidence multilayer gratings for the extreme ultraviolet region: experimental mea surements 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).
25. J. F. Seely, “Multilayer grating for the extreme ultraviolet spectrometer (EIS), ” in X-Ray Optics, Instruments, and Missions TV, R. B. Hoover and A. B. C. Walker, eds., Proc. SPIE 4138, 174-181 (2000).
26. 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).
27. 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 TV, A. M. Larar and M. G. Mlync-zak, eds., Proc. SPIE 4485 (to be published).
28. L. I. Goray, “Modified integral method and real electromagnetic properties of echelles, ” in Diffractive and Holographic Technologies for Tntegrated Photonic Systems, R. I. Suther- land, D. W. Prather, and I. Cindrich, eds., Proc. SPIE 4291, 13-24 (2001).
29. M. Neviere and F. Montiel, “Soft-x-ray multilayer coated ech-elle gratings: electromagnetic and phenomenological study, ” J. Opt. Soc. Am. A 13, 811-818 (1996).
30. A. Pomp, “The integral method for coated gratings: compu tational cost, ” J. Mod. Opt. 38, 109-120 (1991).
31. 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.”
32. 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).
33. W. Jark, “Enhancement of diffraction grating efficiencies in soft-x-ray region by multilayer coating, ” Opt. Commun. 60, 201-205 (1986).
34. S. Bajt, “Molybdenum-ruthenium/beryllium multilayer coatings, ” J. Vac. Sci. Technol. A 18, 557-559 (2000).
35. A. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflec tion 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.
36. A. T. Arakawa, T. A. Callcott, and Y. C. Chang, “Beryllium (Be), ” in Handbook of Optical Constants of Solids TT, E. D. Palik, ed. (Academic, New York, 1991), pp. 421-433.
37. A. W. Lynch and W. R. Hunter, “Molybdenum (Mo), ” in Handbook ofOptical Constants ofSolids, E. D. Palik, ed. (Academic, New York, 1985), pp. 303-313.