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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 1 — Jan. 1, 2006
  • pp: 155–165

Multilayer resonant subwavelength gratings: effects of waveguide modes and real groove profiles

Leonid I. Goray, Ivan G. Kuznetsov, Sergey Yu. Sadov, and David A. Content  »View Author Affiliations

JOSA A, Vol. 23, Issue 1, pp. 155-165 (2006)

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The boundary integral equation code PCGrate-S(X) is used to analyze diffraction on Hubble Space Telescope Cosmic Origins Spectrograph gratings at different boundary shapes and layer thicknesses. An effect of resonance anomalies excited in nonconformal dielectric layers overcoated on the surface of metallic grating on the efficiency is studied for the first time to our knowledge. Refractive indices (RIs) for bulk Mg F 2 taken from well-known references are found to be not suitable for thin optical layers at wavelengths between 115 and 170 nm . A method based on scale fitting of calculated and measured grating efficiencies is outlined for derivation of thin-film optical constants at hard to measure wavelengths. The calculated efficiency based on real boundary profiles and derived RIs of the G185M subwavelength grating is shown to fit within 9.6% or better to the measured data.

© 2006 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics
(260.7190) Physical optics : Ultraviolet
(310.2790) Thin films : Guided waves
(310.6860) Thin films : Thin films, optical properties

ToC Category:

Leonid I. Goray, Ivan G. Kuznetsov, Sergey Yu. Sadov, and David A. Content, "Multilayer resonant subwavelength gratings: effects of waveguide modes and real groove profiles," J. Opt. Soc. Am. A 23, 155-165 (2006)

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  1. J. C. Green, "Cosmic Origins Spectrograph," in UV, Optical, and IR Space Telescopes and Instruments, J.B.Breckinridge and P.Jakobsen, eds., Proc. SPIE 4013, 352-359 (2000).
  2. I. G. Kuznetsov, E. Wilkinson, D. A. Content, R. A. Boucarut, and T. J. Madison, "Grating efficiencies comparison study: calculations versus metrology for various types of high groove density gratings at VUV-UV wavelengths," in Optical Modeling and Performance Predictions, M.A.Kahan, ed., Proc. SPIE 5178, 267-277 (2004).
  3. R. Grange, V. Dauer, M. Saisse, M. Nevière, J. Flamand, and F. Bonnemason, "6000-g/mm holographic flight gratings for the high resolution Far Ultraviolet Spectroscopic Explorer: efficiency, resolution and stray light measurements," in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W.R.McKinney and C.A.Palmer, eds., Proc. SPIE 3450, 103-112 (1998).
  4. V. Dauer, "Optical constants of lithium fluoride thin films in the far ultraviolet," J. Opt. Soc. Am. B 17, 300-303 (2000). [CrossRef]
  5. E.Palik, ed., Handbook of Optical Constant of Solids (Academic, 1991), Vol. 2.
  6. J. Larruquert and R. Keski-Kuha, "Far ultraviolet optical properties of MgF2 films deposited by ion-beam sputtering and their application as protective coatings for Al," Opt. Commun. 215, 93-99 (2003). [CrossRef]
  7. See website at www.pcgrate.com.
  8. D. A. Content, P. Arsenovic, I. G. Kuznetsov, and T. Hadjimichael, "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, 405-416 (2001).
  9. L. I. Goray and S. Yu. Sadov, "Numerical modeling of coated gratings in sensitive cases," in Diffractive Optics and Micro-Optics, R.Magnusson, ed., Vol. 75of OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 365-379.
  10. D. Maystre, "A new general integral theory for dielectric coated gratings," J. Opt. Soc. Am. 68, 490-495 (1978). [CrossRef]
  11. A. Pomp, "The integral method for coated gratings: computational cost," J. Mod. Opt. 38, 109-120 (1991). [CrossRef]
  12. B. Kleemann, A. Mitreiter, and F. Wyrowski, "Integral equation method with parametrization of grating profile: theory and experiments," J. Mod. Opt. 43, 1323-1349 (1996). [CrossRef]
  13. J. T. Beale and M.-C. Lai, "A method for computing nearly singular integrals," SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 38, 1902-1925 (2001).
  14. K. E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind (Cambridge U. Press, 1997). [CrossRef]
  15. G. Elschner and I. Graham, "An optimal order collocation method for first kind boundary integral equations on polygons," Numer. Math. 70, 1-31 (1995). [CrossRef]
  16. R. Kress, "A Nyström method for boundary integral equations in domains with corners," Numer. Math. 58, 145-161 (1990). [CrossRef]
  17. P. Laubin, "High order convergence for collocation of second kind boundary integral equations on polygons," Numer. Math. 79, 107-140 (1998). [CrossRef]
  18. R. Kress, I. Sloan, and F. Stenger, "A sinc quadrature method for the double layer integral equation in planar domain with corners," J. Integral Equ. Appl. 10, 291-317 (1998). [CrossRef]
  19. C. M. Linton, "The Green's function for two-dimensional Helmholtz equation in periodic domains," J. Eng. Math. 33, 377-402 (1998). [CrossRef]
  20. R.Petit, ed., Electromagnetic Theory of Gratings (Springer, 1980). [CrossRef]
  21. A. Aho, J. Hopcroft, and J. Ullman, The Design and Analysis of Computer Algorithms (Addison-Wesley, 1976).
  22. D. Knuth, The Art of Computer Programming (Addison-Wesley, 1998), Vol. 2.
  23. I. G. Kuznetsov, D. A. Content, R. A. Boucarut, and T. J. Madison, "Design, performance and reliability of a high angular resolution, wide angular range, large aperture fully automated UV scatterometer," in Optical Spectroscopic Techniques, Remote Sensing, and Instrumentation for Atmospheric and Space Research IV, A.M.Larar and M.G.Mlynczak, eds., Proc. SPIE 4485, 417-428 (2001).
  24. J. F. Seely, L. I. Goray, D. L. Windt, B. Kjornrattanawanich, Yu. A. Uspenskii, and A. V. Vinogradov, "Extreme ultraviolet optical constants for the design and fabrication of multilayer gratings," in Optical Constants of Materials for UV to X-Ray Wavelengths, R.Soufli and J.F.Seely, eds., Proc. SPIE 5538, 43-52 (2004).
  25. E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel-Dekker, 1997).
  26. American Institute of Physics Handbook (McGraw-Hill, 1972).
  27. R. Keski-Kuha, NASA GSFC, Code 551, Greenbelt, Maryland 20771 (personal communication 2005).
  28. E. Spiller, Soft X-ray Optics (SPIE Press, 1994). [CrossRef]
  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).

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