References

I. I. Goray and L. I. Goray, “Computer system configured in support of solving NP-complete problems at high speed,” United State Patent No. 6,636,840 B1, International Intellectual Group, Inc., Oct. 21, 2003.

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L. I. Goray, J. F. Seely, and S. Yu. Sadov, “Spectral separation of the efficiencies of the inside and outside orders of soft-x-ray-extreme-ultraviolet gratings at near normal incidence,” J. Appl. Phys., vol. 100, No. 9, 2006, pp. 094901-1-13.

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L. I. Goray, I. G. Kuznetsov, S. Yu. Sadov, and D. A. Content, “Multilayer resonant subwavelength gratings: effects of waveguide modes and real groove profiles,” J. Opt. Soc. Am A, vol. 23, No. 1, 2006, pp. 155-165.

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L. I. Goray, “Numerical analysis of the efficiency of multilayer-coated gratings using integral method,” Nuclear Inst. and Methods in Physics Research A, vol. 536, No. 1-2, 2005, pp. 211-221.

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L. I. Goray and G. Schmidt, “Boundary Integral Equation Methods for Conical Diffraction and Short Waves,” Ch.# 12 in Gratings: Theory and Numeric Applications, Second Revisited Edition, E. Popov, ed. (Institut Fresnel, AMU, 2014).

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L. I. Goray and J. F. Seely, “Efficiencies of master, replica, and multilayer gratings for the soft x-ray – EUV range: modeling based on the modified integral method and comparisons to measurements,” Appl. Opt., vol. 41, No. 7, 2002, pp. 1434-1445.

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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., SPIE Proc., vol. 4291, 2001, pp.1-12.

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J. Seely, B. Kjornrattanawanich, L. Goray, Y. Feng, and J. Bremer, “Characterization of zone plate properties using monochromatic synchrotron radiation in the 2 to 20 nm wavelength range,” Appl. Opt., vol. 50, No. 18, 2011, pp. 3015–3020.

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J. F. Seely, L. I. Goray, B. Kjornrattanawanich, J. M. Laming, G. E. Holland, K. A. Flanagan, R. K. Heilmann, C.-H. Chang, M. L. Schattenburg, and A. P. Rasmussen, “Efficiency of a grazing incidence off-plane grating in the soft x-ray region,” Appl. Opt., vol. 45, No. 8, 2006, pp. 1680-1687.

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D. L. Voronov, E. H. Anderson, R. Cambie, S. Cabrini, S. D. Dhuey, L. I. Goray, E. M. Gullikson, F. Salmassi, T. Warwick, V. V. Yashchuk, and H. A. Padmore, “A 10,000 groove/mm multilayer coated grating for EUV spectroscopy,” Opt. Express, vol. 19, No. 7, 2011, pp. 6320–6325.

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L. I. Goray and G. Schmidt, “Solving conical diffraction grating problems with integral equations,” J. Opt. Soc. Am. A, vol. 27, No. 3, 2010, pp. 585–597.

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L. I. Goray, N. I. Chkhalo, and G. E. Tsyrlin, “Determining angles of incidence and heights of quantum dot faces by analyzing X-ray diffuse and specular scattering,” Technical Physics, vol. 54, No. 4, 2009, pp. 561–568.

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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., SPIE Proc., vol. 5538, 2004, pp. 43-52.

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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., SPIE Proc., vol. 5178, 2004, pp. 267-277.

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C.-H. Chang, J. C. Montoya, M. Akilian, A. Lapsa, M. Li, K. A. Flanagan, A. P. Rasmussen, J. F. Seely, J. M. Laming, B. Kjornrattanawanich, and L. I. Goray, “High fidelity blazed grating replication using nanoimprint lithography,” J. Vac. Sci. Technol. B, vol. 22, No. 6, pp. 3260-3264, 2004.

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J. F. Seely, C. M. Brown, D. L. Windt, S. Donguy, and B. Kjornrattanawanich, “Normal-Incidence Efficiencies of multilayer-coated laminar gratings for the Extreme-Ultraviolet Imaging Spectrometer on the Solar-B mission,” Appl. Opt., vol. 43, No. 7, 2004, pp. 1463-1471.

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L. I. Goray, “Specular and diffuse scattering from random asperities of any profile using the rigorous method for x-rays and neutrons,” H. Bosse, B. Bodermann, and R. M. Silver, eds., SPIE Proc., vol. 7390, 2009, pp. 73900V-1–11.

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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., vol.41, No. 10, 2002, pp. 1846-1851.

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D. L. Voronov, E. H. Anderson, R. Cambie, L. I. Goray, P. Gawlitza, E. M.Gullikson, F. Salmassi, T. Warwick, V. V. Yashchuk, H. A. Padmore, “Development of near atomically perfect diffraction gratings for EUV and soft x-rays with very high efficiency and resolving power,” Journal of Physics: Conference Series C, vol. 425, 2013, pp. 152006-1–4.

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W. R. Hunter, M. P. Kowalski, J. C. Rife, and R. G. Gruddace, “Investigation of the properties of an ion-etched plane laminar holographic grating,” Appl. Opt., vol. 40, No. 34, 2001, pp. 6157-6165.

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T. C. Blasiak and S. L. Zheleznyak, “Diffraction grating having enhanced blaze performance at two wavelengths,” United State Patent No. 6,067,197, Spectronic Instruments, Inc., May 23, 2000.

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L. I. Goray, “Off-plane grazing-incidence fan-groove blazed grating to serve as a high-efficiency spectral purity filter for EUV lithography,” in Advances in X-Ray/EUV Optics, Components, and Applications, A. M. Khounsary and C. Morawe, eds., SPIE Proc., vol. 6317, 2006., pp. 0O-1-9.

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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., SPIE Proc., vol. 4291, 2001, pp. 13-24.

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M. R. Haas, E. F. Erickson, J. A. Baltz, S. W. J. Colgan, D. H. Lynch, J. McGuire, R. K. Pina, T. L. Roellig, J. P. Simpson, C. M. Telesco, J. Wolf, and E. T. Young, “Preliminary optical design of AIRES: an airborne infrared echelle spectrometer for SOFIA,” in Infrared Astronomical Instrumentation, A. M. Fowler, ed., SPIE Proc., vol. 3354, 1998, pp. 940-951.

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A. Rathsfeld, G. Schmidt, and B. H. Kleemann, “On a Fast Integral Equation Method for Diffraction Gratings,” Commun. Comput. Phys., vol. 1, No. 6, 2006, pp. 984-1009.

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N. Dechamps, N. de Beaucoudrey, C. Bourlier, and S. Toutain, “Fast numerical method for electromagnetic scattering by rough layered interfaces: Propagation-inside-layer expansion method,” J. Opt. Soc. Am. A, vol. 23, No. 2, 2006, pp. 359-369.

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Diffraction Gratings Handbook, C. Palmer, ed., 6th, Newport Corp. Press, Rochester, 2005, 265 p.

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Light Propagation in Periodic Media: Differential Theory and Design, M. Neviere and E. Popov, in Optical Engineering Series/81, Marcel Dekker, New York – Basel, 2002, 410 p.

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M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces, “Waves Random Media, vol. 11, No. 3, 2001, pp. R103–R137.

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Scattering of Electromagnetics Waves: Numerical Simulations, L. Tsang, J. A. Kong, K.-H. Ding, and C. O. Ao, Wiley, 2001, 736 p.

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Diffraction Gratings and Applications, E. G. Loewen, and E. Popov, in Optical Engineering Series/58, Marcel Dekker, New York – Basel – Hong Kong, 1997, 601 p.

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L.I. Goray and G. Schmidt, “Analysis of two-dimensional photonic band gaps of any rod shape and conductivity using a conical-integral-equation method,” Phys. Rev. E, vol. 85, 2012, pp. 036701-1–12.

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Diffraction Gratings, in SPIE Milestones series/MS83, D. R. Maystre, ed., SPIE Optical Engineering Press, Bellingham, Washington, USA, 1993, 732 p.

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Diffraction Gratings, M. C. Hutley, in Techniques of Physics/6, Academic Press, New York – London, 1982, 330 p.

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Electromagnetic Theory of Gratings, in Topics in Current Physics/22, R. Petit, ed., Springer-Verlag – Berlin – Heidelberg – New York, 1980, 286 p.

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B. 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, vol. 54, 1993, pp.181-342. Updated optical constants can be obtained at

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Handbook of optical constant of solids, II, III, E. D. Palik, ed., Academic Press, in Handbook Series, New York, 1985, 1991, and 1997, 804 p., 1096 p., and 999 p.

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American Institute of Physics Handbook, 3rd ed., D. E. Gray., ed., New York, McGraw-Hill, 1972, pp. 6-107.

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L. I. Goray, “Rigorous solution for electromagnetic scattering from multilayer structures having asperities of any kind in X-ray–EUV ranges,” SPIE Proc. 6617, 2007, p. 661719.

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L. I. Goray, G. E. Cirlin, E. Alves, Yu. B. Samsonenko, A. A. Tonkih, N. K. Polyakov, V. A. Egorov, “Determination of the structural properties of multiple quantum dot ensembles based on a rigorous X-ray specular and diffuse scattering analysis and comparison with measurements,” Proc. of the 15th Int. Symp. “Nanostructures: Physics and Technology”, 2007, pp. 118-119.

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Ivan I. Goray, “On polynomial solvability of the Hamiltonian cycle problem for graphs of degree less than or equal to 3,” arXiv: 1007.0235v1 [math.OC], 1 Jul, 2010, 27 p.

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L. I. Goray, “Application of the boundary integral equation method to very small wavelength-to-period diffraction problems,” Waves Random Media, vol. 20, No. 4, 2010, pp. 569–586.

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L. I. Goray, “Application of the rigorous method to x-ray and neutron beam scattering on rough surfaces,” J. Appl. Phys., 2010, vol. 108, pp. 033516-1–10.

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L. Goray and M. Lubov, “Nonlinear continuum growth model of multiscale reliefs as applied to rigorous analysis of multilayer short-wave scattering intensity. I. Gratings,” J. Appl. Cryst., vol. 46, 2013, pp. 926–932.

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