Reference 1

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.

LINK

Reference 2

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.

LINK

Reference 3

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.

LINK

Reference 4

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.

LINK

Reference 5

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).

LINK

Reference 6

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.

LINK

Reference 7

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.

LINK

Reference 8

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.

LINK

Reference 9

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.

LINK

Reference 10

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.

LINK

Reference 11

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.

LINK

Reference 12

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.

LINK

Reference 13

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.

LINK

Reference 14

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.

LINK

Reference 15

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.

LINK

Reference 16

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.

LINK

Reference 17

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.

LINK

Reference 18

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.

LINK

Reference 19

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.

LINK

Reference 20

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.

LINK

Reference 21

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.

LINK

Reference 22

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.

LINK

Reference 23

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.

LINK

Reference 24

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.

LINK

Reference 25

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.

LINK

Reference 26

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.

LINK

Reference 27

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

LINK

Reference 28

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.

LINK

Reference 29

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

LINK

Reference 30

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

LINK

Reference 31

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.

LINK

Reference 32

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.

LINK

Reference 33

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

LINK

Reference 34

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

LINK

Reference 35

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

LINK

Reference 36

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

LINK

Reference 37

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.

LINK

Reference 38

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

LINK

Reference 39

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.

LINK

Reference 40

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.

LINK

Reference 41

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.

LINK

Reference 42

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.

LINK

Reference 43

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.

LINK

Reference 44

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.

LINK