Aug 01, 2014
PCGrateS(X) release 6.6 32/64bit is available We issue PCGrateS(X) 32/64bit software in the 6.6 releaseversion. 
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Jul 01, 2014
Chapter is published in ebook Gratings: Theory and Numeric Applications 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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Mar 21, 2014
PCGrateS(X) v. 6.5 32/64bit is updated PCGrate®S(X) update of v. 6.5 32/64bit is available 
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Sep 09, 2013
Efficiency Certificate # 6 is issued online Efficiency Certificate for a Flight Multilayer Mo/Si Lamellar Grating in the EUV Range and TM polarization is presented. 
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Jun 05, 2013
Paper is published in Journal of Physics C
“Development of near atomically perfect diffraction gratings for EUV and soft xrays with very high efficiency and resolving power,” 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.

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Jun 04, 2013
Discounts are announced for powerful PCGrateSX v.6.1 software The prices of all program types from PCGrateSX v.6.1 series w/o limitations are reduced by more than 26%, in the average. 
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May 28, 2013
Presentation at Days on Diffraction 2013
The talk "Solution of 3D scattering problems from 2D ones in short waves," is presented at the DD’13 annual meeting. 
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May 06, 2013
Paper is published in Journal of Applied Crystallography
“Nonlinear continuum growth model of multiscale reliefs as applied to rigorous analysis of multilayer shortwave scattering intensity. I. Gratings,” L. Goray and M. Lubov.

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Sep 18, 2012
Presentation at XTOP2012
The talk "Xray scattering on rough and profiled surfaces: rigorous analysis and a nonlinear model of film growth," is presented at the 11th Biennial Conference on High Resolution XRay Diffraction and Imaging.

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Sep 17, 2012
Presentation at XTOP2012
The talk "Development of ultrahigh efficiency multilayercoated blazed diffraction gratings for EUV and soft xrays applications," is presented at the 11th Biennial Conference on High Resolution XRay Diffraction and Imaging.

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PCGrateS(X) release 6.6 32/64bit is available
PCGrate®S(X) v. 6.6 32/64bit software with many adds and improvements is available for a release as from August 1, 2014. The new optical mounting (“Fix Focus”) and relevant photon energy unit (“eV”) were added to this version. Fix Focus is an optical mount configuration for a reflected order where the reflected order is observed at a fixed ratio c of polar diffraction and incidence angle cosines that is used at xrayEUV synchrotron radiation sources in plane grating focusing monochromators. In version 6.6, the “ E(1) refl” and the “ E(1) trans” buttons were added to quickly plot efficiency of reflected/transmitted order #1 graphs. If there are multiple suitable scanning parameters, then an additional dialog appears and you have to choose one. Conical diffraction algorithms to predict reflection grating efficiencies in short waves were substantially improved.
A lot of minor changes were implemented both in the code and the documentation. The last Sentinel® HASP HL driver installer was included to the version.
Important: input and output data formats (grt and pcg types) were changed ! In order to convert .grt files from PCGrate v. 6.5 32/64bit software to .grt files for PCGrate v. 6.6 you can use the provided converter tool.
Click here to download PCGrate DEMO v.6.6 Complete.

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Chapter is published in ebook Gratings: Theory and Numeric Applications
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)
INTRODUCTION
This work is part of research that has been pursued by the authors over a long period of time for the purpose of developing accurate and fast numerical algorithms, including the commercial packages PCGrate and DiPoG [12.1, 12.2] designed to model multilayered gratings having mostly onedimensional periodicity (1D), including roughness, and working in all, including the shortest, optical wavelength ranges at arbitrary optical mounts.
The boundary integral equation theory or, briey, integral method (IM) is presently universally recognized as one of the most developed and exible approaches to an accurate numerical solution of diffraction grating problems (see, e.g., Ref. 12.3 and Ch. 4 and references therein). Viewed in the historical context, this method was the rst to offer a solution to vector problems of light diffraction by optical gratings and to demonstrate remarkable agreement with experimental data. This should be attributed to the high accuracy and good convergence of the method, especially for the TM polarization plane. It does not involve limitations similar to those characteristic of the CoupledWave Analysis (CWA), and it provides a better convergence. The disadvantages of this method include its being mathematically complicated, as well as numerous "peculiarities" involved in numerical realization. In particular, quasiperiodic Greens functions and their derivatives appearing as kernels in the integral operators require sophisticated lattice sum techniques to evaluate. Moreover, application of the IM to cases of heterogeneous or anisotropic media meets with difculties; however, with the volume integral method it is possible to overcome these difculties easily. Nevertheless, it is on the basis of this theory that all the wellknown problems of diffraction by periodic and nonperiodic structures in optics and other elds have been solved. In many cases it offers the only possible way to follow up in research. The exibility and universality inherent in the IM, in particular, enable one rather easily to reduce the problem of radiation of Gaussian waves or of a localized source to that of planewave incidence, for which scientists all over the world have a set of numerical solutions. Generalizations of the IM have recently been proposed for arbitrarily proled 1D multilayer gratings [12.4], randomlyrough xrayextremeultraviolet (EUV) gratings and mirrors [12.5, 12.6], conical diffraction gratings including materials with a negative permittivity and permeability (metamaterials) [12.7, 12.8], biperiodic anisotropic structures using a variation formulation [12.9], Fresnel zone plates and diffraction optical elements [12.10, 12.11], and twodimensional (2D) [12.12, 12.13] and threedimensional (3D) [12.14] photonic crystals (inclusions) of some geometries, among others.
The IM is so pivotal that one can indicate the few areas where it can be modied and improved to solve particular diffraction problems. By convention they are: (1) physical model—choice of boundary types, boundary conditions, layer and substrate refractive indices, and radiation conditions; (2) mathematical structure—integral representations using potentials or integral formulas and a multilayer scheme; (3) method of approximation and discretization—discretization schemes, choice of basis (trial) and test (weighting) functions, and treatment of coincident points and corners in boundary prole curves; (4) lowlevel details—calculations and optimization of kernel functions, mesh of discretization (collocation) points, quadrature rules, and solution of linear algebraic systems; (5) implementation enhancements—memory caching, other implementation details. A selfconsistent explanation of the existing IMs is beyond the primary scope of the present study. The main purpose of this Chapter is to present a complete description in general operator form of the two IMs applied to 1D multilayer gratings working in conical diffraction mounts and in short waves. Our study also includes the calculus of grating absorption in the explicit form and scattering intensity of randomlyrough gratings using Monte Carlo simulations. For other formal IM treatments and their comparisons, one should rather look to the references of this Chapter as well as to Ch. 4 and to references therein.
Various kinds of electromagnetic features of different nature can exist and be explored in complex grating structures: Bragg and Brewster resonances, Rayleigh anomalies and groove shape features, waveguiding and Fanotype modes, etc. In conical diffraction, the inuence of possible types of waves can be mixed. For the purposes of this Chapter, we chose three important types, among many others, of diffraction grating problems to include them in Section 12.9 "Examples of numerical results". They are: bare dielectric or metallic gratings of standard groove shapes working in conical diffraction in the resonance domain; shallow highconductive or dielectric gratings of various boundary shapes, including closed ones, working in different mounts and supporting polaritonplasmon excitation or Bragg diffraction in the visibleinfrared range; bare and multilayer gratings working in grazingconical or nearnormal inplane diffraction in the soft xrayEUV range.
Copyright © 2014 by Université d'AixMarseille, All Rights Reserved [ISBN: 9782853999434]

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PCGrate®S(X) update of v. 6.5 32/64bit is available
PCGrate®S(X) v. 6.5 32/64bit software with some improvements and a few minor bugs fixed is available for an update as from March 21, 2014. The version update supports Windows ^{®} 8(.1) and UAC “On” for users having nonadministrative privileges. A few minor bugs connected with (1) conical diffraction calculus for Absolute plane borders in Separating Solver, (2) input (grttype) file opening by doubleclicking and (3) paralleling under plane sections for plane gratings were fixed in updated PCGrate®S(X) v. 6.5 32/64bit series. Export and import of Microsoft® Excel and text files in Border Profile Editor were extended.
Important: input and output data formats (grt and pcg types) were not changed !
Click here to download updated PCGrate DEMO v.6.5 Complete.

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Efficiency Certificate # 6 is issued online
Efficiency Certificate for a Flight Multilayer Mo/Si Lamellar Grating in the EUV Range and TM polarization is presented. The complete results of the grating efficiency and scattering light investigation and all relevant information about the computation and measurement processes can be obtained from the downloading page ( Cert_4200_hololam_MoSi_EUV.zip file). Various files both *.xlsx (MS Excel® 2010) and *.grt, *.ggp, *.ri, *.ari, & *.pcg (PCGrate®S(X)™ v.6.5) formats relating to this grating efficiency and scattering intensity certification are included in the package. You can view the later by the PCGrate Demo v.6.5 Complete (updated on the 25 ^{th} July, 2012).

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Paper is published in Journal of Physics C
Development of near atomically perfect diffraction gratings for EUV and soft xrays with very high efficiency and resolving power
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
ABSTRACT
Multilayercoated Blazed Gratings (MBG) can offer high diffraction efficiency in a very high diffraction order and are therefore of great interest for highresolution EUV and soft xray spectroscopy techniques such as Resonance Inelastic Xray Scattering. However, realization of the MBG concept requires nanoscale precision in fabrication of a sawtooth substrate with atomically smooth facets, and reproduction of the blazed groove profile in the course of conformal growth of a multilayer coating. We report on recent progress achieved in the development, fabrication, and characterization of ultradense MBGs for EUV and soft xrays. As a result of thorough optimization of all steps of the fabrication process, an absolute diffraction efficiency as high as 44% and 12.7% was achieved for a 5250 l/mm grating in the EUV and soft xray regions respectively. This work now shows a direct route to achieving high diffraction efficiency in high order at wavelengths throughout the soft xray energy range with revolutionary applications in synchrotron science.

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PCGrate®SX of v. 6.1 32bit is discounted
The prices of all the types of software from the last PCGrateSX v. 6.1 w/o limitations cut down by more than 26%, in the average. The price of updated from April 16, 2010 PCGrateSX XMLtype software is 1,999 Euros ($2,599), GUItype  2,999 Euros ($3,899), and Completetype  3,999 Euros ($5,199). We allow additional discounts for earlier and permanent Customers.
This version enables the calculations both multilayer resonance and any small wavelengthtoperiod ratio cases at very high speed using two independent solvers (Normal and Resonance) based on the rigorous boundary integral equation method (modified). The solvers have different behavior and mutually complementary capabilities for many difficult cases such as deep gratings with arbitrary border profiles including measured ones and with random roughness, gratings having any number of very thin layers, grazing incidence, xray—EUV ranges, echelles, etc.
PCGrate®SX v.6.1 32bit series have three types: GUI, XML, and Complete. PCGrate®SX v.6.1 series codes have: the minimal value of the wavelengthtoperiod ratio lambda/d of 2.E13, the maximal number of propagating diffraction orders of 10,000, and the maximal number of layers of the grating surface multilayer material of 5,000. The PCGrateSX v. 6.1 XML and PCGrateSX v.6.1 Complete types make it possible to calculate the grating efficiency from the command line with input/output data in XML format. The PCGrateSX v.6.1 GUI and PCGrateSX v.6.1 Complete types make it possible to obtain the calculated data using the Graphical User Interface and work with the results including saving, coping, exporting, plotting, printing, etc. The type is determined by the HASP® HL USB key, which is shipped separately to the product.
Click here to download updated PCGrate DEMO v.6.1 Complete.

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Presentation at the Days on Diffraction International Conference, May 27  31, 2013, St. Petersburg, Russia
Solution of 3D scattering problems from 2D ones in short waves
L. I. Goray
ABSTRACT
The paper reports on development of a boundary integral equation technique of characterization of scattering by rough threedimensional (3D) surfaces at a short wavelength of λ. The effect of roughness on the mirror scattering intensity can be rigorously taken into account with the model in which an uneven surface is represented by a grating with a large period of d_{i} in different perpendicular planes i, which includes an appropriate number of random asperities with a correlation length of ξ_{i}. The code analyzes the complex structures which, while being multilayer gratings from a mathematical viewpoint, are actually rough surfaces for d_{i}>>ξ_{i}. If ξ_{i}~λ and the number of orders is large, the continuous angular distribution of the energy reflected from randomly rough boundaries can be described by a discrete distribution η(#) in order # of a grating [1]. A study of the scattering intensity starts with obtaining statistical realizations of profile boundaries of the structure to be analyzed, after which one calculates the intensity for each realization, to end with the intensity averaged out over all realizations. By selecting large enough samples, one comes eventually to properly averaged properties of the rough surface; however, this approach does not involve approximations, including averaging by the Monte Carlo method. The more general case of biperiodic gratings (or 3D surfaces) may be considered in a similar way or by expressing the solution of the 3D Helmholtz equation through solutions of the 2D equation described below, an approach which may be resorted to in some cases [2]. General equivalent rules for determination of the efficiencies of reflected orders of biperiodic gratings from those calculated for oneperiodic gratings can be found, for example, in [3]. The general approach used is based on expansion of the efficiency of a bigrating with profile boundaries symmetric relative to the horizontal plane in a Taylor series in powers of a boundary profile depth h, with the principal terms of the series retained in the h<d case. Then the efficiencies e_{0,}_{m}^{+} and e_{0,}_{n}^{+} of the orders numbered (0,m) and (n,0) propagating in the upper (+) medium for arbitrary linear polarization of light can be defined through the leading (quadratic in h) terms of the expansion as
e_{0,}_{m}^{+ } = e_{0,1}^{+}e_{m}_{,2}^{+ }/ R; e_{n}_{,0}^{+ } = e_{n}_{,1}^{+}e_{0,2}^{+ }/ R, (1)
where e_{n}_{(}_{m}_{),1(2)}^{+} are the values of the efficiencies of the corresponding mutually perpendicular oneperiodic gratings calculated with the position of the polarization vector left unchanged, and R is the Fresnel reflection coefficient of the grating material. For nondeterministic surface functions some modification of the general approach is required. As follows from a comparison with the results of rigorous calculations performed in [3] and by the present author, the approximate relations (1) give a highaccuracy solution for cosθ_{i}h_{i}<<d_{i} and λ<d_{i}, where θ_{i} is an incidence angle. In the cases where one minus real part of the refractive index and imaginary part of the material are small, h can be large enough.
References
[1] Goray L. I., 2010, Application of the rigorous method to xray and neutron beam scattering on rough surfaces, J. Appl. Phys., Vol. 108, pp. 033516110.
[2] Goray L.I., 2011, Solution of the inverse problem of diffraction from lowdimensional periodically arranged nanocrystals, Proc. SPIE, Vol. 8083, 80830L112.
[3] Petit, R., ed., 1980, Electromagnetic Theory of Gratings (Springer, Berlin).
© 2013 `Days on Diffraction', POMI.

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Paper is published in Journal of Applied Crystallography
Analysis of twodimensional photonic band gaps of any rod shape and conductivity using a conicalintegralequation method
L. I. Goray and G. Schmidt
ABSTRACT
It is shown that taking into proper account certain terms in the nonlinear continuum equation of thinfilm growth makes it applicable to the simulation of the surface of multilayer gratings with large boundary profile heights and/or gradient jumps. The proposed model describes smoothing and displacement of Mo/Si and Al/Zr boundaries of gratings grown on Si substrates with a blazed groove profile by magnetron sputtering and ionbeam deposition. Computer simulation of the growth of multilayer Mo/Si and Al/Zr gratings has been conducted. Absolute diffraction efficiencies of Mo/Si and Al/Zr gratings in the extreme UV range have been found within the framework of boundary integral equations applied to the calculated boundary profiles. It has been demonstrated that the integrated approach to the calculation of boundary profiles and of the intensity of shortwave scattering by multilayer gratings developed here opens up a way to perform studies comparable in accuracy to measurements with synchrotron radiation, at least for known materials and growth techniques..
The paper is published in JACr. Click here to download the full text.

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Presentation at the 11^{th} Biennial Conference on High Resolution XRay Diffraction and Imaging (XTOP12), September 1520, 2012, St. Petersburg, Russia
Xray scattering on rough and profiled surfaces: rigorous analysis and a nonlinear model of film growth
Goray L.I., Lubov M.N.
ABSTRACT
Understanding of the evolution of surface profiles and roughness of gratings, random asperities, quantum wires and dots, nanowhiskers, etc., during growth is required for further technological improvement. Xray scattering on surfaces with different types of nanoasperities (periodic, random, and selforganized ones, as well as their combinations) is considered based on the rigorous electromagnetic theory and a nonlinear continuum model of surface growth.
It is wellknown that linear continuum models of surface growth and evolution (see, for example, Ref. [1]) cannot reasonably reproduce the PSD spectra of the films deposited on a strongly profiled substrate or on a flat substrate with an rms roughness/correlation length of more than about a few nm. The linear continuum equation used in the models does not properly treat the complexity of the processes of island nucleation, growth and coalescence on profiled surfaces leading to a significant discrepancy of the predicted and measured PSD spectra [2]. The nonlinear growth model proposed in the present work accounts for the nonlinear growth effects and deals with a substrate that is a general rough grating with a groove spacing larger than the width/correlation length of the substrate's asperities. The temporal evolution of the surface height distribution (h(r,t) (r is the radiusvector and t is time) is a function of its derivatives and a stochastic term η(r,t):
∂h(r,t)/∂t=f[grad h(r,t), grad^{2}h(r,t),…] + ·(r,t).
The function f is the sum of linear grad^{n}h(r,t) and nonlinear grad^{l}([grad^{n}h(r,t)]^{k}), (l, k, n ∩ N), terms; the latter describes nonlinear effects and influence of the surface profile on the growth kinetics and resulting surface morphology. This model is capable simulating the growth of various crystalline, polycrystalline, and amorphous multilayers on planar and structured substrates. The model is used to predict the roughening and smoothing behaviors of Mo/Si, Al/Zr, and GaAs/AlGaAs films.
The boundary integral equation method (MIM, Ref. [3]), where the border structure is considered as a 2D grating with wavelength λ to period d ratios of much less than one, is used to obtain absolute specular and nonspecular xray intensities. Note that even for 1D surfaces and, especially, in the EUV and xray range, finding an exact solution to the problem of scattering of electromagnetic waves from a profiled surface is extremely difficult for any rigorous method. In spite of the convergence and accuracy problems, ensemble averaging via Monte Carlo simulations is required in order to obtain scattering intensities. A generalization of MIM has been recently proposed [4] to describe rough multilayer gratings that is suitable for present calculus (see Figure).
The authors are grateful to D. L. Voronov, Yu. V. Trushin, V. V. Yashchuk, and W. McKinney for useful discussions.
References
1. C. Herring, in The Physics of Powder Metallurgy, ed. by W. E. Kingston (McGrawHill, New York, 1951), 143.
2. D. L. Voronov, E. H. Anderson, R. Cambie, E. M. Gullikson, F. Salmassi, T. Warwick, V. V. Yashchuk, and H. A. Padmore, Proc. of SPIE (2011) 8139, 81390B.
3. L. I. Goray, J. Appl. Phys. (2010) 108, 033516.
4. L. I. Goray, Wav. Rand. Med. (2010) 20, 569.
© 2012 Ioffe Physical Technical Institute of the Russian Academy of Sciences.

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Presentation at the 11^{th} Biennial Conference on High Resolution XRay Diffraction and Imaging (XTOP12), September 1520, 2012, St. Petersburg, Russia
Development of ultrahigh efficiency multilayercoated blazed diffraction gratings for EUV and soft xrays applications
Voronov D.L., Anderson E. H., Cambie R., Goray L.I., Gullikson E.M., Salmassi F., Warwick T., Yashchuk V.V., Padmore H.A
ABSTRACT
We report on recent progress achieved at the Advanced Light Source (ALS) on development, fabrication, and characterization of ultrahigh efficiency multilayercoated blazed gratings (MBG) suitable for EUV and soft xray applications. As diffraction elements, MBGs have several important advantages compared with sinusoidal or laminar gratings. First, with blazed gratings most of the incoming radiation m ay potentially be diffracted into one specific, desired, diffracted order. Second, use of high efficiency multilayer coatings potentially allows extending the advantages of normal incidence grating spectrometer designs to EUV and soft x ray wavelengths. In order to realize this potential, the MBG must have a nanoperiod structure with an ideal sawtooth groove profile, coherently replicated over the entire structure and ensured to have an extremely low microroughness of the substrate's and multilayer's interfacial surfaces.
Using ebeam and interference lithography techniques followed by wet anisotropic etching of silicon [1], we fabricated sawtooth substrates with groove densities up to 10,000 lines/mm having nearatomically plane groove facets. The multilayers are deposited on the substrates by magnetron sputtering in Argon. With crosssectional transmissionelectron microscopy (TEM), we show that careful optimization of the deposition parameters [2] allows us to avoid significant smoothing of the groove profile and increase of the surface roughness. This observation is in excellent agreement with the results of diffraction measurements. An absolute efficiency of 44% was achieved for the first blazed order of a 5250 lines/mm MBG (consisting of 30 Mo/Si bilayers) at a wavelength of 13.1 nm. Simulations of diffraction efficiency of soft xray MBGs, based on the integral method for solving Maxwell's equations for a periodic structure [3], show that the efficiency of an optimized grating relative to the reflectance of the multilayer can approach 100%.
We also discuss a route to achieving high diffraction efficiency in high order at wavelengths throughout the soft xray energy range with revolutionary applications in synchrotron science.
The authors are grateful to R. M. Feshchenko, V. V. Kondratenko, Y. P. Pershin, A. G. Ponomarenko, and A. V. Vinogradov for very useful discussions. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, Material Science Division, of the U.S. Department of Energy under Contract No. DEAC0205CH11231 at Lawrence Berkeley National Laboratory.
References
1. D. L. Voronov, E. H. Anderson, R. Cambie, S. Dhuey, E. M. Gullikson, F. Salmassi, T. Warwick, V. V. Yashchuk, and H. A. Padmore, Nucl. Instr. and Meth. (2011) A649(1), 156.
2. D. L. Voronov, E. H. Anderson, E. M. Gullikson, F. Salmassi, T. Warwick, V. V. Yashchuk, and H.A. Padmore, Opt. Lett. (2012) (in press).
3. PCGrate® software (http://www.pcgrate.com/about/pcgrates/sxseries).
© 2012 Ioffe Physical Technical Institute of the Russian Academy of Sciences.

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