Mar 05, 2012
Paper is published in Physical Review E "Analysis of twodimensional photonic band gaps of any rod shape and conductivity using a conicalintegralequation method," L. I. Goray and G. Schmidt. 
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Jan 16, 2012
Discounts are announced for new PCGrateS v.6.5 software The prices of all program types from the last PCGrateS v.6.5 series are reduced by 20%. 
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Nov 14, 2011
PCGrateS(X) update 6.5 32/64bit is available
We issue PCGrateS(X) 32/64bit software in the 6.5 updated version.

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Aug 10, 2011
PCGrateS(X) update 6.5 32/64bit is available We issue PCGrateS(X) 32/64bit software in the 6.5 updated version. 
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Jun 15, 2011
Paper is published in Applied Optics "Characterization of zone plate properties using monochromatic synchrotron radiation in the
2 to 20 nm wavelength range," J. Seely, B. Kjornrattanawanich, L. Goray, Y. Feng, and J. Bremer.

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Jun 06, 2011
PCGrateS(X) release 6.5 32/64bit is available
We issue PCGrateS(X) 32/64bit software in the 6.5 releaseversion. 
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May 31, 2011
Presentation at Days on Diffraction 2011 The report "Integral equation based inverse diffraction problem solving for
lowdimensional periodicallyarranged nanocrystals," is presented at the DD annual meeting. 
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May 24, 2011
Presentation at Optical Metrology 2011 The report “Solution of the inverse problem of diffraction from lowdimensional periodically arranged nanocrystalsis" is presented at the SPIE Europe meeting. 
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Mar 28, 2011
Paper is published in Optics Express "A 10,000 groove/mm multilayer coated grating for EUV spectroscopy," 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 
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Nov 15, 2010
Paper is published in Waves in Random and Complex Media "Application of the boundary integral equation method to very small wavelengthtoperiod diffraction problems," L. I. Goray. 
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Paper is published in Physical Review E
Analysis of twodimensional photonic band gaps of any rod shape and conductivity using a conicalintegralequation method
L. I. Goray and G. Schmidt
ABSTRACT
The conicalboundaryintegralequation method has been proposed for calculation of the sensitive optical response of twodimensional photonic band gaps (PBGs), including dielectric, absorbing, and highconductive rods of various shapes working in any wavelength range. It is possible to determine the diffracted field by computing the scattering matrices separately for any grating boundary profile. The computation of the matrices is based on the solution of a 2x2 system of singular integral equations at each interface between two different materials. The advantage of our integral formulation is that the discretization of the integral equation system and the factorization of the discrete matrices, which takes the majority of the computing time, are carried out only once for a boundary. It turns out that a small number of collocation points per boundary combined with a high convergence rate can provide an adequate description of the dependence on diffracted energy of very different PBGs illuminated at arbitrary incident and polarization angles. The numerical results presented describe the significant impact of rod shape on diffraction in PBGs supporting polaritonplasmon excitation, particularly in the vicinity of resonances and at high filling ratios. The diffracted energy response calculated vs the array cell geometry parameters was found to vary from a few up to a few hundred percent. The influence of other types of anomalies (i.e., waveguide anomalies, cavity modes, FabryPerot and Bragg resonances, Rayleigh orders, etc.), conductivity, and polarization states on the optical response is demonstrated.
The paper is published in PRE. Click here to download the full text.

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Discounts are announced for new PCGrateS v.6.5 32/64bit series software
The prices of all the types of software from the last PCGrateS v.6.5 series are cut down by 20%. The price of updated from 14 November PCGrateS XMLtype software is 3,199 Euros ($4,159), GUItype  4,299 Euros ($5,589), and Completetype  6,499 Euros ($8,449). We allow additional discounts for earlier and permanent Customers.
This version enables the calculations both multilayer resonance and small wavelengthtoperiod ratio cases at very high speed using two independent solvers based on the modified boundary integral equation method, i.e. Penetrating and Separating. The solvers have different behavior and mutually complementary capabilities for many difficult cases such as deep & shallow gratings & rough mirrors with very thin layers, grazing incidence, xrays, and photonic crystals.
PCGrate^{®}S v.6.5 32/64bit series have three types: GUI, XML, and Complete. PCGrate^{®}S v.6.5 series codes have the minimal value of the wavelengthtoperiod ratio lambda/d of 0.02 and the maximal number of layers of the grating surface multilayer material of 20. The PCGrateS v. 6.5 XML and PCGrateS v.6.5 Complete types make it possible to calculate the grating efficiency from the command line with input/output data in XML format. The PCGrateS v.6.5 GUI and PCGrateS v.6.5 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 with the product.
Click here to download updated PCGrate DEMO v.6.5 Complete.

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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 is updated. A few minor bugs were fixed and some improvements were made in updated PCGrate®S(X) v. 6.5 32/64bit series. The software is available for update as from November 14, 2011.
Important: input data format (grttype) was changed!
Click here to download updated PCGrate DEMO v.6.5 Complete.

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PCGrate®S(X) update of v. 6.5 32/64bit is available
PCGrate®S(X) v. 6.5 32/64bit updated software is available. PCGrate®S(X) v. 6.5 32/64bit series software with minor bugs fixed and some improvements is available for update as from August 10, 2011.
Click here to download updated PCGrate DEMO v.6.5 Complete.

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Paper is published in Applied Optics
Characterization of zone plate properties using monochromatic synchrotron radiation in the
2 to 20 nm wavelength range
J. Seely, B. Kjornrattanawanich, L. Goray, Y. Feng, and J. Bremer
ABSTRACT
A zone plate composed of Mo zones having 4mm outermost zone diameter, 100nm outermost zone width, and supported on a silicon nitride membrane was characterized using monochromatic synchrotron radiation in the 2 to 20 nm wavelength range. The zero and first order efficiencies were measured and compared to ab initio calculations that account for the optical properties of the materials, the width and shape of the zones, and multiplelayer thinfilm effects. It is shown that the thicknesses of the Mo zones and the membrane and the ratio of the zone width to zone period can be independently determined from the measured diffraction efficiencies in the zero and first orders and that the computational code can be used to reliably design zone plates that are optimized for applications such as solar irradiance monitors in the extreme ultraviolet region.
OCIS codes: 050.1950, 050.1960, 340.7480.
© 2010 Optical Society of America.
The paper is published in AO. Click here to download the full text.

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PCGrate®S(X) release 6.5 32/64bit is available
PCGrate®S(X) v. 6.5 32/64bit series software with some changes and improvements in comparison with version 6.4 is available for release as from June 6, 2011. A fast iterative method for solving linear systems of algebraic equations based on the Full Orthogonalization Method (FOM) is added to the Computation algorithm group of the Separating solver. The Separating solver was improved by accounting boundary horizontal shifts. Accuracy parameter options are added to the Scanning option item. Any combinations of accuracy parameters now can be specified easily by default and / or customized scanning values. The uninstalling procedure was changed to take into account any file format changes. A lot of minor changes and improvements were implemented both in the code and the documentation.
The PCGrate®S(X) v. 6.5 32/64bit series toolkit, which is designed for exact efficiency modeling of relief and phase diffraction gratings and rough mirrors, combines the brilliant performance of the earlier implementations of PCGrates with the modern Graphical User Interface with 3D and 2D Open GL plots and expands noticeably the set of supported features including two different solvers, paralleling, and the capability to calculate data from the command line using XMLformat input/output files. With PCGrateS(X) v. 6.5 32/64bit series software one can simulate effects of scattering in periodical and nonperiodical structures having multilayer micro/nanoroughnesses of various nature, design variablegroovedepth (VGD) and variablelinespaced (VLS) multisection gratings, model gratings covered with very thin or/and thick layers having arbitrary profiled borders including real and nonfunction ones, calculate photonic crystals and aspherical gratings, and work with conical mountings and nonplanar incident waves as well as with a general polarization state.
This version enables the calculations both multilayer resonance and small wavelengthtoperiod ratio cases at very high speed using two independent solvers based on the modified boundary integral equation method, i.e. Penetrating and Separating. The solvers have different behavior and mutually complementary capabilities for many difficult cases such as deep and shallow gratings and mirrors with very thin layers, grazing incidence, and photonic crystals.
PCGrate®S(X) v. 6.5 32/64bit has two series: S and SX; and each series have three types: PCGrate®S(X) v. 6.5 GUI, PCGrate®S(X) v. 6.5 XML and PCGrate®S(X) v. 6.5 Complete. PCGrate®S v. 6.5 series have the minimal value of the wavelengthtoperiod ratio of 0.02 and the maximal number of layers of the grating surface multilayer material of 20. PCGrate®SX v. 6.5 series have the minimal value of the wavelength of 0.01 nm (there is no a restriction on wavelengthtoperiod ratios) and the maximal number of layers of the grating surface multilayer material of 10 000. The PCGrateS(X) v. 6.5 XML and PCGrateS(X) v. 6.5 Complete types make it possible to calculate the grating efficiency from the command line with input/output data in XML format. The PCGrateS(X) v. 6.5 GUI and PCGrateS(X) v. 6.5 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 a Sentinel HASP® HL USB key, which is shipped with the product. Software has different input and output formats as compared with v. 6.4.
Click here to download PCGrate DEMO v.6.5 Complete.

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Presentation at the Days on Diffraction International Conference, May 30  June 3, 2011, St. Petersburg, Russia
Integral equation based inverse diffraction problem solving for
lowdimensional periodicallyarranged nanocrystals
L. I. Goray
ABSTRACT
Carrier confinement in lowdimensional periodicallyarranged nanocrystals (LDPAN) leads to the dependence of the operating wavelength in LDPANbased optoelectronic devices on the average size, shape, and material properties of heterostructures. Scatterometry as a non diffractionlimited optical method is applied to LDPAN (i.e. quantum dots, nanowhiskers, their combinations, etc) which are arranged on periodical masks. We propose numerical algorithms for the morphology determination of periodic relief nanostructures from light diffraction patterns measured in the UVIR wavelength range. The solution of the direct 3D diffraction problem is reduced for some symmetrical LDPAN to the solution of boundary integral equations for the 2D or even 1D Helmholtz equation. The ratio wavelengthtoperiod is small for typical inverse scattering problems and so the modified boundary integral equation method has to be applied to obtain accurate results at a fast convergence rate for the direct problem. The inverse problem is formulated as a nonlinear operator equation in the Euclidean space with an assumed set of unknown structural parameters of nanocrystals (height, width, slope angles, and refractive indices) and a given set of determined efficiency and phase shift values. The operator maps the sought structural parameters to the amplitudes of diffraction orders. The present approach employs the gradient LevenbergMarquardt method to solve the operator equation. This type of iterations is close to the GaussNewton method, but more efficient and stable for poor or improper input data due
to an additional regularization parameter. The inverse problem, mathematically, severely is illposed and regularization techniques have to be used to improve the solution. Unfortunately, such a regularization is not enough even for simplest geometry considerations and serious restrictions to the number and values of reconstructed parameters must be applied. Here we consider problems with a few polygonaltype boundary profiles having several edge points only. The method can be applied to LDPAN grown in different material systems (group IIIV, IV, IIVI, their combinations, etc) by various techniques (MBE, MOCVD, MOVPE, etc).
© 2011 Days on Diffraction.

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Presentation at SPIE Europe Optical Metrology, the Modeling Aspects of Optical Metrology Conference, June 2326, 2011, Munich, Germany
Specular and diffuse scattering from random asperities of any profile using the rigorous method for xrays and neutrons
L. I. Goray
ABSTRACT
The paper reports on development of an integral and nondestructive technique of characterization of lowdimensional periodically arranged nanocrystals (LDPAN) by spectroscopic scatterometry in the UVIR ranges. Some approaches to the solution of direct and inverse problems in scatterometry are addressed. For the solution of the direct problem, the author has chosen the universal method of boundary integral equations, which has demonstrated a broad range of applicability and a high accuracy. Cases are analyzed in which a complicated threedimensional diffraction problem involving 2D gratings can be reduced to a twodimensional one with 1D gratings, or multilayer mirrors with plane boundaries. An algorithm is proposed for the solution of a system of nonlinear operator equations with an arbitrary, but limited set of unknown LDPAN structural parameters, and a given set of measured values of diffraction efficiency. The functional to be minimized in the course of solution of the inverse problem is identified, and methods of its regularization and for monitoring the accuracy of the solution are proposed. A Fortran code written with the use of the LöwenbergMarkwardt gradient method has turned out an efficient way to the solution of model problems for a Si grating with a trapezoidal profile.. DOI: 10.1117/12.889418.
© 2011 SPIE.
The report is published in SPIE. Click here to download the full text.

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Paper is published in Optics Express
A 10,000 groove/mm multilayer coated grating for EUV spectroscopy
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
ABSTRACT
Ultrahigh spectral resolution in the EUV and soft xray energy ranges requires the use of very high line density gratings with optimal design resulting in use of a Blazed Multilayer Grating (BMG) structure. Here we demonstrate the production of nearatomically perfect Si blazed substrates with an ultrahigh groove density (10,000 l/mm) together with the measured and theoretical performance of an Al/Zr multilayer coating on the grating. A 1st order absolute efficiency of 13% and 24.6% was achieved at incidence angles of 11ş and 36ş respectively. Crosssectional TEM shows the effect of smoothing caused by the surface mobility of deposited atoms and we correlate this effect with a reduction in peak diffraction efficiency. This work shows the high performance that can be achieved with BMGs based on smallperiod anisotropic etched Si substrates, but also the constraints imposed by the surface mobility of deposited species. OCIS codes: codes: (050.1950) Diffraction gratings; (340.7480) Xrays, soft xrays, extreme ultraviolet.
© 2010 Optical Society of America.
The paper is published in OE. Click here to download the full text.

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Paper is published in Waves in Random and Complex Media
Application of the boundary integral equation method to very small wavelengthtoperiod diffraction problems
L. I. Goray
ABSTRACT
Diffraction from 1D multilayer gratings having arbitrary border profiles including edges is considered for small wavelengthtoperiod (λ / d) ratios, the most difficult case for any rigorous numerical method. The boundary integral equation theory is so flexible that we can indicate a few areas where it can be modified. In this work, special attention is paid to the main aspects of the Modified Boundary Integral Equation Method for λ / d << 1 as well as to a more general treatment of the energy conservation law applicable to multilayer absorption gratings. Three types of small λ / d problems are known from optical applications: (a) shallow gratings working in the Xray and extreme ultraviolet ranges, both at near normal and grazing angles, (b) deep echelle gratings with a steep working facet illuminated along its normal by light of any wavelength, and (c) rough mirrors and gratings in which rough boundaries can be represented by a larged grating, and which contain a number of random asperities illuminated at any angle and wavelength. Numerical examples of diverse inplane diffraction problems are presented. DOI: 10.1080/17455030.2010.510857.
© 2010 Taylor & Francis.
The paper is published in WRM. Click here to download the full text.

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