PCGrate-S(X) Series–


is the software for exact calculations by the modified boundary integral equation method in X-ray to meter wavelength range of the diffraction order efficiency and diffuse light intensity (ghosts) of plane/concave/convex multilayer relief & phase gratings, rough mirrors, photonic crystals, manyshaped, with any border profiles, working in conical mounts with general polarization states & non-planar incident waves, as well as taking into account rigorously various roughness types.


The PCGrate®-S(X) v.6.6-6.7 32/64-bit series toolkit, which is designed for exact efficiency modeling of relief & phase diffraction gratings and rough mirrors, combines the brilliant performance of the earlier implementations of PCGrates with the modern Graphical User Interface with 3-D & 2-D 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 XML-format input/output files. With PCGrate-S(X) v.6.6-6.7 32/64-bit series software one can simulate rigorously effects of scattering in periodical and non-periodical structures having multilayer micro/nano-roughnesses of various nature, design variable-groove-depth (VGD) & variable-line-spaced (VLS) multi-section gratings, model gratings covered with very thin or/and thick layers having arbitrary profiled borders including real & non-function ones, calculate photonic crystals & aspherical gratings, and work with conical mountings & non-planar incident waves including Gaussian ones as well as with a general polarization state. PCGrate®-S(X) 32/64-bit versions 6.6-6.7 are very recent (v.6.6 recently updated) and much more powerful in respect to the old 32-bit v.6.1 code. These new versions run both 64- and 32-bit applications and it is more suitable for complex grating modeling using intensive paralleling. It has two different and powerful solvers: Penetrating and Separating. Both of them are based on the modified boundary integral equation method and have complementary capabilities. The principal difference between two versions (vs v.6.1) is that vs.6.6-6.7 simulate not only periodical gratings but also randomly-rough mirrors with any (including non-Gaussian) roughness statistics to obtain exact efficiencies and diffuse light intensities (ghosts between orders). With vs.6.6-6.7 one can model multilayer gratings having randomly-rough real boundaries. The new Border Profile Editor includes the tool for randomization of such boundaries. Vs.6.6-6.7 is much more suitable and accurate for concave/convex grating simulations. It is also convenient for modeling of 1D and 2D photonic crystals and gratings with varied groove space and groove depth (boundary shape). Vs.6.6-6.7 support Gaussian incident waves and extremely grazing incidence for multilayer X-ray gratings. There are a lot of other new features and peculiarities in vs.6.6-6.7. PCGrate®-S(X) v.6.7 32/64-bit software has many adds and improvements in comparison with v. 6.6. In v. 6.7 the logic of scanning over different parameters was divided into two branches. First branch, which is 1D scanning is direct analogy of scanning functionality of previous versions, it allows only independent scanning over one parameter. The new feature 2D scannings – second branch – was added to this version. 2D scannings allow user to vary two parameters together in order to solve grating efficiency tasks. In version 6.7, the 3D Plots were added to better represent the results of 2D scannings mode solutions. The 3D Plots include same functionality as 2D plots for 1D scannings with some enhancements, such as meshes over the plotted surfaces with variable nodes’ density. A lot of other minor changes & improvements were implemented both in the v.6.7 code and the documentation..

Maximal number of layers   Maximal number of points per boundary   Wavelength   Diffraction orders range   Number of plane waves & plane sections   Maximal thickness-to-period ratio   GUI & XML output formats   Near-zone field output  
3   100   From x-rays to meters   ±40   3 × 3   0.25   Yes   Yes  

The Demo versions of PCGrate-S(X) v.6.6-6.7 32/64-bit Complete have several restrictions.

The PCGrate Demos v.6.6-6.7 32/64-bit for Microsoft® Windows® 32/64-bit requires:

  • Microsoft® Windows® Vista/Server 2008/7/Server 2012/8(.1)/10 or higher installed (Server 2012 or Windows 10 are recommended).
  • PC-compatible (Intel® or AMD® modern multi-core processors are recommended for better performance) single- or multi-processor computer.
  • At least 0.5 GB of free RAM per core (thread) (1 GB or more per core (thread) are recommended for complex problem modeling using paralleling).
  • Minimum 1 GB of free storage space (10 GB or more are recommended for storing complex problem results).
  • Web and e-mail access for technical support and program updates.
Title Info Date Size
PCGrate Demo v.6.7.1 PCGrate®-S(X)™ v.6.7.1 32/64-bit Complete Demo zip archive July 2020 105 Mb
PCGrate Demo v.6.6 PCGrate®-S(X)™ v.6.6 32/64-bit Complete Demo zip archive November 2020 80 Mb
PCGrate presentation PCGrate PDF presentation September 2023 5 Mb

The HCP Package

A Brief Overview

The optimization algorithm “HCP Solver” is an approximate polynomial algorithm with O(1.5N3). It is based on the concept of successive iterative decreases in cycle length, in which the iterative procedure begins with a randomly chosen cycle. As different edges of the graph are assigned the weights 0 and 1, the cycle length is determined in view of the edges with the unit weight. Each iteration is completed by replacement of several edges in the cycle. In this case the cycle length either decreases or remains unchanged. A Hamiltonian cycle in the graph exists if its length is equal to zero (H = 0). The graphical viewer for graphs and the generator of leaper graphs stored in TSPLIB-format (*.hcp) are included in the package.

The TSMP Package

A Brief Overview  

The TSMP-1 (Traveling SalesMan Problem) code is intended for solving the problem of the precise determination of the length and path of a minimal Hamiltonian cycle (cycles) of a weighed network (the Traveling Salesman Problem, the TSP) in a time that polynomially depends on the network’s dimension (the number of its nodes); and it also relates to the construction (on this basis) of algorithms of polynomial complexity to solve so-called NP-complete problems of discrete mathematics. The essence of this problem is as follows: to find in a network given a cycle sequence of passing the edges in such a way that it includes all the nodes of the network one and only one time (i.e. the passage of the edges is a Hamiltonian cycle), and the sum of the edge weights of the cycle under consideration (the length of the cycle) is minimal among all possible cycles of the network (at least not greater than the length of any other cycles having similar properties). The research program including the source code and documentation can be obtained from this page (TSMP-1.zip file). Input and output files from TSPLIB – Gerd Reinelt’s library of TSP instances – are included in the package.  

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec ullamcorper mattis, pulvinar dapibus leo.

The HCP v. 1.0 and TSMP-1 v. 1.0 software for Microsoft® Windows® 32/64-bit require:

  • Microsoft® Windows® XP, Server 2003 or higher installed.    
  • PC-compatible (Pentium® or higher for better performance) single-processor computer.
  • At least 64 MB of free RAM.  
  • Minimum 10 MB of free hard disk space.
  • Web and e-mail access for technical support and program updates.
Title Info Size
TSMP TSMP-1 code zip archive 3 Mb
HCP Hamiltonian Cycle Problem Solver zip archive 1 Mb