A Brief Overview of the PCGrate-S(X) Series

PCGrate®-S(X) v.6.6-6.7 32/64-bit calculates the diffraction efficiency and near-zone diffraction field for such kinds of 1-D reflection and transmission relief & phase gratings (holographic, ruled, and others) and 1-D & 2-D photonic crystals as those with arbitrary shape multilayer (that have different borders or non-uniform vertical thicknesses along the grating period), variable groove depth or/and space, concave & convex, in conical mounts, irradiated by non-planar waves, in general polarization states, with various periodical & random layers’ roughnesses, and in a super wide spectral region. The rigorous boundary integral equation method5 employed in the analysis of diffraction grating efficiency3,19 is extended here to the case of non-periodical structures of any kind including calculation of diffuse intensities & ghosts and non-function border profiles.42–44 A tool for random asperities generating, in particular with Gaussian correlation function, is included (see Figure #27) with a possibility to add microroughness on one facet (part) of a border profile (see Figure #15). The updated PCGrate 6.6-6.7 Border Profile Editor has new features to generate rough border profiless of any kind and border profiles of the cubic spline type. The software has two independent multilayer solvers, which are based on different calculation schemes.  

The PCGrate 6.6-6.7 32/64-bit Separating solver is based on the newly developed single-boundary integral-equation Scattering solver and the Scattering-matrix approach to multilayer diffraction.28,32 By the definition, it requires homogeneous media separated two adjacent corrugated regions by fictitious planes (see Figure #30). The distance between such planes may be arbitrary including very close to zero. The Separating solver is primarily intended for efficiency calculations of dielectric rods of arbitrary shape and refractive index such as 2-D photonic crystals, any uncoated gratings including rough ones, and specific types of coated gratings and mirrors. It is indispensable for the x-ray-VUV gratings and mirrors covered with one or many plane or rather thick conformal coatings and, especially, for grazing incidence.  

The earlier implemented and now improved the PCGrate 6.6-6.7 32/64-bit Penetrating solver is based on the multi-boundary marching scheme2,35 and it doesn’t require a separation between two adjacent corrugated regions (see Figure #31).4This is vital in the modeling of many coated gratings (echelles, multilayer x-ray-VUV, thin-oxidized, etc.). So, the Penetrating solver is more general in this sense. In the PCGrate-S(X) v. 6.6-6.7 program the default solver type is Penetrating. As a rule, the Penetrating solver takes more time than Separating one to solve such problems due to considering the absolute plane border as a corrugated boundary and solving the integral equations on each physical boundary (it also depends on number of +/- terms/orders taking into account).  PCGrate®-S(X) v. 6.7.1 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 (see Figure 9) – second branch – was added to this version. 2D scannings allow user to vary two parameters together in order to solve grating efficiency tasks (see, e.g., Figure 16). 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 (see, e.g., Figure 23). A lot of other minor changes & improvements were implemented both in the v.6.7 code and the documentation.  

The Limits and Constraints of Series and Types of the PCGrate®-S(X) Software  

PCGrate®-S(X) v.6.6-6.7 32/64-bit have two series: S and SX; and each series have three types: PCGrate®-S(X) GUI, PCGrate®-S(X) XML and PCGrate®-S(X) Complete. PCGrate®-S series have the minimal value of the wavelength-to-period ratio λ/d of 0.02 and the maximal number of layers of the grating surface multilayer material of 20. PCGrate®-SX series have the minimal value of the wavelength λ of 0.01 nm (there is no a restriction on wavelength-to-period ratios) and the maximal number of layers of the grating surface multilayer material of 10 000 for v. 6.6-6.7. The PCGrate-S(X) XML and PCGrate-S(X) Complete types make it possible to calculate the grating efficiency from the command line with input/output data in XML format. The PCGrate-S(X) GUI and PCGrate-S(X) 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.

Key parameter S-series** v6.6 SX-series** v6.6
Wavelength From x-rays to meters
Minimal wavelength-to-period ratio 0.02 2e-13
Diffraction order range ±100 ±10000
Maximal number of layers 20 10000
Non-periodical structures,
non-function border profiles
& photonic crystals		 Yes
Rigorously accounting random
roughness		 Yes
Gaussian beams, concave/convex
& VLS gratings		 Yes
Key parameter S-series** v6.7.1 SX-series** v6.7.1
Wavelength From x-rays to meters
Minimal wavelength-to-period ratio 0.02 2e-13
Diffraction order range ±100 ±10000
Maximal number of layers 20 10000
Non-periodical structures,
non-function border profiles
& photonic crystals		 Yes
Rigorously accounting random
roughness		 Yes
Gaussian beams, concave/convex
& VLS gratings		 Yes
Additional 2D scanning and 3D plot capabilities Yes

The PCGrate-S(X) v.6.6-6.7 32/64-bit softwarefor Microsoft® Windows® 32/64-bit requires:  

  • Microsoft® Windows® Vista/Server 2008/7/Server 2012/8(.1)/10 or higher installed (Windows 10 or Server 2012 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.