Based on this analysis and the fact that highly efficient gratings are desired for astronomical spectroscopy (which would lead toward extensive use of blazed metallic reflection coatings), we chose PCGrate to calculate the efficiencies from the metrology-derived grating profiles (It is also significant that PCGrate is much faster).

Dr. David A. Content et al.19

PURPOSES AND TASKS

The effective use of diffraction gratings in optical and electronic systems calls for an understanding of how grating parameters affect the system range and performance. An accurate knowledge of the diffraction efficiency over the entire wavelength (or other parameter) range is essential for both accurate performance analysis and optimizing the design of many grating-based applications. By way of illustration, the grating parameters chosen such as groove profile and spacing can be used. The complete efficiency performance therewith would be obtained over the entire wavelength range used for a given geometric configuration of the system. As an example of the latter case, a grating system at the design stage can be modeled by scanning variations of the appropriate parameters such as blaze angle, grating depth, layer thickness or refractive index. Upon optimization, the results can be used to select a standard available grating or become a basis of the custom design. The relevant part of the system layout can be incorporated directly into this efficiency performance analysis. Producers of grating structures can easily appreciate the tremendous benefits arising from reduction in the test and measurement times, both of which are of fundamental importance for the grating production process.

BASIS AND TESTING  

ThePCGrate® software is based on the modified method of boundary integral equations (the modified integral method2-7 – MIM). The PCGrate programs enable the user to accurately solve the periodic boundary value problems which describe the incidence of a light beam on the relief or phase diffraction grating and rough mirror. Our codes are indispensable for efficiency calculations in the following problems:  

  • The x-ray – EUV range and small wavelength-to-period ratios.  
  • Echelles and grisms at diffraction order numbers ranging from low to very high.  
  • Taking rigorously into account periodical and random roughnesses of any kinds.  
  • Rigorously accounting diffuse light intensity (ghosts).  
  • Pulse compression and high conductivity.  
  • 1-D & 2-D photonic crystals and multilayers with rough and non-conformal borders.  
  • Very deep reflection and transmission grooves.  
  • Non-planar incident waves and concave/convex grating shapes.  
  • Any polarization states and other peculiarities.  

The codes are especially convenient and accurate for modeling with the real border profile function. An example of this type is the case of groove profiles determined by: an atomic-force microscope (AFM), a transmission electron microscope (TEM), a micro-interferometer, a stylus profilometer, and also by indirect methods like actual growth modeling, etc. Several different series of the PCGratehave been releasedsince we started:forDOS,forWindows 16-bit, “2000”for Windows 32-bit, and “S(X)” for later versions of Windows 32/64-bit. The efficiency data obtained by the PCGrates were compared with experimental data2,3,6,8–24, with numerous calculated data4,5,7,25 and with the results of other experiments27,28,31–35.Some details of the grating efficiency calculations and well-known examples of sources of refractive indices data are presented in the Efficiency TestLab.  

COMPARISON

The PCGrate®-S(X)™ series is the most flexible and powerful software for efficiency and near-zone field predictions of various types of plane and shaped multilayer gratings & rough mirrors exposed to either plane or non- planar waves. The PCGrate-S(X) programs incorporated all the advantages of the previous program versions and still provided many entirely new features and very fast computation, the latter being of the utmost importance for up-to-date grating efficiency modeling in the super-wide range of parameters. For most problems both the speed and the accuracy of calculation increase many times (up to several orders!) as compared with the earlier PCGrate 2000* software, as the newer series make use of the smart internal cache of the program, parallel processing, and the new mathematics. They have the 2-D & 3-D OpenGL input-output graphics, powerful Border Profile & Refractive Indices Editors, very extended wavelength and other parameter regions, a highly increased maximum order number for echelles and x-ray grating calculations, totally improved multilayer capabilities, and a possibility of calculating the efficiency of gratings from the command line and of saving or converting input/output data in XML-format files. The later permits one to use any alternative codes and tools in which the grating efficiency or the field calculations are a part of the more general task.   The most recent PCGrate-S(X) v.6.6-6.7 32/64-bit series software enables the calculations both multilayer resonance and small wavelength-to-period ratio cases at high speed using one of two independent solvers, i.e. Penetrating and Separating. The solvers have different behavior and mutually complementary capabilities for many difficult cases such as coated gratings with thin layers, randomly rough periodical or non-periodical structures, grazing incidence, and photonic crystals. The new ‘Randomize profile’ and ‘Randomize profile using correlation length’ options in Border Profile Editor convert different border profiles into those of Randomized polygonal type (see Figure #27 ). You can choose amount of randomized points to be used for the conversion, the rms roughness (relative to the period), the correlation length, the maximal deviation-to-rms ratio, and the X-axis shift for randomizing (relative to the period), i.e. the part of a period where the randomization won’t take effect (see Figure #15). Cubic spline is added to the list of supported border profiles, which is a mostly convinient type for computations using non-function border profiles. By PCGrate-S(X) v.6.6-6.7 one can easily simulate variable-groove-depth (VGD) and variable-line-spaced (VLS) sectioned gratings, as well as non-planar incident waves including Gaussian ones.