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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.
The PCGrate® software is based on the modified method of integral equations (the modified integral method 2-7 - 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 orders ranging from low to very high.
Taking into account roughness of any kinds and inter-diffusion.
Pulse compression and high conductivity.
1-D & 2-D photonic crystals and multilayers with 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 groove profile function. An example of this type is the case of groove profile borders 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 efficiency modeling, etc. Several different series of the PCGrate have been released since we started: for DOS, for Windows 16-bit, "2000" for Windows 32-bit, and " S(X)" for later versions of Windows 32-bit. The efficiency data obtained by the PCGrates were compared with experimental data 2,3,6,8-24, with numerous calculated data 4,5,7,25 and with the results of other experiments 27,28,31-35. Some details of the grating efficiency calculations and well-known examples of sources of refractive indices data are presented in the Efficiency TestLab.
The PCGrate®-S(X)™ series is the most flexible and powerful software for efficiency and near-field predictions of various types of plane and shaped gratings & 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 superwide 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 version makes use of the smart internal cache of the program, parallel processing, and the new mathematics. The computation time decreases significantly, in particular for calculations with Trapezoidal, Triangular, Sawtooth, and Polygonal border profile types when the Equal X-interval check-box is checked. One of the most important advantages of the newer version is that the speed difference between the earlier and the new programs increases noticeably when the main accuracy parameter grows. The latest software version includes several new options which make it possible to improve convergence of calculations when considering challenging efficiency problems for some kinds of reflection and transmission gratings, and especially, in the case of TM polarization and with real groove profiles. It has the 2-D & 3-D OpenGL input-output graphics, powerful Groove Profile & Refractive Indices Editors, a very extended wavelength region, a highly increased maximum order for echelles and diffuse scattering, and totally improved multilayer capabilities including closed borders.
The most recent PCGrate-S(X) v.6.1 and PCGrate-S(X) v.6.2 series also provide a possibility of calculating the efficiency of gratings from the command line and of saving or converting input/output data in XML-format files. This permits one to use any alternative codes and tools in which the grating efficiency or the field amplitude calculations are a part of the more general task. PCGrate-S(X) v.6.2 series software enables the calculations both multilayer resonance and small wavelength-to-period ratio cases at very 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, rough periodical or non-periodical structures, and photonic crystals. The new 'Randomize profile' option in Border Profile Editor converts any Trapezoidal, Lamellar, Triangular, Sawtooth, Polygonal or Trigonometric border profile into that of the randomized Polygonal type (see Figure #27 ). You can also choose the rms roughness (relative to the period), the correlation length, amount of randomized points to be used for the conversion, 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 ).
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