The Crossed Grating software of a diffraction grating analysis and design that would run on a PC was developed from 1999 by Dr. Nikolai Lyndin senior physicist of General Physics Institute, Moscow, lyndin@ran.gpi.ru. For many years the author is involved with solving scientific and practical problems of using multilayer grating structures in grating couplers, biochemistry sensors, laser resonator modes selection and others. The Crossed Grating software is a natural extension of one dimensional MC Grating software package and from the beginning the grating software was designed for personal use to insure a maximum convenience for the user.

Features

Crossed Grating software package is designed to run on any Windows® OS. The interface is written in Delphi while the most critical matrix routines are taken from Lapack 3.1.1 package and rewritten in C++. The Lapack routines DLL is optimized for Intel processors and provides calculation speed close to the speed of original Intel® Math Kernel Library (Intel® MKL) routines. The software is intended to calculate crossed gratings with a smooth (Chandezon method^1-5) and a binary (Modal method^6-9) profiles. The «Normal Vector Field» idea^10-12 with automatic generation of NV-Field is implemented. This provides the fasters known convergence for dielectric crossed gratings of a binary profile.
The Crossed Grating code is hardware protected with a HASP HL USB dongle.

Generally the Crossed Grating software is intended to calculate the diffraction efficiencies (power) and complex amplitude (module, phase or real, imagine part) of diffracted waves in superstrate (cover) and substrate under incidence of a plane wave from the cover. Also a complex field and power flow components in the structure and ambient medium can be calculated. If the structure hasn't a grating region at all the software considers this structure as a simple multilayer stack that has only reflected and transmitted waves (zero diffraction orders) and the calculations became very fast.

The multidimensional optimization method is based on the approach suggested by Davidon (1959), and further developed by Fletcher and Powell. The Davidon - Fletcher - Powell method¹³ is a Quasi-Newton Method also known as a Variable Metrics Method. Almost every incident wave, and structure parameters, including refractive indexes, can be set as variables. There isn't any restriction on optimization search area except a physical meaning of the variable parameters (for example a layer thickness can not be negative). Several methods of a criterion function construction allow solving variety of design and inverse structure reconstruction problems.

The Main material catalog contains dispersion data of many dielectric, metal and semiconductor materials. For the user convenience a frequently used materials can be copied into a custom catalog. The user can edit any material in this catalog or add any new material.

The Crossed Grating code has interface analogous to the the MC Grating code interfaces adapted for particular code possibilities. The main form is a container for independent project editor windows. Editor window may display a text with a structure parameters or a text table with results of calculation. The graphic tools take data from the results text table. This seems to be reasonable because the user has an opportunity to edit the data and display in a graphic form a saved data files. The user can change the results precision and diffraction orders of interest displayed in the text table without repeating calculation because a complete result data is kept in a PC memory. The structure parameters can be edited as from the text window or from dialog window "Settings". Dialog windows are also used to access any other options.

The Crossed Grating software demo version has only one restriction: it sets all refractive indexes multiple to 0.5. For this reason a material catalog can be used only as a reference and refractive indexes can not be set as a variable parameters in optimization procedure. Nevertheless the Crossed Grating demo version remains enough flexibility to serve for education and training needs.

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3. Lifeng Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited”, J. Opt. Soc. Am. 11, 2816-2828 (1994).
4. Lifeng Li, G. Granet, J. P. Plumey, and J. Chandezon, “Some topics in extending the C method to multilayer gratings of different profiles”, Pure Appl. Opt. 5, 141-156 (1996).
5. G. Granet, “Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings”, J. Opt. Soc. Am. A 15, 1121-1131 (1998).
6. Lifeng Li, «A modal analysis of lamella diffraction gratings in conical mountings», Journal of Modern Optics, 40, 553-573 (1993);
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8. L. Li, «Use of Fourier series in the analysis of discontinuous periodic structures», J. Opt. Soc. Am. A 13, No. 9, p. 1870 (1996).
9. N. Lyndin, O. Parriaux and A.V. Tishchenko, «Modal analysis and suppression of the FMM instabilities in highly conductive gratings», J. Opt. Soc. Am. A, Vol. 24, No. 12, p. 3781 (2007).
10. Evgeni Popov, Michel Nevie`re, «Grating theory: new equations in Fourier space leading to fast converging results for TM polarization», J. Opt. Soc. Am. A 17, No. 10, p. 1773 (2000).
11. Evgeni Popov, Michel Nevie`re, «Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media», J. Opt. Soc. Am. A 18, No. 11, p. 2886 (2001).
12. Thomas Schuster, Johannes Ruoff, Norbert Kerwien, Stephan Rafler, and Wolfgang Osten1, «Normal vector method for convergence improvement using the RCWA for crossed gratings», J. Opt. Soc. Am. A 24, No. 9, p. 2880 (2007).
13. R. Fletcher, M.J.D. Powell, «A rapidly convergent descent method for minimization», The Computer Journal, 6 163-168 (1963).