# Publications The MC Grating bibliography: 27 papers on the methods the codes implement, by the authors of MC Grating, and computed with it; 23 in full text, and how to cite MC Grating. Canonical: https://mcgrating.com/references.html The literature the six codes implement, the work of the authors of MC Grating, and results computed with it. Numbered as on the site since 2012, so that [17] in the text means the same paper everywhere. Each hosted paper has its own page with a short account of what it contributes and which code uses it; the full text is linked from there. ## Methods the codes implement 1. [1] [J Chandezon, G Raoult and D Maystre, “A new theoretical method for diffraction gratings and its numerical application”, J. Opt. **11**, 235-241 (1980).](https://mcgrating.com/publications/chandezon-1980-new-theoretical-method.html) [doi:10.1088/0150-536x/11/4/005](https://doi.org/10.1088/0150-536x/11/4/005)[About this paper](https://mcgrating.com/publications/chandezon-1980-new-theoretical-method.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [The C method (Chandezon)](https://mcgrating.com/features/c-method.html), [Les équations de Maxwell sous forme covariante](https://mcgrating.com/publications/chandezon-maxwell-equations-covariant-form.html), [Publications](https://mcgrating.com/references.html) 2. [2] [J. Chandezon, M. T. Dupuis, G. Cornet and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region”, J. Opt. Soc. Am. **72**, 839 (1982).](https://mcgrating.com/publications/chandezon-1982-multicoated-gratings.html) [doi:10.1364/josa.72.000839](https://doi.org/10.1364/josa.72.000839)[About this paper](https://mcgrating.com/publications/chandezon-1982-multicoated-gratings.html)Cited on: [The C method (Chandezon)](https://mcgrating.com/features/c-method.html), [A new theoretical method for diffraction gratings and its numerical application](https://mcgrating.com/publications/chandezon-1980-new-theoretical-method.html), [Publications](https://mcgrating.com/references.html) 3. [3] [Lifeng Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al revisited”, J. Opt. Soc. Am. A **11**, 2816 (1994).](https://mcgrating.com/publications/li-1994-differential-method-chandezon-revisited.html) [doi:10.1364/josaa.11.002816](https://doi.org/10.1364/josaa.11.002816)[About this paper](https://mcgrating.com/publications/li-1994-differential-method-chandezon-revisited.html)Cited on: [The C method (Chandezon)](https://mcgrating.com/features/c-method.html) 4. [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).](https://mcgrating.com/publications/li-1996-extending-the-c-method.html) [doi:10.1088/0963-9659/5/2/002](https://doi.org/10.1088/0963-9659/5/2/002)[About this paper](https://mcgrating.com/publications/li-1996-extending-the-c-method.html)Cited on: [The C method (Chandezon)](https://mcgrating.com/features/c-method.html), [Multicoated gratings: a differential formalism applicable in the entire optical region](https://mcgrating.com/publications/chandezon-1982-multicoated-gratings.html) 5. [5] [I.C. Botten, M.S. Craig, R.C. McPhedran, J.L. Adams and J.R. Andrewartha, “The Dielectric Lamellar Diffraction Grating”, Optica Acta: International Journal of Optics **28**, 413-428 (1981).](https://mcgrating.com/publications/botten-1981-dielectric-lamellar-grating.html) [doi:10.1080/713820571](https://doi.org/10.1080/713820571)[About this paper](https://mcgrating.com/publications/botten-1981-dielectric-lamellar-grating.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html), [Publications](https://mcgrating.com/references.html) 6. [6] [L.C. Botten, M.S. Craig, R.C. McPhedran, J.L. Adams and J.R. Andrewartha, “The Finitely Conducting Lamellar Diffraction Grating”, Optica Acta: International Journal of Optics **28**, 1087-1102 (1981).](https://mcgrating.com/publications/botten-1981-finitely-conducting-lamellar-grating.html) [doi:10.1080/713820680](https://doi.org/10.1080/713820680)[About this paper](https://mcgrating.com/publications/botten-1981-finitely-conducting-lamellar-grating.html)Cited on: [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html) 7. [7] [L.C. Botten, M.S. Craig and R.C. McPhedran, “Highly Conducting Lamellar Diffraction Gratings”, Optica Acta: International Journal of Optics **28**, 1103-1106 (1981).](https://mcgrating.com/publications/botten-1981-highly-conducting-lamellar-gratings.html) [doi:10.1080/713820701](https://doi.org/10.1080/713820701)[About this paper](https://mcgrating.com/publications/botten-1981-highly-conducting-lamellar-gratings.html)Cited on: [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html) 8. [8] [Lifeng Li, “A Modal Analysis of Lamellar Diffraction Gratings in Conical Mountings”, Journal of Modern Optics **40**, 553-573 (1993).](https://mcgrating.com/publications/li-1993-modal-analysis-lamellar-conical.html) [doi:10.1080/09500349314550631](https://doi.org/10.1080/09500349314550631)[About this paper](https://mcgrating.com/publications/li-1993-modal-analysis-lamellar-conical.html)Cited on: [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html) 9. [9] [Maud Foresti, Ludivine Menez and Alexander V. Tishchenko, “Modal method in deep metal-dielectric gratings: the decisive role of hidden modes”, J. Opt. Soc. Am. A **23**, 2501 (2006).](https://mcgrating.com/publications/foresti-2006-hidden-modes-deep-metal-dielectric-gratings.html) [doi:10.1364/josaa.23.002501](https://doi.org/10.1364/josaa.23.002501)[About this paper](https://mcgrating.com/publications/foresti-2006-hidden-modes-deep-metal-dielectric-gratings.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html) 10. [10] [Philippe Lalanne and G. Michael Morris, “Highly improved convergence of the coupled-wave method for TM polarization”, J. Opt. Soc. Am. A **13**, 779 (1996).](https://mcgrating.com/publications/lalanne-1996-improved-convergence-tm.html) [doi:10.1364/josaa.13.000779](https://doi.org/10.1364/josaa.13.000779)[About this paper](https://mcgrating.com/publications/lalanne-1996-improved-convergence-tm.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html), [Publications](https://mcgrating.com/references.html) 11. [11] [Lifeng Li, “Use of Fourier series in the analysis of discontinuous periodic structures”, J. Opt. Soc. Am. A **13**, 1870 (1996).](https://mcgrating.com/publications/li-1996-fourier-series-discontinuous.html) [doi:10.1364/josaa.13.001870](https://doi.org/10.1364/josaa.13.001870)[About this paper](https://mcgrating.com/publications/li-1996-fourier-series-discontinuous.html)Cited on: [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html), [Highly improved convergence of the coupled-wave method for TM polarization](https://mcgrating.com/publications/lalanne-1996-improved-convergence-tm.html), [Publications](https://mcgrating.com/references.html) 12. [14] R. Fletcher and M. J. D. Powell, “A Rapidly Convergent Descent Method for Minimization”, The Computer Journal **6**, 163-168 (1963). [doi:10.1093/comjnl/6.2.163](https://doi.org/10.1093/comjnl/6.2.163)No copy hostedCited on: [Optimization](https://mcgrating.com/features/optimization.html), [Products](https://mcgrating.com/products.html) 13. [20] [Gérard 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 (1998).](https://mcgrating.com/publications/granet-1998-chandezon-method-crossed-gratings.html) [doi:10.1364/josaa.15.001121](https://doi.org/10.1364/josaa.15.001121)[About this paper](https://mcgrating.com/publications/granet-1998-chandezon-method-crossed-gratings.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [The C method (Chandezon)](https://mcgrating.com/features/c-method.html), [Publications](https://mcgrating.com/references.html) 14. [21] [Evgeni Popov and Michel Nevière, “Grating theory: new equations in Fourier space leading to fast converging results for TM polarization”, J. Opt. Soc. Am. A **17**, 1773 (2000).](https://mcgrating.com/publications/popov-2000-fourier-space-tm-polarization.html) [doi:10.1364/josaa.17.001773](https://doi.org/10.1364/josaa.17.001773)[About this paper](https://mcgrating.com/publications/popov-2000-fourier-space-tm-polarization.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html) 15. [22] [Evgeny Popov and Michel Nevière, “Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media”, J. Opt. Soc. Am. A **18**, 2886 (2001).](https://mcgrating.com/publications/popov-2001-maxwell-equations-fourier-space.html) [doi:10.1364/josaa.18.002886](https://doi.org/10.1364/josaa.18.002886)[About this paper](https://mcgrating.com/publications/popov-2001-maxwell-equations-fourier-space.html)Cited on: [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html) 16. [23] [Thomas Schuster, Johannes Ruoff, Norbert Kerwien, Stephan Rafler and Wolfgang Osten, “Normal vector method for convergence improvement using the RCWA for crossed gratings”, J. Opt. Soc. Am. A **24**, 2880 (2007).](https://mcgrating.com/publications/schuster-2007-normal-vector-method-rcwa.html) [doi:10.1364/josaa.24.002880](https://doi.org/10.1364/josaa.24.002880)[About this paper](https://mcgrating.com/publications/schuster-2007-normal-vector-method-rcwa.html)Cited on: [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html), [Use of Fourier series in the analysis of discontinuous periodic structures](https://mcgrating.com/publications/li-1996-fourier-series-discontinuous.html), [Publications](https://mcgrating.com/references.html) 17. [25] [Jean Chandezon, “Les équations de Maxwell sous forme covariante”, Thesis chapter, Université de Clermont-Ferrand ().](https://mcgrating.com/publications/chandezon-maxwell-equations-covariant-form.html) [About this paper](https://mcgrating.com/publications/chandezon-maxwell-equations-covariant-form.html)Cited on: [The C method (Chandezon)](https://mcgrating.com/features/c-method.html) 18. [26] Jean Chandezon and Gérard Granet, “Diffraction by gratings: from the C-method to the stochastic C-method”, J. Opt. Soc. Am. A **41**, 1675 (2024). [doi:10.1364/JOSAA.530262](https://doi.org/10.1364/JOSAA.530262)No copy hostedCited on: [The C method (Chandezon)](https://mcgrating.com/features/c-method.html), [Stochastic C-method](https://mcgrating.com/features/stochastic-c-method.html), [Products](https://mcgrating.com/products.html) ## Work by the authors of MC Grating 1. [12] [Nikolay M. Lyndin, Olivier Parriaux and Alexander V. Tishchenko, “Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings”, J. Opt. Soc. Am. A **24**, 3781 (2007).](https://mcgrating.com/publications/lyndin-2007-fmm-instabilities.html) [doi:10.1364/josaa.24.003781](https://doi.org/10.1364/josaa.24.003781)[About this paper](https://mcgrating.com/publications/lyndin-2007-fmm-instabilities.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html), [Publications](https://mcgrating.com/references.html) 2. [13] [S M Loktev, N M Lyndin, O Parriaux, V A Sychugov and A V Tishchenko, “Reflection of a finite light beam from a finite waveguide grating”, Quantum Electron. **27**, 445-449 (1997).](https://mcgrating.com/publications/loktev-1997-finite-beam-finite-waveguide-grating.html) [doi:10.1070/qe1997v027n05abeh000959](https://doi.org/10.1070/qe1997v027n05abeh000959)[About this paper](https://mcgrating.com/publications/loktev-1997-finite-beam-finite-waveguide-grating.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [Resonance search](https://mcgrating.com/features/resonance-search.html), [Products](https://mcgrating.com/products.html) 3. [15] N. M. Lyndin, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, "Analytical methods and apparatus employing an optical sensor device with refractive index modulation", US Patent 6, 218, 194 April 17, 2001 No copy hostedCited on: [Products](https://mcgrating.com/products.html) 4. [16] N. M. Lyndin, "Optical grating structures and method for their manufacture", PCT Patent WO/2002/082130 October 17, 2002 No copy hostedCited on: [Products](https://mcgrating.com/products.html) ## Results computed with MC Grating 1. [17] [V A Sychugov, V A Mikhailov, V A Kondratyuk, N M Lyndin, J Frahm, A I Zagumennyi, Yu D Zavartsev and P A Studenikin, “Short-wavelength (λ = 914 nm) microlaser operating on an Nd3+:YVO4 crystal”, Quantum Electron. **30**, 13-14 (2000).](https://mcgrating.com/publications/sychugov-2000-914nm-microlaser.html) [doi:10.1070/qe2000v030n01abeh001648](https://doi.org/10.1070/qe2000v030n01abeh001648)[About this paper](https://mcgrating.com/publications/sychugov-2000-914nm-microlaser.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [Optimization](https://mcgrating.com/features/optimization.html), [Products](https://mcgrating.com/products.html), [Examples](https://mcgrating.com/try-examples.html) 2. [18] [Nathalie Destouches, Jean-Claude Pommier, Olivier Parriaux, Tina Clausnitzer, Nikolai Lyndin and Svetlen Tonchev, “Narrow band resonant grating of 100% reflection under normal incidence”, Opt. Express **14**, 12613 (2006).](https://mcgrating.com/publications/destouches-2006-narrow-band-resonant-grating.html) [doi:10.1364/oe.14.012613](https://doi.org/10.1364/oe.14.012613)[About this paper](https://mcgrating.com/publications/destouches-2006-narrow-band-resonant-grating.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [Products](https://mcgrating.com/products.html) 3. [19] [N. Lyndin, M. Flury, S. Tonchev, R. Fechner and O. Parriaux, “Design and fabrication of an all-dielectric grating with top-hat high diffraction efficiency over a broad spectral range”, J. Eur. Opt. Soc.-Rapid Publ. **2**, 07019 (2007).](https://mcgrating.com/publications/lyndin-2007-top-hat-dielectric-grating.html) [doi:10.2971/jeos.2007.07019](https://doi.org/10.2971/jeos.2007.07019)[About this paper](https://mcgrating.com/publications/lyndin-2007-top-hat-dielectric-grating.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [Products](https://mcgrating.com/products.html) 4. [24] [S I Derzhavin, O A Dyukel' and N M Lyndin, “Coherent summation of the radiation of a single-mode laser diode array”, Quantum Electron. **42**, 561-564 (2012).](https://mcgrating.com/publications/derzhavin-2012-coherent-summation-laser-diode-array.html) [doi:10.1070/qe2012v042n06abeh014826](https://doi.org/10.1070/qe2012v042n06abeh014826)[About this paper](https://mcgrating.com/publications/derzhavin-2012-coherent-summation-laser-diode-array.html)Cited on: [About MC Grating Software](https://mcgrating.com/about.html), [Products](https://mcgrating.com/products.html), [Examples](https://mcgrating.com/try-examples.html) 5. [27] [I.M. Akhmedzhanov, J. Kh. Nurligareev and B.A. Usievich, “Modal analysis of the quasi-resonant extinction ratio enhancement in the amorphous silicon wire grid polarizer”, Opt. Commun. **549**, 129912 (2023).](https://mcgrating.com/publications/akhmedzhanov-2023-wire-grid-polarizer-extinction-ratio.html) [doi:10.1016/j.optcom.2023.129912](https://doi.org/10.1016/j.optcom.2023.129912)[About this paper](https://mcgrating.com/publications/akhmedzhanov-2023-wire-grid-polarizer-extinction-ratio.html)Cited on: [The modal method (RCWA / FMM)](https://mcgrating.com/features/modal-method.html), [Products](https://mcgrating.com/products.html) A second, separate list of eight papers accompanies the [modes-interference study](https://mcgrating.com/modes-interference.html#references). ## How to cite MC Grating If MC Grating contributed to a published result, we ask that you acknowledge the software by citing it. There is no software paper yet, so the durable form is the software itself: ``` N. M. Lyndin and B. A. Usievich, MC Grating Software, version 2026-05-25, General Physics Institute, Moscow. https://mcgrating.com ``` In addition, one may fairly cite the papers describing the method the result rests on: - **Diffraction efficiencies by the modal codes** (Modal Collinear, Modal Conical, Modal Crossed): the Fourier modal method with the correct factorization rules — [Li 1996](https://mcgrating.com/publications/li-1996-fourier-series-discontinuous.html) [[11](https://mcgrating.com/references.html#ref-11)] and [Lalanne and Morris 1996](https://mcgrating.com/publications/lalanne-1996-improved-convergence-tm.html) [[10](https://mcgrating.com/references.html#ref-10)]; for the true-mode method, [Botten et al. 1981](https://mcgrating.com/publications/botten-1981-dielectric-lamellar-grating.html) [[5](https://mcgrating.com/references.html#ref-5)]. - **Results from the Chandezon codes** (Chandezon Collinear, Chandezon Conical): [Chandezon, Maystre and Raoult 1980](https://mcgrating.com/publications/chandezon-1980-new-theoretical-method.html) [[1](https://mcgrating.com/references.html#ref-1)] and, for multilayers, [Chandezon et al. 1982](https://mcgrating.com/publications/chandezon-1982-multicoated-gratings.html) [[2](https://mcgrating.com/references.html#ref-2)]. - **Crossed gratings:** [Schuster et al. 2007](https://mcgrating.com/publications/schuster-2007-normal-vector-method-rcwa.html) [[23](https://mcgrating.com/references.html#ref-23)] for Modal Crossed, [Granet 1998](https://mcgrating.com/publications/granet-1998-chandezon-method-crossed-gratings.html) [[20](https://mcgrating.com/references.html#ref-20)] for Chandezon Crossed. - **Metallic gratings under TM incidence with the modal codes:** [Lyndin, Parriaux and Tishchenko 2007](https://mcgrating.com/publications/lyndin-2007-fmm-instabilities.html) [[12](https://mcgrating.com/references.html#ref-12)]. A sentence for a methods section, to adapt: > Diffraction efficiencies were computed by the Fourier modal method [Li 1996] as implemented in MC Grating Software (version 2026-05-25, General Physics Institute, Moscow, https://mcgrating.com). Journals differ in how they cite software; follow your journal's form where it has one.