Approaches to the algorithmization of the rigorous coupled-wave analysis
Antonov A.I., Vasin L.A., Greisukh G.I.

 

Penza State University of Architecture and Construction, Penza, Russia

Abstract:
Coefficients required for the algorithmization and implementation of the rigorous coupled-waves analysis are derived for a Fourier series expansion of the permittivity of a linear-sawtooth relief with positive tangent of the working surface angle and vertical backward slope. Approaches to the implementation of the rigorous coupled-waves analysis are described and compared in terms of stability and efficiency, namely, the approach of a purposeful transformation of the transmission matrix and the approach of Gaussian illuminations. It was concluded that the most appropriate approach for determining the diffraction efficiency for cases of deep diffraction structures is the approach of purposeful transformation of the transmission matrix.

Keywords:
diffraction efficiency, permittivity, Maxwell’s equations, rigorous coupled-wave analysis.

Citation:
Antonov AI, Vasin LA, Greisukh GI. Approaches to the algorithmization of the rigorous coupled-wave analysis. Computer Optics 2019; 43(2): 209-219. DOI: 10.18287/2412-6179-2019-43-2-209-219.

References:

  1. Greisukh GI, Danilov VA, Stepanov SA, Antonov AI, Usievich BA. Minimization of the total depth of internal sawtooth reliefs of a two-layer relief-phase diffraction microstructure. Optics and Spectroscopy 2018; 124(1): 98-102.
  2. Greisukh GI, Danilov VA, Stepanov SA, Antonov AI, Usievich BA. Spectral and angular dependences of efficiency of three-layer relief-phase diffraction elements of the IR range. Optics and spectroscopy 2018; 125(1): 60-64.
  3. Greisukh GI, Danilov VA, Stepanov SA, Antonov AI, Usievich BA. Harmonic kinoform lens: Diffraction efficiency and chromatism. Optics and spectroscopy 2018; 125(2): 232-237.
  4. Greisukh GI, Danilov VA, Stepanov SA, Antonov AI, Usievich BA. Spectral and angular dependence of the efficiency of a two-layer and single-relief sawtooth microstructure. Computer Optics 2018; 42(1): 38-43. DOI: 10.18287/2412-6179-2018-42-1-38-43.
  5. Moharam MG, Gaylord TK. Diffraction analysis of dielectric surface-relief gratings. J Opt Soc Am 1982; 72(10): 1385-1392.
  6. Moharam MG, Grann EB, Pommet DA, Gaylord TK. Formulation for stable and efficient implementation ofthe rigorous coupled-wave analysis of binary gratings. J Opt Soc Am 1995; 12(5): 1068-1076.
  7. Moharam MG, Grann EB, Pommet DA, Gaylord TK. Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach. J Opt Soc Am 1995; 12(5): 1077-1086.
  8. Li L. Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings. J Opt Soc Am 1996; 13(6): 1024-1035.
  9. Redheffer R. Difference equations and functional equations in transmission-line theory. Modern Mathematics for the Engineer 1961; 12: 282-337.
  10. CEM Lectures. Source: < http://emlab.utep.edu/academics.htm >.
  11. Solimeno S, Crosignani B, DiPorto P. Guiding, diffraction, and confinement of optical radianion. Orlando, FL: Academic Press Inc; 1989.
  12. Tikhonov AN, Vasil'eva AB, Sveshnikov AG. Differential equations. Berlin, Heidelberg: Springer-Verlag; 1985.
  13. Kiryanov D, Kiryanova E. Computational science. Hungham, MA: Infinity Science Press LLC; 2007.
  14. Ilyin VA, Poznyak EG. Fundamentals of mathematical analysis: Volumes 1 and 2. Part II. Moscow: “Fizmatlit” Publisher; 1982.
  15. Prokhorov General Physics Institute. Source: < http://www.gpi.ru >.
  16. Grating Diffraction Calculator. Source: < http://kjinnovation.com/GD-Calc.html >.
  17. MATLAB. Source: < https://uk.mathworks.com/products /matlab.html >.
  18. Wolfram Mathematica. Source: < http://www.wolfram.com /mathematica.html >.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20