Asymptotic methods of solving problems of diffraction by non-periodic structures
S.I. Kharitonov, L.L. Doskolovich, N.L. Kazanskiy

 

Image Processing Systems Institute оf RAS, – Branch of the FSRC “Crystallography and Photonics” RAS,
Samara National Research University

Full text of article: Russian language.

 PDF

Abstract:
An asymptotic method for calculating the complex amplitude of a light field in the case of diffraction by non-periodic band gap structures. The novelty of the approach consists in the expansion of the solution of the integral equation into a basis that describes the propagation of light through a DOE within the geometrical optics approximation and changes into a basis of plane waves used in the calculation of diffraction gratings. We present the results of focusing into a point by a gradient-index diffractive optical element with a band-gap structure.  Simulation results confirm the efficiency of the proposed method.

Keywords:
diffractive optical element (DOE), asymptotic method, coupled-wave analysis, aperiodic structure, quasi-periodic structure, microrelief.

Citation:
Kharitonov SI, Doskolovich LL, Kazanskiy NL. Asymptotic methods for solving problems of diffraction by non-periodic structures. Computer Optics 2017; 41(2): 160-168. DOI: 10.18287/2412-6179-2017-41-2-160-168.

References:

  1. Doskolovich LL, Kazanskiy NL, Kharitonov SI, Usplenjev GV. Focusators for laser-branding. Optics and Lasers in Engineering 1991; 15(5): 311-322. DOI: 10.1016/0143-8166(91)90018-O.
  2. Golub MA, Doskolovich LL, Kazanskiy NL, Kharitonov SI, Soifer VA. Computer generated diffractive multi-focal lens. Journal of Modern Optics 1992; 39(6): 1245-1251. DOI: 10.1080/713823549.
  3. Kazanskiy NL, Kharitonov SI, Soifer VA Simulation of DOE-aided focusing devices. Optical Memory & Neural Networks 2000; 9(3): 191-200.
  4. Kazanskiy NL, Kharitonov SI, Soifer VA, Volkov AV. Investigation of Lighting Devices Based on Diffractive Optical Elements. Optical Memory & Neural Networks 2000; 9(4): 301-312.
  5. Doskolovich LL, Kharitonov SI, Petrova OI, Soifer VA. A gradient method for design of varied - depth binary diffraction grating. Optics and Lasers in Engineering 1998; 29(4-5): 249-259. DOI: 10.1016/S0143-8166(97)00113-9.
  6. Doskolovich LL, Bigliatti S, Kharitonov SI, Petrova OI. Design of lenses for the focusing into a line [In Russian]. Computer Optics 2000; 20: 29-34.
  7. Bezus EA, Doskolovich LL, Kazanskiy NL, Soifer VA, Kharitonov SI, Pizzi M, Perlo P. The design of the diffractive optical elements to focus surface plasmons [In Russian]. Computer Optics 2009; 33(2): 185-192.
  8. Golub MA, Kazanskii NL, Sisakyan NI, Soifer VA, Kharitonov SI. Diffraction calculation for an optical element which focuses into a ring. Optoelectronics, Instrumentation, and Data Processing 1987; 23(6): 7-14.
  9. Golub MA Kazansky NL, Sissakian IN, Soifer VA, Kharitonov SI. Evaluation of the diffraction blur focal-term line geometroopticheskih focusators [In Russian]. Computer Optics 1989; 5: 34-38.
  10. Golub MA, Kazanskii NL, Sisakiyan IN, Soifer VA, Kharitonov SI. Diffraction calculation of the field intensity near the focal line of a focuser. Optics and Spektroskopy 1989; 67(6): 814-815.
  11. Golub MA, Doskolovich LL, Kazansky NL, Soifer VA, Kharitonov SI. Application of Pseudo optics to calculate the fields of diffractive optical elements [In Russian]. Scientific Instrument 1993; 3(1): 38-46.
  12. Kazanskiy NL, Kharitonov SI, Soifer VA. Application of a pseudogeometrical optical approach for calculation of the field formed by a focusator. Optics & Laser Technology 1996; 28(4): 297-300. DOI: 10.1016/0030-3992(95)00103-4.
  13. Dmitriev AYu, Doskolovich LL, Kharitonov SI. Asymptotic computation of the light field intensity for a diffractive optical element to focus into a line [In Russian]. Computer Optics 2008; 32(2): 195-200.
  14. Kharitonov SI, Doskolovich LL, Kazanskiy NL. The asymptotic solution of the scalar wave equation [In Russian]. Computer Optics 2003; 25: 49-53.
  15. Doskolovich LL, Kharitonov SI, Kazanskiy NL, Tulupova EA, Skuratov SA. Asymptotic solutions of the Helmholtz equation for pseudoperiodic structures [In Russian]. Computer Optics 2005; 27: 50-55.
  16. Doskolovich LL, Kazanskiy NL, Moses MA, Kharitonov SI. Asymptotic methods for solving problems of diffraction by the DOE [In Russian]. Computer Optics 2006; 30: 49-52.
  17. Guizal B, Barchiesi D, Felbacq D. Electromagnetic beam diffraction by a finite lamellar structure: an aperiodic coupled-wave method. J Opt Soc Am A 2003; 20(12): 2274-2280. DOI: 10.1364/JOSAA.20.002274.
  18. Häyrynen T, de Lasson JR, Gregersen N. Open-geometry Fourier modal method: modeling nanophotonic structures in infinite domains. J Opt Soc Am A 2016; 33(7): 1298-1306. DOI: 10.1364/JOSAA.33.001298.
  19. Kazanskiy NL, Kalyaev ML, Kharitonov SI. Compact notation of Maxwell's set of equations in the spatial-frequency representation [In Russian]. Antennas 2007, 10: 13-21.
  20. Kharitonov SI, Doskolovich LL, Kazanskiy NL, Kalyaev ML. The asymptotic method of calculation of the field of optical elements with the structure of the band-swarm [In Russian]. Computer Optics 2007; 31(4): 7-18.
  21. Doskolovich LL, Kazanskiy NL, Kharitonov SI. Integral representations of solutions of Maxwell's equations for anisotropic media [In Russian]. Computer Optics 2010; 34(1): 52-57.
  22. Doskolovich LL, Kazanskiy NL, Kharitonov SI. Solutions of Maxwell's equations in the integral form of a spectrum of surface plasmons [In Russian]. Computer Optics 2008; 32(2): 151-154.
  23. Doskolovich LL, Kazanskiy NL, Soifer VA, Kharitonov SI. The non-linear pre-emphasis phase to focus in the focal line [In Russian]. Scientific Instrument 1993; 3(1): 24-37.
  24. Doskolovich LL, Kazanskiy NL, Kharitonov SI, Tzaregorodzev AYe. A method for estimating the DOE's energy efficiency. Optics and Laser Technology 1995; 27(4): 219-221. DOI: 10.1016/0030-3992(95)93748-G.

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail: journal@computeroptics.ru; Phones: +7 (846) 332-56-22, Fax: +7 (846) 332-56-20