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On the condition of total backward reflection for a diffraction grating on a mirror operating in Littrow mounting
E.A. Bezus 1,2, D.A. Bykov 2,1, L.L. Doskolovich 2,1

Samara National Research University,
Moskovskoye Shosse 34, Samara, 443086, Russia;
Image Processing Systems Institute, NRC “Kurchatov Institute”,
Molodogvardeyskaya Str. 151, Samara, 443001, Russia

 PDF, 855 kB

DOI: 10.18287/2412-6179-CO-1528

Pages: 362-368.

Full text of article: Russian language.

Abstract:
Optical properties of a structure consisting of a diffraction grating operating in the Littrow geometry, a plane-parallel dielectric layer, and a mirror that completely reflects the incident radiation are considered. A condition is obtained that is imposed on the scattering matrix elements of a diffraction grating, under which, by choosing the thickness of the dielectric layer, it is possible to obtain total backward reflection, i.e., to direct all the energy of the incident wave to the –1st reflected diffraction order. The results of numerical simulations within the framework of the electromagnetic theory of diffraction completely confirm the obtained theoretical results.

Keywords:
diffraction grating, Littrow mounting, Bragg mirror, –1st diffraction order, Fourier modal method.

Citation:
Bezus EA, Bykov DA, Doskolovich LL. On the condition of total backward reflection for a diffraction grating on a mirror operating in Littrow mounting. Computer Optics 2025; 49(3): 362-368. DOI: 10.18287/2412-6179-CO-1528.

Acknowledgements:
This work was partly funded by the Ministry of Science and Higher Education of the Russian Federation within state assignment to Samara University, FSSS-2024-0014 (Theoretical investigation of the possibility of obtaining a zero of the zeroth diffraction order) and NRC “Kurchatov Institute”  (Numerical investigation of an example of the diffractive structure).

References:

  1. Rittenhouse D. Explanation of an optical deception. Trans Amer Phil Soc 1786; 2: 37-42. DOI: 10.2307/1005164.
  2. Wood RW. On a remarkable case of uneven distribution of light in a diffraction grating spectrum. Proc Phys Soc London 1902; 18(1): 269-306. DOI: 10.1088/1478-7814/18/1/325.
  3. Hessel A, Oliner AA. A new theory of Wood’s anomalies on optical gratings. Appl Opt 1995; 4(10): 1275-1297. DOI: 10.1364/AO.4.001275.
  4. Loewen EG, Popov T. Diffraction gratings and applications. Boca Raton: CRC Press; 1997. ISBN: 9781315214849.
  5. Collin S. Nanostructure arrays in free-space: optical properties and applications. Rep Prog Phys 2014; 77(12): 126402. DOI: 10.1088/0034-4885/77/12/126402.
  6. Bonod N, Neauport J. Diffraction gratings: from principles to applications in high-intensity lasers. Adv Opt Photonics 2016; 8(1): 156-199. DOI: 10.1364/AOP.8.000156.
  7. Qiao P, Yang W, Chang-Hasnain CJ. Recent advances in high-contrast metastructures, metasurfaces, and photonic crystals. Adv Opt Photonics 2018; 10(1): 180-245. DOI: 10.1364/AOP.10.000180.
  8. Quaranta G, Basset G, Martin OJF, Gallinet B. Recent advances in resonant waveguide gratings. Laser Photonics Rev 2018; 12(9): 1800017. DOI: 10.1002/lpor.201800017.
  9. Khonina SN, Kapitonov YV. Simulation of the spatial distribution of scattered light under illumination of a resonant diffraction grating with structured light. Computer Optics 2023; 47(6): 927-937. DOI: 10.18287/2412-6179-CO-1404.
  10. Bykov DA, Bezus EA, Doskolovich LL. Coupled-mode theory for resonant gratings with a varying period. Computer Optics 2023; 47(3): 341-349. DOI: 10.18287/2412-6179-CO-1232.
  11. Svakhin AS, Sychugov VA, Tikhomirov AE. Efficient diffraction elements for TE-polarized waves. Sov Phys Tech Phys 1991; 36: 1038-1040.
  12. Svakhin AS, Sychugov VA, Tikhomirov AE. Diffraction gratings with high optical strength for laser resonators. Quantum Electron 1994; 24(3): 233-235. DOI: 10.1070/QE1994v024n03ABEH000060.
  13. Perry MD, Boyd RD, Britten JA, Decker D, Shore BW, Shannon C, Shults E. High-efficiency multilayer dielectric diffraction gratings. Opt Lett 1995; 20(8): 940-942. DOI: 10.1364/OL.20.000940.
  14. Shore BW, Perry MD, Britten JA, Boyd RD, Feit MD, Nguyen HT, Chow R, Loomis GE, Li L. Design of high-efficiency dielectric reflection gratings. J Opt Soc Am A 1997; 14(5): 1124-1136. DOI: 10.1364/JOSAA.14.001124.
  15. Tishchenko AV, Sychugov VA. High grating efficiency by energy accumulation in a leaky mode. Opt Quantum Electron 2000; 32(6-8): 1027-1031. DOI: 10.1023/A:1007055604507.
  16. Destouches N, Tishchenko AV, Pommier JC S. Reynaud S, Parriaux O, Tonchev S, Ahmed MA. 99% efficiency measured in the −1st order of a resonant grating. Opt Express 2005; 13(9): 3230-3235. DOI: 10.1364/OPEX.13.003230.
  17. Flury M, Tishchenko AV, Parriaux O. The leaky mode resonance condition ensures 100% diffraction efficiency of mirror-based resonant gratings. J Lightw Technol 2007; 25(7): 1870-1878. DOI: 10.1109/JLT.2007.899187.
  18. Popov E, Tsonev L, Maystre D. Gratings–general properties of the Littrow mounting and energy flow distribution. J Mod Opt 1990; 37(3): 367-377. DOI: 10.1080/09500349014550421.
  19. Li L. Internal mechanism of perfect-reflector-backed dielectric gratings to achieve 100% diffraction efficiency. J Opt Soc Am A 2024; 41(2): 252-260. DOI: 10.1364/JOSAA.511422.
  20. Moharam MG, Grann EB, Pommet DA, Gaylord TK. Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings. J Opt Soc Am A 1995; 12(5): 1068-1076. DOI: 10.1364/JOSAA.12.001068.
  21. Li L. Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings. J Opt Soc Am A 1996; 13(5): 1024-1035. DOI: 10.1364/JOSAA.13.001024.
  22. Khaleghi SSM, Karimi P, Khavasi A. On-chip second-order spatial derivative of an optical beam by a periodic ridge. Opt Express 2020; 28(18): 26481-26491. DOI: 10.1364/OE.399484.
  23. Xu H, Shi Y. Silicon-waveguide-integrated high-quality metagrating supporting bound state in the continuum. Laser Photonics Rev 2020; 14(6): 1900430. DOI: 10.1002/lpor.201900430.
  24. Bezus EA, Doskolovich LL, Soifer VA. Near-wavelength diffraction gratings for surface plasmon polaritons. Opt Lett 2015; 40(21): 4935-4938. DOI: 10.1364/OL.40.004935.
  25. Bezus EA, Doskolovich LL. Broadband mirrors for surface plasmon polaritons using integrated high-contrast diffraction gratings. Opt Express 2021; 29(3): 4022-4034. DOI: 10.1364/OE.415259.
  26. Bezus EA, Bykov DA, Doskolovich, LL. Integrated diffraction gratings on the Bloch surface wave platform supporting bound states in the continuum. Nanophotonics 2021; 10(17): 4331-4340. DOI: 10.1515/nanoph-2021-0352.

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