ru/ ru

ISSN: 1023-5086


ISSN: 1023-5086

Scientific and technical

Opticheskii Zhurnal

A full-text English translation of the journal is published by Optica Publishing Group under the title “Journal of Optical Technology”

Article submission Подать статью
Больше информации Back

DOI: 10.17586/1023-5086-2023-90-05-50-62

УДК: 535.421, 535.417

Diffraction efficiency and the formfactor effect of holograms (review)

For Russian citation (Opticheskii Zhurnal):
Мешалкин А.Ю., Шойдин С.А. Дифракционная эффективность и эффект формфактора голограмм (обзор) // Оптический журнал. 2023. Т. 90. № 5. С. 50–62.   Meshalkin А.Yu., Shoydin S.A. Diffraction efficiency and the formfactor effect of holograms (review) [in Russian] // Opticheskii Zhurnal. 2023. V. 90. № 5. P. 50–62.
For citation (Journal of Optical Technology):
Alexei Yu. Meshalkin and Sergey A. Shoydin, "Diffraction efficiency and form factor effect of holograms," Journal of Optical Technology. 90(5), 254-261 (2023)

Subject of study. Influence of the formfactor effect on the diffraction efficiency of holograms in various holographic materials. Aim of study. To review publications on the analysis of the diffraction efficiency of two-dimensional and three-dimensional holograms depending on the shape of the recording beams. Method. Holographic exposure of photosensitive media makes it possible to register the formed interference pattern in the medium in the form of periodic modulation of the refractive index, surface relief, optical absorption coefficient, or other parameters. The measurement and analysis of the diffraction efficiency showed its dependence both on the degree of modulation of the recording medium and on the shape of the recording beams. Main results. Based on the results of the review, it can be concluded that it is important to take into account the cross interaction of two nonlinear effects — the nonlinearity of the diffraction efficiency and the exposure nonlinearity over the hologram field. Manifestations of this cross-effect have been noticed and by other authors, but often explained by other reasons. Its some non-detectability and hidden effect can be explained by the manifestation only in the presence of two indicated nonlinearities simultaneously with the presence of local maxima in them. In all other cases the formfactor effect disappears. The areas of manifestation of the formfactor effect in holographic experiments are shown, as an effect that generates restrictions on the main "power" parameters of holograms, such as diffraction efficiency and optimal exposure. The manifestation of the formfactor effect is immanent in the holographic recording of complex images, since it cannot be eliminated completely, but can only be weakened in the initial section of the exposure. Practical significance. Along with the indicated restrictive properties, the formfactor effect makes it possible in-situ measuring the kinetics of holograms recording with high accuracy, without involving additional complex equipment. This method was patented. Its influence can be significant; the formfactor in holography cannot be attributed to small corrections of the main result. It manifests itself in the main, "power" characteristics, similar to the fundamental manifestation of the formfactor in the gravitational interactions of irregularly shaped bodies or in interatomic interactions.


holography, interference, holographic interference fringes, Bragg diffraction, Raman–Nath diffraction, diffraction efficiency, formfactor

OCIS codes: 090.1760


Bagbaya I.D. On the history of the diffraction grating [in Russian] // Soviet Physics Uspekhi. 1973. V. 15. № 5. P. 660–661.

  1. Klein W.R. Theoretical efficiency of Bragg devices // Proc. IEEE. 1966. V. 54. P. 803–804.
  2. Nath N.S.N. The diffraction of light by high frequency sound waves: Generalised theory // Proc. Indian Acad. Sci. (Math. Sci.). 1936. V. 4. P. 222–242.
  3. Kogelnik H. Coupled wave theory for thick hologram gratings // Bell Syst. Tech. J. 1969. V. 48. P. 2909–2947.
  4. Goodman J.W. Introduction to Fourier optics. 2nd ed. N.Y.: McGraw-Hill, 1988. 441 p. P. 82.
  5. Goodman J.W. Introduction to Fourier optics. 2nd ed. N.Y.: McGraw-Hill, 1988. 441 p. P. 340.
  6. Goodman J.W. Introduction to Fourier optics. 2nd ed. N.Y.: McGraw-Hill, 1988. 441 p. P. 343.
  7. Shoydin S.A. Requirements to lasers and formfactor of holograms // Opt. Mem. Neural Networks. 2016. V. 25. P. 95–101.
  8. Shoydin S.A. A method of achieving the maximum diffraction efficiency of holograms based on optimizing the formfactor [in Russian] // Comput. Opt. 2016. V. 40. № 4. P. 501–507.

10. Meshalkin A.Y., Shoydin S.A. Form factor of holograms in the Raman–Nath diffraction mode [in Russian] // Abstracts of the XVI International. Conf. Holography and Appl. Opt. Technol. — HOLOEXPO-2019. St. Petersburg, Russia. 2019. Р. 279–289.

11. Shoydin S.A., Meshalkin A.Y., Kovalev M.S. Formfactor of a hologram on a chalcogenide glassy semiconductor and azopolymer // Opt. Mater. Exp. 2020. V. 10. № 8. P. 1819–1825.

12. Gallego S., Ortuno M., Neipp C., et al. Overmodulation effects in volume holograms recorded on photopolymers // Opt. Commun. 2003. V. 215. P. 263–269.

13. Sullivan A.C., Alim M.D., Glugla D.J., еt al. Holographic analysis of photopolymers // Event: SPIE Optics + Optoelectronics, 2017. Prague, Czech Republic. V. 10233.

14. Ciapurin I.V., Glebov L.B., Smirnov V.I. Modeling of Gaussian beam diffraction on volume Bragg gratings in PTR glass // Proc. SPIE. 2005. V. 5742.

15. Sabel T., Marga C.L. Volume holography: Novel materials, methods and applications // in Holographic Materials and Optical Systems. Eds. by Naydenova I., Nazarova D., Babeva T. / London: IntechOpen, 2017.

16. Jelken J., Henkel C., Santer S. Solving an old puzzle: Fine structure of diffraction spots from an azo-polymer surface relief grating // Appl. Phys. B. 2019. V. 125. P. 218.

17. Jelken J., Henkel C., Santer S. Polarization controlled fine structure of diffraction spots from an optically induced grating // Appl. Phys. Lett. 2020. V. 116. P. 051601.

18. Stolz D., Strobelt J., Leven M., et al. One-step fabrication of surface relief dot-matrix holograms using supramolecular azopolymer thin films // Proc. SPIE. 2021. V. 11710. P. 1171008.

19. Sobolewska A., Bartkiewicz S. On the long time holographic grating recording process in azo-polymer // Appl. Phys. Lett. 2009. V. 95. P. 123302.

20. Golub P., Kurioz Yu., Sheremet N., et al. Director modulation of nematic liquid crystal on photosensitive chalcogenide surface // Molecular Cryst. Liquid Cryst. 2018. V. 661. P. 25–37.

21. Meshalkin A., Losmanschii C., Cazac V., et al. Analysis of diffraction efficiency of phase gratings in dependence of grooves number // 2020 Internat. Conf. Information Technol. and Nanotechnol. (ITNT). Samara, Russia. May 26–29, 2020. P. 1–4.

22. Shoydin S.A., Meshalkin A.Y. Method for express analysis of the magnitude of the dynamic range of the photoresponse of a phase holographic material // Patent RU №RU2734093. 2020. Bul. № 29.

23. Meshalkin A.Y., Shoydin S.A. Diffraction method for measuring the dynamic range of the photoresponse of a holographic phase material [in Russian] // Abstracts of the XVII Internat. Conf. Holography and Appl. Opt. Technol. HOLOEXPO-2020. Moscow, Russia. September 08–09, 2020. Р. 235–245.

24. Shoydin S.A., Trifanov A.V. Form-faсtor of the holograms of composite images [in Russian] // Computer Optics. 2018. V. 42. № 3. Р. 362–368.

25. Shoydin S.A. Effect of photo-response nonlinearity on the diffraction efficiency of holograms // Optoelectron. Instrument. Proc. 2019. V. 55. P. 28–31.

26. Znamenskiy V.V. General course of field geophysics: Textbook [in Russian]. Leningrad: Nedra Publ., 1989. 520 р. ISBN: 5-247-00666-6

  1. Bilen'kaya S.I., Bilen'kiy S.M., Kazarinov YU.M., Lapidus L.I. Electromagnetic form factor of the proton and heavy hypothetical particles [in Russian] // Pis'ma v ZHETF. 1974. V. 19. № 9. Р. 613–616.