Abstract

In this work, the formfactor influence on the diffraction efficiency of 2D and 3D phase holograms was analyzed. Experimental results showed that holograms recorded in a chalcogenide glassy semiconductor and an azopolymer have limitations on maximum achievable diffraction efficiency. The coefficient of optimal exposure increase that is necessary to achieve maximum achievable diffraction efficiency was obtained. Due to the difference between the values of the formfactor in the case of the Raman-Nath diffraction and of that in the case of the Bragg diffraction for diffraction on thin (2D) holograms, the value of the formfactor turned out to be larger than that for diffraction on volume (3D) phase holograms.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. A. Shoydin, Lasers. Measurements. Information (St. Petersburg Polytechnical University, 2013)
  2. S. A. Shoydin, “Requirements to Lasers and Formfactor of Holograms,” Opt. Mem. and Neural Networks 23(4), 287–294 (2014).
    [Crossref]
  3. S. A. Shoydin, “A method of achieving the maximum diffraction efficiency of holograms based on optimizing the formfactor,” Comput. Opt. 40(4), 501–507 (2016).
    [Crossref]
  4. S. A. Shoydin and A. Trifanov, “Form-factor of the holograms of composite images,” Comput. Opt. 42(3), 362–368 (2018).
    [Crossref]
  5. S. A. Shoydin, “Effect of Photo-response Nonlinearity on the Diffraction Efficiency of Holograms,” Optoelectron. Instr. Data Process. 55(1), 28–31 (2019).
    [Crossref]
  6. V. E. Privalov, S. A. Shoydin, and A. V. Trifanov, “Formfactor and temporal coherence of laser radiation,” J. Opt. Technol. 85(9), 541–545 (2018).
    [Crossref]
  7. H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
    [Crossref]
  8. S. A. Shoydin, “Requirements to Lasers and Formfactor of Holograms,” Opt. Mem. and Neural Networks 25(2), 95–101 (2016).
    [Crossref]
  9. V. I. Sukhanov, A. V. Veniaminov, A. I. Ryskin, and N. V. Nikonorov, “Developments SOI in the field of bulk recording media for holography,” in Yu.N. Denisyuk - the founder of domestic holography (SPbGUITMO, 2007), pp. 262–276.
  10. E. Achimova, A. Stronski, V. Abashkin, and A. Meshalkin, “Direct surface relief formation on As2S3–Se nanomultilayers in dependence on polarization states of recording beams,” Opt. Mater. (Amsterdam, Neth.) 47, 566–572 (2015).
    [Crossref]
  11. A. Stronski, E. Achimova, O. Paiuk, and A. Meshalkin, “Holographic and e-beam image recording in Ge5As37S58–Se nanomultilayer structures,” Nanoscale Res. Lett. 11(1), 39 (2016).
    [Crossref]
  12. A. Y. Meshalkin, “Reversible polarization recording in As2S3–Se multilayer nanostructures,” Surf. Eng. Appl. Electrochem. 54(4), 407–414 (2018).
    [Crossref]
  13. E. N. Leith and J. Upatnieks, “Wavefront reconstruction with diffused illumination and three-dimensional objects,” J. Opt. Soc. Am. 54(11), 1295 (1964).
    [Crossref]
  14. E. Achimova, “Direct surface relief formation in nanomultilayers based on chalcogenide glasses: A review,” Surf. Eng. Appl. Electrochem. 52(5), 456–468 (2016).
    [Crossref]
  15. A. Meshalkin, C. Losmanschii, A. Prisacar, E. Achimova, V. Abashkin, S. Pogrebnoi, and F. Macaev, “Carbazole-based azopolymers as media for polarization holographic recording,” Adv. Phys. Res. 1(2), 86–98 (2019).
  16. V. Cazac, A. Meshalkin, E. Achimova, and V. Abashkin, “Surface relief and refractive index gratings patterned in chalcogenide glasses and studied by off-axis digital holography,” Appl. Opt. 57(3), 507–513 (2018).
    [Crossref]
  17. A. Meshalkin, S. Robu, E. Achimova, and A. Prisacar, “Direct photoinduced surface relief formation in carbazole-based azopolymer using polarization holographic recording,” J. of Opt. and Adv. Mat. 18(9-10), 763–768 (2016).
  18. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  19. G. Colfield, Optical Holography (Mir, 1982).
  20. T. M. de Jong, D. K. G. de Boer, and C. W. M. Bastiaansen, “Surface-relief and polarization gratings for solar concentrators,” Opt. Express 19(16), 15127–15142 (2011).
    [Crossref]
  21. A. Sobolewska and S. Bartkiewicz, “Three gratings coupling during the holographic grating recording process in azobenzene-functionalized polymer,” Appl. Phys. Lett. 92(25), 253305 (2008).
    [Crossref]

2019 (2)

S. A. Shoydin, “Effect of Photo-response Nonlinearity on the Diffraction Efficiency of Holograms,” Optoelectron. Instr. Data Process. 55(1), 28–31 (2019).
[Crossref]

A. Meshalkin, C. Losmanschii, A. Prisacar, E. Achimova, V. Abashkin, S. Pogrebnoi, and F. Macaev, “Carbazole-based azopolymers as media for polarization holographic recording,” Adv. Phys. Res. 1(2), 86–98 (2019).

2018 (4)

V. Cazac, A. Meshalkin, E. Achimova, and V. Abashkin, “Surface relief and refractive index gratings patterned in chalcogenide glasses and studied by off-axis digital holography,” Appl. Opt. 57(3), 507–513 (2018).
[Crossref]

A. Y. Meshalkin, “Reversible polarization recording in As2S3–Se multilayer nanostructures,” Surf. Eng. Appl. Electrochem. 54(4), 407–414 (2018).
[Crossref]

V. E. Privalov, S. A. Shoydin, and A. V. Trifanov, “Formfactor and temporal coherence of laser radiation,” J. Opt. Technol. 85(9), 541–545 (2018).
[Crossref]

S. A. Shoydin and A. Trifanov, “Form-factor of the holograms of composite images,” Comput. Opt. 42(3), 362–368 (2018).
[Crossref]

2016 (5)

A. Stronski, E. Achimova, O. Paiuk, and A. Meshalkin, “Holographic and e-beam image recording in Ge5As37S58–Se nanomultilayer structures,” Nanoscale Res. Lett. 11(1), 39 (2016).
[Crossref]

S. A. Shoydin, “Requirements to Lasers and Formfactor of Holograms,” Opt. Mem. and Neural Networks 25(2), 95–101 (2016).
[Crossref]

S. A. Shoydin, “A method of achieving the maximum diffraction efficiency of holograms based on optimizing the formfactor,” Comput. Opt. 40(4), 501–507 (2016).
[Crossref]

E. Achimova, “Direct surface relief formation in nanomultilayers based on chalcogenide glasses: A review,” Surf. Eng. Appl. Electrochem. 52(5), 456–468 (2016).
[Crossref]

A. Meshalkin, S. Robu, E. Achimova, and A. Prisacar, “Direct photoinduced surface relief formation in carbazole-based azopolymer using polarization holographic recording,” J. of Opt. and Adv. Mat. 18(9-10), 763–768 (2016).

2015 (1)

E. Achimova, A. Stronski, V. Abashkin, and A. Meshalkin, “Direct surface relief formation on As2S3–Se nanomultilayers in dependence on polarization states of recording beams,” Opt. Mater. (Amsterdam, Neth.) 47, 566–572 (2015).
[Crossref]

2014 (1)

S. A. Shoydin, “Requirements to Lasers and Formfactor of Holograms,” Opt. Mem. and Neural Networks 23(4), 287–294 (2014).
[Crossref]

2011 (1)

2008 (1)

A. Sobolewska and S. Bartkiewicz, “Three gratings coupling during the holographic grating recording process in azobenzene-functionalized polymer,” Appl. Phys. Lett. 92(25), 253305 (2008).
[Crossref]

1969 (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

1964 (1)

Abashkin, V.

A. Meshalkin, C. Losmanschii, A. Prisacar, E. Achimova, V. Abashkin, S. Pogrebnoi, and F. Macaev, “Carbazole-based azopolymers as media for polarization holographic recording,” Adv. Phys. Res. 1(2), 86–98 (2019).

V. Cazac, A. Meshalkin, E. Achimova, and V. Abashkin, “Surface relief and refractive index gratings patterned in chalcogenide glasses and studied by off-axis digital holography,” Appl. Opt. 57(3), 507–513 (2018).
[Crossref]

E. Achimova, A. Stronski, V. Abashkin, and A. Meshalkin, “Direct surface relief formation on As2S3–Se nanomultilayers in dependence on polarization states of recording beams,” Opt. Mater. (Amsterdam, Neth.) 47, 566–572 (2015).
[Crossref]

Achimova, E.

A. Meshalkin, C. Losmanschii, A. Prisacar, E. Achimova, V. Abashkin, S. Pogrebnoi, and F. Macaev, “Carbazole-based azopolymers as media for polarization holographic recording,” Adv. Phys. Res. 1(2), 86–98 (2019).

V. Cazac, A. Meshalkin, E. Achimova, and V. Abashkin, “Surface relief and refractive index gratings patterned in chalcogenide glasses and studied by off-axis digital holography,” Appl. Opt. 57(3), 507–513 (2018).
[Crossref]

E. Achimova, “Direct surface relief formation in nanomultilayers based on chalcogenide glasses: A review,” Surf. Eng. Appl. Electrochem. 52(5), 456–468 (2016).
[Crossref]

A. Meshalkin, S. Robu, E. Achimova, and A. Prisacar, “Direct photoinduced surface relief formation in carbazole-based azopolymer using polarization holographic recording,” J. of Opt. and Adv. Mat. 18(9-10), 763–768 (2016).

A. Stronski, E. Achimova, O. Paiuk, and A. Meshalkin, “Holographic and e-beam image recording in Ge5As37S58–Se nanomultilayer structures,” Nanoscale Res. Lett. 11(1), 39 (2016).
[Crossref]

E. Achimova, A. Stronski, V. Abashkin, and A. Meshalkin, “Direct surface relief formation on As2S3–Se nanomultilayers in dependence on polarization states of recording beams,” Opt. Mater. (Amsterdam, Neth.) 47, 566–572 (2015).
[Crossref]

Bartkiewicz, S.

A. Sobolewska and S. Bartkiewicz, “Three gratings coupling during the holographic grating recording process in azobenzene-functionalized polymer,” Appl. Phys. Lett. 92(25), 253305 (2008).
[Crossref]

Bastiaansen, C. W. M.

Cazac, V.

Colfield, G.

G. Colfield, Optical Holography (Mir, 1982).

de Boer, D. K. G.

de Jong, T. M.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Kogelnik, H.

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Leith, E. N.

Losmanschii, C.

A. Meshalkin, C. Losmanschii, A. Prisacar, E. Achimova, V. Abashkin, S. Pogrebnoi, and F. Macaev, “Carbazole-based azopolymers as media for polarization holographic recording,” Adv. Phys. Res. 1(2), 86–98 (2019).

Macaev, F.

A. Meshalkin, C. Losmanschii, A. Prisacar, E. Achimova, V. Abashkin, S. Pogrebnoi, and F. Macaev, “Carbazole-based azopolymers as media for polarization holographic recording,” Adv. Phys. Res. 1(2), 86–98 (2019).

Meshalkin, A.

A. Meshalkin, C. Losmanschii, A. Prisacar, E. Achimova, V. Abashkin, S. Pogrebnoi, and F. Macaev, “Carbazole-based azopolymers as media for polarization holographic recording,” Adv. Phys. Res. 1(2), 86–98 (2019).

V. Cazac, A. Meshalkin, E. Achimova, and V. Abashkin, “Surface relief and refractive index gratings patterned in chalcogenide glasses and studied by off-axis digital holography,” Appl. Opt. 57(3), 507–513 (2018).
[Crossref]

A. Meshalkin, S. Robu, E. Achimova, and A. Prisacar, “Direct photoinduced surface relief formation in carbazole-based azopolymer using polarization holographic recording,” J. of Opt. and Adv. Mat. 18(9-10), 763–768 (2016).

A. Stronski, E. Achimova, O. Paiuk, and A. Meshalkin, “Holographic and e-beam image recording in Ge5As37S58–Se nanomultilayer structures,” Nanoscale Res. Lett. 11(1), 39 (2016).
[Crossref]

E. Achimova, A. Stronski, V. Abashkin, and A. Meshalkin, “Direct surface relief formation on As2S3–Se nanomultilayers in dependence on polarization states of recording beams,” Opt. Mater. (Amsterdam, Neth.) 47, 566–572 (2015).
[Crossref]

Meshalkin, A. Y.

A. Y. Meshalkin, “Reversible polarization recording in As2S3–Se multilayer nanostructures,” Surf. Eng. Appl. Electrochem. 54(4), 407–414 (2018).
[Crossref]

Nikonorov, N. V.

V. I. Sukhanov, A. V. Veniaminov, A. I. Ryskin, and N. V. Nikonorov, “Developments SOI in the field of bulk recording media for holography,” in Yu.N. Denisyuk - the founder of domestic holography (SPbGUITMO, 2007), pp. 262–276.

Paiuk, O.

A. Stronski, E. Achimova, O. Paiuk, and A. Meshalkin, “Holographic and e-beam image recording in Ge5As37S58–Se nanomultilayer structures,” Nanoscale Res. Lett. 11(1), 39 (2016).
[Crossref]

Pogrebnoi, S.

A. Meshalkin, C. Losmanschii, A. Prisacar, E. Achimova, V. Abashkin, S. Pogrebnoi, and F. Macaev, “Carbazole-based azopolymers as media for polarization holographic recording,” Adv. Phys. Res. 1(2), 86–98 (2019).

Prisacar, A.

A. Meshalkin, C. Losmanschii, A. Prisacar, E. Achimova, V. Abashkin, S. Pogrebnoi, and F. Macaev, “Carbazole-based azopolymers as media for polarization holographic recording,” Adv. Phys. Res. 1(2), 86–98 (2019).

A. Meshalkin, S. Robu, E. Achimova, and A. Prisacar, “Direct photoinduced surface relief formation in carbazole-based azopolymer using polarization holographic recording,” J. of Opt. and Adv. Mat. 18(9-10), 763–768 (2016).

Privalov, V. E.

Robu, S.

A. Meshalkin, S. Robu, E. Achimova, and A. Prisacar, “Direct photoinduced surface relief formation in carbazole-based azopolymer using polarization holographic recording,” J. of Opt. and Adv. Mat. 18(9-10), 763–768 (2016).

Ryskin, A. I.

V. I. Sukhanov, A. V. Veniaminov, A. I. Ryskin, and N. V. Nikonorov, “Developments SOI in the field of bulk recording media for holography,” in Yu.N. Denisyuk - the founder of domestic holography (SPbGUITMO, 2007), pp. 262–276.

Shoydin, S. A.

S. A. Shoydin, “Effect of Photo-response Nonlinearity on the Diffraction Efficiency of Holograms,” Optoelectron. Instr. Data Process. 55(1), 28–31 (2019).
[Crossref]

V. E. Privalov, S. A. Shoydin, and A. V. Trifanov, “Formfactor and temporal coherence of laser radiation,” J. Opt. Technol. 85(9), 541–545 (2018).
[Crossref]

S. A. Shoydin and A. Trifanov, “Form-factor of the holograms of composite images,” Comput. Opt. 42(3), 362–368 (2018).
[Crossref]

S. A. Shoydin, “A method of achieving the maximum diffraction efficiency of holograms based on optimizing the formfactor,” Comput. Opt. 40(4), 501–507 (2016).
[Crossref]

S. A. Shoydin, “Requirements to Lasers and Formfactor of Holograms,” Opt. Mem. and Neural Networks 25(2), 95–101 (2016).
[Crossref]

S. A. Shoydin, “Requirements to Lasers and Formfactor of Holograms,” Opt. Mem. and Neural Networks 23(4), 287–294 (2014).
[Crossref]

S. A. Shoydin, Lasers. Measurements. Information (St. Petersburg Polytechnical University, 2013)

Sobolewska, A.

A. Sobolewska and S. Bartkiewicz, “Three gratings coupling during the holographic grating recording process in azobenzene-functionalized polymer,” Appl. Phys. Lett. 92(25), 253305 (2008).
[Crossref]

Stronski, A.

A. Stronski, E. Achimova, O. Paiuk, and A. Meshalkin, “Holographic and e-beam image recording in Ge5As37S58–Se nanomultilayer structures,” Nanoscale Res. Lett. 11(1), 39 (2016).
[Crossref]

E. Achimova, A. Stronski, V. Abashkin, and A. Meshalkin, “Direct surface relief formation on As2S3–Se nanomultilayers in dependence on polarization states of recording beams,” Opt. Mater. (Amsterdam, Neth.) 47, 566–572 (2015).
[Crossref]

Sukhanov, V. I.

V. I. Sukhanov, A. V. Veniaminov, A. I. Ryskin, and N. V. Nikonorov, “Developments SOI in the field of bulk recording media for holography,” in Yu.N. Denisyuk - the founder of domestic holography (SPbGUITMO, 2007), pp. 262–276.

Trifanov, A.

S. A. Shoydin and A. Trifanov, “Form-factor of the holograms of composite images,” Comput. Opt. 42(3), 362–368 (2018).
[Crossref]

Trifanov, A. V.

Upatnieks, J.

Veniaminov, A. V.

V. I. Sukhanov, A. V. Veniaminov, A. I. Ryskin, and N. V. Nikonorov, “Developments SOI in the field of bulk recording media for holography,” in Yu.N. Denisyuk - the founder of domestic holography (SPbGUITMO, 2007), pp. 262–276.

Adv. Phys. Res. (1)

A. Meshalkin, C. Losmanschii, A. Prisacar, E. Achimova, V. Abashkin, S. Pogrebnoi, and F. Macaev, “Carbazole-based azopolymers as media for polarization holographic recording,” Adv. Phys. Res. 1(2), 86–98 (2019).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Sobolewska and S. Bartkiewicz, “Three gratings coupling during the holographic grating recording process in azobenzene-functionalized polymer,” Appl. Phys. Lett. 92(25), 253305 (2008).
[Crossref]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48(9), 2909–2947 (1969).
[Crossref]

Comput. Opt. (2)

S. A. Shoydin, “A method of achieving the maximum diffraction efficiency of holograms based on optimizing the formfactor,” Comput. Opt. 40(4), 501–507 (2016).
[Crossref]

S. A. Shoydin and A. Trifanov, “Form-factor of the holograms of composite images,” Comput. Opt. 42(3), 362–368 (2018).
[Crossref]

J. of Opt. and Adv. Mat. (1)

A. Meshalkin, S. Robu, E. Achimova, and A. Prisacar, “Direct photoinduced surface relief formation in carbazole-based azopolymer using polarization holographic recording,” J. of Opt. and Adv. Mat. 18(9-10), 763–768 (2016).

J. Opt. Soc. Am. (1)

J. Opt. Technol. (1)

Nanoscale Res. Lett. (1)

A. Stronski, E. Achimova, O. Paiuk, and A. Meshalkin, “Holographic and e-beam image recording in Ge5As37S58–Se nanomultilayer structures,” Nanoscale Res. Lett. 11(1), 39 (2016).
[Crossref]

Opt. Express (1)

Opt. Mater. (Amsterdam, Neth.) (1)

E. Achimova, A. Stronski, V. Abashkin, and A. Meshalkin, “Direct surface relief formation on As2S3–Se nanomultilayers in dependence on polarization states of recording beams,” Opt. Mater. (Amsterdam, Neth.) 47, 566–572 (2015).
[Crossref]

Opt. Mem. and Neural Networks (2)

S. A. Shoydin, “Requirements to Lasers and Formfactor of Holograms,” Opt. Mem. and Neural Networks 25(2), 95–101 (2016).
[Crossref]

S. A. Shoydin, “Requirements to Lasers and Formfactor of Holograms,” Opt. Mem. and Neural Networks 23(4), 287–294 (2014).
[Crossref]

Optoelectron. Instr. Data Process. (1)

S. A. Shoydin, “Effect of Photo-response Nonlinearity on the Diffraction Efficiency of Holograms,” Optoelectron. Instr. Data Process. 55(1), 28–31 (2019).
[Crossref]

Surf. Eng. Appl. Electrochem. (2)

A. Y. Meshalkin, “Reversible polarization recording in As2S3–Se multilayer nanostructures,” Surf. Eng. Appl. Electrochem. 54(4), 407–414 (2018).
[Crossref]

E. Achimova, “Direct surface relief formation in nanomultilayers based on chalcogenide glasses: A review,” Surf. Eng. Appl. Electrochem. 52(5), 456–468 (2016).
[Crossref]

Other (4)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

G. Colfield, Optical Holography (Mir, 1982).

V. I. Sukhanov, A. V. Veniaminov, A. I. Ryskin, and N. V. Nikonorov, “Developments SOI in the field of bulk recording media for holography,” in Yu.N. Denisyuk - the founder of domestic holography (SPbGUITMO, 2007), pp. 262–276.

S. A. Shoydin, Lasers. Measurements. Information (St. Petersburg Polytechnical University, 2013)

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1. The evolution of first-order diffraction efficiency of a hologram recorded by Gaussian beams. Increase of the exposure from (a) to (c) first leads to an increase in η (a), then to a dip in the center (b) and again to an increase in η (c).
Fig. 2.
Fig. 2. Dependence of the average diffraction efficiency ηmax on exposure. (a) Theoretical plot: the solid curve represents the diffraction efficiency according to Eq. (1) with the Gaussian form E(x,y) for determining Ψ; the dashed curve is the diffraction efficiency for the case E(x,y) = const with Ψ = 1, normalized to the maximum of the solid curve Ω = 0.41 in accordance with Eq. (2), for the convenience of comparison. (b) Experimental graph: 1st curve – nonlinear photoresponse of the refractive index Δn of the holographic material Reoxan depending on the exposure; 2nd curve – dependence of the average diffraction efficiency on exposure.
Fig. 3.
Fig. 3. Holographic recording scheme of relief phase gratings. DPSS laser – diode-pumped solid-state single-mode (TEM00) laser; BS – beam splitter; M – mirrors; λ/2 – half-wave plates; LD – laser diode; S – recording media; PD – silicon photodiodes.
Fig. 4.
Fig. 4. (a) Diffraction efficiency of 0, 1 and 2 orders of the phase sinusoidal grating depending on the amplitude of the phase contrast Δφ and the relief depth h (for a material with a refractive index of n = 2.5, at a wavelength of λ = 650 nm). (b) The experimentally obtained kinetics of diffraction efficiency of zero η0 and first η1 orders in the case of recording on a CGS
Fig. 5.
Fig. 5. Intensity profiles in interference patterns: (a) when two beams are mixed with a Gaussian intensity distribution; (b) when two beams are mixed with a uniform intensity distribution.
Fig. 6.
Fig. 6. The dependences of the first-order diffraction efficiency η1 for the recorded gratings using homogeneous beams (red) and beams with a Gaussian intensity distribution (blue).
Fig. 7.
Fig. 7. The evolution of the first-order diffraction pattern of the hologram recorded using Gaussian beams a) on the azopolymer and b) on the CGS. Rings with zero diffraction efficiency, similar to Fig. 1, are clearly visible. The appearance and increase in the number of rings with increasing exposure is seen, similarly to Fig. 1.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

η max = 1 S sin 2 [ β E ( x , y ) V ( x , y ) ] d x d y
η = Ω sin 2 [ Ψ f ( E V ) ]