Abstract

We study diffraction of Bessel vortex beams with topological charges of ±1 and ±2 and a wavelength of 130 µm on two-dimensional amplitude periodic gratings. Results of simulations and experiments at the Novosibirsk Free Electron Laser facility show that there appear periodic patterns in the planes corresponding to the classical main and fractional Talbot planes, but instead of self-images of the holes, there are observed periodic lattices of annular vortex microbeams with topological charges corresponding to the charge of the beam illuminating the grating. The ring diameters are the same for beams with different topological charges, but they are proportional to the grating period and inversely proportional to the diameter of the beam illuminating the grating.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
  33. B. A. Knyazev, Yu. Yu. Choporova, M. S. Mitkov, V. S. Pavelyev, and B. O. Volodkin, “Generation of terahertz surface plasmon polaritons using nondiffractive Bessel beams with orbital angular momentum,” Phys. Rev. Lett. 115, 163901 (2015).
    [Crossref] [PubMed]
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    [Crossref]

2018 (2)

H. Gao, Y. Li, L. Chen, J. Jin, M. Pu, X. Li, P. Gao, C. Wang, X. Luo, and M. Hong, “Quasi-Talbot effect of orbital angular momentum beams for generation of optical vortex arrays by multiplexing metasurface design,” Nanoscale,  10, 666–671 (2018).
[Crossref]

D. Herbi, S. Rasouli, and M. Yaganeh, “Intensity based measurement of the topological charge alteration by the diffraction of vortex beams from amplitude sinusoidal radial grating,” J. Opt. Soc. Am. B 35, 724–730 (2018).
[Crossref]

2017 (4)

C. Schnebelin and H. G. de Chatellus, “Fractional Fourier transform-based description of the Talbot effect: application to analog signal processing,” Appl. Opt.,  56, A62–A68 (2017).
[Crossref]

J. S. Rodrigues, C. V. Mendes, E. J. Fonseca, and A. J. Jesus-Silva, “Talbot effect in optical lattices with topological charge,” Opt. Lett. 42, 3944–39472017.
[Crossref] [PubMed]

M. Aymerich, D. Nieto, E. Álvarez, and M. T. Flores-Arias, “Laser surface microstructuring of biocompatible materials using a microlens array and the Talbot effect: evaluation of the cell adhesion,” Materials 10, 10020214 (2017).
[Crossref]

Yu. Yu. Choporova, B. A. Knyazev, G. N. Kulipanov, V. S. Pavelyev, M. A. Scheglov, N. A. Vinokurov, B. O. Volodkin, and V. N. Zhabin, “High-power Bessel beams with orbital angular momentum in the terahertz range,” Phys. Rev. A 96, 023846 (2017).
[Crossref]

2016 (3)

Y. Lu, B. Jiang, S. Lü, Y. Liu, S. Li, Z. Cao, and X. Qi, “Arrays of Gaussian vortex, Bessel and Airy beams by computer-generated hologram,” Opt. Commun. 363, 85–90 (2016).
[Crossref]

A. Sabatyan and S. M. T. Balanoji, “Square array of optical vortices generated by multiregion spiral square zone plate,” JOSAA 33, 1793–1797(2016).
[Crossref]

P. Panthong, S. Srisuphaphon, A. Pattanaporkratana, S. Chiangga, and S. A. Deachapunya, “Study of optical vortices with the Talbot effect,” J. Opt. 18, 035602 (2016).
[Crossref]

2015 (3)

B. A. Knyazev, Yu. Yu. Choporova, M. S. Mitkov, V. S. Pavelyev, and B. O. Volodkin, “Generation of terahertz surface plasmon polaritons using nondiffractive Bessel beams with orbital angular momentum,” Phys. Rev. Lett. 115, 163901 (2015).
[Crossref] [PubMed]

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Seredniakov, O. A. Shevchenko, A. N. Skrinsky, S. L. Veber, and N. A. Vinokurov, “Novosibirsk free electron laser: facility description and recent experiments,” IEEE Trans. THz Sci. Technol. 5, 798–809 (2015).
[Crossref]

Yu. Yu. Choporova, B. A. Knyazev, and M. S. Mitkov, “Classical holography in the terahertz range: recording and reconstruction techniques,” IEEE Trans. THz Sci. Technol. 5, 836–844 (2015).
[Crossref]

2014 (1)

O. Emile and J. Emile, “Young’s double-slit interference pattern from a twisted beam,” Appl. Phys. B 117, 487–491 (2014).
[Crossref]

2013 (3)

2012 (1)

N. Gao and C. Xie, “Experimental demonstration of free-space optical vortex transmutation with polygonal lenses,” Opti. Lett.,  37, 3255–3257 (2012).
[Crossref]

2011 (1)

B. A. Knyazev, V. S. Cherkassky, Y. Choporova Y., V. Gerasimov V., M. G. Vlasenko, M. A. Demýanenko, and D. G. Esaev, “Real-time imaging using a high-power monochromatic terahertz source: comparative description of imaging techniques with examples of application,” J. Infrared Millim. THz Waves 32, 1207–1222 (2011).
[Crossref]

2010 (1)

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97, 211108 (2010)
[Crossref]

2009 (3)

2008 (1)

M. A. Demyanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90 fps microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett.,  92, 131116 (2008).
[Crossref]

2006 (3)

J. Courtial, R. Zambrini, M. R. Dennis, and M. Vasnetsov, “Angular momentum of optical vortex arrays,” Opt.Expr.,  14, 938–949 (2006).

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, “Observation of topological transformations of optical vortices in two-dimensional photonic lattices,” Opt. Expr.,  14, 8317–8327 (2006).
[Crossref]

H. I. Sztul and R. R. Alfano, “Double-slit interference with Laguerre-Gaussian beams,” Opt. Lett. 31, 999–1001 (2006).
[Crossref] [PubMed]

2002 (1)

2001 (1)

1994 (1)

1992 (1)

L. Allen, M. W. C. Beijersbergen, R.J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

1965 (1)

1836 (1)

H.F. Talbot, “Facts relating to optical science,” Philos. Mag. Ser. 3, 401–407 (1836).

Alfano, R. R.

Allen, L.

L. Allen, M. W. C. Beijersbergen, R.J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Álvarez, E.

M. Aymerich, D. Nieto, E. Álvarez, and M. T. Flores-Arias, “Laser surface microstructuring of biocompatible materials using a microlens array and the Talbot effect: evaluation of the cell adhesion,” Materials 10, 10020214 (2017).
[Crossref]

Andrés, P.

Andrews, D. L.

D. L. Andrews and M. Babiker, The angular momentum of light. (Cambrige University Press, 2013).

Araiza-E, M.

Arrizón, V.

Aseev, A. L.

Aymerich, M.

M. Aymerich, D. Nieto, E. Álvarez, and M. T. Flores-Arias, “Laser surface microstructuring of biocompatible materials using a microlens array and the Talbot effect: evaluation of the cell adhesion,” Materials 10, 10020214 (2017).
[Crossref]

Babiker, M.

D. L. Andrews and M. Babiker, The angular momentum of light. (Cambrige University Press, 2013).

Bagryanskaya, E. G.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Seredniakov, O. A. Shevchenko, A. N. Skrinsky, S. L. Veber, and N. A. Vinokurov, “Novosibirsk free electron laser: facility description and recent experiments,” IEEE Trans. THz Sci. Technol. 5, 798–809 (2015).
[Crossref]

Balanoji, S. M. T.

A. Sabatyan and S. M. T. Balanoji, “Square array of optical vortices generated by multiregion spiral square zone plate,” JOSAA 33, 1793–1797(2016).
[Crossref]

Beijersbergen, M. W. C.

L. Allen, M. W. C. Beijersbergen, R.J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Bezryadina, A.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, “Observation of topological transformations of optical vortices in two-dimensional photonic lattices,” Opt. Expr.,  14, 8317–8327 (2006).
[Crossref]

Brasselet, E.

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97, 211108 (2010)
[Crossref]

Cao, Z.

Y. Lu, B. Jiang, S. Lü, Y. Liu, S. Li, Z. Cao, and X. Qi, “Arrays of Gaussian vortex, Bessel and Airy beams by computer-generated hologram,” Opt. Commun. 363, 85–90 (2016).
[Crossref]

Chen, L.

H. Gao, Y. Li, L. Chen, J. Jin, M. Pu, X. Li, P. Gao, C. Wang, X. Luo, and M. Hong, “Quasi-Talbot effect of orbital angular momentum beams for generation of optical vortex arrays by multiplexing metasurface design,” Nanoscale,  10, 666–671 (2018).
[Crossref]

Chen, Z.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, “Observation of topological transformations of optical vortices in two-dimensional photonic lattices,” Opt. Expr.,  14, 8317–8327 (2006).
[Crossref]

Cherkassky, V. S.

B. A. Knyazev, V. S. Cherkassky, Y. Choporova Y., V. Gerasimov V., M. G. Vlasenko, M. A. Demýanenko, and D. G. Esaev, “Real-time imaging using a high-power monochromatic terahertz source: comparative description of imaging techniques with examples of application,” J. Infrared Millim. THz Waves 32, 1207–1222 (2011).
[Crossref]

B. A. Knyazev, V. S. Cherkassky, Y. Y. Choporova, V. V. Gerasimov, and M. G. Vlasenko, “The Talbot effect in the terahertz spectral range,” in Proceedings of the 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz), Rome, Italy, 5–10 Sept 2010, 5612558.

Chervenkov, S.

Chesnokov, E. N.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Seredniakov, O. A. Shevchenko, A. N. Skrinsky, S. L. Veber, and N. A. Vinokurov, “Novosibirsk free electron laser: facility description and recent experiments,” IEEE Trans. THz Sci. Technol. 5, 798–809 (2015).
[Crossref]

Chiangga, S.

P. Panthong, S. Srisuphaphon, A. Pattanaporkratana, S. Chiangga, and S. A. Deachapunya, “Study of optical vortices with the Talbot effect,” J. Opt. 18, 035602 (2016).
[Crossref]

Choporova, Y. Y.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Seredniakov, O. A. Shevchenko, A. N. Skrinsky, S. L. Veber, and N. A. Vinokurov, “Novosibirsk free electron laser: facility description and recent experiments,” IEEE Trans. THz Sci. Technol. 5, 798–809 (2015).
[Crossref]

B. A. Knyazev, V. S. Cherkassky, Y. Y. Choporova, V. V. Gerasimov, and M. G. Vlasenko, “The Talbot effect in the terahertz spectral range,” in Proceedings of the 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz), Rome, Italy, 5–10 Sept 2010, 5612558.

Choporova, Yu. Yu.

Yu. Yu. Choporova, B. A. Knyazev, G. N. Kulipanov, V. S. Pavelyev, M. A. Scheglov, N. A. Vinokurov, B. O. Volodkin, and V. N. Zhabin, “High-power Bessel beams with orbital angular momentum in the terahertz range,” Phys. Rev. A 96, 023846 (2017).
[Crossref]

B. A. Knyazev, Yu. Yu. Choporova, M. S. Mitkov, V. S. Pavelyev, and B. O. Volodkin, “Generation of terahertz surface plasmon polaritons using nondiffractive Bessel beams with orbital angular momentum,” Phys. Rev. Lett. 115, 163901 (2015).
[Crossref] [PubMed]

Yu. Yu. Choporova, B. A. Knyazev, and M. S. Mitkov, “Classical holography in the terahertz range: recording and reconstruction techniques,” IEEE Trans. THz Sci. Technol. 5, 836–844 (2015).
[Crossref]

Choporova Y., Y.

B. A. Knyazev, V. S. Cherkassky, Y. Choporova Y., V. Gerasimov V., M. G. Vlasenko, M. A. Demýanenko, and D. G. Esaev, “Real-time imaging using a high-power monochromatic terahertz source: comparative description of imaging techniques with examples of application,” J. Infrared Millim. THz Waves 32, 1207–1222 (2011).
[Crossref]

Climent, V.

Courtial, J.

J. Courtial, R. Zambrini, M. R. Dennis, and M. Vasnetsov, “Angular momentum of optical vortex arrays,” Opt.Expr.,  14, 938–949 (2006).

Dashti, M.

de Chatellus, H. G.

Deachapunya, S. A.

P. Panthong, S. Srisuphaphon, A. Pattanaporkratana, S. Chiangga, and S. A. Deachapunya, “Study of optical vortices with the Talbot effect,” J. Opt. 18, 035602 (2016).
[Crossref]

Demyanenko, M. A.

M. A. Demyanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90 fps microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett.,  92, 131116 (2008).
[Crossref]

Demýanenko, M. A.

B. A. Knyazev, V. S. Cherkassky, Y. Choporova Y., V. Gerasimov V., M. G. Vlasenko, M. A. Demýanenko, and D. G. Esaev, “Real-time imaging using a high-power monochromatic terahertz source: comparative description of imaging techniques with examples of application,” J. Infrared Millim. THz Waves 32, 1207–1222 (2011).
[Crossref]

M. A. Demýanenko, D. G. Esaev, V. N. Ovsyuk, B. I. Fomin, A. L. Aseev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Microbolometer detector arrays for the infrared and terahertz ranges,” J. Opt. Technol. 76, 739–743 (2009).
[Crossref]

Dennis, M. R.

J. Courtial, R. Zambrini, M. R. Dennis, and M. Vasnetsov, “Angular momentum of optical vortex arrays,” Opt.Expr.,  14, 938–949 (2006).

Desyatnikov, A. S.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, “Observation of topological transformations of optical vortices in two-dimensional photonic lattices,” Opt. Expr.,  14, 8317–8327 (2006).
[Crossref]

Dreischuh, A.

Emile, J.

O. Emile and J. Emile, “Young’s double-slit interference pattern from a twisted beam,” Appl. Phys. B 117, 487–491 (2014).
[Crossref]

Emile, O.

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B. A. Knyazev, Yu. Yu. Choporova, M. S. Mitkov, V. S. Pavelyev, and B. O. Volodkin, “Generation of terahertz surface plasmon polaritons using nondiffractive Bessel beams with orbital angular momentum,” Phys. Rev. Lett. 115, 163901 (2015).
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Yu. Yu. Choporova, B. A. Knyazev, and M. S. Mitkov, “Classical holography in the terahertz range: recording and reconstruction techniques,” IEEE Trans. THz Sci. Technol. 5, 836–844 (2015).
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B. A. Knyazev, V. S. Cherkassky, Y. Choporova Y., V. Gerasimov V., M. G. Vlasenko, M. A. Demýanenko, and D. G. Esaev, “Real-time imaging using a high-power monochromatic terahertz source: comparative description of imaging techniques with examples of application,” J. Infrared Millim. THz Waves 32, 1207–1222 (2011).
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B. A. Knyazev, V. S. Cherkassky, Y. Y. Choporova, V. V. Gerasimov, and M. G. Vlasenko, “The Talbot effect in the terahertz spectral range,” in Proceedings of the 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz), Rome, Italy, 5–10 Sept 2010, 5612558.

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Yu. Yu. Choporova, B. A. Knyazev, and M. S. Mitkov, “Classical holography in the terahertz range: recording and reconstruction techniques,” IEEE Trans. THz Sci. Technol. 5, 836–844 (2015).
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B. A. Knyazev, Yu. Yu. Choporova, M. S. Mitkov, V. S. Pavelyev, and B. O. Volodkin, “Generation of terahertz surface plasmon polaritons using nondiffractive Bessel beams with orbital angular momentum,” Phys. Rev. Lett. 115, 163901 (2015).
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M. Aymerich, D. Nieto, E. Álvarez, and M. T. Flores-Arias, “Laser surface microstructuring of biocompatible materials using a microlens array and the Talbot effect: evaluation of the cell adhesion,” Materials 10, 10020214 (2017).
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Pavelyev, V. S.

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B. A. Knyazev, Yu. Yu. Choporova, M. S. Mitkov, V. S. Pavelyev, and B. O. Volodkin, “Generation of terahertz surface plasmon polaritons using nondiffractive Bessel beams with orbital angular momentum,” Phys. Rev. Lett. 115, 163901 (2015).
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G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Seredniakov, O. A. Shevchenko, A. N. Skrinsky, S. L. Veber, and N. A. Vinokurov, “Novosibirsk free electron laser: facility description and recent experiments,” IEEE Trans. THz Sci. Technol. 5, 798–809 (2015).
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G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Seredniakov, O. A. Shevchenko, A. N. Skrinsky, S. L. Veber, and N. A. Vinokurov, “Novosibirsk free electron laser: facility description and recent experiments,” IEEE Trans. THz Sci. Technol. 5, 798–809 (2015).
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H. Gao, Y. Li, L. Chen, J. Jin, M. Pu, X. Li, P. Gao, C. Wang, X. Luo, and M. Hong, “Quasi-Talbot effect of orbital angular momentum beams for generation of optical vortex arrays by multiplexing metasurface design,” Nanoscale,  10, 666–671 (2018).
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Y. Lu, B. Jiang, S. Lü, Y. Liu, S. Li, Z. Cao, and X. Qi, “Arrays of Gaussian vortex, Bessel and Airy beams by computer-generated hologram,” Opt. Commun. 363, 85–90 (2016).
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Yu. Yu. Choporova, B. A. Knyazev, G. N. Kulipanov, V. S. Pavelyev, M. A. Scheglov, N. A. Vinokurov, B. O. Volodkin, and V. N. Zhabin, “High-power Bessel beams with orbital angular momentum in the terahertz range,” Phys. Rev. A 96, 023846 (2017).
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G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Seredniakov, O. A. Shevchenko, A. N. Skrinsky, S. L. Veber, and N. A. Vinokurov, “Novosibirsk free electron laser: facility description and recent experiments,” IEEE Trans. THz Sci. Technol. 5, 798–809 (2015).
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D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282, 2692–2698 (2009).
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G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Seredniakov, O. A. Shevchenko, A. N. Skrinsky, S. L. Veber, and N. A. Vinokurov, “Novosibirsk free electron laser: facility description and recent experiments,” IEEE Trans. THz Sci. Technol. 5, 798–809 (2015).
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Yu. Yu. Choporova, B. A. Knyazev, G. N. Kulipanov, V. S. Pavelyev, M. A. Scheglov, N. A. Vinokurov, B. O. Volodkin, and V. N. Zhabin, “High-power Bessel beams with orbital angular momentum in the terahertz range,” Phys. Rev. A 96, 023846 (2017).
[Crossref]

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Seredniakov, O. A. Shevchenko, A. N. Skrinsky, S. L. Veber, and N. A. Vinokurov, “Novosibirsk free electron laser: facility description and recent experiments,” IEEE Trans. THz Sci. Technol. 5, 798–809 (2015).
[Crossref]

M. A. Demýanenko, D. G. Esaev, V. N. Ovsyuk, B. I. Fomin, A. L. Aseev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Microbolometer detector arrays for the infrared and terahertz ranges,” J. Opt. Technol. 76, 739–743 (2009).
[Crossref]

M. A. Demyanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90 fps microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett.,  92, 131116 (2008).
[Crossref]

Vlasenko, M. G.

B. A. Knyazev, V. S. Cherkassky, Y. Choporova Y., V. Gerasimov V., M. G. Vlasenko, M. A. Demýanenko, and D. G. Esaev, “Real-time imaging using a high-power monochromatic terahertz source: comparative description of imaging techniques with examples of application,” J. Infrared Millim. THz Waves 32, 1207–1222 (2011).
[Crossref]

B. A. Knyazev, V. S. Cherkassky, Y. Y. Choporova, V. V. Gerasimov, and M. G. Vlasenko, “The Talbot effect in the terahertz spectral range,” in Proceedings of the 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz), Rome, Italy, 5–10 Sept 2010, 5612558.

Volodkin, B. O.

Yu. Yu. Choporova, B. A. Knyazev, G. N. Kulipanov, V. S. Pavelyev, M. A. Scheglov, N. A. Vinokurov, B. O. Volodkin, and V. N. Zhabin, “High-power Bessel beams with orbital angular momentum in the terahertz range,” Phys. Rev. A 96, 023846 (2017).
[Crossref]

B. A. Knyazev, Yu. Yu. Choporova, M. S. Mitkov, V. S. Pavelyev, and B. O. Volodkin, “Generation of terahertz surface plasmon polaritons using nondiffractive Bessel beams with orbital angular momentum,” Phys. Rev. Lett. 115, 163901 (2015).
[Crossref] [PubMed]

Vyas, S.

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282, 2692–2698 (2009).
[Crossref]

Walther, H.

Wang, C.

H. Gao, Y. Li, L. Chen, J. Jin, M. Pu, X. Li, P. Gao, C. Wang, X. Luo, and M. Hong, “Quasi-Talbot effect of orbital angular momentum beams for generation of optical vortex arrays by multiplexing metasurface design,” Nanoscale,  10, 666–671 (2018).
[Crossref]

Wen, J. M.

Westerholm, J.

Winthrop, J. T.

Woerdman, J. P.

L. Allen, M. W. C. Beijersbergen, R.J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Worthihgton, C. R.

Xiao, M.

Xie, C.

N. Gao and C. Xie, “Experimental demonstration of free-space optical vortex transmutation with polygonal lenses,” Opti. Lett.,  37, 3255–3257 (2012).
[Crossref]

Yaganeh, M.

Yeganeh, M.

Young, J.

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, “Observation of topological transformations of optical vortices in two-dimensional photonic lattices,” Opt. Expr.,  14, 8317–8327 (2006).
[Crossref]

Zambrini, R.

J. Courtial, R. Zambrini, M. R. Dennis, and M. Vasnetsov, “Angular momentum of optical vortex arrays,” Opt.Expr.,  14, 938–949 (2006).

Zhabin, V. N.

Yu. Yu. Choporova, B. A. Knyazev, G. N. Kulipanov, V. S. Pavelyev, M. A. Scheglov, N. A. Vinokurov, B. O. Volodkin, and V. N. Zhabin, “High-power Bessel beams with orbital angular momentum in the terahertz range,” Phys. Rev. A 96, 023846 (2017).
[Crossref]

Zhang, Y.

Žukauskas, A.

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97, 211108 (2010)
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. B (1)

O. Emile and J. Emile, “Young’s double-slit interference pattern from a twisted beam,” Appl. Phys. B 117, 487–491 (2014).
[Crossref]

Appl. Phys. Lett. (2)

M. A. Demyanenko, D. G. Esaev, B. A. Knyazev, G. N. Kulipanov, and N. A. Vinokurov, “Imaging with a 90 fps microbolometer focal plane array and high-power terahertz free electron laser,” Appl. Phys. Lett.,  92, 131116 (2008).
[Crossref]

E. Brasselet, M. Malinauskas, A. Žukauskas, and S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97, 211108 (2010)
[Crossref]

IEEE Trans. THz Sci. Technol. (2)

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Seredniakov, O. A. Shevchenko, A. N. Skrinsky, S. L. Veber, and N. A. Vinokurov, “Novosibirsk free electron laser: facility description and recent experiments,” IEEE Trans. THz Sci. Technol. 5, 798–809 (2015).
[Crossref]

Yu. Yu. Choporova, B. A. Knyazev, and M. S. Mitkov, “Classical holography in the terahertz range: recording and reconstruction techniques,” IEEE Trans. THz Sci. Technol. 5, 836–844 (2015).
[Crossref]

J. Infrared Millim. THz Waves (1)

B. A. Knyazev, V. S. Cherkassky, Y. Choporova Y., V. Gerasimov V., M. G. Vlasenko, M. A. Demýanenko, and D. G. Esaev, “Real-time imaging using a high-power monochromatic terahertz source: comparative description of imaging techniques with examples of application,” J. Infrared Millim. THz Waves 32, 1207–1222 (2011).
[Crossref]

J. Opt. (2)

A. Ferrando and M. A. García-March, “Theory for the control of dark rays by means of discrete symmetry diffractive elements,” J. Opt.,  15, 044014 (2013).
[Crossref]

P. Panthong, S. Srisuphaphon, A. Pattanaporkratana, S. Chiangga, and S. A. Deachapunya, “Study of optical vortices with the Talbot effect,” J. Opt. 18, 035602 (2016).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

J. Opt. Technol. (1)

JOSAA (1)

A. Sabatyan and S. M. T. Balanoji, “Square array of optical vortices generated by multiregion spiral square zone plate,” JOSAA 33, 1793–1797(2016).
[Crossref]

Materials (1)

M. Aymerich, D. Nieto, E. Álvarez, and M. T. Flores-Arias, “Laser surface microstructuring of biocompatible materials using a microlens array and the Talbot effect: evaluation of the cell adhesion,” Materials 10, 10020214 (2017).
[Crossref]

Nanoscale (1)

H. Gao, Y. Li, L. Chen, J. Jin, M. Pu, X. Li, P. Gao, C. Wang, X. Luo, and M. Hong, “Quasi-Talbot effect of orbital angular momentum beams for generation of optical vortex arrays by multiplexing metasurface design,” Nanoscale,  10, 666–671 (2018).
[Crossref]

Opt. Commun. (2)

Y. Lu, B. Jiang, S. Lü, Y. Liu, S. Li, Z. Cao, and X. Qi, “Arrays of Gaussian vortex, Bessel and Airy beams by computer-generated hologram,” Opt. Commun. 363, 85–90 (2016).
[Crossref]

D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282, 2692–2698 (2009).
[Crossref]

Opt. Expr. (1)

A. Bezryadina, D. N. Neshev, A. S. Desyatnikov, J. Young, Z. Chen, and Y. S. Kivshar, “Observation of topological transformations of optical vortices in two-dimensional photonic lattices,” Opt. Expr.,  14, 8317–8327 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Opt.Expr. (1)

J. Courtial, R. Zambrini, M. R. Dennis, and M. Vasnetsov, “Angular momentum of optical vortex arrays,” Opt.Expr.,  14, 938–949 (2006).

Opti. Lett. (1)

N. Gao and C. Xie, “Experimental demonstration of free-space optical vortex transmutation with polygonal lenses,” Opti. Lett.,  37, 3255–3257 (2012).
[Crossref]

Philos. Mag. Ser. (1)

H.F. Talbot, “Facts relating to optical science,” Philos. Mag. Ser. 3, 401–407 (1836).

Phys. Rev. A (2)

L. Allen, M. W. C. Beijersbergen, R.J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185 (1992).
[Crossref] [PubMed]

Yu. Yu. Choporova, B. A. Knyazev, G. N. Kulipanov, V. S. Pavelyev, M. A. Scheglov, N. A. Vinokurov, B. O. Volodkin, and V. N. Zhabin, “High-power Bessel beams with orbital angular momentum in the terahertz range,” Phys. Rev. A 96, 023846 (2017).
[Crossref]

Phys. Rev. Lett. (1)

B. A. Knyazev, Yu. Yu. Choporova, M. S. Mitkov, V. S. Pavelyev, and B. O. Volodkin, “Generation of terahertz surface plasmon polaritons using nondiffractive Bessel beams with orbital angular momentum,” Phys. Rev. Lett. 115, 163901 (2015).
[Crossref] [PubMed]

Other (3)

D. L. Andrews and M. Babiker, The angular momentum of light. (Cambrige University Press, 2013).

B. A. Knyazev and V. G. Serbo, “Photon beams with non-zero projection of orbital momentum – new results,” Physics Uspekhi (to be published in May2018).

B. A. Knyazev, V. S. Cherkassky, Y. Y. Choporova, V. V. Gerasimov, and M. G. Vlasenko, “The Talbot effect in the terahertz spectral range,” in Proceedings of the 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz), Rome, Italy, 5–10 Sept 2010, 5612558.

Supplementary Material (2)

NameDescription
» Visualization 1       This is a videofilm for the diffraction of Bessel vortex beam on amplitude grating with round holes (hole diameter is 1 mm, period is 4 mm):diffraction patterns vs. distance wavelength is 130 um (simulation).
» Visualization 2       This is a videofilm for the diffraction of Bessel vortex beam on amplitude grating with round holes (hole diameter is 1 mm, period is 4 mm):diffraction patterns vs. distance wavelength is 130 um (experiment at Novosubirsk Free Electron Laser Facilit

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Figures (7)

Fig. 1
Fig. 1 Experimental schematic. The Gaussian beam of the Novosibirsk free electron laser with a waist of 15 mm is incident on a silicon phase binary axicon and transforms into a Bessel beam. The initial diameter of the first ring of the Bessel beams is 1.8 mm for l = ±1 and 3.8 mm for l = ±2. A spatial Fourier spectrum of the beam recorded in the lens focus is shown in the inset. A telescope consisting of an exchangeable silicon lens and f = 250 mm parabolic mirror expands the beam (the magnification is 3.3 or 5 times). Diffraction patterns are recorded with a terahertz microbolometer camera moving by a motorized translation stage.
Fig. 2
Fig. 2 Classical Talbot effect (simulation). Images of the diffraction patterns in the Talbot planes: the gratings are illuminated by a Gaussian wave with a plane front, λ = 130 µm. In each frame, the brightness is proportional to the radiation intensity and the local phase of the beam can be determined from the color palette shown in the top of the figure. The frame size here and below is 16.32 × 12.24 mm.
Fig. 3
Fig. 3 Quasi-Talbot effect (simulation). Images in the planes corresponding to the Talbot distances. The gratings are illuminated by the expanded (M = 5) Bessel beam with a topological charge l = +1, λ = 130 µm.
Fig. 4
Fig. 4 Talbot distances vs. grating period. Perfect vortex beamlet arrays are formed in the distances marked with circles for the gratings with D = 1 mm illuminated by the expanded (M = 5) Bessel beam. The circle sizes are proportional to the diameters of the annular vortex beamlets. Additional simulations, as well as experiments, showed that the distances and diameters of the beam rings are the same for beams with the topological charges l = ±1 and ±2.
Fig. 5
Fig. 5 Beamlet characteristics vs. illuminating beam and grating parameters (simulations). a, Intensity and phase of beamlets for different topological charges. b, Change in beamlet characteristics with increase in openings. c, Distribution of the intensity of the diffraction pattern with increasing diameter of the beam illuminating the grating. Beam diameters correspond to the telescope magnification M = 2.5, 3.3, 5, and 10, respectively; the field of view is 30 × 30 mm.
Fig. 6
Fig. 6 Ring diameters of vortex beamlets in the half-Talbot planes as a function of (a) Talbot distances and (b) diameter of illuminating beam. Each point in plot (a) corresponds to a grating whose period is indicated by a number near the point. The diameters of illuminating beam of 6 and 9 mm corresponds to telescope magnification of 3.3 and 5, respectively. The results are presented for a beam with l = +1.
Fig. 7
Fig. 7 Comparison of experimentally observed diffraction patterns (Exp) with results of simulations (Sim). The upper set of frames is obtained for the Bessel beams the diameter of first ring of which was 9 mm for l = +1 and 15 mm for l = +2. The bottom set demonstrates the patterns obtained for illuminating beams which diameters were 1.5 times less. The experimental frames are extracted from terahertz videos. Examples of videos are presented in Visualization 1 and Visualization 2.

Equations (3)

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z N = N L T , N = 1 , 2 , 3 ,
z = 2 p 2 λ ( N 1 + n m ) ,
E ( ρ , θ , z ) = J l ( κ ρ ) exp [ i ( k z z + l θ ) ] ,

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