Abstract

We experimentally demonstrate and theoretically predict a new and unprecedented optical carpet that includes all the geometric shadow and far-field and near-field diffraction patterns at the transverse plane in the diffraction from a radial grating illuminated by a plane wavefront. The main feature of using radial grating is the continuous change of the spatial period along the radial direction. Therefore, the geometric shadow, and the near-field and far-field diffraction regimes are mixed at various propagation distances, and the traditional definitions for the different diffraction regimes would not apply here. We show that for a given propagation distance, at a certain radial distance the shadow regime changes to the near-field regime and at another certain radial distance, the diffraction pattern changes from a near-field to a far-field case.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Intensity-based measuring of the topological charge alteration by the diffraction of vortex beams from amplitude sinusoidal radial gratings

Davud Hebri, Saifollah Rasouli, and Mohammad Yeganeh
J. Opt. Soc. Am. B 35(4) 724-730 (2018)

Phases of Talbot patterns in angular self-imaging

Hugues Guillet de Chatellus, Eric Lacot, Olivier Hugon, Olivier Jacquin, Naïma Khebbache, and José Azaña
J. Opt. Soc. Am. A 32(6) 1132-1139 (2015)

References

  • View by:
  • |
  • |
  • |

  1. Lord Rayleigh, “XXV. On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
    [Crossref]
  2. H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Philos. Mag. 9(56), 401–407 (1836).
    [Crossref]
  3. M. K. Oberthaler, S. Bernet, E. M. Rasel, J. Schmiedmayer, and A. Zeilinger, “Inertial sensing with classical atomic beams,” Phys. Rev. A 54, 3165–3176 (1996).
    [Crossref]
  4. J. Azana and H. Guillet de Chatellus, “Angular Talbot effect,” Phys. Rev. Lett. 112, 213902 (2014).
    [Crossref]
  5. S. Rasouli, M. Dashti, and A. N. Ramaprakash, “An adjustable, high sensitivity, wide dynamic range two channel wave-front sensor based on moiré deflectometry,” Opt. Express 18, 23906–23915 (2010).
    [Crossref]
  6. M. Yeganeh, S. Rasouli, M. Dashti, S. Slussarenko, E. Santamato, and E. Karimi, “Reconstructing the Poynting vector skew angle and wavefront of optical vortex beams via two-channel moiré deflectometery,” Opt. Lett. 38, 887–889 (2013).
    [Crossref]
  7. S. Rasouli and M. Taghi Tavassoly, “Application of the moiré deflectometry on divergent laser beam to the measurement of the angle of arrival fluctuations and the refractive index structure constant in the turbulent atmosphere,” Opt. Lett. 33, 980–982 (2008).
    [Crossref]
  8. M. Dashti and S. Rasouli, “Measurement and statistical analysis of the wavefront distortions induced by atmospheric turbulence using two-channel moiré deflectometry,” J. Opt. 14, 095704 (2012).
    [Crossref]
  9. F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
    [Crossref]
  10. J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photon. 5, 83–130 (2013).
    [Crossref]
  11. Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
    [Crossref]
  12. B. J. McMorran and A. D. Cronin, “An electron Talbot interferometer,” New J. Phys. 11, 033021 (2009).
    [Crossref]
  13. J. A. Salas, K. Varga, J. A. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93, 104305 (2016).
    [Crossref]
  14. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
    [Crossref]
  15. M. R. Dennis, N. I. Zheludev, and F. J. G. de Abajo, “The plasmon Talbot effect,” Opt. Express 15, 9692–9700 (2007).
    [Crossref]
  16. T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
    [Crossref]
  17. S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach, “Spin wave diffraction and perfect imaging of a grating,” Phys. Rev. Lett. 108, 047204 (2012).
    [Crossref]
  18. X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107, 033902 (2011).
    [Crossref]
  19. S. Deachapunya, S. Srisuphaphon, P. Panthong, T. Photia, K. Boonkham, and S. Chiangga, “Realization of the single photon Talbot effect with a spatial light modulator,” Opt. Express 24, 20029–20035 (2016).
    [Crossref]
  20. H. Guillet de Chatellus, E. Lacot, W. Glastre, O. Jacquin, and O. Hugon, “Theory of Talbot lasers,” Phys. Rev. A 88, 033828 (2013).
    [Crossref]
  21. R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
    [Crossref]
  22. M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
    [Crossref]
  23. B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88, 100404 (2002).
    [Crossref]
  24. L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
    [Crossref]
  25. S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
    [Crossref]
  26. M. Berry, I. Marzoli, and W. Schleich, “Quantum carpets, carpets of light,” Phys. World 14, 39–46 (2001).
    [Crossref]
  27. W. B. Case, M. Tomandl, S. Deachapunya, and M. Arndt, “Realization of optical carpets in the Talbot and Talbot-Lau configurations,” Opt. Express 17, 20966–20974 (2009).
    [Crossref]
  28. S. Rasouli and D. Hebri, “Contrast enhanced quarter-Talbot images,” J. Opt. Soc. Am. A 34, 2145–2156 (2017).
  29. P. Szwaykowski, “Self-imaging in polar coordinates,” J. Opt. Soc. Am. A 5, 185–191 (1988).
    [Crossref]
  30. J. Alonso and E. Bernabeu, “Spatial evolution of Gaussian beams diffracted by radial gratings,” Opt. Commun. 98, 323–330 (1993).
    [Crossref]
  31. J. Alonso and E. Bernabeu, “Use of effective focal lengths to describe laser-beam evolution after diffraction in radial gratings,” J. Opt. Soc. Am. A 10, 1963–1970 (1993).
    [Crossref]
  32. B. E. A. Saleh, M. C. Teich, and B. E. Saleh, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991).
  33. G. B. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, 1985).
  34. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  35. A. Jeffrey and D. Zwillinger, eds., Table of Integrals, Series, and Products (Academic, 2007).
  36. S. Rasouli, D. Hebri, and A. M. Khazaei, “Investigation of various behaviors of near- and far-field diffractions from multiplicatively separable structures in the x and y directions, and a detailed study of the near-field diffraction patterns of 2D multiplicatively separable periodic structures using the contrast variation method,” J. Opt. 19, 095601 (2017).
    [Crossref]
  37. S. Rasouli, D. Hebri, and M. Yeganeh, Department of Physics, IASBS, Zanjan, Iran, are preparing a manuscript to be called “Intensity based measuring of the topological charge alteration by the aid of diffraction of vortex beams from amplitude sinusoidal radial gratings” (in preparation).

2017 (2)

S. Rasouli and D. Hebri, “Contrast enhanced quarter-Talbot images,” J. Opt. Soc. Am. A 34, 2145–2156 (2017).

S. Rasouli, D. Hebri, and A. M. Khazaei, “Investigation of various behaviors of near- and far-field diffractions from multiplicatively separable structures in the x and y directions, and a detailed study of the near-field diffraction patterns of 2D multiplicatively separable periodic structures using the contrast variation method,” J. Opt. 19, 095601 (2017).
[Crossref]

2016 (3)

S. Deachapunya, S. Srisuphaphon, P. Panthong, T. Photia, K. Boonkham, and S. Chiangga, “Realization of the single photon Talbot effect with a spatial light modulator,” Opt. Express 24, 20029–20035 (2016).
[Crossref]

J. A. Salas, K. Varga, J. A. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93, 104305 (2016).
[Crossref]

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

2014 (2)

J. Azana and H. Guillet de Chatellus, “Angular Talbot effect,” Phys. Rev. Lett. 112, 213902 (2014).
[Crossref]

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

2013 (3)

2012 (2)

S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach, “Spin wave diffraction and perfect imaging of a grating,” Phys. Rev. Lett. 108, 047204 (2012).
[Crossref]

M. Dashti and S. Rasouli, “Measurement and statistical analysis of the wavefront distortions induced by atmospheric turbulence using two-channel moiré deflectometry,” J. Opt. 14, 095704 (2012).
[Crossref]

2011 (1)

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

2010 (2)

2009 (2)

2008 (1)

2007 (1)

2005 (1)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

2003 (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

2002 (1)

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88, 100404 (2002).
[Crossref]

2001 (1)

M. Berry, I. Marzoli, and W. Schleich, “Quantum carpets, carpets of light,” Phys. World 14, 39–46 (2001).
[Crossref]

1999 (1)

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

1996 (1)

M. K. Oberthaler, S. Bernet, E. M. Rasel, J. Schmiedmayer, and A. Zeilinger, “Inertial sensing with classical atomic beams,” Phys. Rev. A 54, 3165–3176 (1996).
[Crossref]

1995 (1)

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

1993 (2)

J. Alonso and E. Bernabeu, “Spatial evolution of Gaussian beams diffracted by radial gratings,” Opt. Commun. 98, 323–330 (1993).
[Crossref]

J. Alonso and E. Bernabeu, “Use of effective focal lengths to describe laser-beam evolution after diffraction in radial gratings,” J. Opt. Soc. Am. A 10, 1963–1970 (1993).
[Crossref]

1989 (1)

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[Crossref]

1988 (1)

1881 (1)

Lord Rayleigh, “XXV. On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
[Crossref]

1836 (1)

H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Philos. Mag. 9(56), 401–407 (1836).
[Crossref]

Aghion, S.

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

Ahlén, O.

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

Alonso, J.

J. Alonso and E. Bernabeu, “Use of effective focal lengths to describe laser-beam evolution after diffraction in radial gratings,” J. Opt. Soc. Am. A 10, 1963–1970 (1993).
[Crossref]

J. Alonso and E. Bernabeu, “Spatial evolution of Gaussian beams diffracted by radial gratings,” Opt. Commun. 98, 323–330 (1993).
[Crossref]

Amsler, C.

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

Arfken, G. B.

G. B. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, 1985).

Ariga, A.

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

Ariga, T.

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

Arndt, M.

W. B. Case, M. Tomandl, S. Deachapunya, and M. Arndt, “Realization of optical carpets in the Talbot and Talbot-Lau configurations,” Opt. Express 17, 20966–20974 (2009).
[Crossref]

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88, 100404 (2002).
[Crossref]

Azana, J.

J. Azana and H. Guillet de Chatellus, “Angular Talbot effect,” Phys. Rev. Lett. 112, 213902 (2014).
[Crossref]

Belov, A. S.

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

Berggren, K.

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

Bernabeu, E.

J. Alonso and E. Bernabeu, “Spatial evolution of Gaussian beams diffracted by radial gratings,” Opt. Commun. 98, 323–330 (1993).
[Crossref]

J. Alonso and E. Bernabeu, “Use of effective focal lengths to describe laser-beam evolution after diffraction in radial gratings,” J. Opt. Soc. Am. A 10, 1963–1970 (1993).
[Crossref]

Bernet, S.

M. K. Oberthaler, S. Bernet, E. M. Rasel, J. Schmiedmayer, and A. Zeilinger, “Inertial sensing with classical atomic beams,” Phys. Rev. A 54, 3165–3176 (1996).
[Crossref]

Berry, M.

M. Berry, I. Marzoli, and W. Schleich, “Quantum carpets, carpets of light,” Phys. World 14, 39–46 (2001).
[Crossref]

Bevan, K. H.

J. A. Salas, K. Varga, J. A. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93, 104305 (2016).
[Crossref]

Bonomi, G.

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

Boonkham, K.

Bräunig, P.

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

Bremer, J.

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

Brezger, B.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88, 100404 (2002).
[Crossref]

Brusa, R. S.

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

Case, W. B.

Chapman, M. S.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

Chiangga, S.

Christodoulides, D. N.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Clark, C. W.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Cronin, A. D.

B. J. McMorran and A. D. Cronin, “An electron Talbot interferometer,” New J. Phys. 11, 033021 (2009).
[Crossref]

D’Amato, F. X.

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[Crossref]

Dashti, M.

de Abajo, F. J. G.

Deachapunya, S.

Deng, L.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Dennis, M. R.

Denschlag, J.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Edwards, M.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Egorov, O. A.

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

Ekstrom, C. R.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

Estrecho, E.

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

Gao, T.

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

Glastre, W.

H. Guillet de Chatellus, E. Lacot, W. Glastre, O. Jacquin, and O. Hugon, “Theory of Talbot lasers,” Phys. Rev. A 88, 033828 (2013).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Guillet de Chatellus, H.

J. Azana and H. Guillet de Chatellus, “Angular Talbot effect,” Phys. Rev. Lett. 112, 213902 (2014).
[Crossref]

H. Guillet de Chatellus, E. Lacot, W. Glastre, O. Jacquin, and O. Hugon, “Theory of Talbot lasers,” Phys. Rev. A 88, 033828 (2013).
[Crossref]

Hackermüller, L.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88, 100404 (2002).
[Crossref]

Hagley, E. W.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Hammond, T. D.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

Hansen, W.

S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach, “Spin wave diffraction and perfect imaging of a grating,” Phys. Rev. Lett. 108, 047204 (2012).
[Crossref]

Hebri, D.

S. Rasouli, D. Hebri, and A. M. Khazaei, “Investigation of various behaviors of near- and far-field diffractions from multiplicatively separable structures in the x and y directions, and a detailed study of the near-field diffraction patterns of 2D multiplicatively separable periodic structures using the contrast variation method,” J. Opt. 19, 095601 (2017).
[Crossref]

S. Rasouli and D. Hebri, “Contrast enhanced quarter-Talbot images,” J. Opt. Soc. Am. A 34, 2145–2156 (2017).

S. Rasouli, D. Hebri, and M. Yeganeh, Department of Physics, IASBS, Zanjan, Iran, are preparing a manuscript to be called “Intensity based measuring of the topological charge alteration by the aid of diffraction of vortex beams from amplitude sinusoidal radial gratings” (in preparation).

Heitmann, D.

S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach, “Spin wave diffraction and perfect imaging of a grating,” Phys. Rev. Lett. 108, 047204 (2012).
[Crossref]

Helmerson, K.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Hoefling, S.

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

Hugon, O.

H. Guillet de Chatellus, E. Lacot, W. Glastre, O. Jacquin, and O. Hugon, “Theory of Talbot lasers,” Phys. Rev. A 88, 033828 (2013).
[Crossref]

Iwanow, R.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Jacquin, O.

H. Guillet de Chatellus, E. Lacot, W. Glastre, O. Jacquin, and O. Hugon, “Theory of Talbot lasers,” Phys. Rev. A 88, 033828 (2013).
[Crossref]

Kamp, M.

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

Karimi, E.

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Khazaei, A. M.

S. Rasouli, D. Hebri, and A. M. Khazaei, “Investigation of various behaviors of near- and far-field diffractions from multiplicatively separable structures in the x and y directions, and a detailed study of the near-field diffraction patterns of 2D multiplicatively separable periodic structures using the contrast variation method,” J. Opt. 19, 095601 (2017).
[Crossref]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Lacot, E.

H. Guillet de Chatellus, E. Lacot, W. Glastre, O. Jacquin, and O. Hugon, “Theory of Talbot lasers,” Phys. Rev. A 88, 033828 (2013).
[Crossref]

Li, G.

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

Lord Rayleigh,

Lord Rayleigh, “XXV. On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
[Crossref]

Luo, K. H.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Ma, X.

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

Mansfeld, S.

S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach, “Spin wave diffraction and perfect imaging of a grating,” Phys. Rev. Lett. 108, 047204 (2012).
[Crossref]

Martens, K.

S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach, “Spin wave diffraction and perfect imaging of a grating,” Phys. Rev. Lett. 108, 047204 (2012).
[Crossref]

Marzoli, I.

M. Berry, I. Marzoli, and W. Schleich, “Quantum carpets, carpets of light,” Phys. World 14, 39–46 (2001).
[Crossref]

May-Arrioja, D. A.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

McMorran, B. J.

B. J. McMorran and A. D. Cronin, “An electron Talbot interferometer,” New J. Phys. 11, 033021 (2009).
[Crossref]

Mendach, S.

S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach, “Spin wave diffraction and perfect imaging of a grating,” Phys. Rev. Lett. 108, 047204 (2012).
[Crossref]

Min, Y.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Momose, A.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Oberthaler, M. K.

M. K. Oberthaler, S. Bernet, E. M. Rasel, J. Schmiedmayer, and A. Zeilinger, “Inertial sensing with classical atomic beams,” Phys. Rev. A 54, 3165–3176 (1996).
[Crossref]

Ostrovskaya, E. A.

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

Panthong, P.

Petschinka, J.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88, 100404 (2002).
[Crossref]

Phillips, W. D.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Photia, T.

Pritchard, D. E.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

Ramaprakash, A. N.

Rasel, E. M.

M. K. Oberthaler, S. Bernet, E. M. Rasel, J. Schmiedmayer, and A. Zeilinger, “Inertial sensing with classical atomic beams,” Phys. Rev. A 54, 3165–3176 (1996).
[Crossref]

Rasouli, S.

S. Rasouli and D. Hebri, “Contrast enhanced quarter-Talbot images,” J. Opt. Soc. Am. A 34, 2145–2156 (2017).

S. Rasouli, D. Hebri, and A. M. Khazaei, “Investigation of various behaviors of near- and far-field diffractions from multiplicatively separable structures in the x and y directions, and a detailed study of the near-field diffraction patterns of 2D multiplicatively separable periodic structures using the contrast variation method,” J. Opt. 19, 095601 (2017).
[Crossref]

M. Yeganeh, S. Rasouli, M. Dashti, S. Slussarenko, E. Santamato, and E. Karimi, “Reconstructing the Poynting vector skew angle and wavefront of optical vortex beams via two-channel moiré deflectometery,” Opt. Lett. 38, 887–889 (2013).
[Crossref]

M. Dashti and S. Rasouli, “Measurement and statistical analysis of the wavefront distortions induced by atmospheric turbulence using two-channel moiré deflectometry,” J. Opt. 14, 095704 (2012).
[Crossref]

S. Rasouli, M. Dashti, and A. N. Ramaprakash, “An adjustable, high sensitivity, wide dynamic range two channel wave-front sensor based on moiré deflectometry,” Opt. Express 18, 23906–23915 (2010).
[Crossref]

S. Rasouli and M. Taghi Tavassoly, “Application of the moiré deflectometry on divergent laser beam to the measurement of the angle of arrival fluctuations and the refractive index structure constant in the turbulent atmosphere,” Opt. Lett. 33, 980–982 (2008).
[Crossref]

S. Rasouli, D. Hebri, and M. Yeganeh, Department of Physics, IASBS, Zanjan, Iran, are preparing a manuscript to be called “Intensity based measuring of the topological charge alteration by the aid of diffraction of vortex beams from amplitude sinusoidal radial gratings” (in preparation).

Rolston, S. L.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Roychoudhuri, C.

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[Crossref]

Salas, J. A.

J. A. Salas, K. Varga, J. A. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93, 104305 (2016).
[Crossref]

Saleh, B. E.

B. E. A. Saleh, M. C. Teich, and B. E. Saleh, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991).

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, and B. E. Saleh, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991).

Santamato, E.

Schleich, W.

M. Berry, I. Marzoli, and W. Schleich, “Quantum carpets, carpets of light,” Phys. World 14, 39–46 (2001).
[Crossref]

Schmiedmayer, J.

M. K. Oberthaler, S. Bernet, E. M. Rasel, J. Schmiedmayer, and A. Zeilinger, “Inertial sensing with classical atomic beams,” Phys. Rev. A 54, 3165–3176 (1996).
[Crossref]

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

Schneider, C.

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

Siebert, E. T.

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[Crossref]

Simsarian, J. E.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

Slussarenko, S.

Sohler, W.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Song, X. B.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Srisuphaphon, S.

Stegeman, G. I.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Suzuki, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Szwaykowski, P.

Taghi Tavassoly, M.

Takai, K.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Talbot, H. F.

H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Philos. Mag. 9(56), 401–407 (1836).
[Crossref]

Tannian, B. E.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

Teich, M. C.

B. E. A. Saleh, M. C. Teich, and B. E. Saleh, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991).

Toedt, J. N.

S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach, “Spin wave diffraction and perfect imaging of a grating,” Phys. Rev. Lett. 108, 047204 (2012).
[Crossref]

Tomandl, M.

Topp, J.

S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach, “Spin wave diffraction and perfect imaging of a grating,” Phys. Rev. Lett. 108, 047204 (2012).
[Crossref]

Truscott, A. G.

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

Uttenthaler, S.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88, 100404 (2002).
[Crossref]

Varga, K.

J. A. Salas, K. Varga, J. A. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93, 104305 (2016).
[Crossref]

Wang, H. B.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Wang, K.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Wehinger, S.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

Wen, J.

Winkler, K.

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

Wu, L. A.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Xiao, M.

Xiong, J.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Yan, J. A.

J. A. Salas, K. Varga, J. A. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93, 104305 (2016).
[Crossref]

Yeganeh, M.

M. Yeganeh, S. Rasouli, M. Dashti, S. Slussarenko, E. Santamato, and E. Karimi, “Reconstructing the Poynting vector skew angle and wavefront of optical vortex beams via two-channel moiré deflectometery,” Opt. Lett. 38, 887–889 (2013).
[Crossref]

S. Rasouli, D. Hebri, and M. Yeganeh, Department of Physics, IASBS, Zanjan, Iran, are preparing a manuscript to be called “Intensity based measuring of the topological charge alteration by the aid of diffraction of vortex beams from amplitude sinusoidal radial gratings” (in preparation).

Zeilinger, A.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88, 100404 (2002).
[Crossref]

M. K. Oberthaler, S. Bernet, E. M. Rasel, J. Schmiedmayer, and A. Zeilinger, “Inertial sensing with classical atomic beams,” Phys. Rev. A 54, 3165–3176 (1996).
[Crossref]

Zhang, X.

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Zhang, Y.

Zheludev, N. I.

Zhu, S. N.

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (1)

F. X. D’Amato, E. T. Siebert, and C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[Crossref]

J. Opt. (2)

M. Dashti and S. Rasouli, “Measurement and statistical analysis of the wavefront distortions induced by atmospheric turbulence using two-channel moiré deflectometry,” J. Opt. 14, 095704 (2012).
[Crossref]

S. Rasouli, D. Hebri, and A. M. Khazaei, “Investigation of various behaviors of near- and far-field diffractions from multiplicatively separable structures in the x and y directions, and a detailed study of the near-field diffraction patterns of 2D multiplicatively separable periodic structures using the contrast variation method,” J. Opt. 19, 095601 (2017).
[Crossref]

J. Opt. Soc. Am. A (3)

Jpn. J. Appl. Phys. (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Nat. Commun. (1)

S. Aghion, O. Ahlén, C. Amsler, A. Ariga, T. Ariga, A. S. Belov, K. Berggren, G. Bonomi, P. Bräunig, J. Bremer, and R. S. Brusa, “A moiré deflectometer for antimatter,” Nat. Commun. 5, 4538 (2014).
[Crossref]

New J. Phys. (1)

B. J. McMorran and A. D. Cronin, “An electron Talbot interferometer,” New J. Phys. 11, 033021 (2009).
[Crossref]

Opt. Commun. (1)

J. Alonso and E. Bernabeu, “Spatial evolution of Gaussian beams diffracted by radial gratings,” Opt. Commun. 98, 323–330 (1993).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Philos. Mag. (2)

Lord Rayleigh, “XXV. On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
[Crossref]

H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Philos. Mag. 9(56), 401–407 (1836).
[Crossref]

Phys. Rev. A (3)

M. K. Oberthaler, S. Bernet, E. M. Rasel, J. Schmiedmayer, and A. Zeilinger, “Inertial sensing with classical atomic beams,” Phys. Rev. A 54, 3165–3176 (1996).
[Crossref]

H. Guillet de Chatellus, E. Lacot, W. Glastre, O. Jacquin, and O. Hugon, “Theory of Talbot lasers,” Phys. Rev. A 88, 033828 (2013).
[Crossref]

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
[Crossref]

Phys. Rev. B (1)

J. A. Salas, K. Varga, J. A. Yan, and K. H. Bevan, “Electron Talbot effect on graphene,” Phys. Rev. B 93, 104305 (2016).
[Crossref]

Phys. Rev. Lett. (8)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

J. Azana and H. Guillet de Chatellus, “Angular Talbot effect,” Phys. Rev. Lett. 112, 213902 (2014).
[Crossref]

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
[Crossref]

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88, 100404 (2002).
[Crossref]

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
[Crossref]

T. Gao, E. Estrecho, G. Li, O. A. Egorov, X. Ma, K. Winkler, M. Kamp, C. Schneider, S. Hoefling, A. G. Truscott, and E. A. Ostrovskaya, “Talbot effect for exciton polaritons,” Phys. Rev. Lett. 117, 097403 (2016).
[Crossref]

S. Mansfeld, J. Topp, K. Martens, J. N. Toedt, W. Hansen, D. Heitmann, and S. Mendach, “Spin wave diffraction and perfect imaging of a grating,” Phys. Rev. Lett. 108, 047204 (2012).
[Crossref]

X. B. Song, H. B. Wang, J. Xiong, K. Wang, X. Zhang, K. H. Luo, and L. A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Phys. World (1)

M. Berry, I. Marzoli, and W. Schleich, “Quantum carpets, carpets of light,” Phys. World 14, 39–46 (2001).
[Crossref]

Other (5)

B. E. A. Saleh, M. C. Teich, and B. E. Saleh, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 1991).

G. B. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, 1985).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

A. Jeffrey and D. Zwillinger, eds., Table of Integrals, Series, and Products (Academic, 2007).

S. Rasouli, D. Hebri, and M. Yeganeh, Department of Physics, IASBS, Zanjan, Iran, are preparing a manuscript to be called “Intensity based measuring of the topological charge alteration by the aid of diffraction of vortex beams from amplitude sinusoidal radial gratings” (in preparation).

Supplementary Material (3)

NameDescription
» Visualization 1       The movie presents transverse plane Talbot carpet of a sinusoidal amplitude radial grating at different propagation distances and corresponding intensity profiles along azimuthal and radial directions.
» Visualization 2       The movie presents transverse plane Talbot carpet of a sinusoidal amplitude radial grating at different propagation distances.
» Visualization 3       The movie presents transverse plane Talbot carpet of a binary amplitude radial grating at different propagation distances.

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 (11)

Fig. 1.
Fig. 1. Illustration of the diffraction geometry.
Fig. 2.
Fig. 2. Illustration of two typical amplitude radial gratings with spoke numbers of m=20 having (a) sinusoidal and (b) binary transmission profiles.
Fig. 3.
Fig. 3. (a) Calculated diffraction pattern for three sinusoidal amplitude radial gratings with 5, 50, and 75 spokes at distance 100 cm from the gratings, and (b) projection of a sector of the theoretically produced transverse plane Talbot carpet from the polar coordinates to the Cartesian coordinates. (c) Calculated intensity profiles at radii equal to the locations of first and second subimages (A and C plots) and first half-Talbot and Talbot images (B and D plots). (d) Intensity profiles along two radial lines passing through locations of the extrema values of the shadow image. (e) Calculated visibility of the Talbot carpet as a function of radial distance from the optical axis. Corresponding locations of the plots are shown in (b) by the same letters. Values of the intensities are normalized to the value of the incident beam’s intensity (see also Visualization 1 and Visualization 2).
Fig. 4.
Fig. 4. Experimental diffraction pattern from an amplitude radial grating with a sinusoidal profile and spoke number of m=50 at a propagation distance equal to 100 cm recorded directly on the active area of the camera. Real size of pattern is 23.4  mm×15.6  mm, and wavelength of the impinging light was 532 nm.
Fig. 5.
Fig. 5. Talbot carpets produced at the transverse planes by diffraction from amplitude radial gratings with sinusoidal profiles and spoke numbers of 5, 50, and 75 at different distances of 100 cm, 150 cm, and 200 cm from the gratings. Simulated and experimentally recorded patterns are illustrated by red and green colors, respectively. Real size of all patterns is 3  cm×3  cm.
Fig. 6.
Fig. 6. Calculated (first row) and experimentally recorded (second row) diffraction patterns for a sinusoidal amplitude radial grating with 50 spokes at three different conventional near-field distances from the structure. Real size of all patterns is 10  mm×10  mm.
Fig. 7.
Fig. 7. Splitting of the space into geometric shadow and far-field and near-field diffraction regimes for a typical amplitude radial grating. Green surface splits the geometric shadow from the near-field diffraction regime, and blue surface splits the near-field and far-field diffraction regimes from each other.
Fig. 8.
Fig. 8. Calculated diffraction patterns for three binary amplitude radial gratings with 4, 50, and 75 spokes at propagation distance of 100 cm.
Fig. 9.
Fig. 9. Experimental diffraction pattern from an amplitude radial grating with a binary profile and spoke number of m=50 at a propagation distance of 100 cm. The pattern is directly recorded on the sensitive area of the camera, and its real size is 23.4  mm×15.6  mm.
Fig. 10.
Fig. 10. Simulated and experimentally recorded diffraction patterns from three different radial binary amplitude gratings having binary profiles. The parameters of the gratings are the same as the case of Fig. 5, and diffraction planes are considered at propagation distances of 100 cm, 150 cm, 200 cm, and 490 cm.
Fig. 11.
Fig. 11. Calculated (first row) and experimentally recorded (second row) diffraction patterns of a binary amplitude radial grating with 50 spokes at different almost conventional near-field distances (see also Visualization 3). Real size of all patterns is 10  mm×10  mm.

Equations (27)

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

g(x,y)=h0f(x,y)eiα[(xx)2+(yy)2]dxdy,
g(r,θ)=h0eiαr2002πrdrdθf(r,θ)eiαr2e2iαrrcos(θθ),
f(r,θ)=fR(r)fΘ(θ).
g(r,θ)=h0eiαr20+rdrfR(r)eiαr202πdθfΘ(θ)e2iαrrcos(θθ).
e2iαrrcos(θθ)=n=+(i)nJn(2πρr)ein(θθ),
fΘ(θ)=m=+cmeimθ,
Hn{f(r)}=2π0+f(r)Jn(2πρr)rdr,
g(r,θ)=h0eiαr2n=+cn(i)neinθHn{fR(r)eiαr2},
02πei(mn)θdθ=2πδm,n,
g(r,θ)=h0eiαr2×{c0H0{eiαr2}+n=1+(cneinθ+cneinθ)(i)nHn{eiαr2}},
Hn{f(r)}=(1)nHn{f(r)}.
Hn{eiαr2}=b4(πα)32ei(b28αnπ4)×[Jn+12(b28α)+iJn12(b28α)],
H0{eiαr2}=iπαeiπ2ρ2α.
g(r,θ)=eikz×{c0+ReiR2n=1+π2(i)n2+1(cneinθ+cneinθ)×[Jn+12(R2)+iJn12(R2)]},
t(θ)=fΘ(θ)=12[1+cos(mθ)]=12+14(eimθ+eimθ),
g(r,θ)=eikz2×{1+ReiR2π2(i)m2+1[Jm+12(R2)+iJm12(R2)]cos(mθ)}.
rout=m2π2λz.
rT1=m2πλz/2.
V(r)=I(r,θmax)I(r,θmin)I(r,θmax)+I(r,θmin).
Jm(R2)2πR2cos(R2mπ2π4).
g(r,θ)=eikz2{1+cos(mθ)},
Jm(R2)1Γ(m+1)(R22)m,
g(r,θ)=eikz2×{1+π(i)m2+1RmeiR2[R2+i(m+1)2(m2)(m+1)Γ(m+12)]cos(mθ)}.
rin=mλzπ.
t(θ)=12(1+sgn  cos(mθ))=12+l=1+(Aleimlθ+Aleimlθ),
fΘ(θ)=12+12l=1+sinc(lπ2)(eimlθ+eimlθ).
g(r,θ)=eikz2×{1+ReiR2l=1gl[Jml+12(R2)+iJml12(R2)]cos(mlθ)},

Metrics