Abstract

We theoretically study discrete Talbot self-imaging in hexagonal, square, and irregular two-dimensional waveguide arrays. Different from its counterpart in a continuous system, the periods of the input fields must belong to {1, 2, 3, 4, 6} for Talbot self-imaging. Also, the combinations of the input periods cannot be 3 & 4, or 4 & 6 along two different directions, which distinguishes itself from the one-dimensional discrete Talbot effect.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics

Jianming Wen, Yong Zhang, and Min Xiao
Adv. Opt. Photon. 5(1) 83-130 (2013)

Discrete plasmonic Talbot effect in subwavelength metal waveguide arrays

Yueke Wang, Keya Zhou, Xueru Zhang, Kun Yang, Yuxiao Wang, Yinglin Song, and Shutian Liu
Opt. Lett. 35(5) 685-687 (2010)

Talbot effect in weakly coupled monolayer graphene sheet arrays

Yang Fan, Bing Wang, Kai Wang, Hua Long, and Peixiang Lu
Opt. Lett. 39(12) 3371-3373 (2014)

References

  • View by:
  • |
  • |
  • |

  1. H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401–407 (1836).
  2. K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–108 (1989).
  3. J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
    [Crossref]
  4. L. Rayleigh, “On copying diffraction gratings and some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
    [Crossref]
  5. V. V. Antyukhov, A. F. Glova, O. R. Kachurin, F. V. Lebedev, V. V. Likhanskii, A. P. Napartovich, and V. D. Pismennyi, “Effective phase locking of an array of lasers,” JETP Lett. 44, 78 (1986).
  6. A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik (Stuttg.) 79, 41–45 (1988).
  7. J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55(4), 334 (1989).
    [Crossref]
  8. D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, “Modal analysis of linear Talbot-cavity semiconductor lasers,” Opt. Lett. 16(11), 823–825 (1991).
    [Crossref] [PubMed]
  9. T. Jannson and J. Jannson, “Temporal self-imaging effect in single-mode fibers,” J. Opt. Soc. Am. 71, 1373–1376 (1981).
  10. J. Azaña, “Spectral Talbot phenomena of frequency combs induced by cross-phase modulation in optical fibers,” Opt. Lett. 30(3), 227–229 (2005).
    [Crossref] [PubMed]
  11. P. Peterson, A. Gavrielides, and M. Sharma, “Extraction characteristics of a one dimensional Talbot cavity with stochastic propagation phase,” Opt. Express 8(12), 670–681 (2001).
    [Crossref] [PubMed]
  12. 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(5), 053902 (2005).
    [Crossref] [PubMed]
  13. H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-Symmetric Talbot Effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
    [Crossref] [PubMed]
  14. 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(1), R14–R17 (1995).
    [Crossref] [PubMed]
  15. J. F. Clauser and S. Li, “Talbot-vonLau atom interferometry with cold slow potassium,” Phys. Rev. A 49(4), R2213–R2216 (1994).
    [Crossref] [PubMed]
  16. Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
    [Crossref] [PubMed]
  17. J. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, “Theory of nonlinear Talbot effect,” J. Opt. Soc. Am. B 28(2), 275–280 (2011).
  18. D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
    [Crossref] [PubMed]
  19. 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(26), 5407–5411 (1999).
    [Crossref]
  20. J. M. Cowley, Diffraction Physics (Elsevier, 1995).
  21. L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278(1), 23–27 (2007).
    [Crossref]
  22. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
    [Crossref] [PubMed]
  23. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, 1976).
  24. Z. Chen, D. Liu, Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett. 37(4), 689–691 (2012).
    [Crossref] [PubMed]
  25. L. W. Zhu, X. Yin, Z. Hong, and C. S. Guo, “Reciprocal vector theory for diffractive self-imaging,” J. Opt. Soc. Am. A 25(1), 203–210 (2008).
    [Crossref] [PubMed]

2014 (1)

D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
[Crossref] [PubMed]

2013 (1)

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
[Crossref]

2012 (2)

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-Symmetric Talbot Effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

Z. Chen, D. Liu, Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett. 37(4), 689–691 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

2008 (1)

2007 (1)

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278(1), 23–27 (2007).
[Crossref]

2005 (2)

J. Azaña, “Spectral Talbot phenomena of frequency combs induced by cross-phase modulation in optical fibers,” Opt. Lett. 30(3), 227–229 (2005).
[Crossref] [PubMed]

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(5), 053902 (2005).
[Crossref] [PubMed]

2003 (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

2001 (1)

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(26), 5407–5411 (1999).
[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(1), R14–R17 (1995).
[Crossref] [PubMed]

1994 (1)

J. F. Clauser and S. Li, “Talbot-vonLau atom interferometry with cold slow potassium,” Phys. Rev. A 49(4), R2213–R2216 (1994).
[Crossref] [PubMed]

1991 (1)

1989 (2)

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–108 (1989).

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55(4), 334 (1989).
[Crossref]

1988 (1)

A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik (Stuttg.) 79, 41–45 (1988).

1986 (1)

V. V. Antyukhov, A. F. Glova, O. R. Kachurin, F. V. Lebedev, V. V. Likhanskii, A. P. Napartovich, and V. D. Pismennyi, “Effective phase locking of an array of lasers,” JETP Lett. 44, 78 (1986).

1981 (1)

1881 (1)

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

1836 (1)

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

Antyukhov, V. V.

V. V. Antyukhov, A. F. Glova, O. R. Kachurin, F. V. Lebedev, V. V. Likhanskii, A. P. Napartovich, and V. D. Pismennyi, “Effective phase locking of an array of lasers,” JETP Lett. 44, 78 (1986).

Azaña, J.

Bernabeu, E.

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278(1), 23–27 (2007).
[Crossref]

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(1), R14–R17 (1995).
[Crossref] [PubMed]

Chen, Z.

D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
[Crossref] [PubMed]

Z. Chen, D. Liu, Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett. 37(4), 689–691 (2012).
[Crossref] [PubMed]

Christodoulides, D. N.

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-Symmetric Talbot Effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

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(5), 053902 (2005).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

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(26), 5407–5411 (1999).
[Crossref]

Clauser, J. F.

J. F. Clauser and S. Li, “Talbot-vonLau atom interferometry with cold slow potassium,” Phys. Rev. A 49(4), R2213–R2216 (1994).
[Crossref] [PubMed]

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(26), 5407–5411 (1999).
[Crossref]

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(26), 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(26), 5407–5411 (1999).
[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(1), R14–R17 (1995).
[Crossref] [PubMed]

Gavrielides, A.

Glova, A. F.

V. V. Antyukhov, A. F. Glova, O. R. Kachurin, F. V. Lebedev, V. V. Likhanskii, A. P. Napartovich, and V. D. Pismennyi, “Effective phase locking of an array of lasers,” JETP Lett. 44, 78 (1986).

Guo, C. S.

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(26), 5407–5411 (1999).
[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(1), R14–R17 (1995).
[Crossref] [PubMed]

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(26), 5407–5411 (1999).
[Crossref]

Hong, Z.

Hu, X.

D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
[Crossref] [PubMed]

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(5), 053902 (2005).
[Crossref] [PubMed]

Jannson, J.

Jannson, T.

Kachurin, O. R.

V. V. Antyukhov, A. F. Glova, O. R. Kachurin, F. V. Lebedev, V. V. Likhanskii, A. P. Napartovich, and V. D. Pismennyi, “Effective phase locking of an array of lasers,” JETP Lett. 44, 78 (1986).

Kottos, T.

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-Symmetric Talbot Effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

Kovanis, V.

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-Symmetric Talbot Effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

Lebedev, F. V.

V. V. Antyukhov, A. F. Glova, O. R. Kachurin, F. V. Lebedev, V. V. Likhanskii, A. P. Napartovich, and V. D. Pismennyi, “Effective phase locking of an array of lasers,” JETP Lett. 44, 78 (1986).

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

Leger, J. R.

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55(4), 334 (1989).
[Crossref]

Li, S.

J. F. Clauser and S. Li, “Talbot-vonLau atom interferometry with cold slow potassium,” Phys. Rev. A 49(4), R2213–R2216 (1994).
[Crossref] [PubMed]

Likhanskii, V. V.

V. V. Antyukhov, A. F. Glova, O. R. Kachurin, F. V. Lebedev, V. V. Likhanskii, A. P. Napartovich, and V. D. Pismennyi, “Effective phase locking of an array of lasers,” JETP Lett. 44, 78 (1986).

Liu, D.

D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
[Crossref] [PubMed]

Z. Chen, D. Liu, Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett. 37(4), 689–691 (2012).
[Crossref] [PubMed]

Lohmann, A. W.

A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik (Stuttg.) 79, 41–45 (1988).

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(5), 053902 (2005).
[Crossref] [PubMed]

Mehuys, D.

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(5), 053902 (2005).
[Crossref] [PubMed]

Napartovich, A. P.

V. V. Antyukhov, A. F. Glova, O. R. Kachurin, F. V. Lebedev, V. V. Likhanskii, A. P. Napartovich, and V. D. Pismennyi, “Effective phase locking of an array of lasers,” JETP Lett. 44, 78 (1986).

Patorski, K.

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–108 (1989).

Peterson, P.

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(26), 5407–5411 (1999).
[Crossref]

Pismennyi, V. D.

V. V. Antyukhov, A. F. Glova, O. R. Kachurin, F. V. Lebedev, V. V. Likhanskii, A. P. Napartovich, and V. D. Pismennyi, “Effective phase locking of an array of lasers,” JETP Lett. 44, 78 (1986).

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(1), R14–R17 (1995).
[Crossref] [PubMed]

Ramezani, H.

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-Symmetric Talbot Effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

Rayleigh, L.

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

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(26), 5407–5411 (1999).
[Crossref]

Sanchez-Brea, L. M.

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278(1), 23–27 (2007).
[Crossref]

Schmiedmayer, J.

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(1), R14–R17 (1995).
[Crossref] [PubMed]

Sharma, M.

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

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(26), 5407–5411 (1999).
[Crossref]

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(5), 053902 (2005).
[Crossref] [PubMed]

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(5), 053902 (2005).
[Crossref] [PubMed]

Streifer, W.

Talbot, H. F.

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

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(1), R14–R17 (1995).
[Crossref] [PubMed]

Torcal-Milla, F. J.

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278(1), 23–27 (2007).
[Crossref]

Vitebskiy, I.

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-Symmetric Talbot Effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

Waarts, R. G.

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(1), R14–R17 (1995).
[Crossref] [PubMed]

Wei, D.

D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
[Crossref] [PubMed]

Welch, D. F.

Wen, J.

D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
[Crossref] [PubMed]

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
[Crossref]

Z. Chen, D. Liu, Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett. 37(4), 689–691 (2012).
[Crossref] [PubMed]

J. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, “Theory of nonlinear Talbot effect,” J. Opt. Soc. Am. B 28(2), 275–280 (2011).

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

Xiao, M.

D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
[Crossref] [PubMed]

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
[Crossref]

Z. Chen, D. Liu, Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett. 37(4), 689–691 (2012).
[Crossref] [PubMed]

J. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, “Theory of nonlinear Talbot effect,” J. Opt. Soc. Am. B 28(2), 275–280 (2011).

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

Yin, X.

Zhang, Y.

D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
[Crossref] [PubMed]

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
[Crossref]

Z. Chen, D. Liu, Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett. 37(4), 689–691 (2012).
[Crossref] [PubMed]

J. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, “Theory of nonlinear Talbot effect,” J. Opt. Soc. Am. B 28(2), 275–280 (2011).

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

Zhao, G.

D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
[Crossref] [PubMed]

Zhu, L. W.

Zhu, S. N.

D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
[Crossref] [PubMed]

Z. Chen, D. Liu, Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett. 37(4), 689–691 (2012).
[Crossref] [PubMed]

J. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, “Theory of nonlinear Talbot effect,” J. Opt. Soc. Am. B 28(2), 275–280 (2011).

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photonics 5(1), 83–130 (2013).
[Crossref]

Appl. Phys. Lett. (1)

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55(4), 334 (1989).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

JETP Lett. (1)

V. V. Antyukhov, A. F. Glova, O. R. Kachurin, F. V. Lebedev, V. V. Likhanskii, A. P. Napartovich, and V. D. Pismennyi, “Effective phase locking of an array of lasers,” JETP Lett. 44, 78 (1986).

Nature (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

Opt. Commun. (1)

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278(1), 23–27 (2007).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Optik (Stuttg.) (1)

A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik (Stuttg.) 79, 41–45 (1988).

Philos. Mag. (2)

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

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

Phys. Rev. A (2)

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(1), R14–R17 (1995).
[Crossref] [PubMed]

J. F. Clauser and S. Li, “Talbot-vonLau atom interferometry with cold slow potassium,” Phys. Rev. A 49(4), R2213–R2216 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

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(5), 053902 (2005).
[Crossref] [PubMed]

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-Symmetric Talbot Effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

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(26), 5407–5411 (1999).
[Crossref]

Prog. Opt. (1)

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–108 (1989).

Sci. Rep. (1)

D. Liu, Y. Zhang, J. Wen, Z. Chen, D. Wei, X. Hu, G. Zhao, S. N. Zhu, and M. Xiao, “Diffraction interference induced superfocusing in nonlinear Talbot effect,” Sci. Rep. 4, 6134 (2014).
[Crossref] [PubMed]

Other (2)

J. M. Cowley, Diffraction Physics (Elsevier, 1995).

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, 1976).

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 (4)

Fig. 1
Fig. 1 Sketches of a waveguide array structure in real space (a) and in reciprocal space (b). In our model, only the nearest and next nearest neighbors of a waveguide are considered as marked in the red polygon in (a). The red points in (b) stand for all possible ( k 1 , k 2 ) to realize Talbot self-imaging with input periods of N 1 = N 2 =3 .
Fig. 2
Fig. 2 The first row is the simulated intensity patterns with input periods of N1 = 2 and N2 = 4. (a) shows the structure of the waveguide array and the input fields. (b)-(e) are the corresponding Talbot images at z T /4 , z T /3 , z T /2 , and z T planes. The second row is the simulated patterns with input periods of N1 = N2 = 3. (f) presents the array structure and the input periods. (g)-(j) are the the corresponding Talbot images at z T /4 , z T /3 , z T /2 , and z T planes. The insets in (a) and (f) show the base vectors of the hexagonal array.
Fig. 3
Fig. 3 The first row is the simulated patterns with α 1 = α 2 =0 . (a) shows the array structure, and the input periods. (b)-(e) are the corresponding Talbot images at z T /4 , z T /3 , z T /2 , and z T planes. The second row shows the case of α 1 =1/10 and α 2 =0 . (f) is the array structure. (g)-(j) are the corresponding Talbot images at z T /4 , z T /3 , z T /2 , and z T planes. The input periods are N1 = N2 = 3. The insets in (a) and (f) show the base vectors of the square array.
Fig. 4
Fig. 4 The first row shows the simulated patterns with θ<π/3 . (a) is the array structure. (b)-(e) are the corresponding Talbot images at z T /4 , z T /3 , z T /2 , and z T planes. The second row is the calculated patterns with π/3θ<π/2 . (f) is the structure of waveguide array. (g)-(j) are the corresponding Talbot images at z T /4 , z T /3 , z T /2 , and z T planes. The input periods are N1 = N2 = 3. The insets in (a) and (f) show the base vectors of the irregular arrays.

Equations (23)

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

R = l 1 a 1 + l 2 a 2 =( l 1 , l 2 ),
i d U ( l 1 , l 2 ) dz +κ[ U ( l 1 +1, l 2 ) + U ( l 1 1, l 2 ) + U ( l 1 , l 2 +1 ) + U ( l 1 , l 2 1 ) ]+κ [ α 1 ( U ( l 1 +1, l 2 1 ) + U ( l 1 1, l 2 +1 ) )+ α 2 ( U ( l 1 +1, l 2 +1 ) + U ( l 1 1, l 2 1 ) ) ]=0,
α 1 { >1 θ< π 3 =1 θ= π 3 <1 θ> π 3 , α 2 { = α 1 θ= π 2 =0 other .
U ( l 1 , l 2 ) ( z )=exp( i R K )exp( iλz ),
K = k 1 b 1 + k 2 b 2 =( k 1 , k 2 ),
U ( l 1 , l 2 ) = U ( l 1 +α N 1 , l 2 +β N 2 ) ,
α N 1 k 1 +β N 2 k 2 =m,
k 1 = d 1 N 1 , d 1 =0,1... N 1 1 k 2 = d 2 N 2 , d 2 =0,1... N 2 1.
λ( k 1 , k 2 )=2κ[ cos( 2π k 1 )+cos( 2π k 2 )+ α 1 cos( 2π( k 1 k 2 ) )+ α 2 cos( 2π( k 1 + k 2 ) ) ].
λ( k 1 , k 2 ) λ( k 1 ' , k 2 ' ) = p q ,
λ( k 1 , k 2 )λ( 0,0 ) λ( k 1 ' , k 2 ' )λ( 0,0 ) = p q
cos( 2π k 1 )1 cos( 2π k 1 ' )1 = p q ,
cos( d 1 2π N 1 )= T d 1 ( cos( 2π N 1 ) )= i=0 [ d 1 2 ] c i ( d 1 ) ( cos( 2π N 1 ) ) d 1 2i
c i ( d 1 ) = d 1 2 ( 1 ) i ( d 1 i1 )! i!( d 1 2i )! 2 d 1 2i .
cos( 2π )=cos( 2π N 1 N 1 )= T N 1 ( cos( 2π N 1 ) )=1
2 N 1 1 ( cos( 2π N 1 ) ) N 1 +...+ c [ N 1 /2 ] N 1 cos( 2π N 1 )an=0
U ( l 1 , l 2 ) ( z )= c ( k 1 , k 2 ) exp( 2πi( l 1 k 1 + l 2 k 2 ) ) exp( i λ ( k 1 , k 2 ) z ).
I ( l 1 , l 2 ) ( z )= c 0 + c 1 cos( ( λ 1 λ 2 )z )+...+ c m cos( ( λ i λ j )z )+...,
z T =F( 2π | λ i λ j | ),
{ I ( 0,0 ) = 1 64 [ 30+24cos( 4κz )+10cos( 8κz ) ] I ( 0,1 ) = I ( 0,3 ) = I ( 1,1 ) = I ( 1,3 ) = 1 32 [ 1cos( 8κz ) ] I ( 0,2 ) = I ( 1,2 ) = 1 64 [ 68cos( 4κz )+2cos( 8κz ) ] I ( 1,0 ) = 1 64 [ 148cos( 4κz )6cos( 8κz ) ] .
{ I ( 0,0 ) = 1 81 [ 41+12cos( 6κz )+4cos( 9κz )+24cos( 3κz ) ] I ( 0,1 ) = I ( 0,2 ) = I ( 1,2 ) = I ( 1,0 ) = I ( 2,0 ) = I ( 2,1 ) = 2 81 [ 1cos( 9κz ) ] I ( 1,1 ) = I ( 2,2 ) = 1 81 [ 14+4cos( 9κz )6cos( 6κz )12cos( 3κz ) ]
{ I ( 0,0 ) = 1 81 [ 33+8cos( ( 3+6 α 1 )κz )+8cos( ( 6+3 α 1 )κz )+32cos( ( 33 α 1 )κz ) ] I ( 0,1 ) = I ( 1,0 ) = I ( 0,2 ) = I ( 2,0 ) = 1 81 [ 6+2cos( ( 3+6 α 1 )κz )4cos( ( 6+3 α 1 )κz )4cos( ( 33 α 1 )κz ) ] I ( 1,1 ) = I ( 2,2 ) = I ( 1,2 ) = I ( 2,1 ) = 1 81 [ 64cos( ( 3+6 α 1 )κz )+2cos( ( 6+3 α 1 )κz )4cos( ( 33 α 1 )κz ) ]
{ I ( 0,0 ) = 1 81 [ 25+8cos( ( 3+3 α 1 )κz )+4cos( 6κz )+4cos( ( 6+3 α 1 )κz ) +16cos( ( 33 α 1 )κz )+16cos( 3κz )+8cos( 3 α 1 κz ) ] I ( 0,1 ) = I ( 1,0 ) = I ( 0,2 ) = I ( 2,0 ) = 1 81 [ 2cos( ( 3+3 α 1 )κz )2cos( 6κz )2cos( ( 6+3 α 1 )κz ) 2cos( ( 33 α 1 )κz )2cos( 3κz )+2cos( 3 α 1 κz )+4 ] I ( 1,1 ) = I ( 2,2 ) = 1 81 [ 104cos( ( 3+3 α 1 )κz )2cos( 6κz )+4cos( ( 6+3 α 1 )κz ) +4cos( ( 33 α 1 )κz )8cos( 3κz )4cos( 3 α 1 κz ) ] I ( 1,2 ) = I ( 2,1 ) = 1 81 [ 104cos( ( 3+3 α 1 )κz )+4cos( 6κz )2cos( ( 6+3 α 1 )κz ) 8cos( ( 33 α 1 )κz )+4cos( 3κz )4cos( 3 α 1 κz ) ]

Metrics