Abstract

We demonstrate the fractional second-harmonic (SH) Talbot effect in a hexagonally poled LiTaO3 crystal. We carefully record the SH Talbot images at 1/2, 1/3, and 1/4 Talbot lengths, which are well matched with the simulated images by using the modified Rayleigh–Sommerfeld diffraction formula. A simplified model with a hexagonal array is adopted in the simulations. Also, we use a modified reciprocal vector theory to analytically explain the evolution of the SH array at fractional Talbot lengths. Our results show that the images are sensitive to the duty circle and the background of the array.

© 2012 Optical Society of America

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X. Song, H. Wang, J. Xiong, K. Wang, X. Zhang, K. Luo, and L. Wu, Phys. Rev. Lett. 107, 033902 (2011).
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J. M. Wen, S. Du, H. Chen, and M. Xiao, Appl. Phys. Lett. 98, 081108 (2011).
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Y. Zhang, J. M. Wen, S. N. Zhu, and M. Xiao, Phys. Rev. Lett. 104, 183901 (2010).
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K. H. Luo, J. M. Wen, X. H. Chen, Q. Liu, M. Xiao, and L. A. Wu, Phys. Rev. A 80, 043820 (2009).
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Chen, H.

J. M. Wen, S. Du, H. Chen, and M. Xiao, Appl. Phys. Lett. 98, 081108 (2011).
[Crossref]

Chen, X. H.

K. H. Luo, J. M. Wen, X. H. Chen, Q. Liu, M. Xiao, and L. A. Wu, Phys. Rev. A 80, 043820 (2009).
[Crossref]

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B. J. McMorran and A. D. Cronin, New J. Phys. 11, 033021 (2009).
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[Crossref]

Du, S.

J. M. Wen, S. Du, H. Chen, and M. Xiao, Appl. Phys. Lett. 98, 081108 (2011).
[Crossref]

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Gronzweig, and C. David, Nat. Mater. 7, 134 (2008).
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[Crossref]

Guo, C.-S.

Hong, Z.-P.

Huang, X.

Iwanow, R.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Gronzweig, and C. David, Nat. Mater. 7, 134 (2008).
[Crossref]

Leger, J.

Liu, Q.

K. H. Luo, J. M. Wen, X. H. Chen, Q. Liu, M. Xiao, and L. A. Wu, Phys. Rev. A 80, 043820 (2009).
[Crossref]

Lu, Z.

Luo, K.

X. Song, H. Wang, J. Xiong, K. Wang, X. Zhang, K. Luo, and L. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Luo, K. H.

K. H. Luo, J. M. Wen, X. H. Chen, Q. Liu, M. Xiao, and L. A. Wu, Phys. Rev. A 80, 043820 (2009).
[Crossref]

May-Arrioja, D. A.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

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B. J. McMorran and A. D. Cronin, New J. Phys. 11, 033021 (2009).
[Crossref]

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S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
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K. Patorski, Prog. Opt. 27, 1 (1989).
[Crossref]

Peier, P.

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F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Gronzweig, and C. David, Nat. Mater. 7, 134 (2008).
[Crossref]

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[Crossref]

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X. Song, H. Wang, J. Xiong, K. Wang, X. Zhang, K. Luo, and L. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Wen, J. M.

J. M. Wen, S. Du, H. Chen, and M. Xiao, Appl. Phys. Lett. 98, 081108 (2011).
[Crossref]

J. M. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, J. Opt. Soc. Am. B 28, 275 (2011).
[Crossref]

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

K. H. Luo, J. M. Wen, X. H. Chen, Q. Liu, M. Xiao, and L. A. Wu, Phys. Rev. A 80, 043820 (2009).
[Crossref]

Wu, L.

X. Song, H. Wang, J. Xiong, K. Wang, X. Zhang, K. Luo, and L. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Wu, L. A.

K. H. Luo, J. M. Wen, X. H. Chen, Q. Liu, M. Xiao, and L. A. Wu, Phys. Rev. A 80, 043820 (2009).
[Crossref]

Xiao, M.

J. M. Wen, S. Du, H. Chen, and M. Xiao, Appl. Phys. Lett. 98, 081108 (2011).
[Crossref]

J. M. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, J. Opt. Soc. Am. B 28, 275 (2011).
[Crossref]

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

K. H. Luo, J. M. Wen, X. H. Chen, Q. Liu, M. Xiao, and L. A. Wu, Phys. Rev. A 80, 043820 (2009).
[Crossref]

Xiong, J.

X. Song, H. Wang, J. Xiong, K. Wang, X. Zhang, K. Luo, and L. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Yin, X.

Zhang, X.

X. Song, H. Wang, J. Xiong, K. Wang, X. Zhang, K. Luo, and L. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

Zhang, Y.

J. M. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, J. Opt. Soc. Am. B 28, 275 (2011).
[Crossref]

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

Zhao, W. S.

Zhou, C.

Zhu, L.-W.

Zhu, S.

S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
[Crossref]

Zhu, S. N.

J. M. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, J. Opt. Soc. Am. B 28, 275 (2011).
[Crossref]

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

Zhu, Y.

S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. M. Wen, S. Du, H. Chen, and M. Xiao, Appl. Phys. Lett. 98, 081108 (2011).
[Crossref]

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

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

Nat. Mater. (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Gronzweig, and C. David, Nat. Mater. 7, 134 (2008).
[Crossref]

New J. Phys. (1)

B. J. McMorran and A. D. Cronin, New J. Phys. 11, 033021 (2009).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

K. H. Luo, J. M. Wen, X. H. Chen, Q. Liu, M. Xiao, and L. A. Wu, Phys. Rev. A 80, 043820 (2009).
[Crossref]

Phys. Rev. Lett. (3)

X. Song, H. Wang, J. Xiong, K. Wang, X. Zhang, K. Luo, and L. Wu, Phys. Rev. Lett. 107, 033902 (2011).
[Crossref]

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

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

Prog. Opt. (1)

K. Patorski, Prog. Opt. 27, 1 (1989).
[Crossref]

Science (1)

S. Zhu, Y. Zhu, and N. Ming, Science 278, 843 (1997).
[Crossref]

Other (1)

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

Supplementary Material (1)

» Media 1: AVI (4002 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

The SEM image of the hexagonally poled LiTaO 3 crystal.

Fig. 2.
Fig. 2.

Experimental setup.

Fig. 3.
Fig. 3.

(a) SH pattern at few micrometers away from the sample output surface. (b) Recorded SH self-imaging at the first SH Talbot plane. (c) Modeled object used in our simulations. (d) Simulated mage at the first SH Talbot plane.

Fig. 4.
Fig. 4.

Recorded fractional self-images at 1 / N SH Talbot lengths in CCD camera (a)  N = 2 , (b)  N = 3 , (c)  N = 4 ) and (d)–(f) their corresponding numerical simulations, respectively (Media 1).

Equations (1)

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U ( r 1 ) = 2 i λ Σ U i ( r ) t ( r ) exp ( i k | r 01 | ) | r 01 | cos ( n , r 01 ) d s ,

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