Abstract

We report on an experimental generation of Airy beams by four-wave mixing (FWM) in atomic vapor cells. This is achieved by using a non-degenerate FWM process, which occurs with two Gaussian pump beams and one Airy signal beam in hot Rubidium vapor. After satisfying the phase matching condition, a FWM field with the profile of an Airy beam can be generated. In our experiment, the diffraction-free and self-healing behaviors of the generated FWM beam are examined. The results shown that the generated FWM beam is an Airy beam. The nonlinear generation process can be extended to other configurations in the atomic medium, which will be useful for manipulation and application of Airy beams in atomic systems.

© 2014 Optical Society of America

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    [CrossRef]
  2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  3. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. N. K. Efremidis and D. N. Christodoulides, Opt. Lett. 35, 4045 (2010).
    [CrossRef]
  9. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
    [CrossRef]
  10. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2014 (1)

C. Hang and G. Huang, Phys. Rev. A 89, 013821 (2014).
[CrossRef]

2013 (2)

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, Nature 494, 331 (2013).
[CrossRef]

Y.-Y. Li, L. Li, Y.-X. Lu, X.-X. Zhao, K.-W. Xu, Y.-Q. Zhang, and Y.-P. Zhang, Opt. Express 21, 8311 (2013).
[CrossRef]

2012 (4)

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

F. Zhuang, J. Shen, X. Du, and D. Zhao, Opt. Lett. 37, 3054 (2012).
[CrossRef]

D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Opt. Lett. 37, 3270 (2012).
[CrossRef]

D.-S. Ding, Z.-Y. Zhou, W. Huang, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Phys. Rev. A 86, 033803 (2012).
[CrossRef]

2011 (3)

2010 (8)

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581 (2010).
[CrossRef]

A. Salandrino and D. N. Christodoulides, Opt. Lett. 35, 2082 (2010).
[CrossRef]

Y. Hu, S. Huang, P. Zhang, C. Lou, J. Xu, and Z. Chen, Opt. Lett. 35, 3952 (2010).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Opt. Lett. 35, 4045 (2010).
[CrossRef]

I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
[CrossRef]

S. Jia, J. Lee, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

2009 (2)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

2008 (4)

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Q.-F. Chen, B.-S. Shi, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 78, 053810 (2008).
[CrossRef]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef]

Q.-F. Chen, B.-S. Shi, M. Feng, Y.-S. Zhang, and G.-C. Guo, Opt. Express 16, 21708 (2008).
[CrossRef]

2007 (2)

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

2003 (1)

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef]

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

André, A.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef]

Arie, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, Nature 494, 331 (2013).
[CrossRef]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
[CrossRef]

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581 (2010).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Broky, J.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Chen, Q.-F.

Q.-F. Chen, B.-S. Shi, M. Feng, Y.-S. Zhang, and G.-C. Guo, Opt. Express 16, 21708 (2008).
[CrossRef]

Q.-F. Chen, B.-S. Shi, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 78, 053810 (2008).
[CrossRef]

Chen, Z.

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Christodoulides, D. N.

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Ding, D.-S.

D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Opt. Lett. 37, 3270 (2012).
[CrossRef]

D.-S. Ding, Z.-Y. Zhou, W. Huang, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Phys. Rev. A 86, 033803 (2012).
[CrossRef]

Dogariu, A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dolev, I.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581 (2010).
[CrossRef]

I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
[CrossRef]

Du, X.

Efremidis, N. K.

Eisaman, M. D.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef]

Ellenbogen, T.

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581 (2010).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Feng, M.

Fleischer, J. W.

S. Jia, J. Lee, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef]

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Gorshkov, A. V.

N. B. Phillips, A. V. Gorshkov, and I. Novikova, Phys. Rev. A 83, 063823 (2011).
[CrossRef]

Gover, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, Nature 494, 331 (2013).
[CrossRef]

Guo, G.-C.

D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Opt. Lett. 37, 3270 (2012).
[CrossRef]

D.-S. Ding, Z.-Y. Zhou, W. Huang, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Phys. Rev. A 86, 033803 (2012).
[CrossRef]

Q.-F. Chen, B.-S. Shi, M. Feng, Y.-S. Zhang, and G.-C. Guo, Opt. Express 16, 21708 (2008).
[CrossRef]

Q.-F. Chen, B.-S. Shi, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 78, 053810 (2008).
[CrossRef]

Hang, C.

C. Hang and G. Huang, Phys. Rev. A 89, 013821 (2014).
[CrossRef]

Hu, Y.

Huang, G.

C. Hang and G. Huang, Phys. Rev. A 89, 013821 (2014).
[CrossRef]

Huang, S.

Huang, W.

D.-S. Ding, Z.-Y. Zhou, W. Huang, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Phys. Rev. A 86, 033803 (2012).
[CrossRef]

Jia, S.

S. Jia, J. Lee, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef]

Kaminer, I.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Lee, J.

S. Jia, J. Lee, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef]

Lereah, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, Nature 494, 331 (2013).
[CrossRef]

Li, L.

Li, Y.-Y.

Lilach, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, Nature 494, 331 (2013).
[CrossRef]

Liu, S.

Lou, C.

Lu, Y.-X.

Lukin, M. D.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef]

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Novikova, I.

N. B. Phillips, A. V. Gorshkov, and I. Novikova, Phys. Rev. A 83, 063823 (2011).
[CrossRef]

Papazoglou, D. G.

D. G. Papazoglou, N. K. Efremidis, and D. N. Christodoulides, Opt. Lett. 36, 1842 (2011).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Phillips, D. F.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef]

Phillips, N. B.

N. B. Phillips, A. V. Gorshkov, and I. Novikova, Phys. Rev. A 83, 063823 (2011).
[CrossRef]

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Salandrino, A.

Segev, M.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

Shapira, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

Shen, J.

Shi, B.-S.

D.-S. Ding, Z.-Y. Zhou, W. Huang, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Phys. Rev. A 86, 033803 (2012).
[CrossRef]

D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Opt. Lett. 37, 3270 (2012).
[CrossRef]

Q.-F. Chen, B.-S. Shi, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 78, 053810 (2008).
[CrossRef]

Q.-F. Chen, B.-S. Shi, M. Feng, Y.-S. Zhang, and G.-C. Guo, Opt. Express 16, 21708 (2008).
[CrossRef]

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Song, D.

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

van der Wal, C. H.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef]

Voloch-Bloch, N.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, Nature 494, 331 (2013).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Walsworth, R. L.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

Xu, J.

Xu, K.-W.

Ye, Z.

Zhang, P.

Zhang, Y.-P.

Zhang, Y.-Q.

Zhang, Y.-S.

Q.-F. Chen, B.-S. Shi, M. Feng, Y.-S. Zhang, and G.-C. Guo, Opt. Express 16, 21708 (2008).
[CrossRef]

Q.-F. Chen, B.-S. Shi, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 78, 053810 (2008).
[CrossRef]

Zhao, D.

Zhao, J.

Zhao, X.-X.

Zhou, Z.-Y.

D.-S. Ding, Z.-Y. Zhou, W. Huang, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Phys. Rev. A 86, 033803 (2012).
[CrossRef]

D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Opt. Lett. 37, 3270 (2012).
[CrossRef]

Zhuang, F.

Zibrov, A. S.

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef]

Zou, X.-B.

D.-S. Ding, Z.-Y. Zhou, W. Huang, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Phys. Rev. A 86, 033803 (2012).
[CrossRef]

D.-S. Ding, Z.-Y. Zhou, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Opt. Lett. 37, 3270 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
[CrossRef]

Nat. Photonics (3)

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Nature (1)

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, Nature 494, 331 (2013).
[CrossRef]

Opt. Express (3)

Opt. Lett. (9)

Phys. Rev. A (4)

N. B. Phillips, A. V. Gorshkov, and I. Novikova, Phys. Rev. A 83, 063823 (2011).
[CrossRef]

D.-S. Ding, Z.-Y. Zhou, W. Huang, B.-S. Shi, X.-B. Zou, and G.-C. Guo, Phys. Rev. A 86, 033803 (2012).
[CrossRef]

C. Hang and G. Huang, Phys. Rev. A 89, 013821 (2014).
[CrossRef]

Q.-F. Chen, B.-S. Shi, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 78, 053810 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

S. Jia, J. Lee, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Science (2)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of four wave mixing in the non-degenerate geometry. The two strong pump beams with frequencies ωF and ωB counterpropagate along the z axis. The signal beam crossed with the two pump beams at a small angle. Under the phase matching condition, the FWM beam can be generated which propagates nearly in the opposite direction of the signal beam. (b) Four-level double Λ system, coupled with forward and backward pump beams, the ωS and ωA denote the signal field and generated FWM beam, respectively.

Fig. 2.
Fig. 2.

Experimental setup, with abbreviations: SAS, saturated absorption spectroscopy; PBS, polarizing beam splitter; SLM, spatial light modulator; and CCD, charge-coupled device.

Fig. 3.
Fig. 3.

Recorded beams’ profile with a CCD. (a) The Airy beam generated by SLM. (b) The Airy beam generated by FWM. The right part of the image is the profile of leaked backward pump beam.

Fig. 4.
Fig. 4.

Recorded propagation dynamics of the FWM beam as a function of distance. (a) z=45cm, (b) z=55cm, and (c) z=65cm. (d), (e), and (f) are cross sections of the beam intensity in xz plane at corresponding distances.

Fig. 5.
Fig. 5.

Self-healing of FWM beam when its main lobe is blocked. Observed intensity profile at (a) z=45cm, (b) z=55cm, (c) z=65cm, and (d) z=75cm, where z is the distance between the center of the Rb cell and the CCD.

Equations (1)

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PA=6ε0EFEBES*.

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