Abstract

In this Letter, we demonstrate the general propagation dynamics of an Airy beam (AiB) carrying unit phase singularity, i.e., optical vortices (OVs). For the OV with a unit charge, theoretical analysis indicates that the OV carried by the AiB will propagate along the parabolic trajectory with an acceleration velocity twice as fast as conventional AiBs before a critical position. Thereafter, the AiB main lobe destroyed by OV will be reconstructed and the phase singularity will reappear in the middle of the AiB profile.

© 2010 Optical Society of America

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  1. M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
    [CrossRef]
  2. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef] [PubMed]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  4. I. M. Besieris and A. M. Shaarawi, Opt. Lett. 32, 2447 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
    [CrossRef] [PubMed]
  8. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
    [CrossRef] [PubMed]
  9. H. I. Sztul and R. R. Alfano, Opt. Express 16, 9411 (2008).
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  10. H. T. Dai, X. W. Sun, D. Luo, and Y. J. Liu, Opt. Express 17, 19365 (2009).
    [CrossRef] [PubMed]
  11. D. M. Cottrell, J. A. Davis, and T. M. Hazard, Opt. Lett. 34, 2634 (2009).
    [CrossRef] [PubMed]
  12. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
  14. Y. L. Gu and G. Gbur, Opt. Lett. 35, 3456 (2010).
    [CrossRef] [PubMed]
  15. J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
    [CrossRef]
  16. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
    [CrossRef] [PubMed]
  17. P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
    [CrossRef] [PubMed]
  18. P. Saari, Opt. Express 16, 10303 (2008).
    [CrossRef] [PubMed]
  19. A. Chong, W. H. Reninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
    [CrossRef]
  20. A. Salandrino and D. N. Christodoulides, Opt. Lett. 35, 2082 (2010).
    [CrossRef] [PubMed]
  21. B. Z. Zhang and D. M. Zhao, Opt. Express 18, 12818 (2010).
    [CrossRef] [PubMed]
  22. W. D. Furlan, F. Gimenez, A. Calatayud, and J. A. Monsoriu, Opt. Express 17, 21891 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
  24. M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
    [CrossRef]

2010 (4)

2009 (8)

J. E. Morris, M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Opt. Express 17, 13236 (2009).
[CrossRef] [PubMed]

D. M. Cottrell, J. A. Davis, and T. M. Hazard, Opt. Lett. 34, 2634 (2009).
[CrossRef] [PubMed]

H. T. Dai, X. W. Sun, D. Luo, and Y. J. Liu, Opt. Express 17, 19365 (2009).
[CrossRef] [PubMed]

W. D. Furlan, F. Gimenez, A. Calatayud, and J. A. Monsoriu, Opt. Express 17, 21891 (2009).
[CrossRef] [PubMed]

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

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef] [PubMed]

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

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[CrossRef]

2008 (6)

2007 (4)

1993 (1)

G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

1979 (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Alfano, R. R.

Arie, A.

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

Balazs, N. L.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Bandres, M. A.

Baumgartl, J.

J. E. Morris, M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Opt. Express 17, 13236 (2009).
[CrossRef] [PubMed]

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[CrossRef]

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

Berry, M. V.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Besieris, I. M.

I. M. Besieris and A. M. Shaarawi, Phys. Rev. E 78, 046605 (2008).
[CrossRef]

I. M. Besieris and A. M. Shaarawi, Opt. Lett. 32, 2447 (2007).
[CrossRef] [PubMed]

Broky, J.

Calatayud, A.

Chong, A.

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

Christodoulides, D. N.

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

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

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

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

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef] [PubMed]

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

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

Cizmar, T.

J. E. Morris, M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Opt. Express 17, 13236 (2009).
[CrossRef] [PubMed]

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[CrossRef]

Cottrell, D. M.

Dai, H. T.

Davis, J. A.

Dholakia, K.

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[CrossRef]

J. E. Morris, M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Opt. Express 17, 13236 (2009).
[CrossRef] [PubMed]

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

Dogariu, A.

Ellenbogen, T.

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

Furlan, W. D.

Ganany-Padowicz, A.

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

Gbur, G.

Gimenez, F.

Gu, Y. L.

Gutierrez-Vega, J. C.

Hazard, T. M.

Indebetouw, G.

G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

Kolesik, M.

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef] [PubMed]

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

Liu, Y. J.

Luo, D.

Mazilu, M.

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[CrossRef]

J. E. Morris, M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Opt. Express 17, 13236 (2009).
[CrossRef] [PubMed]

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

Moloney, J.

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef] [PubMed]

Moloney, J. V.

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

Monsoriu, J. A.

Morris, J. E.

Polynkin, P.

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

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef] [PubMed]

Reninger, W. H.

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

Saari, P.

Salandrino, A.

Shaarawi, A. M.

I. M. Besieris and A. M. Shaarawi, Phys. Rev. E 78, 046605 (2008).
[CrossRef]

I. M. Besieris and A. M. Shaarawi, Opt. Lett. 32, 2447 (2007).
[CrossRef] [PubMed]

Siviloglou, G. A.

Sun, X. W.

Sztul, H. I.

Voloch-Bloch, N.

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

Wise, F. W.

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

Zhang, B. Z.

Zhao, D. M.

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

J. Mod. Opt. (1)

G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

Nat. Photon. (3)

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

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

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

Opt. Express (8)

Opt. Lett. (6)

Phys. Rev. E (1)

I. M. Besieris and A. M. Shaarawi, Phys. Rev. E 78, 046605 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef] [PubMed]

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

Proc. SPIE (1)

M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[CrossRef]

Science (1)

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

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Figures (4)

Fig. 1
Fig. 1

Intensity profile of the OV carried by the AiBs located at (a) position z = 34.38 cm and the three individual components (b) I 1 , (c) I 2 , and (d) I 3 . The beam parameters are all set as a = 0.05 , x 0 = y 0 = 100 μm , and x d = y d = 300 μm with a 633 nm laser illuminating.

Fig. 2
Fig. 2

Superposition between the OV and the AiB main lobe at the location close to critical distance z s . (a) z = 0.7 z s , (b) z = 0.9 z s , (c) z = 1.1 z s , and (d) z = 1.3 z s .

Fig. 3
Fig. 3

Propagation of AiBs with OV after critical distance z s : (a)–(d) show the intensity distribution located at 1 z s , 1.7 z s , 2.3 z s , and 3 z s , respectively; (e)–(h) show the corresponding phase distribution—the phase singularity positions have been highlighted by blue arrows.

Fig. 4
Fig. 4

Trajectory of the main lobe peak of AiBs with (red open circles) and without (blue stars) OV after the critical position z s .

Equations (8)

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u ( x , y , z = 0 ) = Ai ( x / x 0 ) Ai ( y / y 0 ) exp [ a ( x / x 0 + y / y 0 ) ] × [ ( x x d ) + i ( y y d ) ] l ,
u ( x , y , z ) = i k 2 π z exp ( i k 2 z ( ( x 1 x ) 2 + ( y 1 y ) 2 ) ) u ( x 1 , y 1 , z = 0 ) d x 1 d y 1 = Fre T { u ( x , y , z ) } .
u ( x , y , z ) = Fre T { Ai ( x / x 0 ) Ai ( y / y 0 ) exp [ a ( x / x 0 + y / y 0 ) ] × [ ( x x d ) ± i ( y y d ) ] } .
u ( x , y , z ) = 1 k x 0 y 0 exp ( p ( x , y , z ) ) ( I 1 + I 2 + I 3 ) ,
p ( x , y , z ) = a ( x x 0 + y y 0 ) 2 a ( x m ( z ) x 0 + y m ( z ) y 0 ) + i [ z 2 k ( x x 0 3 + y y 0 3 ) + a 2 z 2 k ( 1 x 0 2 + 1 y 0 2 ) z 3 12 k 3 ( 1 x 0 6 + 1 y 0 6 ) ] ,
I 1 = k x 0 y 0 Ai ( q ( x ) ) Ai ( q ( y ) ) ( ( x x d 2 x m ( z ) ) ± i ( y y d 2 y m ( z ) ) ) ,
I 2 = x 0 z Ai ( q ( x ) ) ( A i ( q ( y ) ) + a Ai ( q ( y ) ) ) ,
I 3 = i y 0 z Ai ( q ( y ) ) ( Ai ( q ( x ) ) + a Ai ( q ( x ) ) ) ,

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