Abstract

In a numerical investigation, we demonstrate the existence and curious evolution of vortices in a ladder-type three-level nonlinear atomic vapor with linear, cubic, and quintic susceptibilities considered simultaneously with the dressing effect. We find that the number of beads and topological charge of the incident beam, as well as its size, greatly affect the formation and evolution of vortices. To determine the number of induced vortices and the corresponding rotation direction, we give common rules associated with the initial conditions coming from various incident beams.

© 2012 Optical Society of America

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References

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  1. R. Voogd, M. Singh, and J. Braat, Proc. SPIE 5380, 387 (2004).
    [CrossRef]
  2. V. Tikhonenko, J. Christou, and B. Luther-Daves, J. Opt. Soc. Am. B 12, 2046 (1995).
    [CrossRef]
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    [CrossRef]
  4. D. Grier, Nat. Photonics 424, 810 (2003).
    [CrossRef]
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    [CrossRef]
  6. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
    [CrossRef]
  7. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
    [CrossRef]
  8. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
    [CrossRef]
  9. S. Skupin, M. Saffman, and W. Królikowski, Phys. Rev. Lett. 98, 263902 (2007).
    [CrossRef]
  10. D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, Phys. Rev. Lett. 97, 073904 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. Y. Zhang and M. Xiao, Multi-Wave Mixing Processes: From Ultrafast Polarization Beats to Electromagnetically Induced Transparency (HEP & Springer, 2009).
  14. Y. Zhang, S. Skupin, F. Maucher, A. G. Pour, K. Lu, and W. Królikowski, Opt. Express 18, 27846 (2010).
    [CrossRef]
  15. G. Molina-Terriza and L. Torner, J. Opt. Soc. Am. B 17, 1197 (2000).
    [CrossRef]
  16. Y. J. He, H. Z. Wang, and B. A. Malomed, Opt. Express 15, 17502 (2007).
    [CrossRef]
  17. D. A. Steck, “Sodium D line data,” http://steck.us/alkalidata (2000).
  18. S. Liu, C. Ma, Y. Zhang, and K. Lu, Opt. Commun. 285, 1934 (2012).
    [CrossRef]
  19. J. Masajada and B. Dubik, Opt. Commun. 198, 21 (2001).
    [CrossRef]
  20. Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, Phys. Rev. Lett. 78, 2948 (1997).
    [CrossRef]
  21. S. Sang, Z. Wu, J. Sun, H. Lan, Y. Zhang, X. Zhang, and Y. Zhang, IEEE Photon. J. 4, 1973 (2012).

2012 (2)

S. Liu, C. Ma, Y. Zhang, and K. Lu, Opt. Commun. 285, 1934 (2012).
[CrossRef]

S. Sang, Z. Wu, J. Sun, H. Lan, Y. Zhang, X. Zhang, and Y. Zhang, IEEE Photon. J. 4, 1973 (2012).

2010 (1)

2008 (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

2007 (2)

S. Skupin, M. Saffman, and W. Królikowski, Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef]

Y. J. He, H. Z. Wang, and B. A. Malomed, Opt. Express 15, 17502 (2007).
[CrossRef]

2006 (2)

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef]

2005 (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

2004 (2)

R. Voogd, M. Singh, and J. Braat, Proc. SPIE 5380, 387 (2004).
[CrossRef]

K. Crabtree, J. A. Davis, and I. Moreno, Appl. Opt. 43, 1360 (2004).
[CrossRef]

2003 (2)

D. Grier, Nat. Photonics 424, 810 (2003).
[CrossRef]

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. Lett. 90, 120403 (2003).
[CrossRef]

2001 (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

J. Masajada and B. Dubik, Opt. Commun. 198, 21 (2001).
[CrossRef]

2000 (1)

1997 (2)

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

1995 (1)

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Braat, J.

R. Voogd, M. Singh, and J. Braat, Proc. SPIE 5380, 387 (2004).
[CrossRef]

Chen, Z.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Christou, J.

Crabtree, K.

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

Davis, J. A.

Desyatnikov, A. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

Dubik, B.

J. Masajada and B. Dubik, Opt. Commun. 198, 21 (2001).
[CrossRef]

Frantzeskakis, D. J.

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. Lett. 90, 120403 (2003).
[CrossRef]

Grier, D.

D. Grier, Nat. Photonics 424, 810 (2003).
[CrossRef]

He, Y. J.

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Kartashov, Y. V.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

Kevrekidis, P. G.

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. Lett. 90, 120403 (2003).
[CrossRef]

Kivshar, Y. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. Lett. 90, 120403 (2003).
[CrossRef]

Królikowski, W.

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Lan, H.

S. Sang, Z. Wu, J. Sun, H. Lan, Y. Zhang, X. Zhang, and Y. Zhang, IEEE Photon. J. 4, 1973 (2012).

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

Liu, S.

S. Liu, C. Ma, Y. Zhang, and K. Lu, Opt. Commun. 285, 1934 (2012).
[CrossRef]

Lu, K.

Luther-Daves, B.

Ma, C.

S. Liu, C. Ma, Y. Zhang, and K. Lu, Opt. Commun. 285, 1934 (2012).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Maker, P. D.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Malomed, B. A.

Y. J. He, H. Z. Wang, and B. A. Malomed, Opt. Express 15, 17502 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. Lett. 90, 120403 (2003).
[CrossRef]

Masajada, J.

J. Masajada and B. Dubik, Opt. Commun. 198, 21 (2001).
[CrossRef]

Maucher, F.

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

Michinel, H.

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

Molina-Terriza, G.

Moreno, I.

Muller, R. E.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Paz-Alonso, M. J.

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef]

Pérez-García, V. M.

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef]

Pour, A. G.

Saffman, M.

S. Skupin, M. Saffman, and W. Królikowski, Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef]

Sang, S.

S. Sang, Z. Wu, J. Sun, H. Lan, Y. Zhang, X. Zhang, and Y. Zhang, IEEE Photon. J. 4, 1973 (2012).

Sasada, H.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Shimizu, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Singh, M.

R. Voogd, M. Singh, and J. Braat, Proc. SPIE 5380, 387 (2004).
[CrossRef]

Skupin, S.

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Sun, J.

S. Sang, Z. Wu, J. Sun, H. Lan, Y. Zhang, X. Zhang, and Y. Zhang, IEEE Photon. J. 4, 1973 (2012).

Theocharis, G.

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. Lett. 90, 120403 (2003).
[CrossRef]

Tikhonenko, V.

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Torner, L.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

G. Molina-Terriza and L. Torner, J. Opt. Soc. Am. B 17, 1197 (2000).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Voogd, R.

R. Voogd, M. Singh, and J. Braat, Proc. SPIE 5380, 387 (2004).
[CrossRef]

Wang, H. Z.

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Wilson, D. W.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Wu, Z.

S. Sang, Z. Wu, J. Sun, H. Lan, Y. Zhang, X. Zhang, and Y. Zhang, IEEE Photon. J. 4, 1973 (2012).

Xiao, M.

Y. Zhang and M. Xiao, Multi-Wave Mixing Processes: From Ultrafast Polarization Beats to Electromagnetically Induced Transparency (HEP & Springer, 2009).

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Zhang, X.

S. Sang, Z. Wu, J. Sun, H. Lan, Y. Zhang, X. Zhang, and Y. Zhang, IEEE Photon. J. 4, 1973 (2012).

Zhang, Y.

S. Sang, Z. Wu, J. Sun, H. Lan, Y. Zhang, X. Zhang, and Y. Zhang, IEEE Photon. J. 4, 1973 (2012).

S. Sang, Z. Wu, J. Sun, H. Lan, Y. Zhang, X. Zhang, and Y. Zhang, IEEE Photon. J. 4, 1973 (2012).

S. Liu, C. Ma, Y. Zhang, and K. Lu, Opt. Commun. 285, 1934 (2012).
[CrossRef]

Y. Zhang, S. Skupin, F. Maucher, A. G. Pour, K. Lu, and W. Królikowski, Opt. Express 18, 27846 (2010).
[CrossRef]

Y. Zhang and M. Xiao, Multi-Wave Mixing Processes: From Ultrafast Polarization Beats to Electromagnetically Induced Transparency (HEP & Springer, 2009).

Appl. Opt. (1)

IEEE Photon. J. (1)

S. Sang, Z. Wu, J. Sun, H. Lan, Y. Zhang, X. Zhang, and Y. Zhang, IEEE Photon. J. 4, 1973 (2012).

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

Nat. Photonics (1)

D. Grier, Nat. Photonics 424, 810 (2003).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Opt. Commun. (2)

S. Liu, C. Ma, Y. Zhang, and K. Lu, Opt. Commun. 285, 1934 (2012).
[CrossRef]

J. Masajada and B. Dubik, Opt. Commun. 198, 21 (2001).
[CrossRef]

Opt. Express (2)

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Phys. Rev. Lett. (6)

S. Skupin, M. Saffman, and W. Królikowski, Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, Phys. Rev. Lett. 97, 073904 (2006).
[CrossRef]

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. Lett. 90, 120403 (2003).
[CrossRef]

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef]

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, Phys. Rev. Lett. 78, 4713 (1997).
[CrossRef]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, Phys. Rev. Lett. 78, 2948 (1997).
[CrossRef]

Proc. SPIE (1)

R. Voogd, M. Singh, and J. Braat, Proc. SPIE 5380, 387 (2004).
[CrossRef]

Prog. Opt. (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

Other (2)

Y. Zhang and M. Xiao, Multi-Wave Mixing Processes: From Ultrafast Polarization Beats to Electromagnetically Induced Transparency (HEP & Springer, 2009).

D. A. Steck, “Sodium D line data,” http://steck.us/alkalidata (2000).

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Figures (4)

Fig. 1.
Fig. 1.

(a), (b) Evolution of vortex incidences for several propagation distances and for l = 0 and l = 1 , respectively; (c), (d) output intensities (left panels) and phases (right panels) of vortices with l = 3 and l = 6 , respectively. The color bars and physical scales of the transverse plane shown here are the same in all other figures.

Fig. 2.
Fig. 2.

(a)–(f) Evolution outputs at z = 15 cm , from a crescent input ( n = 0.5 ) corresponding to l = 5.5 , 1.5 , 0.5 , 0.5, 1.5, and 5.5, respectively. The top and bottom insets present the input and output phases, respectively.

Fig. 3.
Fig. 3.

Evolutions of azimuthon incidences with n = 2 and B = 0.5 for (a)  l = 6 , (b)  2 , (c)  1 , (d) 1, (e) 2, and (f) 6, respectively. The figure setup is as in Fig. 2.

Fig. 4.
Fig. 4.

(a)–(c) Evolution of an azimuthon with l = 9 , n = 3 , B = 0.5 , r 0 = 40 μm at different propagation distances. (d)–(f) azimuthons with r 0 = 30 μm at 30 cm with ( l = 9 , n = 3 ), ( l = 9 , n = 2 ), and ( l = 4 , n = 2 ), respectively. The top row is the intensities; the bottom row is the phases.

Tables (1)

Tables Icon

Table 1. Properties of the Induced Vortices from Necklace and Azimuthon Incidences with Different l and n Values

Equations (2)

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

i z ψ + 1 i β 2 k 2 ψ + k 2 χ ψ = 0 ,
ψ ( z = 0 , r , θ ) = A sech [ ( r R 0 ) / r 0 ] × [ cos ( n θ ) + i B sin ( n θ ) ] exp ( i l θ ) ,

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