Abstract

We study the propagation properties of an Airy beam through a four-level electromagnetic induced transparency (EIT) atomic vapor. The analytical expression for the Airy beam passing through the ABCD optical system of the EIT vapor is deduced and employed to analyze the propagation characteristics of the beam. It is shown that both the deflection position and the intensity of the Airy beam can be modulated by the Rabi frequency of the control light. Such a tunable optical behavior may have some potential applications in medicine science.

© 2012 Optical Society of America

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  1. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef]
  2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 2139011 (2007).
    [CrossRef]
  3. J. E. Morris, M. Mazilu, J. Baumgartl, T. Cizmar, and K. Dholakia, Opt. Express 17, 13236 (2009).
    [CrossRef]
  4. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
    [CrossRef]
  5. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
    [CrossRef]
  6. J. Baumgartl, M. Mazilu, and K. Dholakia, Nature Photon. 2, 675 (2008).
    [CrossRef]
  7. A. Salandrino and D. N. Christodoulides, Opt. Lett. 35, 2082 (2010).
    [CrossRef]
  8. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nature Photon. 4, 103 (2010).
    [CrossRef]
  9. Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, Opt. Lett. 36, 3230 (2011).
    [CrossRef]
  10. Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, Opt. Lett. 35, 2260 (2010).
    [CrossRef]
  11. I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
    [CrossRef]
  12. S. E. Harris, Phys. Today 50, 36 (1997).
    [CrossRef]
  13. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
    [CrossRef]
  14. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
    [CrossRef]
  15. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
    [CrossRef]
  16. F. Zhuang, X. Du, and D. Zhao, Opt. Lett. 36, 939 (2011).
    [CrossRef]
  17. J. Q. Shen, Phys. Rev. A 84, 063841 (2011).
    [CrossRef]
  18. J. Q. Shen, Opt. Commun. 283, 4546 (2010).
    [CrossRef]
  19. J. D. Jackson, Classical Electrodynamics3rd ed. (Wiley & Sons, 1998).
  20. S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).

2011

Z. Ye, S. Liu, C. Lou, P. Zhang, Y. Hu, D. Song, J. Zhao, and Z. Chen, Opt. Lett. 36, 3230 (2011).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

F. Zhuang, X. Du, and D. Zhao, Opt. Lett. 36, 939 (2011).
[CrossRef]

J. Q. Shen, Phys. Rev. A 84, 063841 (2011).
[CrossRef]

2010

J. Q. Shen, Opt. Commun. 283, 4546 (2010).
[CrossRef]

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, Opt. Lett. 35, 2260 (2010).
[CrossRef]

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

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

2009

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

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, Nature Photon. 3, 395 (2009).
[CrossRef]

2008

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

2007

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, 2139011 (2007).
[CrossRef]

1999

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

1997

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

1996

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef]

1995

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

Arie, A.

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

Baumgartl, J.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 2139011 (2007).
[CrossRef]

Chen, Z.

Chong, A.

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

Christodoulides, D. N.

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

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

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

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[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, 2139011 (2007).
[CrossRef]

Cizmar, T.

Dholakia, K.

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 2139011 (2007).
[CrossRef]

Du, X.

Dunn, M. H.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

Ellenbogen, T.

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

Fry, E. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Fulton, D. J.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

Ganany-Padowicz, A.

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

Harris, S. E.

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

Hollberg, L.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Hu, Y.

Huang, S.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics3rd ed. (Wiley & Sons, 1998).

Kaminer, I.

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

Kash, M. M.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Kolesik, M.

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

Liu, S.

Lou, C.

Lukin, M. D.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Mazilu, M.

Moloney, J. V.

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

Morris, J. E.

Moseley, R. R.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[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, Nature Photon. 4, 103 (2010).
[CrossRef]

Rostovtsev, Y.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Salandrino, A.

Sautenkov, V. A.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Scully, M. O.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Segev, M.

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

Shen, J. Q.

J. Q. Shen, Phys. Rev. A 84, 063841 (2011).
[CrossRef]

J. Q. Shen, Opt. Commun. 283, 4546 (2010).
[CrossRef]

Shepherd, S.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

Sinclair, B. D.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[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, 2139011 (2007).
[CrossRef]

Song, D.

Voloch-Bloch, N.

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

Wang, S.

S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).

Welch, G. R.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Wise, F. W.

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

Xu, J.

Ye, Z.

Zhang, P.

Zhao, D.

F. Zhuang, X. Du, and D. Zhao, Opt. Lett. 36, 939 (2011).
[CrossRef]

S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).

Zhao, J.

Zhuang, F.

Zibrov, A. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Nature Photon.

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

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

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

Opt. Commun.

J. Q. Shen, Opt. Commun. 283, 4546 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef]

J. Q. Shen, Phys. Rev. A 84, 063841 (2011).
[CrossRef]

Phys. Rev. Lett.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 2139011 (2007).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef]

Phys. Today

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

Science

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

Other

J. D. Jackson, Classical Electrodynamics3rd ed. (Wiley & Sons, 1998).

S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the double-control four-level atomic system interacting with the probe and control light fields.

Fig. 2.
Fig. 2.

Changes in the lateral position of a finite energy Airy beam on propagation through the EIT vapor with the Rabi frequency (a) Ωc=6.0×107Hz; (b) Ωc=6.5×107Hz; (c) Ωc=7.5×107Hz; (d) Ωc=1.5×108Hz.

Fig. 3.
Fig. 3.

Propagation dynamics (normalized intensity) of a finite energy Airy beam through the EIT vapor with different Rabi frequency (a) Ωc=6.0×107Hz; (b) Ωc=6.5×107Hz; (c) Ωc=7.5×107Hz; (d) Ωc=1.5×108Hz.

Fig. 4.
Fig. 4.

Changes of the intensity of the Airy beam at the positive position (x=0.3mm, z=300mm) along with the Rabi frequency.

Equations (10)

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

ε=1+Nβe1Nβe/3,
βe=i|D13|2ε0D[γ22+i(ΔpΔc)][γ22+i(ΔpΔc)],
D=(Γ32+iΔp)[γ22+i(ΔpΔc)][γ22+i(ΔpΔc)]+14Ωc*Ωc[γ22+i(ΔpΔc)]+14Ωc*Ωc[γ22+i(ΔpΔc)],
iuξ+122us2=0,
[ABCD]=[1zn01],
u(x)=ik2πBu(x1)exp[ik2B(Ax122x1x+Dx2)]dx1,
u(x1)=Ai(x1x0)exp(a0x1x0)
Ai(x)=exp(iu33+ixu)du
u(x)=1AAi(xAx0B24A2k2x04+ia0BAkx02)exp(ikCx22A)×exp(a0xAx0a0B22A2k2x04iB312A3k3x06+ia02B2Akx02+iBx2A2kx03),
xc=B24Ak2x03

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