Abstract

We study the self-imaging and image-transforming properties of a probe field in a cold atomic medium with electromagnetically induced transparency (EIT). Due to the similarities between the gradient-index medium and the inhomogeneous index distribution of an EIT medium under the conditions of a negative probe detuning and a Gaussian control field, we find based on analytical investigations that there exists a kind of electromagnetically induced self-imaging phenomenon in cold atomic media. Numerical simulations clearly show that electromagnetically induced self-imaging is observable and controllable.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Patorski, Prog. Opt. 27, 1 (1989), and references therein.
    [CrossRef]
  2. C. Gomez-Reino and E. Larrea, Appl. Opt. 21, 4271 (1982).
    [CrossRef] [PubMed]
  3. C. Gomez-Reino, M. V. Perez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, 2002).
  4. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [CrossRef]
  5. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
    [CrossRef] [PubMed]
  6. H. Y. Ling, Y. Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
    [CrossRef]
  7. H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 71, 043812 (2005).
    [CrossRef]
  8. A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
    [CrossRef] [PubMed]
  9. J. Cheng, S. S. Han, and Y. J. Yan, Phys. Rev. A 72, 021801(R) (2005).
    [CrossRef]
  10. J. Cheng and S. S. Han, Phys. Rev. A 73, 063803 (2006).
    [CrossRef]
  11. S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
    [CrossRef] [PubMed]
  12. S. E. Harris, J. E. Field, and A. Kasapi, Phys. Rev. A 46, R29 (1992).
    [CrossRef] [PubMed]
  13. A. Andre, and M. D. Lukin, Phys. Rev. Lett. 89, 143602 (2002).
    [CrossRef] [PubMed]

2006

J. Cheng and S. S. Han, Phys. Rev. A 73, 063803 (2006).
[CrossRef]

2005

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 71, 043812 (2005).
[CrossRef]

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

J. Cheng, S. S. Han, and Y. J. Yan, Phys. Rev. A 72, 021801(R) (2005).
[CrossRef]

2002

A. Andre, and M. D. Lukin, Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

1998

H. Y. Ling, Y. Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
[CrossRef]

1996

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

1992

S. E. Harris, J. E. Field, and A. Kasapi, Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

1990

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

1989

K. Patorski, Prog. Opt. 27, 1 (1989), and references therein.
[CrossRef]

1982

Andre, A.

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

A. Andre, and M. D. Lukin, Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

Bajcsy, M.

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

Bao, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, 2002).

Cheng, J.

J. Cheng and S. S. Han, Phys. Rev. A 73, 063803 (2006).
[CrossRef]

J. Cheng, S. S. Han, and Y. J. Yan, Phys. Rev. A 72, 021801(R) (2005).
[CrossRef]

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] [PubMed]

Field, J. E.

S. E. Harris, J. E. Field, and A. Kasapi, Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Friedmann, H.

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 71, 043812 (2005).
[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] [PubMed]

Gomez-Reino, C.

C. Gomez-Reino and E. Larrea, Appl. Opt. 21, 4271 (1982).
[CrossRef] [PubMed]

C. Gomez-Reino, M. V. Perez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, 2002).

Han, S. S.

J. Cheng and S. S. Han, Phys. Rev. A 73, 063803 (2006).
[CrossRef]

J. Cheng, S. S. Han, and Y. J. Yan, Phys. Rev. A 72, 021801(R) (2005).
[CrossRef]

Harris, S. E.

S. E. Harris, J. E. Field, and A. Kasapi, Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

Kasapi, A.

S. E. Harris, J. E. Field, and A. Kasapi, Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

Larrea, E.

Li, Y. Q.

H. Y. Ling, Y. Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
[CrossRef]

Ling, H. Y.

H. Y. Ling, Y. Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
[CrossRef]

Lukin, M. D.

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

A. Andre, and M. D. Lukin, Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

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] [PubMed]

Patorski, K.

K. Patorski, Prog. Opt. 27, 1 (1989), and references therein.
[CrossRef]

Perez, M. V.

C. Gomez-Reino, M. V. Perez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, 2002).

Shepherd, S.

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

Shpaisman, H.

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 71, 043812 (2005).
[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] [PubMed]

Wilson-Gordon, A. D.

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 71, 043812 (2005).
[CrossRef]

Xiao, M.

H. Y. Ling, Y. Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
[CrossRef]

Yan, Y. J.

J. Cheng, S. S. Han, and Y. J. Yan, Phys. Rev. A 72, 021801(R) (2005).
[CrossRef]

Zibrov, A. S.

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

Appl. Opt.

Phys. Rev. A

S. E. Harris, J. E. Field, and A. Kasapi, Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

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

H. Y. Ling, Y. Q. Li, and M. Xiao, Phys. Rev. A 57, 1338 (1998).
[CrossRef]

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 71, 043812 (2005).
[CrossRef]

J. Cheng, S. S. Han, and Y. J. Yan, Phys. Rev. A 72, 021801(R) (2005).
[CrossRef]

J. Cheng and S. S. Han, Phys. Rev. A 73, 063803 (2006).
[CrossRef]

Phys. Rev. Lett.

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef] [PubMed]

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

A. Andre, and M. D. Lukin, Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

Prog. Opt.

K. Patorski, Prog. Opt. 27, 1 (1989), and references therein.
[CrossRef]

Rev. Mod. Phys.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Other

C. Gomez-Reino, M. V. Perez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Schematic diagram of electromagnetically induced self-imaging. A probe beam and a control beam are counterpropagated. The probe beam illuminates an object located at z = 0 with a transmission function t ( x , y ) . The right side of the object is occupied by three-level Λ-type atoms, shown in the lower left corner.

Fig. 2
Fig. 2

Normalized intensity distribution of I ( x , y ) at several different planes. Parameters are given in the text.

Fig. 3
Fig. 3

Normalized intensity distribution of I ( x = 0 , y , z ) . Parameters are the same as in Fig. 2.

Equations (8)

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

χ = η Δ p ( Ω c 2 4 Δ p 2 4 Γ 1 2 ) + 2 i Δ p 2 Γ 2 + i Γ 1 ( Ω c 2 + Γ 1 Γ 2 ) 2 [ Ω c 2 + Γ 1 Γ 2 4 Δ p 2 ] 2 + 4 Δ p 2 ( Γ 1 + Γ 2 ) 2 ,
χ ( ω p ) = χ ( 0 ) + χ ( 1 ) Δ p + 1 2 χ ( 2 ) Δ p 2 + .
n 2 ( r ) = ( 1 η Δ p Ω 0 2 ) 2 η Δ p Ω 0 2 σ 2 r 2 ,
n 2 ( x , y ) = n 0 2 [ 1 g 2 ( x 2 + y 2 ) ] ,
E ( x , y , z ) = S d x 0 d y 0 E 0 ( x 0 , y 0 ) G ( x , y , x 0 , y 0 , z ) ,
G ( x , y , x 0 , y 0 , z ) = k n 0 g e i k n 0 z i 2 π sin ( g z ) exp [ i k n 0 g 2 tan ( g z ) ( x 2 + y 2 2 x x 0 + y y 0 cos ( g z ) + x 0 2 + y 0 2 ) ] ,
G ( x , y , x 0 , y 0 , z ) = ( 1 ) m e i k n 0 z δ [ x ( 1 ) m x 0 , y ( 1 ) m y 0 ] .
2 i k ϕ z + ( x x + y y ) ϕ + k 2 χ ϕ = 0 ,

Metrics