Abstract

Under the condition of electromagnetically induced transparency, self-imaging in three-level Λ-type atoms at normal temperature is studied. The influences of the temperature on the position of the self-imaging and the corresponding imaging quality are discussed in detail. Numerical results show that, with the increase of the temperature, the location of the self-imaging linearly moves away from the original object, and the self-imaging quality decreases.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Patorski, Progress in Optics, E. Wolf, ed. (Pergamon, 1989), Vol. 27, Chap. 1, pp. 1-108, and references therein.
    [CrossRef]
  2. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401-407 (1836).
  3. Lord Rayleigh, “On copying diffraction gratings, and on some phenomenon connected therewith,” Philos. Mag. 11, 196-205(1881).
  4. G. S. Agarwal, “Talbot effect in a quadratic index medium,” Opt. Commun. 119, 30-32 (1995).
    [CrossRef]
  5. E. Arimondo, Progress in Optics, E. Wolf, ed. (North-Holland, 1996), Vol. 35, 259 pp.
    [CrossRef]
  6. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36-42 (1997).
    [CrossRef]
  7. K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
    [CrossRef] [PubMed]
  8. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673(1995).
    [CrossRef] [PubMed]
  9. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408-415 (1996).
    [CrossRef] [PubMed]
  10. H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338-1344 (1998).
    [CrossRef]
  11. H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, “Electromagnetically induced waveguiding in double-Λ systems,” Phys. Rev. A 71, 043812 (2005).
    [CrossRef]
  12. J. Cheng and S. S. Han, “Electromagnetically induced self-imaging,” Opt. Lett. 32, 1162-1164 (2007).
    [CrossRef] [PubMed]
  13. P. Zhou and S. Swain, “Collisional-dephasing and Doppler-broadening effects on quantum interference in a Vee atomic system,” J. Opt. Soc. Am. B 15, 2593-2598 (1998).
    [CrossRef]
  14. S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical process using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107-1110 (1990).
    [CrossRef] [PubMed]
  15. R. Kapoor and G. S. Agarwal, “Theory of electromagnetically induced waveguides,” Phys. Rev. A 61, 053818 (2000).
    [CrossRef]
  16. A. Siegman, Lasers (University Science, 1986).
  17. A. Andre and M. D. Lukin, “Manipulating light pulses via dynamically controlled photonic band gap,” Phys. Rev. Lett. 89, 143602 (2002).
    [CrossRef] [PubMed]

2007 (1)

2005 (1)

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, “Electromagnetically induced waveguiding in double-Λ systems,” Phys. Rev. A 71, 043812 (2005).
[CrossRef]

2002 (1)

A. Andre and M. D. Lukin, “Manipulating light pulses via dynamically controlled photonic band gap,” Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

2000 (1)

R. Kapoor and G. S. Agarwal, “Theory of electromagnetically induced waveguides,” Phys. Rev. A 61, 053818 (2000).
[CrossRef]

1998 (2)

P. Zhou and S. Swain, “Collisional-dephasing and Doppler-broadening effects on quantum interference in a Vee atomic system,” J. Opt. Soc. Am. B 15, 2593-2598 (1998).
[CrossRef]

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338-1344 (1998).
[CrossRef]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36-42 (1997).
[CrossRef]

1996 (1)

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

1995 (2)

G. S. Agarwal, “Talbot effect in a quadratic index medium,” Opt. Commun. 119, 30-32 (1995).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673(1995).
[CrossRef] [PubMed]

1991 (1)

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef] [PubMed]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical process using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107-1110 (1990).
[CrossRef] [PubMed]

1881 (1)

Lord Rayleigh, “On copying diffraction gratings, and on some phenomenon connected therewith,” Philos. Mag. 11, 196-205(1881).

1836 (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401-407 (1836).

Agarwal, G. S.

R. Kapoor and G. S. Agarwal, “Theory of electromagnetically induced waveguides,” Phys. Rev. A 61, 053818 (2000).
[CrossRef]

G. S. Agarwal, “Talbot effect in a quadratic index medium,” Opt. Commun. 119, 30-32 (1995).
[CrossRef]

Andre, A.

A. Andre and M. D. Lukin, “Manipulating light pulses via dynamically controlled photonic band gap,” Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

Arimondo, E.

E. Arimondo, Progress in Optics, E. Wolf, ed. (North-Holland, 1996), Vol. 35, 259 pp.
[CrossRef]

Boller, K. J.

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef] [PubMed]

Cheng, J.

Dunn, M. H.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673(1995).
[CrossRef] [PubMed]

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical process using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107-1110 (1990).
[CrossRef] [PubMed]

Friedmann, H.

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, “Electromagnetically induced waveguiding in double-Λ systems,” 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, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673(1995).
[CrossRef] [PubMed]

Han, S. S.

Harris, S. E.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36-42 (1997).
[CrossRef]

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical process using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107-1110 (1990).
[CrossRef] [PubMed]

Imamoglu, A.

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef] [PubMed]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical process using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107-1110 (1990).
[CrossRef] [PubMed]

Kapoor, R.

R. Kapoor and G. S. Agarwal, “Theory of electromagnetically induced waveguides,” Phys. Rev. A 61, 053818 (2000).
[CrossRef]

Li, Y. Q.

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338-1344 (1998).
[CrossRef]

Ling, H. Y.

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338-1344 (1998).
[CrossRef]

Lukin, M. D.

A. Andre and M. D. Lukin, “Manipulating light pulses via dynamically controlled photonic band gap,” Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

Moseley, R. R.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673(1995).
[CrossRef] [PubMed]

Patorski, K.

K. Patorski, Progress in Optics, E. Wolf, ed. (Pergamon, 1989), Vol. 27, Chap. 1, pp. 1-108, and references therein.
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, “On copying diffraction gratings, and on some phenomenon connected therewith,” Philos. Mag. 11, 196-205(1881).

Shepherd, S.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673(1995).
[CrossRef] [PubMed]

Shpaisman, H.

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, “Electromagnetically induced waveguiding in double-Λ systems,” Phys. Rev. A 71, 043812 (2005).
[CrossRef]

Siegman, A.

A. Siegman, Lasers (University Science, 1986).

Sinclair, B. D.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673(1995).
[CrossRef] [PubMed]

Swain, S.

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401-407 (1836).

Wilson-Gordon, A. D.

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, “Electromagnetically induced waveguiding in double-Λ systems,” Phys. Rev. A 71, 043812 (2005).
[CrossRef]

Xiao, M.

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338-1344 (1998).
[CrossRef]

Zhou, P.

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

G. S. Agarwal, “Talbot effect in a quadratic index medium,” Opt. Commun. 119, 30-32 (1995).
[CrossRef]

Opt. Lett. (1)

Philos. Mag. (2)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401-407 (1836).

Lord Rayleigh, “On copying diffraction gratings, and on some phenomenon connected therewith,” Philos. Mag. 11, 196-205(1881).

Phys. Rev. A (4)

R. Kapoor and G. S. Agarwal, “Theory of electromagnetically induced waveguides,” Phys. Rev. A 61, 053818 (2000).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Electromagnetically-induced focusing,” Phys. Rev. A 53, 408-415 (1996).
[CrossRef] [PubMed]

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338-1344 (1998).
[CrossRef]

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, “Electromagnetically induced waveguiding in double-Λ systems,” Phys. Rev. A 71, 043812 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical process using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107-1110 (1990).
[CrossRef] [PubMed]

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593-2596 (1991).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673(1995).
[CrossRef] [PubMed]

A. Andre and M. D. Lukin, “Manipulating light pulses via dynamically controlled photonic band gap,” Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36-42 (1997).
[CrossRef]

Other (3)

K. Patorski, Progress in Optics, E. Wolf, ed. (Pergamon, 1989), Vol. 27, Chap. 1, pp. 1-108, and references therein.
[CrossRef]

E. Arimondo, Progress in Optics, E. Wolf, ed. (North-Holland, 1996), Vol. 35, 259 pp.
[CrossRef]

A. Siegman, Lasers (University Science, 1986).

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 (5)

Fig. 1
Fig. 1

Notation of the focusing system. The control field and the probe field are counterpropagated. A probe beam illuminates an object located at z = 0 with a transmission function t ( x , y ) . The left side of the object is free space, while the right side of the object is occupied by the closed three-level Λ-type atoms ( Rb 87 ) at normal temperature. A three-level Λ-type system is shown in the lower left corner.

Fig. 2
Fig. 2

Real and imaginary parts of χ. Parameters: T = 400 K , λ = 800 nm , Ω 0 = 2 × 10 8 s 1 , η = 2 × 10 5 s 1 , σ = 1 mm , Δ p = 0.4 × 10 6 s 1 , Γ 2 = 3 × 10 3 s 1 , Γ 3 = 3 × 10 6 s 1 .

Fig. 3
Fig. 3

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

Fig. 4
Fig. 4

Original object and the self-imaging in Fig. 3.

Fig. 5
Fig. 5

(a) Influence of the temperature T on the position of the self-imaging z i ; (b) Error factor Q on the self-imaging plane as a function of the temperature T. Parameters are the same as in Fig. 2.

Equations (7)

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

χ = | μ 13 | 2 N ε 0 { 4 Δ p ( Ω c 2 4 Δ p 2 ) 4 Δ p Γ 2 2 ( Ω c 2 + Γ 2 Γ 3 4 Δ p 2 ) 2 + 4 Δ p 2 ( Γ 2 + Γ 3 ) 2 + i 8 Δ p 2 Γ 3 + 2 Γ 2 ( Ω c 2 + Γ 2 Γ 3 ) ( Ω c 2 + Γ 2 Γ 3 4 Δ p 2 ) 2 + 4 Δ p 2 ( Γ 2 + Γ 3 ) 2 } ,
Ω c ( r ) = Ω 0 exp ( r 2 σ 2 ) ,
d N ( v ) = N 0 u π e v 2 / u 2 d v ,
χ ( v ) = η u π e v 2 / u 2 4 Δ p ( Ω c 2 4 Δ p 2 ) 4 Δ p Γ 2 2 + 8 i Δ p 2 Γ 3 + 2 i Γ 2 ( Ω c 2 + Γ 2 Γ 3 ) ( Ω c 2 + Γ 2 Γ 3 4 Δ p 2 ) 2 + 4 Δ p 2 ( Γ 2 + Γ 3 ) 2 d v ,
2 i k ϕ z + 2 ϕ + k 2 χ ϕ = 0 ,
2 = ( 2 x 2 + 2 y 2 ) ,
Q = m , n = 1 M , N | I i m n I o m n | m , n = 1 M , N I o m n

Metrics