Abstract

In this paper, a special gradient-index electromagnetically induced transparency medium is induced with a Gaussian control field, which can be realized in a four-level Rb87 cold atomic cloud. Special directional self-imaging and imaging transforming properties are studied in this work. Simulated results show that a complex object can be imaged in the cold atoms, as the control field substituted with the elliptical Gaussian beam, then the self-imaging is directional, which has potental application in encryption.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Patorski, “The self imaging phenomenon and its applications,” Prog. Opt. 27, 16–20 (1989), and references therein.
    [CrossRef]
  2. C. Gomez-Reino and E. Larrea, “Paraxial imaging and transforming in a medium with gradient-index: transmittance function,” Appl. Opt. 21, 4271–4275 (1982).
    [CrossRef]
  3. C. Gomez-Reino, M. V. Perez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, 2002).
  4. C. F. Wang, J. Cheng, and S. S. Han, “Slow light deflection in the Gaussian pumped atomic medium,” Chin. Opt. Lett. 8, 115–118 (2010).
    [CrossRef]
  5. C. F. Wang, J. Cheng, and S. S. Han, “Manipulating the focal shift in a medium with electromagnetically induced transparency,” J. Mod. Opt. 55, 985–992 (2008).
    [CrossRef]
  6. J. Cheng and S. S. Han, “Electromagnetically induced self-imaging,” Opt. Lett. 32, 1162–1164 (2007).
    [CrossRef]
  7. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
    [CrossRef]
  8. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [CrossRef]
  9. V. G. Arkhipkin and S. A. Myslivets, “All-optical switching in a photonic crystal with a defect containing an N -type four-level atomic system,” Phys. Rev. A 86, 063816 (2012).
    [CrossRef]
  10. J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A 88, 053845 (2013).
    [CrossRef]
  11. G. Heinze, N. Rentzsch, and T. Halfmann, “Multiplexed image storage by electromagnetically induced transparency in a solid,” Phys. Rev. A 86, 053837 (2012).
    [CrossRef]
  12. S. C. Zhang, S. Y. Zhou, M. M. T. Loy, G. K. L. Wong, and S. W. Du, “Optical storage with electromagnetically induced transparency in a dense cold atomic ensemble,” Opt. Lett. 36, 4530–4532 (2011).
    [CrossRef]
  13. 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]
  14. H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
    [CrossRef]
  15. F. X. Zhou, Y. H. Qi, H. Sun, D. J. Chen, J. Yang, Y. P. Niu, and S. Q. Gong, “Electromagnetically induced grating in asymmetric quantum wells via Fano interference,” Opt. Express 21, 12249–12259 (2013).
    [CrossRef]
  16. H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, “Electromagnetically induced waveguiding in double systems,” Phys. Rev. A 71, 043812 (2005).
    [CrossRef]
  17. A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Nonlinear optics with stationary pulses of light,” Phys. Rev. Lett. 94, 063902 (2005).
    [CrossRef]
  18. J. Cheng, S. S. Han, and Y. J. Yan, “Transverse localization and slow propagation of light,” Phys. Rev. A 72, 021801(R) (2005).
    [CrossRef]
  19. J. Cheng and S. S. Han, “Manipulating spectral anomalies of focused pulses in a medium with electromagnetically induced transparency,” Phys. Rev. A 73, 063803 (2006).
    [CrossRef]
  20. S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
    [CrossRef]

2013

J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A 88, 053845 (2013).
[CrossRef]

F. X. Zhou, Y. H. Qi, H. Sun, D. J. Chen, J. Yang, Y. P. Niu, and S. Q. Gong, “Electromagnetically induced grating in asymmetric quantum wells via Fano interference,” Opt. Express 21, 12249–12259 (2013).
[CrossRef]

2012

G. Heinze, N. Rentzsch, and T. Halfmann, “Multiplexed image storage by electromagnetically induced transparency in a solid,” Phys. Rev. A 86, 053837 (2012).
[CrossRef]

V. G. Arkhipkin and S. A. Myslivets, “All-optical switching in a photonic crystal with a defect containing an N -type four-level atomic system,” Phys. Rev. A 86, 063816 (2012).
[CrossRef]

2011

2010

2008

C. F. Wang, J. Cheng, and S. S. Han, “Manipulating the focal shift in a medium with electromagnetically induced transparency,” J. Mod. Opt. 55, 985–992 (2008).
[CrossRef]

2007

2006

J. Cheng and S. S. Han, “Manipulating spectral anomalies of focused pulses in a medium with electromagnetically induced transparency,” Phys. Rev. A 73, 063803 (2006).
[CrossRef]

2005

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

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

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Nonlinear optics with stationary pulses of light,” Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef]

J. Cheng, S. S. Han, and Y. J. Yan, “Transverse localization and slow propagation of light,” Phys. Rev. A 72, 021801(R) (2005).
[CrossRef]

1998

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (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

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

1996

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]

1989

K. Patorski, “The self imaging phenomenon and its applications,” Prog. Opt. 27, 16–20 (1989), and references therein.
[CrossRef]

1982

Andre, A.

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Nonlinear optics with stationary pulses of light,” Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef]

Arkhipkin, V. G.

V. G. Arkhipkin and S. A. Myslivets, “All-optical switching in a photonic crystal with a defect containing an N -type four-level atomic system,” Phys. Rev. A 86, 063816 (2012).
[CrossRef]

Bajcsy, M.

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Nonlinear optics with stationary pulses of light,” Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef]

Bao, C.

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

Bimbard, E.

J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A 88, 053845 (2013).
[CrossRef]

Chen, D. J.

Cheng, J.

C. F. Wang, J. Cheng, and S. S. Han, “Slow light deflection in the Gaussian pumped atomic medium,” Chin. Opt. Lett. 8, 115–118 (2010).
[CrossRef]

C. F. Wang, J. Cheng, and S. S. Han, “Manipulating the focal shift in a medium with electromagnetically induced transparency,” J. Mod. Opt. 55, 985–992 (2008).
[CrossRef]

J. Cheng and S. S. Han, “Electromagnetically induced self-imaging,” Opt. Lett. 32, 1162–1164 (2007).
[CrossRef]

J. Cheng and S. S. Han, “Manipulating spectral anomalies of focused pulses in a medium with electromagnetically induced transparency,” Phys. Rev. A 73, 063803 (2006).
[CrossRef]

J. Cheng, S. S. Han, and Y. J. Yan, “Transverse localization and slow propagation of light,” Phys. Rev. A 72, 021801(R) (2005).
[CrossRef]

Du, S. W.

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]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Friedmann, H.

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, “Electromagnetically induced waveguiding in double 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]

Gomez-Reino, C.

Gong, S. Q.

Grangier, P.

J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A 88, 053845 (2013).
[CrossRef]

Halfmann, T.

G. Heinze, N. Rentzsch, and T. Halfmann, “Multiplexed image storage by electromagnetically induced transparency in a solid,” Phys. Rev. A 86, 053837 (2012).
[CrossRef]

Han, S. S.

C. F. Wang, J. Cheng, and S. S. Han, “Slow light deflection in the Gaussian pumped atomic medium,” Chin. Opt. Lett. 8, 115–118 (2010).
[CrossRef]

C. F. Wang, J. Cheng, and S. S. Han, “Manipulating the focal shift in a medium with electromagnetically induced transparency,” J. Mod. Opt. 55, 985–992 (2008).
[CrossRef]

J. Cheng and S. S. Han, “Electromagnetically induced self-imaging,” Opt. Lett. 32, 1162–1164 (2007).
[CrossRef]

J. Cheng and S. S. Han, “Manipulating spectral anomalies of focused pulses in a medium with electromagnetically induced transparency,” Phys. Rev. A 73, 063803 (2006).
[CrossRef]

J. Cheng, S. S. Han, and Y. J. Yan, “Transverse localization and slow propagation of light,” Phys. Rev. A 72, 021801(R) (2005).
[CrossRef]

Harris, S. E.

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

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

Heinze, G.

G. Heinze, N. Rentzsch, and T. Halfmann, “Multiplexed image storage by electromagnetically induced transparency in a solid,” Phys. Rev. A 86, 053837 (2012).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Larrea, E.

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]

Loy, M. M. T.

Lukin, M. D.

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Nonlinear optics with stationary pulses of light,” Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

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]

Myslivets, S. A.

V. G. Arkhipkin and S. A. Myslivets, “All-optical switching in a photonic crystal with a defect containing an N -type four-level atomic system,” Phys. Rev. A 86, 063816 (2012).
[CrossRef]

Niu, Y. P.

Ourjoumtsev, A.

J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A 88, 053845 (2013).
[CrossRef]

Parigi, V.

J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A 88, 053845 (2013).
[CrossRef]

Patorski, K.

K. Patorski, “The self imaging phenomenon and its applications,” Prog. Opt. 27, 16–20 (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).

Qi, Y. H.

Rentzsch, N.

G. Heinze, N. Rentzsch, and T. Halfmann, “Multiplexed image storage by electromagnetically induced transparency in a solid,” Phys. Rev. A 86, 053837 (2012).
[CrossRef]

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]

Shpaisman, H.

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

Stanojevic, J.

J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A 88, 053845 (2013).
[CrossRef]

Sun, H.

Wang, C. F.

C. F. Wang, J. Cheng, and S. S. Han, “Slow light deflection in the Gaussian pumped atomic medium,” Chin. Opt. Lett. 8, 115–118 (2010).
[CrossRef]

C. F. Wang, J. Cheng, and S. S. Han, “Manipulating the focal shift in a medium with electromagnetically induced transparency,” J. Mod. Opt. 55, 985–992 (2008).
[CrossRef]

Wilson-Gordon, A. D.

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

Wong, G. K. L.

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]

Yamamoto, Y.

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

Yan, Y. J.

J. Cheng, S. S. Han, and Y. J. Yan, “Transverse localization and slow propagation of light,” Phys. Rev. A 72, 021801(R) (2005).
[CrossRef]

Yang, J.

Zhang, S. C.

Zhou, F. X.

Zhou, S. Y.

Zibrov, A. S.

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Nonlinear optics with stationary pulses of light,” Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef]

Appl. Opt.

Chin. Opt. Lett.

J. Mod. Opt.

C. F. Wang, J. Cheng, and S. S. Han, “Manipulating the focal shift in a medium with electromagnetically induced transparency,” J. Mod. Opt. 55, 985–992 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

V. G. Arkhipkin and S. A. Myslivets, “All-optical switching in a photonic crystal with a defect containing an N -type four-level atomic system,” Phys. Rev. A 86, 063816 (2012).
[CrossRef]

J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A 88, 053845 (2013).
[CrossRef]

G. Heinze, N. Rentzsch, and T. Halfmann, “Multiplexed image storage by electromagnetically induced transparency in a solid,” Phys. Rev. A 86, 053837 (2012).
[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]

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 systems,” Phys. Rev. A 71, 043812 (2005).
[CrossRef]

J. Cheng, S. S. Han, and Y. J. Yan, “Transverse localization and slow propagation of light,” Phys. Rev. A 72, 021801(R) (2005).
[CrossRef]

J. Cheng and S. S. Han, “Manipulating spectral anomalies of focused pulses in a medium with electromagnetically induced transparency,” Phys. Rev. A 73, 063803 (2006).
[CrossRef]

Phys. Rev. Lett.

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

A. Andre, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Nonlinear optics with stationary pulses of light,” Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef]

Phys. Today

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

Prog. Opt.

K. Patorski, “The self imaging phenomenon and its applications,” Prog. Opt. 27, 16–20 (1989), and references therein.
[CrossRef]

Rev. Mod. Phys.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (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 (6)

Fig. 1.
Fig. 1.

(a) Schematic diagram of electromagnetically induced self-imaging. (b) Energy schematic for a four-level Rb87 atom.

Fig. 2.
Fig. 2.

Transverse refractive index profile of the atomic medium illuminated by an elliptical Gaussian beam, σx=σy=6.4×104m.

Fig. 3.
Fig. 3.

Normalized intensity distribution I(x,y) at several different planes. (a) z=0, (b) z=21.50mm, (c) z=32.25mm, (d) z=53.75mm, (e) z=64.50mm, and (f) z=86.00mm.

Fig. 4.
Fig. 4.

Refractive index profile of the atomic medium illuminated by an elliptical Gaussian beam; σx=7.15×104m and σy=6.4×104m.

Fig. 5.
Fig. 5.

Normalized intensity distribution (a) I(x,z), as y=0 and (b) I(y,z), as x=0.

Fig. 6.
Fig. 6.

Normalized intensity distribution I(x,z) at several different planes. (a) z=0, (b) z=21.50mm, (c) z=32.25mm, (d) z=53.75mm, (e) z=64.50mm, and (f) z=86.00mm.

Equations (6)

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

χ(ωs)=K(|Ωc|24Δω˜pΔω˜c)4Δω˜sΔω˜pΔω˜c|Ωp|2Δω˜c|Ωc|2Δω˜s,
2ι˙κΔzϕ+(xx+yy)ϕ+κ2χ(ωs)ϕ=0,
n2(r)=n02(1g2r2),
n2(y)=n2(x)=(0.9993)2[1(0.0584)2x2],
n2(x)=(0.9993)2[1(0.0487)2x2],
n2(y)=(0.9993)2[1(0.0584)2y2],

Metrics