Abstract

We theoretically study the stacked optical transients generated from a series of square pulses passing through a cold atomic ensemble. Using the hybrid analysis and fast Fourier transform, we identify the stacked coherent transients [Europhys. Lett. 4, 47 (1987) ] as optical precursors. With slow-light and electromagnetically induced transparency, we obtain nearly 700% transmitted intensity at the transient spikes resulting from the interference between the delayed main field and the stacked optical precursors.

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References

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  1. L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).
  2. K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).
  3. M. D. Crisp, Phys. Rev. A 1, 1604 (1970).
    [CrossRef]
  4. B. Segard, J. Zemmouri, and B. Macke, Europhys. Lett. 4, 47 (1987).
    [CrossRef]
  5. H. Jeong, A. M. C. Dawes, and D. J. Gauthier, Phys. Rev. Lett. 96, 143901 (2006).
    [CrossRef] [PubMed]
  6. E. Varoquaux, G. A. Williams, and O. Avenel, Phys. Rev. B 34, 7617 (1986).
    [CrossRef]
  7. H. Jeong and U. L. Österberg, J. Opt. Soc. Am. B 25, B1 (2008).
    [CrossRef]
  8. H. Jeong and U. L. Österberg, Phys. Rev. A 77, 021803(R) (2008).
    [CrossRef]
  9. F. J. Lynch, R. E. Holland, and M. Hamermesh, Phys. Rev. 120, 513 (1960).
    [CrossRef]
  10. J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
    [CrossRef]
  11. S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 100, 183603 (2008).
    [CrossRef] [PubMed]
  12. S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, Opt. Lett. 33, 2149 (2008).
    [CrossRef] [PubMed]
  13. H. Jeong and S. Du, Phys. Rev. A 79, 011802(R) (2009).
    [CrossRef]
  14. B. Macke and B. Segard, Phys. Rev. A 80, 011803(R) (2009).
    [CrossRef]
  15. D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
    [CrossRef] [PubMed]
  16. B. Macke and B. Segard, Phys. Rev. A 73, 043802 (2006).
    [CrossRef]
  17. W. R. LeFew, S. Venakides, and D. J. Gauthier, Phys. Rev. A 79, 063842 (2009).
    [CrossRef]

2009 (4)

H. Jeong and S. Du, Phys. Rev. A 79, 011802(R) (2009).
[CrossRef]

B. Macke and B. Segard, Phys. Rev. A 80, 011803(R) (2009).
[CrossRef]

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef] [PubMed]

W. R. LeFew, S. Venakides, and D. J. Gauthier, Phys. Rev. A 79, 063842 (2009).
[CrossRef]

2008 (4)

H. Jeong and U. L. Österberg, J. Opt. Soc. Am. B 25, B1 (2008).
[CrossRef]

H. Jeong and U. L. Österberg, Phys. Rev. A 77, 021803(R) (2008).
[CrossRef]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, Opt. Lett. 33, 2149 (2008).
[CrossRef] [PubMed]

2006 (2)

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef] [PubMed]

B. Macke and B. Segard, Phys. Rev. A 73, 043802 (2006).
[CrossRef]

1987 (1)

B. Segard, J. Zemmouri, and B. Macke, Europhys. Lett. 4, 47 (1987).
[CrossRef]

1986 (1)

E. Varoquaux, G. A. Williams, and O. Avenel, Phys. Rev. B 34, 7617 (1986).
[CrossRef]

1984 (1)

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

1970 (1)

M. D. Crisp, Phys. Rev. A 1, 1604 (1970).
[CrossRef]

1960 (1)

F. J. Lynch, R. E. Holland, and M. Hamermesh, Phys. Rev. 120, 513 (1960).
[CrossRef]

Avenel, O.

E. Varoquaux, G. A. Williams, and O. Avenel, Phys. Rev. B 34, 7617 (1986).
[CrossRef]

Balant, A. C.

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

Belthangady, C.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, Opt. Lett. 33, 2149 (2008).
[CrossRef] [PubMed]

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Chen, J. F.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef] [PubMed]

Crisp, M. D.

M. D. Crisp, Phys. Rev. A 1, 1604 (1970).
[CrossRef]

Dawes, A. M. C.

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef] [PubMed]

Du, S.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef] [PubMed]

H. Jeong and S. Du, Phys. Rev. A 79, 011802(R) (2009).
[CrossRef]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, Opt. Lett. 33, 2149 (2008).
[CrossRef] [PubMed]

Gauthier, D. J.

W. R. LeFew, S. Venakides, and D. J. Gauthier, Phys. Rev. A 79, 063842 (2009).
[CrossRef]

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef] [PubMed]

Grischkowsky, D.

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

Hamermesh, M.

F. J. Lynch, R. E. Holland, and M. Hamermesh, Phys. Rev. 120, 513 (1960).
[CrossRef]

Harris, S. E.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, Opt. Lett. 33, 2149 (2008).
[CrossRef] [PubMed]

Holland, R. E.

F. J. Lynch, R. E. Holland, and M. Hamermesh, Phys. Rev. 120, 513 (1960).
[CrossRef]

Jeong, H.

H. Jeong and S. Du, Phys. Rev. A 79, 011802(R) (2009).
[CrossRef]

H. Jeong and U. L. Österberg, Phys. Rev. A 77, 021803(R) (2008).
[CrossRef]

H. Jeong and U. L. Österberg, J. Opt. Soc. Am. B 25, B1 (2008).
[CrossRef]

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef] [PubMed]

Kolchin, P.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, Opt. Lett. 33, 2149 (2008).
[CrossRef] [PubMed]

LeFew, W. R.

W. R. LeFew, S. Venakides, and D. J. Gauthier, Phys. Rev. A 79, 063842 (2009).
[CrossRef]

Loy, M. M. T.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef] [PubMed]

Lynch, F. J.

F. J. Lynch, R. E. Holland, and M. Hamermesh, Phys. Rev. 120, 513 (1960).
[CrossRef]

Macke, B.

B. Macke and B. Segard, Phys. Rev. A 80, 011803(R) (2009).
[CrossRef]

B. Macke and B. Segard, Phys. Rev. A 73, 043802 (2006).
[CrossRef]

B. Segard, J. Zemmouri, and B. Macke, Europhys. Lett. 4, 47 (1987).
[CrossRef]

Österberg, U. L.

H. Jeong and U. L. Österberg, Phys. Rev. A 77, 021803(R) (2008).
[CrossRef]

H. Jeong and U. L. Österberg, J. Opt. Soc. Am. B 25, B1 (2008).
[CrossRef]

Oughstun, K. E.

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).

Rothenberg, J. E.

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

Segard, B.

B. Macke and B. Segard, Phys. Rev. A 80, 011803(R) (2009).
[CrossRef]

B. Macke and B. Segard, Phys. Rev. A 73, 043802 (2006).
[CrossRef]

B. Segard, J. Zemmouri, and B. Macke, Europhys. Lett. 4, 47 (1987).
[CrossRef]

Sherman, G. C.

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).

Varoquaux, E.

E. Varoquaux, G. A. Williams, and O. Avenel, Phys. Rev. B 34, 7617 (1986).
[CrossRef]

Venakides, S.

W. R. LeFew, S. Venakides, and D. J. Gauthier, Phys. Rev. A 79, 063842 (2009).
[CrossRef]

Wei, D.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef] [PubMed]

Williams, G. A.

E. Varoquaux, G. A. Williams, and O. Avenel, Phys. Rev. B 34, 7617 (1986).
[CrossRef]

Wong, G. K. L.

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef] [PubMed]

Yin, G. Y.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, Opt. Lett. 33, 2149 (2008).
[CrossRef] [PubMed]

Zemmouri, J.

B. Segard, J. Zemmouri, and B. Macke, Europhys. Lett. 4, 47 (1987).
[CrossRef]

Europhys. Lett. (1)

B. Segard, J. Zemmouri, and B. Macke, Europhys. Lett. 4, 47 (1987).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. (1)

F. J. Lynch, R. E. Holland, and M. Hamermesh, Phys. Rev. 120, 513 (1960).
[CrossRef]

Phys. Rev. A (6)

B. Macke and B. Segard, Phys. Rev. A 73, 043802 (2006).
[CrossRef]

W. R. LeFew, S. Venakides, and D. J. Gauthier, Phys. Rev. A 79, 063842 (2009).
[CrossRef]

H. Jeong and S. Du, Phys. Rev. A 79, 011802(R) (2009).
[CrossRef]

B. Macke and B. Segard, Phys. Rev. A 80, 011803(R) (2009).
[CrossRef]

H. Jeong and U. L. Österberg, Phys. Rev. A 77, 021803(R) (2008).
[CrossRef]

M. D. Crisp, Phys. Rev. A 1, 1604 (1970).
[CrossRef]

Phys. Rev. B (1)

E. Varoquaux, G. A. Williams, and O. Avenel, Phys. Rev. B 34, 7617 (1986).
[CrossRef]

Phys. Rev. Lett. (4)

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef] [PubMed]

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef] [PubMed]

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, Phys. Rev. Lett. 53, 552 (1984).
[CrossRef]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

Other (2)

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).

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Figures (4)

Fig. 1
Fig. 1

Illustration of a step-off or square pulse propagation through an EIT medium. The carrier frequency of the incident pulse ω p = ω 0 is on resonance of the transition | 1 | 3 . The coupling laser ( ω c ) is on resonance of the transition | 2 | 3 with a Rabi frequency of Ω c .

Fig. 2
Fig. 2

Normalized intensities of (a) total precursors (solid curve) and the main signal (dashed curve) and (b) total intensity at the falling edge of a step-off input pulse.

Fig. 3
Fig. 3

Normalized total intensities composed of optical precursors and delayed main signal in an EIT medium. Input square pulse E ( 0 , t ) is given as a solid line (shifted by 1.2 ). Hybrid analysis [Eqs. (2, 3), solid curves (blue online)] is compared with FFT (dashed curves).

Fig. 4
Fig. 4

Normalized total intensities composed of a stack of optical precursors and delayed main signal for the case of (a) two-level ( Ω c = 0 ) and (b) EIT medium ( Ω c = 4.2 δ ) . The series of square pulses as input E ( 0 , t ) is given as a solid line (shifted by 1.2 ). The hybrid analysis [Eqs. (4, 5, 6), solid curves (blue online)] is compared with FFT (dashed curves).

Equations (6)

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χ ( ω ) = c α 0 ω 0 4 ( Δ + i δ 12 ) δ Ω c 2 4 ( Δ + i δ 12 ) ( Δ + i δ ) ,
E SB ± ( z , t ) ± E 0 J 0 ( 2 α 0 z δ τ ) Θ ( τ ) e δ τ e i ( k 0 z ω 0 τ ) ,
E M ( z , t ) = E 0 0 G EIT ( z , t τ ) d τ ,
E SB stack ( z , t ) = E SB + ( z , t ) + E SB + ( z , t τ 0 ) + i = 1 i = 5 ( 1 ) i E SB + ( z , t τ 0 + t i ) ,
E M stack ( z , t ) = E 0 k = 1 2 τ 0 t 2 k 1 τ 0 t 2 k G EIT ( z , t τ ) d τ + E 0 ( 0 τ 0 t 5 + τ 0 ) G EIT ( z , t τ ) d τ ,
E stack ( z , t ) = E SB stack ( z , t ) + E M stack ( z , t ) .

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