Abstract

We show that light pulses propagating in two-photon absorbing systems may present time delays like slow light produced via coherent population oscillations in one-photon interactions. Two regimes are numerically studied for a simplified two-level system: (a) a light pulse at frequency ω/2 undergoes two-photon absorption (TPA) and is delayed by the absorbing system (two-photon slow light) and (b) a light pulse at frequency ω is delayed in a system prepared by TPA of a light pulse at frequency ω/2 (two-photon-assisted slow light). The study carried out in solutions of dyes and dendrites shows significant delays, low distortion, and good transmission for easily reachable experimental conditions. The working principle can be applied to other media and can be used in telecommunications technology.

© 2011 Optical Society of America

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  1. R. W. Boyd and D. J. Gauthier, Science 326, 1074 (2009).
    [CrossRef] [PubMed]
  2. G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, Science 312, 895 (2006).
    [CrossRef] [PubMed]
  3. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Phys. Rev. Lett. 90, 113903 (2003).
    [CrossRef] [PubMed]
  4. L. Cerdán, R. Weigand, J. M. Guerra Pérez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
    [CrossRef]
  5. P. Sperber and A. Penzkofer, Opt. Quantum Electron. 18, 381 (1986).
    [CrossRef]
  6. M. Drobizhev, A. Karotki, A. Rebane, and C. W. Spangler, Opt. Lett. 26, 1081 (2001).
    [CrossRef]
  7. H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
    [CrossRef]
  8. R. Weigand, M. Wittmann, and J. M. Guerra, Appl. Phys. B 73, 201 (2001).
  9. G. Piredda and R. W. Boyd, J. Europ. Opt. Soc. Rap. Public. 2, 07004 (2007).
    [CrossRef]
  10. H. Shin, A. Schweinsberg, G. Gehring, K. Schwertz, H. J. Chang, R. W. Boyd, Q. Park, and D. J. Gauthier, Opt. Lett. 32, 906 (2007).
    [CrossRef] [PubMed]

2009 (1)

R. W. Boyd and D. J. Gauthier, Science 326, 1074 (2009).
[CrossRef] [PubMed]

2008 (1)

L. Cerdán, R. Weigand, J. M. Guerra Pérez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

2007 (2)

2006 (1)

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, Science 312, 895 (2006).
[CrossRef] [PubMed]

2003 (1)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

2001 (2)

M. Drobizhev, A. Karotki, A. Rebane, and C. W. Spangler, Opt. Lett. 26, 1081 (2001).
[CrossRef]

R. Weigand, M. Wittmann, and J. M. Guerra, Appl. Phys. B 73, 201 (2001).

2000 (1)

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

1986 (1)

P. Sperber and A. Penzkofer, Opt. Quantum Electron. 18, 381 (1986).
[CrossRef]

Barsi, C.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, Science 312, 895 (2006).
[CrossRef] [PubMed]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, Science 326, 1074 (2009).
[CrossRef] [PubMed]

G. Piredda and R. W. Boyd, J. Europ. Opt. Soc. Rap. Public. 2, 07004 (2007).
[CrossRef]

H. Shin, A. Schweinsberg, G. Gehring, K. Schwertz, H. J. Chang, R. W. Boyd, Q. Park, and D. J. Gauthier, Opt. Lett. 32, 906 (2007).
[CrossRef] [PubMed]

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, Science 312, 895 (2006).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

Cerdán, L.

L. Cerdán, R. Weigand, J. M. Guerra Pérez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

Chang, H. J.

Crespo, H.

L. Cerdán, R. Weigand, J. M. Guerra Pérez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

Drobizhev, M.

Fang, Q.

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

Gauthier, D. J.

Gehring, G.

Gehring, G. M.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, Science 312, 895 (2006).
[CrossRef] [PubMed]

Guerra, J. M.

R. Weigand, M. Wittmann, and J. M. Guerra, Appl. Phys. B 73, 201 (2001).

Guerra Pérez, J. M.

L. Cerdán, R. Weigand, J. M. Guerra Pérez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

Jiang, M. H.

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

Karotki, A.

Kostinski, N.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, Science 312, 895 (2006).
[CrossRef] [PubMed]

Lei, H.

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

Park, Q.

Penzkofer, A.

P. Sperber and A. Penzkofer, Opt. Quantum Electron. 18, 381 (1986).
[CrossRef]

Piredda, G.

G. Piredda and R. W. Boyd, J. Europ. Opt. Soc. Rap. Public. 2, 07004 (2007).
[CrossRef]

Rebane, A.

Ren, Y.

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

Schweinsberg, A.

Schwertz, K.

Shin, H.

Spangler, C. W.

Sperber, P.

P. Sperber and A. Penzkofer, Opt. Quantum Electron. 18, 381 (1986).
[CrossRef]

Tian, Y. P.

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

Wang, H. Z.

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

Wang, X. M.

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

Wei, Z. C.

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

Weigand, R.

L. Cerdán, R. Weigand, J. M. Guerra Pérez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

R. Weigand, M. Wittmann, and J. M. Guerra, Appl. Phys. B 73, 201 (2001).

Wittmann, M.

R. Weigand, M. Wittmann, and J. M. Guerra, Appl. Phys. B 73, 201 (2001).

Xu, N. S.

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

Zhao, F. L.

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

Zheng, X. G.

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

Am. J. Phys. (1)

L. Cerdán, R. Weigand, J. M. Guerra Pérez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

Appl. Phys. B (1)

R. Weigand, M. Wittmann, and J. M. Guerra, Appl. Phys. B 73, 201 (2001).

Chem. Phys. Lett. (1)

H. Z. Wang, H. Lei, Z. C. Wei, F. L. Zhao, X. G. Zheng, N. S. Xu, X. M. Wang, Y. Ren, Y. P. Tian, Q. Fang, and M. H. Jiang, Chem. Phys. Lett. 324, 349 (2000).
[CrossRef]

J. Europ. Opt. Soc. Rap. Public. (1)

G. Piredda and R. W. Boyd, J. Europ. Opt. Soc. Rap. Public. 2, 07004 (2007).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

P. Sperber and A. Penzkofer, Opt. Quantum Electron. 18, 381 (1986).
[CrossRef]

Phys. Rev. Lett. (1)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

Science (2)

R. W. Boyd and D. J. Gauthier, Science 326, 1074 (2009).
[CrossRef] [PubMed]

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, Science 312, 895 (2006).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Energy levels diagram for an organic molecule, (b) propagation of a light pulse at ω / 2 through a two-photon absorbing system, (c) propagation of a weak light pulse at ω through a TPA prepared system.

Fig. 2
Fig. 2

Time and fractional delays between reference I ω / 2 ref ( L , t ) and output I ω / 2 out ( L , t ) pulses in a (a) dye solution and (b) dendrite solution at three concentrations (see text). Inset, temporal profiles of a reference and output pulses.

Fig. 3
Fig. 3

Distortion and transmission of calculated I ω / 2 out ( L , t ) pulses in (a) dye solution and (b) dendrite solution at three concentrations (see text).

Fig. 4
Fig. 4

Delay (a), distortion (b) and transmission (b) of a weak pulse (ω, t p = 100 ps (▪, □) or t p = 50 ps (•, ○) traversing a medium prepared by an intense pulse ( ω / 2 , t p = 100 ps ) as a function of their relative time delay (for positive delay, probe arrives later than pump). Inset, temporal profiles of a reference and output pulses.

Equations (5)

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d n 1 ( z , t ) d t = σ ( 2 ) n 1 ( z , t ) I ω / 2 2 ( z , t ) + n n 1 ( z , t ) τ ,
n r ( ω / 2 ) c d I ω / 2 ( z , t ) d t + d I ω / 2 ( z , t ) d z = 2 σ ( 2 ) n 1 ( z , t ) I ω / 2 2 ( z , t ) ,
d n 1 ( z , t ) d t = σ ( 1 ) n 1 ( z , t ) I ω ( z , t ) σ ( 2 ) n 1 ( z , t ) I ω / 2 2 ( z , t ) + n n 1 ( z , t ) τ ,
n r ( ω / 2 ) c d I ω / 2 ( z , t ) d t + d I ω / 2 ( z , t ) d z = 2 σ ( 2 ) n 1 ( z , t ) I ω / 2 2 ( z , t ) ,
n r ( ω ) c d I ω ( z , t ) d t + d I ω ( z , t ) d z = σ ( 1 ) n 1 ( z , t ) I ω ( z , t ) ,

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