Abstract

We show theoretically that the group velocity of light can be slowed down by means of phase coupling in the photorefractive two-wave mixing process. It is shown that the group velocity of light propagating in a photorefractive material could be significantly reduced because of a steep variation of the phase-coupling coefficient with respect to the angular frequency difference between two coupling beams in a two-wave mixing process. The results for the case of a photorefractive Bi12SiO20 crystal are presented and discussed in detail.

© 2004 Optical Society of America

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References

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  1. L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
    [CrossRef]
  2. C. Liu, Z. Dutton, C. H. Behroozl, L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
    [CrossRef] [PubMed]
  3. S. E. Harris, L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
    [CrossRef]
  4. M. D. Lukin, A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
    [CrossRef] [PubMed]
  5. A. B. Matsko, Y. V. Rostovtsev, H. Z. Cummins, M. O. Scully, “Using slow light to enhance acoustic-optical effects: application to squeezed light,” Phys. Rev. Lett. 84, 5752–5755 (2000).
    [CrossRef] [PubMed]
  6. L. Deng, E. W. Hagley, M. Kozuma, D. Akamatsu, M. G. Payne, “Achieving very-low group velocity reduction without electromagnetically induced transparency,” Appl. Phys. Lett. 81, 1168–1170 (2002).
    [CrossRef]
  7. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602-1–4 (2002).
  8. S. H. Lin, K. Y. Hsu, P. Yeh, “Experimental observation of the slowdown of optical beams by a volume-index grating in a photorefractive LiNbO3 crystal,” Opt. Lett. 25, 1582–1584 (2000).
    [CrossRef]
  9. G. C. Valley, “Two-wave mixing with an applied field and a moving grating,” J. Opt. Soc. Am. B 1, 868–873 (1984).
    [CrossRef]
  10. P. Réfrégier, L. Solymer, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
    [CrossRef]
  11. S. L. Sochava, E. V. Mokrushina, V. V. Prokof’ev, S. I. Stepanov, “Experimental comparison of the ac field and the moving grating holographic-recording techniques for Bi12SiO20 and Bi12TiO20 photorefractive crystals,” J. Opt. Soc. Am. B 10, 1600–1604 (1993).
    [CrossRef]
  12. B. Mainguet, F. Le Guiner, G. Picoli, “Moving grating and intrinsic electron-hole resonance in two-wave mixing in photorefractive InP:Fe,” Opt. Lett. 15, 938–940 (1990).
    [CrossRef] [PubMed]
  13. L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).
  14. N. Kukhtarev, V. Markov, S. Odulov, “Transient energy transfer during hologram formation in LiNbO3 in external electric field,” Opt. Commun. 23, 338–343 (1977).
    [CrossRef]
  15. G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
    [CrossRef]
  16. M. J. Damzen, N. Barry, “Intensity-dependent hole-electron competition and photocarrier saturation in BaTiO3 when using intense laser pulses,” J. Opt. Soc. Am. B 10, 600–606 (1993).
    [CrossRef]

2002 (2)

L. Deng, E. W. Hagley, M. Kozuma, D. Akamatsu, M. G. Payne, “Achieving very-low group velocity reduction without electromagnetically induced transparency,” Appl. Phys. Lett. 81, 1168–1170 (2002).
[CrossRef]

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602-1–4 (2002).

2001 (2)

C. Liu, Z. Dutton, C. H. Behroozl, L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

M. D. Lukin, A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef] [PubMed]

2000 (2)

A. B. Matsko, Y. V. Rostovtsev, H. Z. Cummins, M. O. Scully, “Using slow light to enhance acoustic-optical effects: application to squeezed light,” Phys. Rev. Lett. 84, 5752–5755 (2000).
[CrossRef] [PubMed]

S. H. Lin, K. Y. Hsu, P. Yeh, “Experimental observation of the slowdown of optical beams by a volume-index grating in a photorefractive LiNbO3 crystal,” Opt. Lett. 25, 1582–1584 (2000).
[CrossRef]

1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

S. E. Harris, L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

1993 (2)

1990 (1)

1985 (1)

P. Réfrégier, L. Solymer, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[CrossRef]

1984 (1)

1983 (1)

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

1977 (1)

N. Kukhtarev, V. Markov, S. Odulov, “Transient energy transfer during hologram formation in LiNbO3 in external electric field,” Opt. Commun. 23, 338–343 (1977).
[CrossRef]

Akamatsu, D.

L. Deng, E. W. Hagley, M. Kozuma, D. Akamatsu, M. G. Payne, “Achieving very-low group velocity reduction without electromagnetically induced transparency,” Appl. Phys. Lett. 81, 1168–1170 (2002).
[CrossRef]

Barry, N.

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Behroozl, C. H.

C. Liu, Z. Dutton, C. H. Behroozl, L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Cummins, H. Z.

A. B. Matsko, Y. V. Rostovtsev, H. Z. Cummins, M. O. Scully, “Using slow light to enhance acoustic-optical effects: application to squeezed light,” Phys. Rev. Lett. 84, 5752–5755 (2000).
[CrossRef] [PubMed]

Damzen, M. J.

Deng, L.

L. Deng, E. W. Hagley, M. Kozuma, D. Akamatsu, M. G. Payne, “Achieving very-low group velocity reduction without electromagnetically induced transparency,” Appl. Phys. Lett. 81, 1168–1170 (2002).
[CrossRef]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozl, L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Grunnet-Jepsen, A.

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).

Hagley, E. W.

L. Deng, E. W. Hagley, M. Kozuma, D. Akamatsu, M. G. Payne, “Achieving very-low group velocity reduction without electromagnetically induced transparency,” Appl. Phys. Lett. 81, 1168–1170 (2002).
[CrossRef]

Ham, B. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602-1–4 (2002).

Harris, S. E.

S. E. Harris, L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozl, L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

S. E. Harris, L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Hemmer, P. R.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602-1–4 (2002).

Hsu, K. Y.

Huignard, J.-P.

P. Réfrégier, L. Solymer, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[CrossRef]

Imamoglu, A.

M. D. Lukin, A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef] [PubMed]

Kozuma, M.

L. Deng, E. W. Hagley, M. Kozuma, D. Akamatsu, M. G. Payne, “Achieving very-low group velocity reduction without electromagnetically induced transparency,” Appl. Phys. Lett. 81, 1168–1170 (2002).
[CrossRef]

Kukhtarev, N.

N. Kukhtarev, V. Markov, S. Odulov, “Transient energy transfer during hologram formation in LiNbO3 in external electric field,” Opt. Commun. 23, 338–343 (1977).
[CrossRef]

Le Guiner, F.

Lin, S. H.

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozl, L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Lukin, M. D.

M. D. Lukin, A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef] [PubMed]

Mainguet, B.

Markov, V.

N. Kukhtarev, V. Markov, S. Odulov, “Transient energy transfer during hologram formation in LiNbO3 in external electric field,” Opt. Commun. 23, 338–343 (1977).
[CrossRef]

Matsko, A. B.

A. B. Matsko, Y. V. Rostovtsev, H. Z. Cummins, M. O. Scully, “Using slow light to enhance acoustic-optical effects: application to squeezed light,” Phys. Rev. Lett. 84, 5752–5755 (2000).
[CrossRef] [PubMed]

Mokrushina, E. V.

Musser, J. A.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602-1–4 (2002).

Odulov, S.

N. Kukhtarev, V. Markov, S. Odulov, “Transient energy transfer during hologram formation in LiNbO3 in external electric field,” Opt. Commun. 23, 338–343 (1977).
[CrossRef]

Payne, M. G.

L. Deng, E. W. Hagley, M. Kozuma, D. Akamatsu, M. G. Payne, “Achieving very-low group velocity reduction without electromagnetically induced transparency,” Appl. Phys. Lett. 81, 1168–1170 (2002).
[CrossRef]

Picoli, G.

Prokof’ev, V. V.

Rajbenbach, H.

P. Réfrégier, L. Solymer, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[CrossRef]

Réfrégier, P.

P. Réfrégier, L. Solymer, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[CrossRef]

Rostovtsev, Y. V.

A. B. Matsko, Y. V. Rostovtsev, H. Z. Cummins, M. O. Scully, “Using slow light to enhance acoustic-optical effects: application to squeezed light,” Phys. Rev. Lett. 84, 5752–5755 (2000).
[CrossRef] [PubMed]

Scully, M. O.

A. B. Matsko, Y. V. Rostovtsev, H. Z. Cummins, M. O. Scully, “Using slow light to enhance acoustic-optical effects: application to squeezed light,” Phys. Rev. Lett. 84, 5752–5755 (2000).
[CrossRef] [PubMed]

Shahriar, M. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602-1–4 (2002).

Sochava, S. L.

Solymar, L.

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).

Solymer, L.

P. Réfrégier, L. Solymer, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[CrossRef]

Stepanov, S. I.

Sudarshanam, V. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602-1–4 (2002).

Turukhin, A. V.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602-1–4 (2002).

Valley, G. C.

G. C. Valley, “Two-wave mixing with an applied field and a moving grating,” J. Opt. Soc. Am. B 1, 868–873 (1984).
[CrossRef]

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

Webb, D. J.

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).

Yeh, P.

Appl. Phys. Lett. (1)

L. Deng, E. W. Hagley, M. Kozuma, D. Akamatsu, M. G. Payne, “Achieving very-low group velocity reduction without electromagnetically induced transparency,” Appl. Phys. Lett. 81, 1168–1170 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

J. Appl. Phys. (1)

P. Réfrégier, L. Solymer, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–47 (1985).
[CrossRef]

J. Opt. Soc. Am. B (3)

Nature (3)

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

C. Liu, Z. Dutton, C. H. Behroozl, L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

M. D. Lukin, A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef] [PubMed]

Opt. Commun. (1)

N. Kukhtarev, V. Markov, S. Odulov, “Transient energy transfer during hologram formation in LiNbO3 in external electric field,” Opt. Commun. 23, 338–343 (1977).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (3)

A. B. Matsko, Y. V. Rostovtsev, H. Z. Cummins, M. O. Scully, “Using slow light to enhance acoustic-optical effects: application to squeezed light,” Phys. Rev. Lett. 84, 5752–5755 (2000).
[CrossRef] [PubMed]

S. E. Harris, L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88, 023602-1–4 (2002).

Other (1)

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).

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Figures (4)

Fig. 1
Fig. 1

Dispersion curves for (a) Γph, (b) ∂Γph/∂ω1, and (c) v g at various grating spacings Λ with E 0 and I 0 set at 106 V/m and 104 W/m2, respectively, in a photorefractive two-wave mixing process; 1, 10, 20, 30, and 40 are the grating spacing (in micrometers) for the corresponding curves. The material parameters used in the calculation are for a photorefractive BSO crystal and are listed in Table 1.

Fig. 2
Fig. 2

Dependences of (a) Γph and (b) v g on the angular frequency difference Ω with E 0 and Λ set at 106 V/m and 30 μm, respectively. The total incident intensities of the two beams I 0 are 102, 103, 104, and 105 W/m2, as indicated. The material parameters for the BSO crystal used in the calculation are the same as those in Table 1.

Fig. 3
Fig. 3

Dispersion curves for (a) Γph and (b) v g with I 0 = 104 W/m2 and Λ = 30 μm, but at different E0. The solid, dashed, and dotted curves correspond to E0 equal to 106 V/m, 104 V/m, and 0, respectively. The left-vertical coordinate and the bottom-horizontal coordinate denote the case when E 0 = 106 V/m; the right-vertical coordinate and the top-horizontal coordinate denote the cases when E 0 = 104 V/m and E 0 = 0, as indicated by the arrows. Note that the coordinate scales for the two coordinate systems are different. The material parameters for the BSO crystal used in the simulation are the same as those in Table 1.

Fig. 4
Fig. 4

Dependence of the intensity-coupling coefficient Γin on the angular frequency difference Ω with E 0, I 0, and Λ set at 106 V/m, 104 W/m2, and 30 μm, respectively. The material parameters used to calculate the curve are listed in Table 1.

Tables (1)

Tables Icon

Table 1 Material Parameters for a Typical Photorefractive BSO Crystala Used in the Numerical Simulation

Equations (12)

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

I=I01+mReexpiΩt-qx,
E=E0+mReEsc expiΩt-qx,
Esc=-E0-iED1+EDEq+i E0Eq-ΩτE0Eq-i τdiτ-i EDEq.
I1r=ΓinI1I2I1+I2,
Φ1r=ΓphI2I1+I2,
I1r=I10expΓinr,
Φ1r=Γphr-Φ10,
vg=cnb+c Γphω1,
Γphω1=δω1 ReEsc+δ  ReEscω1.
δω1 ReEsc=nb3reff2cEDB-E0AA2+B2,
δ  ReEscω1=δ  ReEscΩ,=πnb3reffτλ1EDτdiτ+EDEq+E02EqA2+B2-2EDB-E0ABτdiτ+EDEq-A E0EqA2+B22.
A=1+EDEq-Ωτ E0Eq,B=E0Eq+Ωττdiτ+EDEq,

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