Abstract

Stimulated photon echoes (SPEs) with time duration comparable to the coherent lifetime and Rabi period have been investigated theoretically and experimentally with an angled beam configuration. The Rabi oscillation effects on both the transmitted field (optical nutation) and the SPE fields are explained by analytic solutions of Maxwell–Bloch equations. The theory also predicts that an echo can exist in the noncausal direction, and this was confirmed by experiments with Tm:YAG crystal.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. L. Shoemaker, in Laser and Coherence Spectroscopy, J. I. Steinfeld, ed. (Plenum, New York, 1978), Chap. 3.
  2. R. M. Macfarlane and R. M. Shelby, in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyankii and R. M. Macfarlane, eds., (Elsevier, New York, 1987), Chap. 3.
  3. L. Allen and I. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).
  4. S. Bernet, B. Kohler, A. Rebane, A. Renn, and U. P. Wild, J. Opt. Soc. Am. B 9, 987 (1992).
    [CrossRef]
  5. A. Rebane, S. Bernet, A. Renn, and Urs P. Wild, Opt. Commun. 86, 7 (1991).
    [CrossRef]
  6. T. Mossberg, Opt. Lett. 7, 77 (1982).
    [CrossRef] [PubMed]
  7. V. V. Samartsev, V. A. Zuikov, and L. A. Nefed’ev, J. Appl. Spectrosc. 59, 766 (1993).
    [CrossRef]
  8. M. Tian, J. Zhao, Z. Cole, R. Reibel, and W. R. Babbitt, J. Opt. Soc. Am. 18, 673 (2001).
    [CrossRef]
  9. N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, Phys. Rev. B 62, 1473 (2000).
    [CrossRef]
  10. Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. Leask, Phys. Rev. B 62, 15443 (2000).
    [CrossRef]

2001 (1)

M. Tian, J. Zhao, Z. Cole, R. Reibel, and W. R. Babbitt, J. Opt. Soc. Am. 18, 673 (2001).
[CrossRef]

2000 (2)

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, Phys. Rev. B 62, 1473 (2000).
[CrossRef]

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. Leask, Phys. Rev. B 62, 15443 (2000).
[CrossRef]

1993 (1)

V. V. Samartsev, V. A. Zuikov, and L. A. Nefed’ev, J. Appl. Spectrosc. 59, 766 (1993).
[CrossRef]

1992 (1)

1991 (1)

A. Rebane, S. Bernet, A. Renn, and Urs P. Wild, Opt. Commun. 86, 7 (1991).
[CrossRef]

1982 (1)

Allen, L.

L. Allen and I. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).

Babbitt, W. R.

M. Tian, J. Zhao, Z. Cole, R. Reibel, and W. R. Babbitt, J. Opt. Soc. Am. 18, 673 (2001).
[CrossRef]

Bernet, S.

S. Bernet, B. Kohler, A. Rebane, A. Renn, and U. P. Wild, J. Opt. Soc. Am. B 9, 987 (1992).
[CrossRef]

A. Rebane, S. Bernet, A. Renn, and Urs P. Wild, Opt. Commun. 86, 7 (1991).
[CrossRef]

Carlsten, J. L.

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, Phys. Rev. B 62, 1473 (2000).
[CrossRef]

Cole, Z.

M. Tian, J. Zhao, Z. Cole, R. Reibel, and W. R. Babbitt, J. Opt. Soc. Am. 18, 673 (2001).
[CrossRef]

Cone, R. L.

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. Leask, Phys. Rev. B 62, 15443 (2000).
[CrossRef]

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, Phys. Rev. B 62, 1473 (2000).
[CrossRef]

Eberly, I. H.

L. Allen and I. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).

Equall, R. W.

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. Leask, Phys. Rev. B 62, 15443 (2000).
[CrossRef]

Kohler, B.

Leask, M. J.

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. Leask, Phys. Rev. B 62, 15443 (2000).
[CrossRef]

Macfarlane, R. M.

R. M. Macfarlane and R. M. Shelby, in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyankii and R. M. Macfarlane, eds., (Elsevier, New York, 1987), Chap. 3.

Mossberg, T.

Nefed’ev, L. A.

V. V. Samartsev, V. A. Zuikov, and L. A. Nefed’ev, J. Appl. Spectrosc. 59, 766 (1993).
[CrossRef]

Rebane, A.

S. Bernet, B. Kohler, A. Rebane, A. Renn, and U. P. Wild, J. Opt. Soc. Am. B 9, 987 (1992).
[CrossRef]

A. Rebane, S. Bernet, A. Renn, and Urs P. Wild, Opt. Commun. 86, 7 (1991).
[CrossRef]

Reibel, R.

M. Tian, J. Zhao, Z. Cole, R. Reibel, and W. R. Babbitt, J. Opt. Soc. Am. 18, 673 (2001).
[CrossRef]

Renn, A.

S. Bernet, B. Kohler, A. Rebane, A. Renn, and U. P. Wild, J. Opt. Soc. Am. B 9, 987 (1992).
[CrossRef]

A. Rebane, S. Bernet, A. Renn, and Urs P. Wild, Opt. Commun. 86, 7 (1991).
[CrossRef]

Samartsev, V. V.

V. V. Samartsev, V. A. Zuikov, and L. A. Nefed’ev, J. Appl. Spectrosc. 59, 766 (1993).
[CrossRef]

Sellin, P. B.

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, Phys. Rev. B 62, 1473 (2000).
[CrossRef]

Shelby, R. M.

R. M. Macfarlane and R. M. Shelby, in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyankii and R. M. Macfarlane, eds., (Elsevier, New York, 1987), Chap. 3.

Shoemaker, R. L.

R. L. Shoemaker, in Laser and Coherence Spectroscopy, J. I. Steinfeld, ed. (Plenum, New York, 1978), Chap. 3.

Strickland, N. M.

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, Phys. Rev. B 62, 1473 (2000).
[CrossRef]

Sun, Y.

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, Phys. Rev. B 62, 1473 (2000).
[CrossRef]

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. Leask, Phys. Rev. B 62, 15443 (2000).
[CrossRef]

Tian, M.

M. Tian, J. Zhao, Z. Cole, R. Reibel, and W. R. Babbitt, J. Opt. Soc. Am. 18, 673 (2001).
[CrossRef]

Wang, G. M.

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. Leask, Phys. Rev. B 62, 15443 (2000).
[CrossRef]

Wild, U. P.

Wild, Urs P.

A. Rebane, S. Bernet, A. Renn, and Urs P. Wild, Opt. Commun. 86, 7 (1991).
[CrossRef]

Zhao, J.

M. Tian, J. Zhao, Z. Cole, R. Reibel, and W. R. Babbitt, J. Opt. Soc. Am. 18, 673 (2001).
[CrossRef]

Zuikov, V. A.

V. V. Samartsev, V. A. Zuikov, and L. A. Nefed’ev, J. Appl. Spectrosc. 59, 766 (1993).
[CrossRef]

J. Appl. Spectrosc. (1)

V. V. Samartsev, V. A. Zuikov, and L. A. Nefed’ev, J. Appl. Spectrosc. 59, 766 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

M. Tian, J. Zhao, Z. Cole, R. Reibel, and W. R. Babbitt, J. Opt. Soc. Am. 18, 673 (2001).
[CrossRef]

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

Opt. Commun. (1)

A. Rebane, S. Bernet, A. Renn, and Urs P. Wild, Opt. Commun. 86, 7 (1991).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (2)

N. M. Strickland, P. B. Sellin, Y. Sun, J. L. Carlsten, and R. L. Cone, Phys. Rev. B 62, 1473 (2000).
[CrossRef]

Y. Sun, G. M. Wang, R. L. Cone, R. W. Equall, and M. J. Leask, Phys. Rev. B 62, 15443 (2000).
[CrossRef]

Other (3)

R. L. Shoemaker, in Laser and Coherence Spectroscopy, J. I. Steinfeld, ed. (Plenum, New York, 1978), Chap. 3.

R. M. Macfarlane and R. M. Shelby, in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyankii and R. M. Macfarlane, eds., (Elsevier, New York, 1987), Chap. 3.

L. Allen and I. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).

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 (3)

Fig. 1
Fig. 1

(a) Angled beam configuration and (b) input timing showing the brief-pulse programming and quasi-continuous probe.

Fig. 2
Fig. 2

Calculated results of the induced fields from a quasi-continuous plane-wave probe in an optically thin spatial–spectral grating with w0<0, Ω0=0.8 MHz, and τ21=0.3 µs. Top trace, optical nutation on the normalized transmitted field. E-t and E+t are the normalized echo fields in the causal and noncausal directions, calculated from Eqs. (6) and (7), respectively.

Fig. 3
Fig. 3

Experimental results for Tm:YAG. The optical power of the echoes in the causal and the noncausal directions is shown for (a) τ21=0.15 µs and (b) 0.3 µs. (c) Optical nutation on the transmission.

Equations (9)

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

uΔ,t=exp-t/T2w0ΔΔ×1-cosΩ02+Δ21/2t/Ω02+Δ2, vΔ,t=exp-t/T2w0Δ×sinΩ02+Δ21/2t/Ω02+Δ2,
pnutexp-t/T2Ω0J0Ω0t,
pechotexp-t/T2Ω0J0Ω0t2-τ2121/2t>τ210t<τ21,
E+t02π-uΔ,t,xdΔdδ,
E-t02π-uΔ,t,xcos 2δ-νΔ,t,xsin 2δdΔdδ,
E+t=CΩ0w0π exp-t/T2J0Ω0t,
E-t=0.5CΩ0g0 exp-t/T2×πexp-Ω0τ21+πJ0Ω0t-τ2221/2--ΔΩ02+Δ2cosΩ02+Δ21/2t×sin Δτ21dΔ,
E+t=0.5CΩ0g0 exp-t/T2×-πexp-Ω0τ21+πJ0Ω0t-τ2121/2+-ΔΩ02+Δ2cosΩ02+Δ21/2t×sin Δτ21dΔ,
E-t=CΩ0w0πexp-t/T2J0Ω0t.

Metrics