Abstract

We observe the two- and three-pulse photon echo emission from a scattering powder, obtained by grinding a Pr3+:Y2SiO5 rare earth doped single crystal. We show that the collective emission is coherently constructed over several grains. A well defined atomic coherence can therefore be created between randomly placed particles. Observation of photon echo on powders as opposed to bulk materials opens the way to faster material development. More generally, time-domain resonant four-wave mixing offers an attractive approach to investigate coherent propagation in scattering media.

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  1. N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon echo,” Phys. Rev. Lett. 13, 567–568 (1964).
    [CrossRef]
  2. I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. 141(1), 391–406 (1966).
    [CrossRef]
  3. M. P. Van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
    [CrossRef] [PubMed]
  4. P.-E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
    [CrossRef] [PubMed]
  5. D. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008).
    [CrossRef]
  6. V. E. Kravtsov, V. M. Agranovich, and K. I. Grigorishin, “Theory of second-harmonic generation in strongly scattering media,” Phys. Rev. B 44(10), 4931–4942 (1991).
    [CrossRef]
  7. M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
    [CrossRef] [PubMed]
  8. J. F. de Boer, A. Lagendijk, R. Sprik, and S. Feng, “Transmission and reflection correlations of second harmonic waves in nonlinear random media,” Phys. Rev. Lett. 71(24), 3947–3950 (1993).
    [CrossRef] [PubMed]
  9. C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87(18), 183903 (2001).
    [CrossRef]
  10. H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000).
    [CrossRef] [PubMed]
  11. T. Wellens and B. Grémaud, “Nonlinear coherent transport of waves in disordered media,” Phys. Rev. Lett. 100(3), 033902 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. T. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7(2), 77–79 (1982).
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  14. X. Wen, S. Chen, and D. D. Dlott, “Time-resolved three-color coherent Raman scattering applied to polycrys-talline and opaque solids,” J. Opt. Soc. Am. B 8, 813–819 (1991).
    [CrossRef]
  15. V. Markushev, N. Ter-Gabriélyan, C. Briskina, V. Belan, and V. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Quantum Electron. 20(7), 773–777 (1990).
    [CrossRef]
  16. M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, “Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316, 265–268 (2007).
    [CrossRef] [PubMed]
  17. M. Colice, F. Schlottau, K. Wagner, R. Mohan, W. Babbitt, I. Lorgeré, and J.-L. Le Gouët, “RF spectrum analysis in spectral hole burning media,” Proc. SPIE 5557, 132 (2004).
    [CrossRef]
  18. J.-L. Le Gouët, F. Bretenaker, and I. Lorgeré, “Atomic processing of optically carried RF signals,” in Advances in Atomic Molecular and Optical Physics (Elsevier, 2007), Vol. 54, pp. 549–613.
    [CrossRef]
  19. W. Tittel, M. Afzelius, R. Cone, T. Chanelière, S. Kroll, S. Moiseev, and M. Sellars, “Photon-echo quantum memory in solid state systems,” Laser Photonics Rev. 4(2), 244–267 (2009).
    [CrossRef]
  20. H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
    [CrossRef] [PubMed]
  21. S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
    [CrossRef] [PubMed]
  22. T. Ito and M. Tomita, “Speckle correlation measurement in a disordered medium observed through second-harmonics generation,” Phys. Rev. E 69, 036610 (2004).
    [CrossRef]
  23. R. M. Macfarlane, Y. Sun, R. L. Cone, C. W. Thiel, and R. W. Equall, “Optical dephasing by disorder modes in yttrium orthosilicate (Y2SiO5) doped with Eu3+,” J. Lumin. 107(1–4), 310–313 (2004).
    [CrossRef]
  24. G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, “10-GHz bandwidth RF spectral analyzer with MHz resolution based on spectral hole burning in Tm3+:YAG,” IEEE Photon. Technol. Lett. 17(11), 2385–2387 (2005).
    [CrossRef]

2009 (2)

T. Wellens and B. Grémaud, “Coherent propagation of waves in dilute random media with weak nonlinearity,” Phys. Rev. A 80(6), 063827 (2009).
[CrossRef]

W. Tittel, M. Afzelius, R. Cone, T. Chanelière, S. Kroll, S. Moiseev, and M. Sellars, “Photon-echo quantum memory in solid state systems,” Laser Photonics Rev. 4(2), 244–267 (2009).
[CrossRef]

2008 (3)

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

T. Wellens and B. Grémaud, “Nonlinear coherent transport of waves in disordered media,” Phys. Rev. Lett. 100(3), 033902 (2008).
[CrossRef] [PubMed]

D. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008).
[CrossRef]

2007 (1)

M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, “Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316, 265–268 (2007).
[CrossRef] [PubMed]

2005 (1)

G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, “10-GHz bandwidth RF spectral analyzer with MHz resolution based on spectral hole burning in Tm3+:YAG,” IEEE Photon. Technol. Lett. 17(11), 2385–2387 (2005).
[CrossRef]

2004 (4)

T. Ito and M. Tomita, “Speckle correlation measurement in a disordered medium observed through second-harmonics generation,” Phys. Rev. E 69, 036610 (2004).
[CrossRef]

R. M. Macfarlane, Y. Sun, R. L. Cone, C. W. Thiel, and R. W. Equall, “Optical dephasing by disorder modes in yttrium orthosilicate (Y2SiO5) doped with Eu3+,” J. Lumin. 107(1–4), 310–313 (2004).
[CrossRef]

M. Colice, F. Schlottau, K. Wagner, R. Mohan, W. Babbitt, I. Lorgeré, and J.-L. Le Gouët, “RF spectrum analysis in spectral hole burning media,” Proc. SPIE 5557, 132 (2004).
[CrossRef]

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

2001 (1)

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87(18), 183903 (2001).
[CrossRef]

2000 (1)

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000).
[CrossRef] [PubMed]

1993 (1)

J. F. de Boer, A. Lagendijk, R. Sprik, and S. Feng, “Transmission and reflection correlations of second harmonic waves in nonlinear random media,” Phys. Rev. Lett. 71(24), 3947–3950 (1993).
[CrossRef] [PubMed]

1991 (2)

V. E. Kravtsov, V. M. Agranovich, and K. I. Grigorishin, “Theory of second-harmonic generation in strongly scattering media,” Phys. Rev. B 44(10), 4931–4942 (1991).
[CrossRef]

X. Wen, S. Chen, and D. D. Dlott, “Time-resolved three-color coherent Raman scattering applied to polycrys-talline and opaque solids,” J. Opt. Soc. Am. B 8, 813–819 (1991).
[CrossRef]

1990 (1)

V. Markushev, N. Ter-Gabriélyan, C. Briskina, V. Belan, and V. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Quantum Electron. 20(7), 773–777 (1990).
[CrossRef]

1988 (1)

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[CrossRef] [PubMed]

1985 (2)

M. P. Van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[CrossRef] [PubMed]

P.-E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
[CrossRef] [PubMed]

1982 (1)

1966 (1)

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. 141(1), 391–406 (1966).
[CrossRef]

1964 (1)

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon echo,” Phys. Rev. Lett. 13, 567–568 (1964).
[CrossRef]

Abella, I. D.

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. 141(1), 391–406 (1966).
[CrossRef]

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon echo,” Phys. Rev. Lett. 13, 567–568 (1964).
[CrossRef]

Afzelius, M.

W. Tittel, M. Afzelius, R. Cone, T. Chanelière, S. Kroll, S. Moiseev, and M. Sellars, “Photon-echo quantum memory in solid state systems,” Laser Photonics Rev. 4(2), 244–267 (2009).
[CrossRef]

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

Agranovich, V. M.

V. E. Kravtsov, V. M. Agranovich, and K. I. Grigorishin, “Theory of second-harmonic generation in strongly scattering media,” Phys. Rev. B 44(10), 4931–4942 (1991).
[CrossRef]

Babbitt, W.

M. Colice, F. Schlottau, K. Wagner, R. Mohan, W. Babbitt, I. Lorgeré, and J.-L. Le Gouët, “RF spectrum analysis in spectral hole burning media,” Proc. SPIE 5557, 132 (2004).
[CrossRef]

Baudrier-Raybaut, M.

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

Belan, V.

V. Markushev, N. Ter-Gabriélyan, C. Briskina, V. Belan, and V. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Quantum Electron. 20(7), 773–777 (1990).
[CrossRef]

Bretenaker, F.

G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, “10-GHz bandwidth RF spectral analyzer with MHz resolution based on spectral hole burning in Tm3+:YAG,” IEEE Photon. Technol. Lett. 17(11), 2385–2387 (2005).
[CrossRef]

J.-L. Le Gouët, F. Bretenaker, and I. Lorgeré, “Atomic processing of optically carried RF signals,” in Advances in Atomic Molecular and Optical Physics (Elsevier, 2007), Vol. 54, pp. 549–613.
[CrossRef]

Briskina, C.

V. Markushev, N. Ter-Gabriélyan, C. Briskina, V. Belan, and V. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Quantum Electron. 20(7), 773–777 (1990).
[CrossRef]

Cao, H.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000).
[CrossRef] [PubMed]

Chanelière, T.

W. Tittel, M. Afzelius, R. Cone, T. Chanelière, S. Kroll, S. Moiseev, and M. Sellars, “Photon-echo quantum memory in solid state systems,” Laser Photonics Rev. 4(2), 244–267 (2009).
[CrossRef]

Chang, R. P. H.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000).
[CrossRef] [PubMed]

Chang, S. H.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000).
[CrossRef] [PubMed]

Chen, S.

Colice, M.

M. Colice, F. Schlottau, K. Wagner, R. Mohan, W. Babbitt, I. Lorgeré, and J.-L. Le Gouët, “RF spectrum analysis in spectral hole burning media,” Proc. SPIE 5557, 132 (2004).
[CrossRef]

Cone, R.

W. Tittel, M. Afzelius, R. Cone, T. Chanelière, S. Kroll, S. Moiseev, and M. Sellars, “Photon-echo quantum memory in solid state systems,” Laser Photonics Rev. 4(2), 244–267 (2009).
[CrossRef]

Cone, R. L.

R. M. Macfarlane, Y. Sun, R. L. Cone, C. W. Thiel, and R. W. Equall, “Optical dephasing by disorder modes in yttrium orthosilicate (Y2SiO5) doped with Eu3+,” J. Lumin. 107(1–4), 310–313 (2004).
[CrossRef]

Crozatier, V.

G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, “10-GHz bandwidth RF spectral analyzer with MHz resolution based on spectral hole burning in Tm3+:YAG,” IEEE Photon. Technol. Lett. 17(11), 2385–2387 (2005).
[CrossRef]

de Boer, J. F.

J. F. de Boer, A. Lagendijk, R. Sprik, and S. Feng, “Transmission and reflection correlations of second harmonic waves in nonlinear random media,” Phys. Rev. Lett. 71(24), 3947–3950 (1993).
[CrossRef] [PubMed]

de Riedmatten, H.

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

Dlott, D. D.

Dogariu, A.

M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, “Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316, 265–268 (2007).
[CrossRef] [PubMed]

Equall, R. W.

R. M. Macfarlane, Y. Sun, R. L. Cone, C. W. Thiel, and R. W. Equall, “Optical dephasing by disorder modes in yttrium orthosilicate (Y2SiO5) doped with Eu3+,” J. Lumin. 107(1–4), 310–313 (2004).
[CrossRef]

Feng, S.

J. F. de Boer, A. Lagendijk, R. Sprik, and S. Feng, “Transmission and reflection correlations of second harmonic waves in nonlinear random media,” Phys. Rev. Lett. 71(24), 3947–3950 (1993).
[CrossRef] [PubMed]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[CrossRef] [PubMed]

Gisin, N.

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

Gorju, G.

G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, “10-GHz bandwidth RF spectral analyzer with MHz resolution based on spectral hole burning in Tm3+:YAG,” IEEE Photon. Technol. Lett. 17(11), 2385–2387 (2005).
[CrossRef]

Grémaud, B.

T. Wellens and B. Grémaud, “Coherent propagation of waves in dilute random media with weak nonlinearity,” Phys. Rev. A 80(6), 063827 (2009).
[CrossRef]

T. Wellens and B. Grémaud, “Nonlinear coherent transport of waves in disordered media,” Phys. Rev. Lett. 100(3), 033902 (2008).
[CrossRef] [PubMed]

Grigorishin, K. I.

V. E. Kravtsov, V. M. Agranovich, and K. I. Grigorishin, “Theory of second-harmonic generation in strongly scattering media,” Phys. Rev. B 44(10), 4931–4942 (1991).
[CrossRef]

Haidar, R.

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

Hartmann, S. R.

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. 141(1), 391–406 (1966).
[CrossRef]

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon echo,” Phys. Rev. Lett. 13, 567–568 (1964).
[CrossRef]

Ho, S. T.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000).
[CrossRef] [PubMed]

Huang, Y.

M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, “Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316, 265–268 (2007).
[CrossRef] [PubMed]

Ito, T.

T. Ito and M. Tomita, “Speckle correlation measurement in a disordered medium observed through second-harmonics generation,” Phys. Rev. E 69, 036610 (2004).
[CrossRef]

Kane, C.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[CrossRef] [PubMed]

Kravtsov, V. E.

V. E. Kravtsov, V. M. Agranovich, and K. I. Grigorishin, “Theory of second-harmonic generation in strongly scattering media,” Phys. Rev. B 44(10), 4931–4942 (1991).
[CrossRef]

Kroll, S.

W. Tittel, M. Afzelius, R. Cone, T. Chanelière, S. Kroll, S. Moiseev, and M. Sellars, “Photon-echo quantum memory in solid state systems,” Laser Photonics Rev. 4(2), 244–267 (2009).
[CrossRef]

Kupecek, P.

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

Kurnit, N. A.

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. 141(1), 391–406 (1966).
[CrossRef]

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon echo,” Phys. Rev. Lett. 13, 567–568 (1964).
[CrossRef]

Lagendijk, A.

J. F. de Boer, A. Lagendijk, R. Sprik, and S. Feng, “Transmission and reflection correlations of second harmonic waves in nonlinear random media,” Phys. Rev. Lett. 71(24), 3947–3950 (1993).
[CrossRef] [PubMed]

M. P. Van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[CrossRef] [PubMed]

Le Gouët, J.-L.

G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, “10-GHz bandwidth RF spectral analyzer with MHz resolution based on spectral hole burning in Tm3+:YAG,” IEEE Photon. Technol. Lett. 17(11), 2385–2387 (2005).
[CrossRef]

M. Colice, F. Schlottau, K. Wagner, R. Mohan, W. Babbitt, I. Lorgeré, and J.-L. Le Gouët, “RF spectrum analysis in spectral hole burning media,” Proc. SPIE 5557, 132 (2004).
[CrossRef]

J.-L. Le Gouët, F. Bretenaker, and I. Lorgeré, “Atomic processing of optically carried RF signals,” in Advances in Atomic Molecular and Optical Physics (Elsevier, 2007), Vol. 54, pp. 549–613.
[CrossRef]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[CrossRef] [PubMed]

Lemasson, P.

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

Liu, X.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000).
[CrossRef] [PubMed]

Lorgeré, I.

G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, “10-GHz bandwidth RF spectral analyzer with MHz resolution based on spectral hole burning in Tm3+:YAG,” IEEE Photon. Technol. Lett. 17(11), 2385–2387 (2005).
[CrossRef]

M. Colice, F. Schlottau, K. Wagner, R. Mohan, W. Babbitt, I. Lorgeré, and J.-L. Le Gouët, “RF spectrum analysis in spectral hole burning media,” Proc. SPIE 5557, 132 (2004).
[CrossRef]

J.-L. Le Gouët, F. Bretenaker, and I. Lorgeré, “Atomic processing of optically carried RF signals,” in Advances in Atomic Molecular and Optical Physics (Elsevier, 2007), Vol. 54, pp. 549–613.
[CrossRef]

Macfarlane, R. M.

R. M. Macfarlane, Y. Sun, R. L. Cone, C. W. Thiel, and R. W. Equall, “Optical dephasing by disorder modes in yttrium orthosilicate (Y2SiO5) doped with Eu3+,” J. Lumin. 107(1–4), 310–313 (2004).
[CrossRef]

Maret, G.

P.-E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
[CrossRef] [PubMed]

Markushev, V.

V. Markushev, N. Ter-Gabriélyan, C. Briskina, V. Belan, and V. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Quantum Electron. 20(7), 773–777 (1990).
[CrossRef]

Mohan, R.

M. Colice, F. Schlottau, K. Wagner, R. Mohan, W. Babbitt, I. Lorgeré, and J.-L. Le Gouët, “RF spectrum analysis in spectral hole burning media,” Proc. SPIE 5557, 132 (2004).
[CrossRef]

Moiseev, S.

W. Tittel, M. Afzelius, R. Cone, T. Chanelière, S. Kroll, S. Moiseev, and M. Sellars, “Photon-echo quantum memory in solid state systems,” Laser Photonics Rev. 4(2), 244–267 (2009).
[CrossRef]

Mossberg, T.

Rosencher, E.

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

Rostovtsev, Y. V.

M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, “Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316, 265–268 (2007).
[CrossRef] [PubMed]

Sautenkov, V. A.

M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, “Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316, 265–268 (2007).
[CrossRef] [PubMed]

Schlottau, F.

M. Colice, F. Schlottau, K. Wagner, R. Mohan, W. Babbitt, I. Lorgeré, and J.-L. Le Gouët, “RF spectrum analysis in spectral hole burning media,” Proc. SPIE 5557, 132 (2004).
[CrossRef]

Scully, M. O.

M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, “Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316, 265–268 (2007).
[CrossRef] [PubMed]

Sebbah, P.

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87(18), 183903 (2001).
[CrossRef]

Seelig, E. W.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000).
[CrossRef] [PubMed]

Sellars, M.

W. Tittel, M. Afzelius, R. Cone, T. Chanelière, S. Kroll, S. Moiseev, and M. Sellars, “Photon-echo quantum memory in solid state systems,” Laser Photonics Rev. 4(2), 244–267 (2009).
[CrossRef]

Simon, C.

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

Sokolov, A. V.

M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, “Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316, 265–268 (2007).
[CrossRef] [PubMed]

Sprik, R.

J. F. de Boer, A. Lagendijk, R. Sprik, and S. Feng, “Transmission and reflection correlations of second harmonic waves in nonlinear random media,” Phys. Rev. Lett. 71(24), 3947–3950 (1993).
[CrossRef] [PubMed]

Staudt, M. U.

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[CrossRef] [PubMed]

Sun, Y.

R. M. Macfarlane, Y. Sun, R. L. Cone, C. W. Thiel, and R. W. Equall, “Optical dephasing by disorder modes in yttrium orthosilicate (Y2SiO5) doped with Eu3+,” J. Lumin. 107(1–4), 310–313 (2004).
[CrossRef]

Ter-Gabriélyan, N.

V. Markushev, N. Ter-Gabriélyan, C. Briskina, V. Belan, and V. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Quantum Electron. 20(7), 773–777 (1990).
[CrossRef]

Thiel, C. W.

R. M. Macfarlane, Y. Sun, R. L. Cone, C. W. Thiel, and R. W. Equall, “Optical dephasing by disorder modes in yttrium orthosilicate (Y2SiO5) doped with Eu3+,” J. Lumin. 107(1–4), 310–313 (2004).
[CrossRef]

Tittel, W.

W. Tittel, M. Afzelius, R. Cone, T. Chanelière, S. Kroll, S. Moiseev, and M. Sellars, “Photon-echo quantum memory in solid state systems,” Laser Photonics Rev. 4(2), 244–267 (2009).
[CrossRef]

Tomita, M.

T. Ito and M. Tomita, “Speckle correlation measurement in a disordered medium observed through second-harmonics generation,” Phys. Rev. E 69, 036610 (2004).
[CrossRef]

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M. P. Van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[CrossRef] [PubMed]

Vanneste, C.

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87(18), 183903 (2001).
[CrossRef]

Wagner, K.

M. Colice, F. Schlottau, K. Wagner, R. Mohan, W. Babbitt, I. Lorgeré, and J.-L. Le Gouët, “RF spectrum analysis in spectral hole burning media,” Proc. SPIE 5557, 132 (2004).
[CrossRef]

Wellens, T.

T. Wellens and B. Grémaud, “Coherent propagation of waves in dilute random media with weak nonlinearity,” Phys. Rev. A 80(6), 063827 (2009).
[CrossRef]

T. Wellens and B. Grémaud, “Nonlinear coherent transport of waves in disordered media,” Phys. Rev. Lett. 100(3), 033902 (2008).
[CrossRef] [PubMed]

Wen, X.

Wiersma, D.

D. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008).
[CrossRef]

Wolf, P.-E.

P.-E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
[CrossRef] [PubMed]

Xu, J. Y.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000).
[CrossRef] [PubMed]

Zhang, D. Z.

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000).
[CrossRef] [PubMed]

Zhi, M.

M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, “Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316, 265–268 (2007).
[CrossRef] [PubMed]

Zolin, V.

V. Markushev, N. Ter-Gabriélyan, C. Briskina, V. Belan, and V. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Quantum Electron. 20(7), 773–777 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G. Gorju, V. Crozatier, I. Lorgeré, J.-L. Le Gouët, and F. Bretenaker, “10-GHz bandwidth RF spectral analyzer with MHz resolution based on spectral hole burning in Tm3+:YAG,” IEEE Photon. Technol. Lett. 17(11), 2385–2387 (2005).
[CrossRef]

J. Lumin. (1)

R. M. Macfarlane, Y. Sun, R. L. Cone, C. W. Thiel, and R. W. Equall, “Optical dephasing by disorder modes in yttrium orthosilicate (Y2SiO5) doped with Eu3+,” J. Lumin. 107(1–4), 310–313 (2004).
[CrossRef]

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

Laser Photonics Rev. (1)

W. Tittel, M. Afzelius, R. Cone, T. Chanelière, S. Kroll, S. Moiseev, and M. Sellars, “Photon-echo quantum memory in solid state systems,” Laser Photonics Rev. 4(2), 244–267 (2009).
[CrossRef]

Nat. Phys. (1)

D. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008).
[CrossRef]

Nature (2)

M. Baudrier-Raybaut, R. Haidar, P. Kupecek, P. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature 432(7015), 374–376 (2004).
[CrossRef] [PubMed]

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. (1)

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, “Photon echoes,” Phys. Rev. 141(1), 391–406 (1966).
[CrossRef]

Phys. Rev. A (1)

T. Wellens and B. Grémaud, “Coherent propagation of waves in dilute random media with weak nonlinearity,” Phys. Rev. A 80(6), 063827 (2009).
[CrossRef]

Phys. Rev. B (1)

V. E. Kravtsov, V. M. Agranovich, and K. I. Grigorishin, “Theory of second-harmonic generation in strongly scattering media,” Phys. Rev. B 44(10), 4931–4942 (1991).
[CrossRef]

Phys. Rev. E (1)

T. Ito and M. Tomita, “Speckle correlation measurement in a disordered medium observed through second-harmonics generation,” Phys. Rev. E 69, 036610 (2004).
[CrossRef]

Phys. Rev. Lett. (8)

M. P. Van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[CrossRef] [PubMed]

P.-E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55(24), 2696–2699 (1985).
[CrossRef] [PubMed]

J. F. de Boer, A. Lagendijk, R. Sprik, and S. Feng, “Transmission and reflection correlations of second harmonic waves in nonlinear random media,” Phys. Rev. Lett. 71(24), 3947–3950 (1993).
[CrossRef] [PubMed]

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87(18), 183903 (2001).
[CrossRef]

H. Cao, J. Y. Xu, D. Z. Zhang, S. H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84(24), 5584–5587 (2000).
[CrossRef] [PubMed]

T. Wellens and B. Grémaud, “Nonlinear coherent transport of waves in disordered media,” Phys. Rev. Lett. 100(3), 033902 (2008).
[CrossRef] [PubMed]

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon echo,” Phys. Rev. Lett. 13, 567–568 (1964).
[CrossRef]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61(7), 834–837 (1988).
[CrossRef] [PubMed]

Proc. SPIE (1)

M. Colice, F. Schlottau, K. Wagner, R. Mohan, W. Babbitt, I. Lorgeré, and J.-L. Le Gouët, “RF spectrum analysis in spectral hole burning media,” Proc. SPIE 5557, 132 (2004).
[CrossRef]

Quantum Electron. (1)

V. Markushev, N. Ter-Gabriélyan, C. Briskina, V. Belan, and V. Zolin, “Stimulated emission kinetics of neodymium powder lasers,” Quantum Electron. 20(7), 773–777 (1990).
[CrossRef]

Science (1)

M. Zhi, A. V. Sokolov, V. A. Sautenkov, Y. V. Rostovtsev, A. Dogariu, Y. Huang, and M. O. Scully, “Optimizing the laser-pulse configuration for coherent Raman spectroscopy,” Science 316, 265–268 (2007).
[CrossRef] [PubMed]

Other (1)

J.-L. Le Gouët, F. Bretenaker, and I. Lorgeré, “Atomic processing of optically carried RF signals,” in Advances in Atomic Molecular and Optical Physics (Elsevier, 2007), Vol. 54, pp. 549–613.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental set-up. P: powder, S: light stop, PD: photodetector.

Fig. 2
Fig. 2

Scattered light intensity recorded for a two-pulse photon echo sequence in a Pr3+:Y2SiO5 powder. Dashed line: Excitation pulses. Solid line: two-pulse echo (intensity × 110). The incident laser power is 32 mW.

Fig. 3
Fig. 3

Three-pulse photon echo heterodyne detection in situation (i): k I = k III = k 1 and k II = k 2. A 10 MHz-shifted probe pulse is used as a local oscillator (LO). (a) Beating is observed when the LO is sent along k II . (b) No beating is observed with a LO along k I .

Fig. 4
Fig. 4

Scattered light intensity recorded for a three-pulse photon echo (3PE) sequence for different excitation pulses time-ordering. The dashed line represents the excitation pulses. Solid lines: (a) situation (i): k I = k III = k 1 and k II = k 2; (b) k I = k II = k 1 and k III = k 2; (c) k I = k II = k III = k 1. The phase matching condition is satisfied for (a), (b) and (c). Two-pulse echos (2PE) are present in cases (b) and (c) (see text for details). (d) Situation (ii): 3PE is not observed.

Fig. 5
Fig. 5

Echo intensity variations with beam angle θ = (k 1, k 2). In situation (i), where k I = k III = k 1 and k II = k 2, the signal decreases to half the maximum value at large angle. In situation (ii), where k I = k 2 and k II = k III = k 1, the signal drops to zero at large angle. The characteristic angle of variation exhibits the same size in both profiles.

Equations (3)

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

E I * ( r ) E I I ( r ) E I I I ( r )
[ E I * ( r ) E I I ( r ) E I I I ( r ) ] coh . = 1 2 < E I * ( r ) E I I ( r ) > E I I I ( r ) + 1 2 < E I * ( r ) E I I I ( r ) > E I I ( r )
= 1 2 < I > [ E I I ( r ) + E I I I ( r ) ]

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