Abstract

Erasure of data stored by use of photon echoes has been investigated as a function of data writing time and data storage time. The results clarify the requirements on laser phase and frequency stability for performing photon-echo data erasure. The analysis of phase and frequency stability of a light source by the photon-echo erasure process is illustrated. A theoretical analysis emphasizing the physical processes that affect the erasure efficiency as well as an extensive discussion of possible error sources are given. Finally, an approach to bit-selective photon-echo data erasure that is insensitive to laser phase and frequency fluctuations is suggested.

© 1996 Optical Society of America

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References

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  1. W. E. Moerner, Persistent Spectral Hole-Burning: Science and Applications (Springer, New York, 1988), Chap. 7, pp. 251–307.
    [Crossref]
  2. T. W. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7, 77 (1982).
    [Crossref] [PubMed]
  3. X. A. Shen, E. Chiang, and R. Kachru, “Time-domain holographic image storage,” Opt. Lett. 19, 1246 (1994).
    [Crossref] [PubMed]
  4. M. Mitsunaga, N. Uesugi, H. Sasaki, and K. Karaki, “Holographic motion picture by Eu3+:Y2SiO5,” Opt. Lett. 19, 752 (1994).
    [Crossref] [PubMed]
  5. E. S. Maniloff, S. B. Altner, S. Bernet, F. R. Graf, A. Renn, and U. P. Wild, “Recording of 6000 holograms by use of spectral hole burning,” Appl. Opt. 34, 4140 (1995).
    [Crossref] [PubMed]
  6. W. R. Babbitt and T. W. Mossberg, “Quasi-two-dimensional time-domain color memories: process limitations and potentials,” J. Opt. Soc. Am. B 11, 1948 (1994).
    [Crossref]
  7. S. Kröll and P. Tidlund, “Recording density limit of photon-echo optical storage with high-speed reading and writing,” Appl. Opt. 32, 7233 (1993).
    [Crossref]
  8. S. Saikan, T. Kishida, A. Imaoka, K. Uchikawa, A. Furusawa, and H. Oosawa, “Optical memory based on heterodyne-detected accumulated photon echoes,” Opt. Lett. 14, 841 (1989).
    [Crossref] [PubMed]
  9. R. Yano, M. Mitsunaga, and N. Uesugi, “Nonlinear laser spectroscopy of Eu3+:Y2SiO5 and its application to time-domain optical memory,” J. Opt. Soc. Am. B 9, 992 (1992).
    [Crossref]
  10. R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179 (1994).
    [Crossref] [PubMed]
  11. Y. S. Bai, W. R. Babbitt, N. W. Carlsson, and T. W. Mossberg, “Real-time optical waveform convolver/cross correlator,” Appl. Phys. Lett. 45, 714 (1984).
    [Crossref]
  12. S. Kröll and U. Elman, “Photon-echo-based logical processing,” Opt. Lett. 18, 1834 (1993).
    [Crossref] [PubMed]
  13. M. Zhu, W. R. Babbitt, and C. M. Jefferson, “Continuous transient optical processing in a solid,” Opt. Lett. 20, 2514 (1995).
    [Crossref]
  14. W. R. Babbitt and T. W. Mossberg, “Spatial routing of optical beams through time-domain spatial-spectral filtering,” Opt. Lett. 20, 910 (1995).
    [Crossref] [PubMed]
  15. H. Sonajalg, A. Débarre, J.-L. Le Gouët, I. Lorgeré, and P. Tchénio, “Phase-encoding technique in time-domain holography: theoretical estimation,” J. Opt. Soc. Am. B 12, 1448 (1995).
    [Crossref]
  16. W. R. Babbitt, “The response of inhomogeneously broadened absorbers to temporally complex light pulses,” Ph.D. dissertation (Harvard University, Cambridge, Mass., 1987).
  17. H. Lin, T. Wang, G. A. Wilson, and T. W. Mossberg, “Experimental demonstration of swept-carrier time-domain optical memory,” Opt. Lett. 20, 91 (1995).
    [Crossref] [PubMed]
  18. X. A. Shen and R. Kachru, “Time-domain optical memory for image storage and high-speed image processing,” Appl. Opt. 32, 5810 (1993).
    [Crossref] [PubMed]
  19. H. Lin, T. Wang, and T. W. Mossberg, “Demonstration of 8-Gbit/in.2 areal storage density based on swept-carrier frequency-selective optical memory,” Opt. Lett. 20, 1658 (1995).
    [Crossref] [PubMed]
  20. E. Y. Xu, S. Kröll, D. L. Huestis, R. Kachru, and M. K. Kim, “Nanosecond image processing using stimulated photon echoes,” Opt. Lett. 15, 562 (1990).
    [Crossref] [PubMed]
  21. N. N. Akhmediev, “Information erasing in the phenomenon of long-lived photon echo,” Opt. Lett. 15, 1035 (1990).
    [Crossref] [PubMed]
  22. W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991 (1979).
    [Crossref]
  23. E. A. Manykin, N. V. Zhamensky, D. V. Marchenko, E. A. Petrenko, and M. A. Selifanov, “Elaboration of rapid data erasure methods in an optical storage device based on the photon echo effect,” Opt. Mem. Neural Networks 1, 239 (1992).
  24. M. Arend, E. Block, and S. R. Hartmann, “Random access processing of optical memory by use of photon-echo interference effects,” Opt. Lett. 18, 1789 (1993).
    [Crossref] [PubMed]
  25. O. V. Tchernyshyov, “On coherent erasure of long-lived photon echo,” Laser Phys. 2, 567 (1992).
  26. U. Elman and S. Kröll, “Statistical modeling and theoretical analysis of the influence of laser phase fluctuations on photon echo data erasure and stimulated photon echoes,” Laser Phys. (to be published).
  27. W. R. Babbitt and T. W. Mossberg, “Mixed binary multiplication of optical signals by convolution in an inhomogeneously broadened absorber,” Appl. Opt. 25, 962 (1986).
    [Crossref] [PubMed]
  28. R. M. Macfarlane and R. M. Shelby, “Coherent transient and holeburning spectroscopy of rare earth ions in solids,” in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii and R. M. Macfarlane, eds. (Elsevier, New York, 1987), p. 111.
  29. J. L. Hall and T. W. Hänsch, “External dye laser frequency stabilizer,” Opt. Lett. 9, 502 (1984).
    [Crossref] [PubMed]
  30. M. Mitsunaga, R. Yano, and N. Uesugi, “Stimulated-photon-echo spectroscopy. II. Echo modulation in Pr3+:YAlO3,” Phys. Rev. B 45, 12760 (1992).
    [Crossref]
  31. A. Szabo and T. Muramoto, “Experimental test of the optical Bloch equations for solids using free-induction decay,” Phys. Rev. A 39, 3992 (1989).
    [Crossref] [PubMed]
  32. M. K. Kim and R. Kachru, “Multiple-bit long-term data storage by backward-stimulated echo in Eu3+:YAlO3,” Opt. Lett. 14, 423 (1989).
    [Crossref] [PubMed]
  33. T. Blasberg and D. Suter, “Nuclear spin relaxation of Pr3+ in YAlO3. A temperature-dependent optical-rf double-resonance study,” Chem. Phys. Lett. 215, 668 (1993).
    [Crossref]
  34. M. Mitsunaga and R. G. Brewer, “Generalized perturbation theory of coherent optical emission,” Phys. Rev. A 32, 1605 (1985).
    [Crossref] [PubMed]
  35. L. E. Erickson, “Optical-pumping effects on Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay,” Phys. Rev. B 42, 3789 (1990).
    [Crossref]
  36. Y. S. Bai and R. Kachru, “Spin-fluctuation-induced optical spectral diffusion in Pr3+:YAlO3,” Phys. Rev. A 44, R6990 (1991).
    [Crossref]

1995 (6)

1994 (4)

1993 (5)

1992 (4)

E. A. Manykin, N. V. Zhamensky, D. V. Marchenko, E. A. Petrenko, and M. A. Selifanov, “Elaboration of rapid data erasure methods in an optical storage device based on the photon echo effect,” Opt. Mem. Neural Networks 1, 239 (1992).

O. V. Tchernyshyov, “On coherent erasure of long-lived photon echo,” Laser Phys. 2, 567 (1992).

M. Mitsunaga, R. Yano, and N. Uesugi, “Stimulated-photon-echo spectroscopy. II. Echo modulation in Pr3+:YAlO3,” Phys. Rev. B 45, 12760 (1992).
[Crossref]

R. Yano, M. Mitsunaga, and N. Uesugi, “Nonlinear laser spectroscopy of Eu3+:Y2SiO5 and its application to time-domain optical memory,” J. Opt. Soc. Am. B 9, 992 (1992).
[Crossref]

1991 (1)

Y. S. Bai and R. Kachru, “Spin-fluctuation-induced optical spectral diffusion in Pr3+:YAlO3,” Phys. Rev. A 44, R6990 (1991).
[Crossref]

1990 (3)

1989 (3)

1986 (1)

1985 (1)

M. Mitsunaga and R. G. Brewer, “Generalized perturbation theory of coherent optical emission,” Phys. Rev. A 32, 1605 (1985).
[Crossref] [PubMed]

1984 (2)

Y. S. Bai, W. R. Babbitt, N. W. Carlsson, and T. W. Mossberg, “Real-time optical waveform convolver/cross correlator,” Appl. Phys. Lett. 45, 714 (1984).
[Crossref]

J. L. Hall and T. W. Hänsch, “External dye laser frequency stabilizer,” Opt. Lett. 9, 502 (1984).
[Crossref] [PubMed]

1982 (1)

1979 (1)

W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991 (1979).
[Crossref]

Akhmediev, N. N.

Altner, S. B.

Arend, M.

Babbitt, W. R.

Bai, Y. S.

Y. S. Bai and R. Kachru, “Spin-fluctuation-induced optical spectral diffusion in Pr3+:YAlO3,” Phys. Rev. A 44, R6990 (1991).
[Crossref]

Y. S. Bai, W. R. Babbitt, N. W. Carlsson, and T. W. Mossberg, “Real-time optical waveform convolver/cross correlator,” Appl. Phys. Lett. 45, 714 (1984).
[Crossref]

Bernet, S.

Blasberg, T.

T. Blasberg and D. Suter, “Nuclear spin relaxation of Pr3+ in YAlO3. A temperature-dependent optical-rf double-resonance study,” Chem. Phys. Lett. 215, 668 (1993).
[Crossref]

Block, E.

Brewer, R. G.

M. Mitsunaga and R. G. Brewer, “Generalized perturbation theory of coherent optical emission,” Phys. Rev. A 32, 1605 (1985).
[Crossref] [PubMed]

Carlsson, N. W.

Y. S. Bai, W. R. Babbitt, N. W. Carlsson, and T. W. Mossberg, “Real-time optical waveform convolver/cross correlator,” Appl. Phys. Lett. 45, 714 (1984).
[Crossref]

Chiang, E.

Cone, R. L.

R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179 (1994).
[Crossref] [PubMed]

Débarre, A.

Elman, U.

S. Kröll and U. Elman, “Photon-echo-based logical processing,” Opt. Lett. 18, 1834 (1993).
[Crossref] [PubMed]

U. Elman and S. Kröll, “Statistical modeling and theoretical analysis of the influence of laser phase fluctuations on photon echo data erasure and stimulated photon echoes,” Laser Phys. (to be published).

Equall, R. W.

R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179 (1994).
[Crossref] [PubMed]

Erickson, L. E.

L. E. Erickson, “Optical-pumping effects on Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay,” Phys. Rev. B 42, 3789 (1990).
[Crossref]

Furusawa, A.

Gouët, J.-L. Le

Graf, F. R.

Hall, J. L.

Hänsch, T. W.

Hartmann, S. R.

Hesselink, W. H.

W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991 (1979).
[Crossref]

Huestis, D. L.

Imaoka, A.

Jefferson, C. M.

Kachru, R.

Karaki, K.

Kim, M. K.

Kishida, T.

Kröll, S.

Lin, H.

Lorgeré, I.

Macfarlane, R. M.

R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179 (1994).
[Crossref] [PubMed]

R. M. Macfarlane and R. M. Shelby, “Coherent transient and holeburning spectroscopy of rare earth ions in solids,” in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii and R. M. Macfarlane, eds. (Elsevier, New York, 1987), p. 111.

Maniloff, E. S.

Manykin, E. A.

E. A. Manykin, N. V. Zhamensky, D. V. Marchenko, E. A. Petrenko, and M. A. Selifanov, “Elaboration of rapid data erasure methods in an optical storage device based on the photon echo effect,” Opt. Mem. Neural Networks 1, 239 (1992).

Marchenko, D. V.

E. A. Manykin, N. V. Zhamensky, D. V. Marchenko, E. A. Petrenko, and M. A. Selifanov, “Elaboration of rapid data erasure methods in an optical storage device based on the photon echo effect,” Opt. Mem. Neural Networks 1, 239 (1992).

Mitsunaga, M.

M. Mitsunaga, N. Uesugi, H. Sasaki, and K. Karaki, “Holographic motion picture by Eu3+:Y2SiO5,” Opt. Lett. 19, 752 (1994).
[Crossref] [PubMed]

R. Yano, M. Mitsunaga, and N. Uesugi, “Nonlinear laser spectroscopy of Eu3+:Y2SiO5 and its application to time-domain optical memory,” J. Opt. Soc. Am. B 9, 992 (1992).
[Crossref]

M. Mitsunaga, R. Yano, and N. Uesugi, “Stimulated-photon-echo spectroscopy. II. Echo modulation in Pr3+:YAlO3,” Phys. Rev. B 45, 12760 (1992).
[Crossref]

M. Mitsunaga and R. G. Brewer, “Generalized perturbation theory of coherent optical emission,” Phys. Rev. A 32, 1605 (1985).
[Crossref] [PubMed]

Moerner, W. E.

W. E. Moerner, Persistent Spectral Hole-Burning: Science and Applications (Springer, New York, 1988), Chap. 7, pp. 251–307.
[Crossref]

Mossberg, T. W.

Muramoto, T.

A. Szabo and T. Muramoto, “Experimental test of the optical Bloch equations for solids using free-induction decay,” Phys. Rev. A 39, 3992 (1989).
[Crossref] [PubMed]

Oosawa, H.

Petrenko, E. A.

E. A. Manykin, N. V. Zhamensky, D. V. Marchenko, E. A. Petrenko, and M. A. Selifanov, “Elaboration of rapid data erasure methods in an optical storage device based on the photon echo effect,” Opt. Mem. Neural Networks 1, 239 (1992).

Renn, A.

Saikan, S.

Sasaki, H.

Selifanov, M. A.

E. A. Manykin, N. V. Zhamensky, D. V. Marchenko, E. A. Petrenko, and M. A. Selifanov, “Elaboration of rapid data erasure methods in an optical storage device based on the photon echo effect,” Opt. Mem. Neural Networks 1, 239 (1992).

Shelby, R. M.

R. M. Macfarlane and R. M. Shelby, “Coherent transient and holeburning spectroscopy of rare earth ions in solids,” in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii and R. M. Macfarlane, eds. (Elsevier, New York, 1987), p. 111.

Shen, X. A.

Sonajalg, H.

Sun, Y.

R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179 (1994).
[Crossref] [PubMed]

Suter, D.

T. Blasberg and D. Suter, “Nuclear spin relaxation of Pr3+ in YAlO3. A temperature-dependent optical-rf double-resonance study,” Chem. Phys. Lett. 215, 668 (1993).
[Crossref]

Szabo, A.

A. Szabo and T. Muramoto, “Experimental test of the optical Bloch equations for solids using free-induction decay,” Phys. Rev. A 39, 3992 (1989).
[Crossref] [PubMed]

Tchénio, P.

Tchernyshyov, O. V.

O. V. Tchernyshyov, “On coherent erasure of long-lived photon echo,” Laser Phys. 2, 567 (1992).

Tidlund, P.

Uchikawa, K.

Uesugi, N.

Wang, T.

Wiersma, D. A.

W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991 (1979).
[Crossref]

Wild, U. P.

Wilson, G. A.

Xu, E. Y.

Yano, R.

R. Yano, M. Mitsunaga, and N. Uesugi, “Nonlinear laser spectroscopy of Eu3+:Y2SiO5 and its application to time-domain optical memory,” J. Opt. Soc. Am. B 9, 992 (1992).
[Crossref]

M. Mitsunaga, R. Yano, and N. Uesugi, “Stimulated-photon-echo spectroscopy. II. Echo modulation in Pr3+:YAlO3,” Phys. Rev. B 45, 12760 (1992).
[Crossref]

Zhamensky, N. V.

E. A. Manykin, N. V. Zhamensky, D. V. Marchenko, E. A. Petrenko, and M. A. Selifanov, “Elaboration of rapid data erasure methods in an optical storage device based on the photon echo effect,” Opt. Mem. Neural Networks 1, 239 (1992).

Zhu, M.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

Y. S. Bai, W. R. Babbitt, N. W. Carlsson, and T. W. Mossberg, “Real-time optical waveform convolver/cross correlator,” Appl. Phys. Lett. 45, 714 (1984).
[Crossref]

Chem. Phys. Lett. (1)

T. Blasberg and D. Suter, “Nuclear spin relaxation of Pr3+ in YAlO3. A temperature-dependent optical-rf double-resonance study,” Chem. Phys. Lett. 215, 668 (1993).
[Crossref]

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

Laser Phys. (1)

O. V. Tchernyshyov, “On coherent erasure of long-lived photon echo,” Laser Phys. 2, 567 (1992).

Opt. Lett. (14)

M. Arend, E. Block, and S. R. Hartmann, “Random access processing of optical memory by use of photon-echo interference effects,” Opt. Lett. 18, 1789 (1993).
[Crossref] [PubMed]

H. Lin, T. Wang, and T. W. Mossberg, “Demonstration of 8-Gbit/in.2 areal storage density based on swept-carrier frequency-selective optical memory,” Opt. Lett. 20, 1658 (1995).
[Crossref] [PubMed]

E. Y. Xu, S. Kröll, D. L. Huestis, R. Kachru, and M. K. Kim, “Nanosecond image processing using stimulated photon echoes,” Opt. Lett. 15, 562 (1990).
[Crossref] [PubMed]

N. N. Akhmediev, “Information erasing in the phenomenon of long-lived photon echo,” Opt. Lett. 15, 1035 (1990).
[Crossref] [PubMed]

M. K. Kim and R. Kachru, “Multiple-bit long-term data storage by backward-stimulated echo in Eu3+:YAlO3,” Opt. Lett. 14, 423 (1989).
[Crossref] [PubMed]

J. L. Hall and T. W. Hänsch, “External dye laser frequency stabilizer,” Opt. Lett. 9, 502 (1984).
[Crossref] [PubMed]

T. W. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7, 77 (1982).
[Crossref] [PubMed]

X. A. Shen, E. Chiang, and R. Kachru, “Time-domain holographic image storage,” Opt. Lett. 19, 1246 (1994).
[Crossref] [PubMed]

M. Mitsunaga, N. Uesugi, H. Sasaki, and K. Karaki, “Holographic motion picture by Eu3+:Y2SiO5,” Opt. Lett. 19, 752 (1994).
[Crossref] [PubMed]

S. Saikan, T. Kishida, A. Imaoka, K. Uchikawa, A. Furusawa, and H. Oosawa, “Optical memory based on heterodyne-detected accumulated photon echoes,” Opt. Lett. 14, 841 (1989).
[Crossref] [PubMed]

H. Lin, T. Wang, G. A. Wilson, and T. W. Mossberg, “Experimental demonstration of swept-carrier time-domain optical memory,” Opt. Lett. 20, 91 (1995).
[Crossref] [PubMed]

S. Kröll and U. Elman, “Photon-echo-based logical processing,” Opt. Lett. 18, 1834 (1993).
[Crossref] [PubMed]

M. Zhu, W. R. Babbitt, and C. M. Jefferson, “Continuous transient optical processing in a solid,” Opt. Lett. 20, 2514 (1995).
[Crossref]

W. R. Babbitt and T. W. Mossberg, “Spatial routing of optical beams through time-domain spatial-spectral filtering,” Opt. Lett. 20, 910 (1995).
[Crossref] [PubMed]

Opt. Mem. Neural Networks (1)

E. A. Manykin, N. V. Zhamensky, D. V. Marchenko, E. A. Petrenko, and M. A. Selifanov, “Elaboration of rapid data erasure methods in an optical storage device based on the photon echo effect,” Opt. Mem. Neural Networks 1, 239 (1992).

Phys. Rev. A (3)

A. Szabo and T. Muramoto, “Experimental test of the optical Bloch equations for solids using free-induction decay,” Phys. Rev. A 39, 3992 (1989).
[Crossref] [PubMed]

M. Mitsunaga and R. G. Brewer, “Generalized perturbation theory of coherent optical emission,” Phys. Rev. A 32, 1605 (1985).
[Crossref] [PubMed]

Y. S. Bai and R. Kachru, “Spin-fluctuation-induced optical spectral diffusion in Pr3+:YAlO3,” Phys. Rev. A 44, R6990 (1991).
[Crossref]

Phys. Rev. B (2)

L. E. Erickson, “Optical-pumping effects on Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay,” Phys. Rev. B 42, 3789 (1990).
[Crossref]

M. Mitsunaga, R. Yano, and N. Uesugi, “Stimulated-photon-echo spectroscopy. II. Echo modulation in Pr3+:YAlO3,” Phys. Rev. B 45, 12760 (1992).
[Crossref]

Phys. Rev. Lett. (2)

W. H. Hesselink and D. A. Wiersma, “Picosecond photon echoes stimulated from an accumulated grating,” Phys. Rev. Lett. 43, 1991 (1979).
[Crossref]

R. W. Equall, Y. Sun, R. L. Cone, and R. M. Macfarlane, “Ultraslow optical dephasing in Eu3+:Y2SiO5,” Phys. Rev. Lett. 72, 2179 (1994).
[Crossref] [PubMed]

Other (4)

W. E. Moerner, Persistent Spectral Hole-Burning: Science and Applications (Springer, New York, 1988), Chap. 7, pp. 251–307.
[Crossref]

W. R. Babbitt, “The response of inhomogeneously broadened absorbers to temporally complex light pulses,” Ph.D. dissertation (Harvard University, Cambridge, Mass., 1987).

U. Elman and S. Kröll, “Statistical modeling and theoretical analysis of the influence of laser phase fluctuations on photon echo data erasure and stimulated photon echoes,” Laser Phys. (to be published).

R. M. Macfarlane and R. M. Shelby, “Coherent transient and holeburning spectroscopy of rare earth ions in solids,” in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii and R. M. Macfarlane, eds. (Elsevier, New York, 1987), p. 111.

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Figures (12)

Fig. 1
Fig. 1

Typical input sequences for photon-echo experiments together with the definition of the time intervals τ, Δ, and σ used subsequently in this paper. a, the first two pulses write (w), and data (d) create a frequency-dependent population grating in the material, which is probed by the read pulse (r). b, By use of several pairs of write and data pulses the population grating by each pair can be added to the population grating created by the previous pairs, leading to an enhanced signal after readout. c, Phase-shifted data pulse in the second pair. The first and the second gratings cancel instead of enhancing each other, which leads to a suppressed or even an eliminated signal.

Fig. 2
Fig. 2

Experimental set up: EOM, electro-optic modulator; AOM is acousto-optic modulators; XTAL, crystal; PMT, photomultiplier tube.

Fig. 3
Fig. 3

Experimental recordings of pulse sequences corresponding to a, Fig. 1b and b, Fig. 1c. The notation for the excitation pulses is the same as in Fig. 1. There are several echo output pulses, denoted E1–E6. As can be seen, not only one but two of the echo output pulses are suppressed when a phase shift is applied. Further discussion is given in the text.

Fig. 4
Fig. 4

Erasure efficiency, as defined in the text, versus the temporal separation between the write and data pulses (τ) in each pair. The rapid decrease of the erasure efficiency as a function of the pulse separation is interpreted as being caused by laser phase fluctuations.

Fig. 5
Fig. 5

Echo signal for two accumulated excitation pulse pairs versus Pockels cell voltage applied to the electro-optic modulator in Fig. 2. For zero voltage the excitation sequence corresponds to that in Fig. 1b. The electro-optic modulator voltage for 180-deg phase shift is ∼420 V. At this voltage the excitation sequence corresponds to the trace in Fig. 1c. Good agreement is obtained between experimental (▲) and theoretical (□) values.

Fig. 6
Fig. 6

Erasure efficiency, as defined in the text, versus the separation between the two excitation pulse pairs for two different separations between the pulses within a pair (▲, 500 ns and ▽, 1000 ns). The decrease in erasure efficiency as a function of pulse pair separation is interpreted as being caused by laser frequency drift.

Fig. 7
Fig. 7

Echo intensity for an excitation sequence as in Fig. 1b as a function of frequency shift applied to the first excitation pulse pair. Darker figures, theory; lighter figures, experiment.

Fig. 8
Fig. 8

Echo intensity for an excitation sequence as in Fig. 1a as function of frequency shift applied to the third pulse, r. Darker figures, theory; lighter figures, experiment.

Fig. 9
Fig. 9

Laser phase shift versus time as calculated from the experimental data in Fig. 4. As discussed in the text, a laser frequency drift of 40 kHz during 10 µs has been assumed in addition to the phase shift.

Fig. 10
Fig. 10

Laser frequency drift versus time calculated from the experimental data in Fig. 6 assuming the frequency drift is 40 kHz after 10 µs. Dark rectangles, τ = 500 ns; light triangles, τ = 1000 ns.

Fig. 11
Fig. 11

Schematic energy-level diagram of the energy levels of relevance for the erasure process. |1〉 is the ground state. The excitation pulses transfer population between states |1〉 and |2〉. A fraction β of the atoms present in state |2〉 after the excitation will decay (radiatively or nonradiatively) to reservoir state |3〉. After a comparatively long time (0.1–1 s) the atoms will decay from the reservoir state back to the ground state.

Fig. 12
Fig. 12

Conceptual view of how the sensitivity of the erasure process to phase and frequency fluctuations can be eliminated. To erase data stored in the sample the sequence is read out. The read pulse and the output are coupled into the erasure loop where the data sequence is amplified, and the read pulse (or the data sequence) is phase shifted by 180 deg. As they enter the sample again the former read pulse now acts as a write pulse for the recalled data sequence. Because of the added phase shift these input pulses will neutralize the existing population grating from which it was originally generated.

Equations (13)

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Eoutt-Ew*ωEdωErωexpiωtdω
Eout(t)-[Ew1*(ω)Ed1(ω)+Ew2*Ed2(ω)]Er(ω)exp(iωt)dω.
Ekt=E0 exp-2t-tkT2-iωkt+ϕk,
Ekω=E exp-Tω+ωk28exp-iω+ωktk+ϕk.
Eoutt=C exp-Tω1-ω2212exp-23 t-teT2×phase factor.
Ioutt=|Eoutpair 1exp-iϕext+Eoutpair 2|2exp-43 t-teT21+e-2γ+2e-γ×cosΔϕ-ϕext+2ω1-ω2t-te/3,
γ=[T(ω1-ω2)]212,
Δϕ=(ω1-ω2)τ+(ϕw1-ϕd1)-(ϕw2-ϕd2).
S1+e-2γ+2e-2γ cos(Δϕ-ϕext).
η=S(ϕext=0)S(ϕext=π)=1+e-2γ+2e-2γ cos(Δϕ)1+e-2γ-2e-2γ cos(Δϕ).
Eout(t)-[Ew1*(ω)Ed1(ω)×exp(-Δ/T1)+Ew2*(ω)Ed2(ω)]×exp(-σ/T1)Er(ω)exp(iωt)dω,
Eout(t)-Ew1*(ω)Ed1(ω)[exp[-(Δ+σ)/T1]+(β/2){1-exp[-(Δ+σ)/T1]}]Er(ω)×exp(iωt)dω+-Ew2*(ω)Ed2(ω)×[exp(-σ/T1)+(β/2)×[1-exp(-σ/T1)]]Er(ω)exp(iωt)dω.
η=exp-Δ+σ/T1+β/21-exp-Δ+σ/T1+exp-σ/T1+β/21-exp-σ/T1exp-Δ+σ/T1+β/21-exp-Δ+σ/T1-exp-σ/T1-β/21-exp-σ/T12.

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