Abstract

The first analysis to our knowledge of the optical data storage density of photon-echo storage is presented. Mainly considering signal-to-noise ratio performance, we calculate the obtainable storage density for data storage and processing using photon echoes to be approximately 100 times the theoretical limit for conventional optical data storage. This limit is similar to that theoretically calculated for data storage by use of persistent spectral hole burning. For storage times longer than the upper-state lifetime the highest densities can, however, be obtained only if all the excited atoms decay, or are transferred, to a different state than that from which they were originally excited. The analysis is restricted to samples with low optical density, and it also assumes that for every data sequence, writing is performed only once. It is therefore not directly applicable to accumulated photon echoes. A significant feature of photon-echo storage and processing is its speed; e.g., addressing 1 kbyte/(spatial point) permits terahertz read and write speeds for transitions with transition probabilities as low as 1000 s−1.

© 1993 Optical Society of America

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References

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  1. T. W. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7, 77–79 (1982).
    [CrossRef] [PubMed]
  2. Y. S. Bai, W. R. Babbitt, N. W. Carlson, T. W. Mossberg, “Real-time optical waveform convolver/cross correlator,” Appl. Phys. Lett. 45, 714–716 (1984).
    [CrossRef]
  3. S. Saikan, T. Kishida, A. Imaoka, K. Uchikawa, A. Furusawa, H. Oosawa, “Optical memory based on heterodyne-detected accumulated photon echoes,” Opt. Lett. 14, 841–843 (1989).
    [CrossRef] [PubMed]
  4. M. Mitsunaga, N. Uesugi, “248-bit optical data storage in Eu3+:YAlO3 by accumulated photon echoes,” Opt. Lett. 15, 195–197 (1990).
    [CrossRef] [PubMed]
  5. V. L. da Silva, Y. Silberberg, J. P. Heritage, E. W. Chase, M. A. Saifi, M. J. Andrejco, “Femtosecond accumulated photon echo in Er-doped fibers,” Opt. Lett. 16, 1340–1342 (1991).
    [CrossRef] [PubMed]
  6. A. Débarre, J.-C. Keller, J.-L. Le Gouët, P. Tchénio, J.-P. Galaup, “Optical information storage in condensed matter with stochastic excitation,” J. Opt. Soc. Am. B 8, 2529–2536 (1991).
    [CrossRef]
  7. S. Kröll, L. E. Jusinski, R. Kachru, “Frequency-chirped copropagating multiple-bit stimulated echo storage and retrieval in Pr3+:YAlO3,” Opt. Lett. 16, 517–519 (1991).
    [CrossRef] [PubMed]
  8. Persistent Spectral Hole Burning: Science and Application, Vol. 16 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991).
  9. W. E. Moerner, Persistent Spectral Hole-Burning: Science and Applications (Springer, New York, 1988), Chap. 7, pp. 251–307.
    [CrossRef]
  10. W. E. Moerner, M. D. Levenson, “Can single-photon processes provide useful materials for frequency-domain optical storage,” J. Opt. Soc. B 2, 915–924 (1985).
    [CrossRef]
  11. N. Murase, K. Horie, M. Terao, M. Ojima, “Theoretical study of the recording density limit of photochemical hole-burning memory,” J. Opt. Soc. Am. B 9, 998–1005 (1992).
    [CrossRef]
  12. M. Mitsunaga, R. Yano, N. Uesugi, “Time- and frequency-domain hybrid optical memory: 1.6-kbit data storage in Eu3+:Y2SiO5,” Opt. Lett. 16, 1890–1892 (1991).
    [CrossRef] [PubMed]
  13. T. W. Mossberg, “Swept-carrier time-domain optical memory,” Opt. Lett. 17, 535–537 (1992).
    [CrossRef] [PubMed]
  14. S. Saikan, K. Uchikawa, H. Ohsawa, “Phase-modulation technique for accumulated photon echo,” Opt. Lett. 16, 10–12 (1991).
    [CrossRef] [PubMed]
  15. X. A. Shen, Y. S. Bai, R. Kachru, “Reprogrammable optical matched filter for biphase-coded pulse compression,” Opt. Lett. 17, 1079–1081 (1992).
    [CrossRef] [PubMed]
  16. I. D. Abella, A. Kurnit, S. R. Hartmann, “Photon echoes,” Phys. Rev. 141, 391–406 (1966).
    [CrossRef]
  17. R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
    [CrossRef]
  18. M.-K. Kim, R. Kachru, “Many-bit optical data storage using stimulated echoes,” Appl. Opt. 28, 2186–2189 (1989).
    [CrossRef] [PubMed]
  19. A. G. Andersson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324–1338 (1955).
    [CrossRef]
  20. R. C. Hilborn, “Einstein coefficients, cross sections, f values, dipole moments, and all that,” Am. J. Phys. 50, 982–986 (1982).
    [CrossRef]
  21. A. C. G. Mitchell, M. W. Zeemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, Cambridge, 1971), Chap. 3, pp. 92–102.
  22. L. E. Erickson, “Optical-pumping effects on Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay,” Phys. Rev. B 42, 3789–3797 (1990).
    [CrossRef]
  23. A. Winnacker, R. M. Shelby, R. M. Macfarlane, “Photon-gated hole burning: a new mechanism using two-step photoionization,” Opt. Lett. 10, 350–352 (1985).
    [CrossRef] [PubMed]
  24. B. E. A. Saleh, M. C. Teich, Fundamentals of PhotonicsWiley, New York, 1991) p. 852.
  25. R. M. Macfarlane, R. M. Shelby, “Coherent transient and hole-burning spectroscopy of rare earth ions in solids,” in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii, R. M. Macfarlane, eds. (Elsevier, New York, 1987), p. 51.
  26. E. L. Hahn, N. S. Shiren, S. L. McCall, “Application of the area theorem to photon echoes,” Phys. Lett. A 37, 265–267 (1971).
    [CrossRef]
  27. R. Friedberg, S. R. Hartmann, “Superradiant damping and absorption,” Phys. Lett. A 37, 285–286 (1971).
    [CrossRef]
  28. X. A. Shen, R. Kachru, “High-speed pattern recognition by using stimulated echoes,” Opt. Lett. 17, 520–522 (1992).
    [CrossRef] [PubMed]
  29. D. Manganaris, P. Talagala, M. K. Kim, “Spatial mixed binary multiplication by photon echoes,” Appl. Opt. 31, 2426–2429 (1992).
    [CrossRef] [PubMed]
  30. W. R. Babbitt, “Optical coherent transient memory systgems,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, W. J. Micelli, S. T. Kowell, eds. Proc. Soc. Photo-Opt. Instrum. Eng.2026, 2026–50 (1993).
  31. Y. S. Bai, R. Kachru, “Coherent time-domain data storage with a spread spectrum generated by random biphase shifting,” Opt. Lett. 18, 1189–1191 (1993).
    [CrossRef] [PubMed]

1993 (1)

1992 (5)

1991 (5)

1990 (2)

M. Mitsunaga, N. Uesugi, “248-bit optical data storage in Eu3+:YAlO3 by accumulated photon echoes,” Opt. Lett. 15, 195–197 (1990).
[CrossRef] [PubMed]

L. E. Erickson, “Optical-pumping effects on Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay,” Phys. Rev. B 42, 3789–3797 (1990).
[CrossRef]

1989 (2)

1985 (2)

W. E. Moerner, M. D. Levenson, “Can single-photon processes provide useful materials for frequency-domain optical storage,” J. Opt. Soc. B 2, 915–924 (1985).
[CrossRef]

A. Winnacker, R. M. Shelby, R. M. Macfarlane, “Photon-gated hole burning: a new mechanism using two-step photoionization,” Opt. Lett. 10, 350–352 (1985).
[CrossRef] [PubMed]

1984 (1)

Y. S. Bai, W. R. Babbitt, N. W. Carlson, T. W. Mossberg, “Real-time optical waveform convolver/cross correlator,” Appl. Phys. Lett. 45, 714–716 (1984).
[CrossRef]

1982 (2)

T. W. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7, 77–79 (1982).
[CrossRef] [PubMed]

R. C. Hilborn, “Einstein coefficients, cross sections, f values, dipole moments, and all that,” Am. J. Phys. 50, 982–986 (1982).
[CrossRef]

1971 (2)

E. L. Hahn, N. S. Shiren, S. L. McCall, “Application of the area theorem to photon echoes,” Phys. Lett. A 37, 265–267 (1971).
[CrossRef]

R. Friedberg, S. R. Hartmann, “Superradiant damping and absorption,” Phys. Lett. A 37, 285–286 (1971).
[CrossRef]

1966 (1)

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

1955 (1)

A. G. Andersson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324–1338 (1955).
[CrossRef]

1954 (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
[CrossRef]

Abella, I. D.

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

Andersson, A. G.

A. G. Andersson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324–1338 (1955).
[CrossRef]

Andrejco, M. J.

Babbitt, W. R.

Y. S. Bai, W. R. Babbitt, N. W. Carlson, T. W. Mossberg, “Real-time optical waveform convolver/cross correlator,” Appl. Phys. Lett. 45, 714–716 (1984).
[CrossRef]

W. R. Babbitt, “Optical coherent transient memory systgems,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, W. J. Micelli, S. T. Kowell, eds. Proc. Soc. Photo-Opt. Instrum. Eng.2026, 2026–50 (1993).

Bai, Y. S.

Carlson, N. W.

Y. S. Bai, W. R. Babbitt, N. W. Carlson, T. W. Mossberg, “Real-time optical waveform convolver/cross correlator,” Appl. Phys. Lett. 45, 714–716 (1984).
[CrossRef]

Chase, E. W.

da Silva, V. L.

Débarre, A.

Dicke, R. H.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
[CrossRef]

Erickson, L. E.

L. E. Erickson, “Optical-pumping effects on Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay,” Phys. Rev. B 42, 3789–3797 (1990).
[CrossRef]

Friedberg, R.

R. Friedberg, S. R. Hartmann, “Superradiant damping and absorption,” Phys. Lett. A 37, 285–286 (1971).
[CrossRef]

Furusawa, A.

Galaup, J.-P.

Garwin, R. L.

A. G. Andersson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324–1338 (1955).
[CrossRef]

Hahn, E. L.

E. L. Hahn, N. S. Shiren, S. L. McCall, “Application of the area theorem to photon echoes,” Phys. Lett. A 37, 265–267 (1971).
[CrossRef]

A. G. Andersson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324–1338 (1955).
[CrossRef]

Hartmann, S. R.

R. Friedberg, S. R. Hartmann, “Superradiant damping and absorption,” Phys. Lett. A 37, 285–286 (1971).
[CrossRef]

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

Heritage, J. P.

Hilborn, R. C.

R. C. Hilborn, “Einstein coefficients, cross sections, f values, dipole moments, and all that,” Am. J. Phys. 50, 982–986 (1982).
[CrossRef]

Horie, K.

Horton, J. W.

A. G. Andersson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324–1338 (1955).
[CrossRef]

Imaoka, A.

Jusinski, L. E.

Kachru, R.

Keller, J.-C.

Kim, M. K.

Kim, M.-K.

Kishida, T.

Kröll, S.

Kurnit, A.

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

Le Gouët, J.-L.

Levenson, M. D.

W. E. Moerner, M. D. Levenson, “Can single-photon processes provide useful materials for frequency-domain optical storage,” J. Opt. Soc. B 2, 915–924 (1985).
[CrossRef]

Macfarlane, R. M.

A. Winnacker, R. M. Shelby, R. M. Macfarlane, “Photon-gated hole burning: a new mechanism using two-step photoionization,” Opt. Lett. 10, 350–352 (1985).
[CrossRef] [PubMed]

R. M. Macfarlane, R. M. Shelby, “Coherent transient and hole-burning spectroscopy of rare earth ions in solids,” in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii, R. M. Macfarlane, eds. (Elsevier, New York, 1987), p. 51.

Manganaris, D.

McCall, S. L.

E. L. Hahn, N. S. Shiren, S. L. McCall, “Application of the area theorem to photon echoes,” Phys. Lett. A 37, 265–267 (1971).
[CrossRef]

Mitchell, A. C. G.

A. C. G. Mitchell, M. W. Zeemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, Cambridge, 1971), Chap. 3, pp. 92–102.

Mitsunaga, M.

Moerner, W. E.

W. E. Moerner, M. D. Levenson, “Can single-photon processes provide useful materials for frequency-domain optical storage,” J. Opt. Soc. B 2, 915–924 (1985).
[CrossRef]

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

Mossberg, T. W.

Murase, N.

Ohsawa, H.

Ojima, M.

Oosawa, H.

Saifi, M. A.

Saikan, S.

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of PhotonicsWiley, New York, 1991) p. 852.

Shelby, R. M.

A. Winnacker, R. M. Shelby, R. M. Macfarlane, “Photon-gated hole burning: a new mechanism using two-step photoionization,” Opt. Lett. 10, 350–352 (1985).
[CrossRef] [PubMed]

R. M. Macfarlane, R. M. Shelby, “Coherent transient and hole-burning spectroscopy of rare earth ions in solids,” in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii, R. M. Macfarlane, eds. (Elsevier, New York, 1987), p. 51.

Shen, X. A.

Shiren, N. S.

E. L. Hahn, N. S. Shiren, S. L. McCall, “Application of the area theorem to photon echoes,” Phys. Lett. A 37, 265–267 (1971).
[CrossRef]

Silberberg, Y.

Talagala, P.

Tchénio, P.

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of PhotonicsWiley, New York, 1991) p. 852.

Terao, M.

Tucker, G. L.

A. G. Andersson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324–1338 (1955).
[CrossRef]

Uchikawa, K.

Uesugi, N.

Walker, R. M.

A. G. Andersson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324–1338 (1955).
[CrossRef]

Winnacker, A.

Yano, R.

Zeemansky, M. W.

A. C. G. Mitchell, M. W. Zeemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, Cambridge, 1971), Chap. 3, pp. 92–102.

Am. J. Phys. (1)

R. C. Hilborn, “Einstein coefficients, cross sections, f values, dipole moments, and all that,” Am. J. Phys. 50, 982–986 (1982).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

Y. S. Bai, W. R. Babbitt, N. W. Carlson, T. W. Mossberg, “Real-time optical waveform convolver/cross correlator,” Appl. Phys. Lett. 45, 714–716 (1984).
[CrossRef]

J. Appl. Phys. (1)

A. G. Andersson, R. L. Garwin, E. L. Hahn, J. W. Horton, G. L. Tucker, R. M. Walker, “Spin echo serial storage memory,” J. Appl. Phys. 26, 1324–1338 (1955).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Opt. Soc. B (1)

W. E. Moerner, M. D. Levenson, “Can single-photon processes provide useful materials for frequency-domain optical storage,” J. Opt. Soc. B 2, 915–924 (1985).
[CrossRef]

Opt. Lett. (12)

T. W. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7, 77–79 (1982).
[CrossRef] [PubMed]

M. Mitsunaga, R. Yano, N. Uesugi, “Time- and frequency-domain hybrid optical memory: 1.6-kbit data storage in Eu3+:Y2SiO5,” Opt. Lett. 16, 1890–1892 (1991).
[CrossRef] [PubMed]

T. W. Mossberg, “Swept-carrier time-domain optical memory,” Opt. Lett. 17, 535–537 (1992).
[CrossRef] [PubMed]

S. Saikan, K. Uchikawa, H. Ohsawa, “Phase-modulation technique for accumulated photon echo,” Opt. Lett. 16, 10–12 (1991).
[CrossRef] [PubMed]

X. A. Shen, Y. S. Bai, R. Kachru, “Reprogrammable optical matched filter for biphase-coded pulse compression,” Opt. Lett. 17, 1079–1081 (1992).
[CrossRef] [PubMed]

S. Kröll, L. E. Jusinski, R. Kachru, “Frequency-chirped copropagating multiple-bit stimulated echo storage and retrieval in Pr3+:YAlO3,” Opt. Lett. 16, 517–519 (1991).
[CrossRef] [PubMed]

S. Saikan, T. Kishida, A. Imaoka, K. Uchikawa, A. Furusawa, H. Oosawa, “Optical memory based on heterodyne-detected accumulated photon echoes,” Opt. Lett. 14, 841–843 (1989).
[CrossRef] [PubMed]

M. Mitsunaga, N. Uesugi, “248-bit optical data storage in Eu3+:YAlO3 by accumulated photon echoes,” Opt. Lett. 15, 195–197 (1990).
[CrossRef] [PubMed]

V. L. da Silva, Y. Silberberg, J. P. Heritage, E. W. Chase, M. A. Saifi, M. J. Andrejco, “Femtosecond accumulated photon echo in Er-doped fibers,” Opt. Lett. 16, 1340–1342 (1991).
[CrossRef] [PubMed]

Y. S. Bai, R. Kachru, “Coherent time-domain data storage with a spread spectrum generated by random biphase shifting,” Opt. Lett. 18, 1189–1191 (1993).
[CrossRef] [PubMed]

A. Winnacker, R. M. Shelby, R. M. Macfarlane, “Photon-gated hole burning: a new mechanism using two-step photoionization,” Opt. Lett. 10, 350–352 (1985).
[CrossRef] [PubMed]

X. A. Shen, R. Kachru, “High-speed pattern recognition by using stimulated echoes,” Opt. Lett. 17, 520–522 (1992).
[CrossRef] [PubMed]

Phys. Lett. A (2)

E. L. Hahn, N. S. Shiren, S. L. McCall, “Application of the area theorem to photon echoes,” Phys. Lett. A 37, 265–267 (1971).
[CrossRef]

R. Friedberg, S. R. Hartmann, “Superradiant damping and absorption,” Phys. Lett. A 37, 285–286 (1971).
[CrossRef]

Phys. Rev. (2)

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

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
[CrossRef]

Phys. Rev. B (1)

L. E. Erickson, “Optical-pumping effects on Raman-heterodyne-detected multipulse rf nuclear-spin-echo decay,” Phys. Rev. B 42, 3789–3797 (1990).
[CrossRef]

Other (6)

B. E. A. Saleh, M. C. Teich, Fundamentals of PhotonicsWiley, New York, 1991) p. 852.

R. M. Macfarlane, R. M. Shelby, “Coherent transient and hole-burning spectroscopy of rare earth ions in solids,” in Spectroscopy of Solids Containing Rare Earth Ions, A. A. Kaplyanskii, R. M. Macfarlane, eds. (Elsevier, New York, 1987), p. 51.

A. C. G. Mitchell, M. W. Zeemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, Cambridge, 1971), Chap. 3, pp. 92–102.

W. R. Babbitt, “Optical coherent transient memory systgems,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, W. J. Micelli, S. T. Kowell, eds. Proc. Soc. Photo-Opt. Instrum. Eng.2026, 2026–50 (1993).

Persistent Spectral Hole Burning: Science and Application, Vol. 16 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991).

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

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Figures (6)

Fig. 1
Fig. 1

Conceptual picture of time-domain optical storage and processing. The write pulse stores the temporal Fourier transform of the data input sequence in the material. The read pulse recalls the stored sequence. Each output data pulse is the correlation of the corresponding input data pulse and the write pulse convoluted with the read pulse.

Fig. 2
Fig. 2

Permitted material parameter space for time-domain optical storage for storage densities equal to 1, 10, and 100 (solid, long-dashed, and short-dashed curves, respectively) times the theoretical limit for conventional optical storage. The permitted area for each case is the triangle-shaped region to the right of the curve. η is the branching ratio; on the vertical axis N is the number of bits addressed in each spatial point, A is the transition probability, and τ is the duration of each data bit.

Fig. 3
Fig. 3

Permitted material parameter space for time-domain optical storage with destructive reading. The storage density equals the theoretical limit for conventional optical storage. The numbers of consecutive readings are 1, 5, and 25 (solid, long-dashed, and short-dashed curves, respectively). The permitted area decreases as the number of reads increase, η and NAτ are the same as in Fig. 2.

Fig. 4
Fig. 4

Thermal considerations set a lower limit for the product NAτ (defined in Figs. 2 and 3) as a function of transition probability A. This lower limit is plotted assuming the highest laser intensity permitted is Imax = 100 W/cm2 (dashed line) and Imax = 10,000 W/cm2 (solid line), respectively.

Fig. 5
Fig. 5

Permitted values for the data bit duration versus the number of bits per point for optical processing with the 3H41D2 transition in Pr:YAlO3. Thick solid lines represent the following: the lower limit on bit duration (τ), set by the inhomogeneous bandwidth, and the upper limit on bit duration times the number of bits per point (τN), set by the homogeneous bandwidth. The thick dashed line is the thermal limit, giving a lowest value of τN. The three pairs of thin lines, the dotted, dashed, and solid ones, are SNR limits for storage densities (N/k2) equal to 1, 10, and 100 times the theoretical limit for conventional optical storage, respectively. The SNR restrictions result in an upper limit on the bit duration. The permissible areas in (N, τ) space for the above three storage densities are shown as diagonally striped, cross-ruled, and filled-in areas, respectively.

Fig. 6
Fig. 6

Same thermal and bandwidth limits as in Fig. 5 are shown together with the SNR limits for a storage density equal to ten times the conventional limit. The permissible area in bit duration versus bits per point space is shown as a diagonally striped area. For each limit the dependence on the transition probability, A, the inhomogeneous dephasing time, T, and the homogeneous dephasing time, T2 is shown. Thus the figure shows how the permissible area changes if these parameters change from their Pr 3H41D2 transition values.

Tables (5)

Tables Icon

Table 1 Limitations of the Analysis

Tables Icon

Table 2 Definition of Variables

Tables Icon

Table 3 Maximum Storage Density (N/k2) a Versus Writing Efficiency (η)

Tables Icon

Table 4 Data Rate versus Transition Probability a

Tables Icon

Table 5 Data Rate versus Bits per Point a

Equations (23)

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

S e = N e 2 p ( t ) 4 .
N e = α n A x L T τ .
S 2 p = ( n 2 A x L T τ ) 2 A τ ( 3 λ 8 L ) .
S = S 2 p η 2 sin 2 θ w sin 2 θ d sin 2 θ r .
θ d = π / ( 2 N ) .
L = 2 A x / λ .
A x = ( k λ ) 2 .
S = 3 π 2 64 ξ n 2 k 6 λ 6 η 2 T 2 N 2 A τ .
N k 2 < π 8 ( 3 ξ ) 1 / 2 n k λ 3 η T τ ( A τ S ) 1 / 2 .
N A τ > 64 3 π 2 ξ 1 n 2 λ 6 1 η 2 ( N k 2 ) 3 S .
T = 4 ( π ln 2 ) 1 / 2 1 λ 2 σ A ,
N k 2 < π 4 ( 3 πξ ln 2 ) 1 / 2 ( n σ L ) η k 1 S 1 A τ .
N A τ < 3 π 2 16 ln 2 ξ η 2 1 S ( n σ L ) 2 ( N / k 2 ) .
S = 3 π 2 64 ξ n 2 k 6 λ 6 η 2 T 2 N 2 A τ ( 1 η 0 ) 2 m ( 1 η ) 2 ( m 1 ) .
d E d τ ћ = π 2 N
I < I th .
d 2 = 3 0 h λ 3 16 π 3 A .
I = 1 2 c 0 E d 2
N A τ > π ( π 6 ) 1 / 2 ( h c λ 3 ) 1 / 2 ( A I th ) 1 / 2 .
τ < 3 π 2 64 ξ n max 2 λ 6 η 2 T 2 S A N ( N / k 2 ) 3 .
τ < 27 π 3 1600 ln 2 ξ η 2 1 S N 1 A 1 ( N / k 2 ) ,
τ > T .
τ < T 2 2 N .

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