Abstract

Storage and subsequent recall of shaped femtosecond waveforms is achieved by performing spectral holography within a femtosecond pulse-shaping apparatus. Readout of the spectral hologram by using a short reference pulse yields both real and time-reversed reconstructions of the original signal. Convolution and correlation operations are achieved by using shaped pulses for readout. These experiments demonstrate the possibility of nonlinear spectral filtering and signal processing of femtosecond optical waveforms.

© 1992 Optical Society of America

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References

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  1. C. Froehly, B. Colombeau, M. Vampouille, in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.
  2. A. M. Weiner, J. P. Heritage, E. M. Kirschner, J. Opt. Soc. Am. B 5, 1563 (1988).
    [CrossRef]
  3. A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, Opt. Lett. 15, 326 (1990).
    [CrossRef] [PubMed]
  4. A. M. Weiner, J. P. Heritage, J. A. Salehi, Opt. Lett. 13, 300 (1988).
    [CrossRef] [PubMed]
  5. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
    [CrossRef] [PubMed]
  6. A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, K. A. Nelson, J. Opt. Soc. Am. B 8, 1264 (1991).
    [CrossRef]
  7. M. Haner, W. S. Warren, Appl. Phys. Lett. 52, 1458 (1988).
    [CrossRef]
  8. T. Kobayashi, A. Morimoto, in Picosecond Electronics and Optoelectronics, Vol. 4 of OSA Proceedings Series, T. C. L. G. Sollner, D. M. Bloom, eds. (Optical Society of America, Washington, D.C., 1989), p. 81.
  9. K. Ema, F. Shimizu, Jpn. J. Appl. Phys. 29, L631 (1990).
    [CrossRef]
  10. D. A. B. Miller, Opt. Lett. 5, 300 (1980).
    [CrossRef] [PubMed]
  11. W. R. Babbitt, T. W Mossberg, Opt. Commun. 65, 185 (1988); M. K. Kim, R. Kachru, Opt. Lett. 14, 423 (1989); A. Rebane, J. Aaviksoo, J. Kuhl, Appl. Phys. Lett. 54, 93 (1989); V. L. da Silva, Y. Silberberg, J. P. Heritage, E. W. Chase, M. A. Saifi, M. J. Andrejco, Opt. Lett. 16, 1340 (1991).
    [CrossRef] [PubMed]
  12. Y. T. Mazurenko, Appl. Phys. B 50, 101 (1990).
    [CrossRef]
  13. D. Gabor, Nature (London) 161, 177 (1948).
    [CrossRef]
  14. S. D. Smith, Holographic Recording Materials (Springer-Verlag, New York, 1977).
    [CrossRef]
  15. J. A. Valdmanis, R. L. Fork, J. P. Gordon, Opt. Lett. 10, 131 (1985).
    [CrossRef] [PubMed]
  16. R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, IEEE J. Quantum Electron. QE-22, 682 (1986).
    [CrossRef]
  17. A. Frenkel, J. P. Heritage, M. Stern, IEEE J. Quantum Electron. 25, 1981 (1989).
    [CrossRef]

1991 (1)

1990 (3)

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, Opt. Lett. 15, 326 (1990).
[CrossRef] [PubMed]

K. Ema, F. Shimizu, Jpn. J. Appl. Phys. 29, L631 (1990).
[CrossRef]

Y. T. Mazurenko, Appl. Phys. B 50, 101 (1990).
[CrossRef]

1989 (1)

A. Frenkel, J. P. Heritage, M. Stern, IEEE J. Quantum Electron. 25, 1981 (1989).
[CrossRef]

1988 (5)

A. M. Weiner, J. P. Heritage, E. M. Kirschner, J. Opt. Soc. Am. B 5, 1563 (1988).
[CrossRef]

W. R. Babbitt, T. W Mossberg, Opt. Commun. 65, 185 (1988); M. K. Kim, R. Kachru, Opt. Lett. 14, 423 (1989); A. Rebane, J. Aaviksoo, J. Kuhl, Appl. Phys. Lett. 54, 93 (1989); V. L. da Silva, Y. Silberberg, J. P. Heritage, E. W. Chase, M. A. Saifi, M. J. Andrejco, Opt. Lett. 16, 1340 (1991).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, J. A. Salehi, Opt. Lett. 13, 300 (1988).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

M. Haner, W. S. Warren, Appl. Phys. Lett. 52, 1458 (1988).
[CrossRef]

1986 (1)

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, IEEE J. Quantum Electron. QE-22, 682 (1986).
[CrossRef]

1985 (1)

1980 (1)

1948 (1)

D. Gabor, Nature (London) 161, 177 (1948).
[CrossRef]

Babbitt, W. R.

W. R. Babbitt, T. W Mossberg, Opt. Commun. 65, 185 (1988); M. K. Kim, R. Kachru, Opt. Lett. 14, 423 (1989); A. Rebane, J. Aaviksoo, J. Kuhl, Appl. Phys. Lett. 54, 93 (1989); V. L. da Silva, Y. Silberberg, J. P. Heritage, E. W. Chase, M. A. Saifi, M. J. Andrejco, Opt. Lett. 16, 1340 (1991).
[CrossRef] [PubMed]

Colombeau, B.

C. Froehly, B. Colombeau, M. Vampouille, in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

Ema, K.

K. Ema, F. Shimizu, Jpn. J. Appl. Phys. 29, L631 (1990).
[CrossRef]

Fork, R. L.

Frenkel, A.

A. Frenkel, J. P. Heritage, M. Stern, IEEE J. Quantum Electron. 25, 1981 (1989).
[CrossRef]

Froehly, C.

C. Froehly, B. Colombeau, M. Vampouille, in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

Gabor, D.

D. Gabor, Nature (London) 161, 177 (1948).
[CrossRef]

Gordon, J. P.

Haner, M.

M. Haner, W. S. Warren, Appl. Phys. Lett. 52, 1458 (1988).
[CrossRef]

Hawkins, R. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

Heritage, J. P.

A. Frenkel, J. P. Heritage, M. Stern, IEEE J. Quantum Electron. 25, 1981 (1989).
[CrossRef]

A. M. Weiner, J. P. Heritage, J. A. Salehi, Opt. Lett. 13, 300 (1988).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, E. M. Kirschner, J. Opt. Soc. Am. B 5, 1563 (1988).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, IEEE J. Quantum Electron. QE-22, 682 (1986).
[CrossRef]

Kirschner, E. M.

A. M. Weiner, J. P. Heritage, E. M. Kirschner, J. Opt. Soc. Am. B 5, 1563 (1988).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

Kobayashi, T.

T. Kobayashi, A. Morimoto, in Picosecond Electronics and Optoelectronics, Vol. 4 of OSA Proceedings Series, T. C. L. G. Sollner, D. M. Bloom, eds. (Optical Society of America, Washington, D.C., 1989), p. 81.

Leaird, D. E.

Mazurenko, Y. T.

Y. T. Mazurenko, Appl. Phys. B 50, 101 (1990).
[CrossRef]

Miller, D. A. B.

Morimoto, A.

T. Kobayashi, A. Morimoto, in Picosecond Electronics and Optoelectronics, Vol. 4 of OSA Proceedings Series, T. C. L. G. Sollner, D. M. Bloom, eds. (Optical Society of America, Washington, D.C., 1989), p. 81.

Mossberg, T. W

W. R. Babbitt, T. W Mossberg, Opt. Commun. 65, 185 (1988); M. K. Kim, R. Kachru, Opt. Lett. 14, 423 (1989); A. Rebane, J. Aaviksoo, J. Kuhl, Appl. Phys. Lett. 54, 93 (1989); V. L. da Silva, Y. Silberberg, J. P. Heritage, E. W. Chase, M. A. Saifi, M. J. Andrejco, Opt. Lett. 16, 1340 (1991).
[CrossRef] [PubMed]

Nelson, K. A.

Patel, J. S.

Salehi, J. A.

Shimizu, F.

K. Ema, F. Shimizu, Jpn. J. Appl. Phys. 29, L631 (1990).
[CrossRef]

Smith, S. D.

S. D. Smith, Holographic Recording Materials (Springer-Verlag, New York, 1977).
[CrossRef]

Stern, M.

A. Frenkel, J. P. Heritage, M. Stern, IEEE J. Quantum Electron. 25, 1981 (1989).
[CrossRef]

Thurston, R. N.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, IEEE J. Quantum Electron. QE-22, 682 (1986).
[CrossRef]

Tomlinson, W. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, IEEE J. Quantum Electron. QE-22, 682 (1986).
[CrossRef]

Valdmanis, J. A.

Vampouille, M.

C. Froehly, B. Colombeau, M. Vampouille, in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

Warren, W. S.

M. Haner, W. S. Warren, Appl. Phys. Lett. 52, 1458 (1988).
[CrossRef]

Weiner, A. M.

Wiederrecht, G. P.

Wullert, J. R.

Appl. Phys. B (1)

Y. T. Mazurenko, Appl. Phys. B 50, 101 (1990).
[CrossRef]

Appl. Phys. Lett. (1)

M. Haner, W. S. Warren, Appl. Phys. Lett. 52, 1458 (1988).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, IEEE J. Quantum Electron. QE-22, 682 (1986).
[CrossRef]

A. Frenkel, J. P. Heritage, M. Stern, IEEE J. Quantum Electron. 25, 1981 (1989).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

K. Ema, F. Shimizu, Jpn. J. Appl. Phys. 29, L631 (1990).
[CrossRef]

Nature (London) (1)

D. Gabor, Nature (London) 161, 177 (1948).
[CrossRef]

Opt. Commun. (1)

W. R. Babbitt, T. W Mossberg, Opt. Commun. 65, 185 (1988); M. K. Kim, R. Kachru, Opt. Lett. 14, 423 (1989); A. Rebane, J. Aaviksoo, J. Kuhl, Appl. Phys. Lett. 54, 93 (1989); V. L. da Silva, Y. Silberberg, J. P. Heritage, E. W. Chase, M. A. Saifi, M. J. Andrejco, Opt. Lett. 16, 1340 (1991).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[CrossRef] [PubMed]

Other (3)

C. Froehly, B. Colombeau, M. Vampouille, in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

T. Kobayashi, A. Morimoto, in Picosecond Electronics and Optoelectronics, Vol. 4 of OSA Proceedings Series, T. C. L. G. Sollner, D. M. Bloom, eds. (Optical Society of America, Washington, D.C., 1989), p. 81.

S. D. Smith, Holographic Recording Materials (Springer-Verlag, New York, 1977).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic illustration of the apparatus for femtosecond spectral holography, (a) Setup for recording the spectral hologram. Only the front half of the pulse-shaping apparatus is shown. The expanded view of the spectral hologram illustrates one possible interference pattern between spectrally dispersed signal and reference beams, (b) Setup for reading out the spectral hologram.

Fig. 2
Fig. 2

Reconstructed waveforms from four separate spectral holograms. The holograms are recordings of short (unshaped) signal pulses delayed by 0, 1, 2, and 3 ps, respectively, as noted on the figure, (a) Real reconstructed pulses read out with kt = kr. (b) Time-reversed pulses read out with kt = ks.

Fig. 3
Fig. 3

Intensity cross-correlation measurements showing holographic storage and recall of a signal pulse distorted by cubic spectral phase modulation. The curves are individually normalized for the same height. (a) Input signal pulse. (b) Real reconstructed output pulse (kt = kr). (c) Time-reversed output pulse (kt = ks).(d)Autocorrelation of the signal field, obtained using a test pulse identical to the signal pulse (with kt = ks). The peak is actually 1.6 times stronger than that in (c).(e)Time-reversed autoconvolution of the signal field, obtained using a test pulse time-reversed with respect to the signal pulse (with kt = ks). The peak is actually 2 times weaker than that in (c).

Equations (1)

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E out ( ω ) E t ( ω ) E r * ( ω ) E s ( ω ) exp [ i ( k t k r + k s ) r ] + E t ( ω ) E r ( ω ) E s * ( ω ) exp [ i ( k t + k r k s ) r ] .

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