Abstract

A nonlinear phase shift is applied to a spectrum of an ultrafast input signal after dispersing it in space. It is shown that when the input is a pulse pair, the output contains new pulses, which are formed both in front of and behind the original pair. We show the analogy between this experiment and photon echoes and discuss the causal properties of this system.

© 1993 Optical Society of America

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References

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  1. J. P. Heritage, A. M. Weiner, R. N. Thurston, Opt. Lett. 10, 609 (1985).
    [Crossref] [PubMed]
  2. A. M. Weiner, J. P. Heritage, E. M. Kirchner, J. Opt. Soc. Am. B 5, 1563 (1988).
    [Crossref]
  3. Preliminary results of this research were presented by V. L. da Silva, Y. Silberberg, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper QFA3.
  4. L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).
  5. Y. Silberberg, V. L. da Silva, J. P. Heritage, E. W. Chase, M. J. Andrejco, IEEE J. Quantum Electron. QE-22, 2369 (1992).
    [Crossref]
  6. P. Saari, R. Kaarli, A. Rebane, J. Opt. Soc. Am. B 3, 527 (1986).
    [Crossref]
  7. W. H. Hesselink, D. A. Wiersma, Phys. Rev. Lett. 43, 1991 (1979).
    [Crossref]
  8. Note that every narrow filter will broaden a short pulse, but in most filters, such as Fabry–Perot-type interference filters, the temporal broadening is asymmetric and the signal is always delayed by the filter. In these filters, which are limited by a K-K relation, the signal is never pushed forward in time.
  9. M. K. Jackson, G. R. Boyer, J. Paye, M. A. Franco, A. Mysyrowicz, Opt. Lett. 17, 1770 (1992).
    [Crossref] [PubMed]
  10. A. M. Weiner, D. E. Leaird, D. H. Reitze, E. G. Paek, Opt. Lett. 17, 224 (1992).
    [Crossref] [PubMed]

1992 (3)

1988 (1)

1986 (1)

1985 (1)

1979 (1)

W. H. Hesselink, D. A. Wiersma, Phys. Rev. Lett. 43, 1991 (1979).
[Crossref]

Allen, L.

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

Andrejco, M. J.

Y. Silberberg, V. L. da Silva, J. P. Heritage, E. W. Chase, M. J. Andrejco, IEEE J. Quantum Electron. QE-22, 2369 (1992).
[Crossref]

Boyer, G. R.

Chase, E. W.

Y. Silberberg, V. L. da Silva, J. P. Heritage, E. W. Chase, M. J. Andrejco, IEEE J. Quantum Electron. QE-22, 2369 (1992).
[Crossref]

da Silva, V. L.

Y. Silberberg, V. L. da Silva, J. P. Heritage, E. W. Chase, M. J. Andrejco, IEEE J. Quantum Electron. QE-22, 2369 (1992).
[Crossref]

Preliminary results of this research were presented by V. L. da Silva, Y. Silberberg, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper QFA3.

Eberly, J. H.

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

Franco, M. A.

Heritage, J. P.

Hesselink, W. H.

W. H. Hesselink, D. A. Wiersma, Phys. Rev. Lett. 43, 1991 (1979).
[Crossref]

Jackson, M. K.

Kaarli, R.

Kirchner, E. M.

Leaird, D. E.

Mysyrowicz, A.

Paek, E. G.

Paye, J.

Rebane, A.

Reitze, D. H.

Saari, P.

Silberberg, Y.

Y. Silberberg, V. L. da Silva, J. P. Heritage, E. W. Chase, M. J. Andrejco, IEEE J. Quantum Electron. QE-22, 2369 (1992).
[Crossref]

Preliminary results of this research were presented by V. L. da Silva, Y. Silberberg, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper QFA3.

Thurston, R. N.

Weiner, A. M.

Wiersma, D. A.

W. H. Hesselink, D. A. Wiersma, Phys. Rev. Lett. 43, 1991 (1979).
[Crossref]

IEEE J. Quantum Electron. (1)

Y. Silberberg, V. L. da Silva, J. P. Heritage, E. W. Chase, M. J. Andrejco, IEEE J. Quantum Electron. QE-22, 2369 (1992).
[Crossref]

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

Opt. Lett. (3)

Phys. Rev. Lett. (1)

W. H. Hesselink, D. A. Wiersma, Phys. Rev. Lett. 43, 1991 (1979).
[Crossref]

Other (3)

Note that every narrow filter will broaden a short pulse, but in most filters, such as Fabry–Perot-type interference filters, the temporal broadening is asymmetric and the signal is always delayed by the filter. In these filters, which are limited by a K-K relation, the signal is never pushed forward in time.

Preliminary results of this research were presented by V. L. da Silva, Y. Silberberg, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper QFA3.

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. The nonlinear medium is a liquid solution producing thermally induced refractive-index changes.

Fig. 2
Fig. 2

Time-resolved signal emerging from the system for three different delays between the input pulses: 0.4 ps (top), 0.8 ps (middle), and 1.3 ps (bottom). The first-order echoes are marked by arrows.

Fig. 3
Fig. 3

Decay of the echo as a function of the delay between the pulses. Circles (crosses) mark the preceding (following) echo intensity. The solid line depicts exponential decay exp(−t/0.375).

Equations (4)

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S i ( ω ) = 2 A ( ω ) cos ( ω Δ t / 2 ) .
S f ( ω ) = S i ( ω ) exp [ i ϕ nl ( ω ) ] ,
ϕ nl ( ω ) = β S i ( ω ) 2 .
ϕ ( ω ) = β S ( ω ) 2 * H ( ω ) ,

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