Abstract

Taking advantage of the slow optical response of low-temperature rare earth ion–doped crystal, we explore the similarity between causality and Fresnel diffraction by a straight edge. We relate these features to spectral resolution and selectivity. The concept is illustrated with experimental data.

© 2000 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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1999 (2)

1995 (1)

1994 (2)

B. H. Kolner, IEEE J. Quantum Electron. 30, 1951 (1994).
[CrossRef]

C. V. Bennett, R. P. Scott, and B. H. Kolner, Appl. Phys. Lett. 65, 2513 (1994).
[CrossRef]

1993 (1)

1992 (1)

1985 (1)

A. Renn, A. J. Meixner, U. Wild, and F. Buckhalter, Chem. Phys. 93, 157 (1985).

1984 (1)

Y. S. Bai, W. R. Babbitt, N. W. Carlson, and T. W. Mossberg, Appl. Phys. Lett. 45, 714 (1984).
[CrossRef]

1980 (1)

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Altner, S. B.

Babbitt, W. R.

Y. S. Bai, W. R. Babbitt, N. W. Carlson, and T. W. Mossberg, Appl. Phys. Lett. 45, 714 (1984).
[CrossRef]

Bai, Y. S.

Y. S. Bai, W. R. Babbitt, N. W. Carlson, and T. W. Mossberg, Appl. Phys. Lett. 45, 714 (1984).
[CrossRef]

Bennett, C. V.

C. V. Bennett and B. H. Kolner, Opt. Lett. 24, 783 (1999).
[CrossRef]

C. V. Bennett, R. P. Scott, and B. H. Kolner, Appl. Phys. Lett. 65, 2513 (1994).
[CrossRef]

Bernet, S.

Buckhalter, F.

A. Renn, A. J. Meixner, U. Wild, and F. Buckhalter, Chem. Phys. 93, 157 (1985).

Carlson, N. W.

Y. S. Bai, W. R. Babbitt, N. W. Carlson, and T. W. Mossberg, Appl. Phys. Lett. 45, 714 (1984).
[CrossRef]

Eckbreth, A. C.

Gouët, J.-L.

Graf, F. R.

Hall, R. J.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Kolner, B. H.

C. V. Bennett and B. H. Kolner, Opt. Lett. 24, 783 (1999).
[CrossRef]

B. H. Kolner, IEEE J. Quantum Electron. 30, 1951 (1994).
[CrossRef]

C. V. Bennett, R. P. Scott, and B. H. Kolner, Appl. Phys. Lett. 65, 2513 (1994).
[CrossRef]

Lohmann, A. W.

Lorgeré, I.

MacFarlane, R.

Maniloff, E. S.

Meixner, A. J.

A. Renn, A. J. Meixner, U. Wild, and F. Buckhalter, Chem. Phys. 93, 157 (1985).

Ménager, L.

Mendlovic, D.

Mossberg, T. W.

Y. S. Bai, W. R. Babbitt, N. W. Carlson, and T. W. Mossberg, Appl. Phys. Lett. 45, 714 (1984).
[CrossRef]

Renn, A.

Scott, R. P.

C. V. Bennett, R. P. Scott, and B. H. Kolner, Appl. Phys. Lett. 65, 2513 (1994).
[CrossRef]

Shirley, J. A.

Wild, U.

A. Renn, A. J. Meixner, U. Wild, and F. Buckhalter, Chem. Phys. 93, 157 (1985).

Wild, U. P.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

C. V. Bennett, R. P. Scott, and B. H. Kolner, Appl. Phys. Lett. 65, 2513 (1994).
[CrossRef]

Y. S. Bai, W. R. Babbitt, N. W. Carlson, and T. W. Mossberg, Appl. Phys. Lett. 45, 714 (1984).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Chem. Phys. (1)

A. Renn, A. J. Meixner, U. Wild, and F. Buckhalter, Chem. Phys. 93, 157 (1985).

IEEE J. Quantum Electron. (1)

B. H. Kolner, IEEE J. Quantum Electron. 30, 1951 (1994).
[CrossRef]

Opt. Lett. (4)

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Figures (4)

Fig. 1
Fig. 1

Box configuration of engraving and probe beams in a four-wave-mixing process.

Fig. 2
Fig. 2

Gray-scale mapping of (a), (b) βP+r,t2 and (c), (d) P+r,t2. The waveform Λt-T propagates upward. At z=1/βτL2=0 causality screens the t<0 half-axis. This obstacle hampers propagation in (a) and (c), in which the waveform is centered at T=0. However, propagation is free in (b) and (d), in which the waveform center is shifted to T=τL. The Fresnel fringes are visible in (a). Transition to the Fraunhofer regime can be observed in (c) and (d).

Fig. 3
Fig. 3

Experimental and calculated signal time–dependent profiles for T=0. Experimental settings: βτL2= (a) 0.7, (b) 1.8, (c) 5.0, (d) 10.2; β= (a) 1.44, (b) 3.6, (c) 10.2, (d) 10.2 MHz/µs. Profiles computed with these setting values fit the experimental data shown in (c) and (d). The best-fit values of βτL2 [(a) 1.46, (b) 3.08] and β [(a) 1.8 MHz/µs, (b) 3.8 MHz/µs] differ significantly from the settings for the data shown in (a) and (b).

Fig. 4
Fig. 4

Experimental and calculated signal time-dependent profiles for T=τL. Experiment settings: βτL2= (a) 0.18, (b) 0.36, (c) 1.8, (d) 5.0; β= (a) 0.36, (b) 0.72, (c) 3.6, (d) 10.2 MHz/µs. The profiles computed with these parameter values fit the experimental data.

Equations (4)

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Pt=0χτEt-τdτ,
Et=E0 exp2iπν0t+iπβt2-ik3r+c.c.
P+β,t=0E0 exp2iπν0t-ik+r×0Λτ-Texpiπβt-τ2dτ+c.c.
limzP+t,β=120E0Λ˜βt-iπΛ˜νβt-νdν,

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