Abstract

We propose a time-domain interferometry method that circumvents the usual sampling rate condition. It was devised for the retrieval of fast optical response functions in low-repetition-rate experiments. Its potential temporal dynamic range matches the spectral resolution and bandwidth requirements of the arbitrarily shaped spectral filters that are engraved in amorphous spectral hole-burning materials.

© 2000 Optical Society of America

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References

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  4. W. P. de Boeij, M. S. Pshnichnikov, and D. A. Wiersma, Chem. Phys. Lett. 238, 1 (1995).
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    [CrossRef]
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    [CrossRef]
  8. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1999 (1)

I. A. Walmsley, Opt. Photon. News 10(4), 29 (1999), and references therein.

1995 (2)

W. P. de Boeij, M. S. Pshnichnikov, and D. A. Wiersma, Chem. Phys. Lett. 238, 1 (1995).

H. Schwoerer, D. Erni, and A. Rebane, J. Opt. Soc. Am. B 12, 1083 (1995).
[CrossRef]

1992 (1)

1991 (1)

K. Minoshima, M. Taiji, and T. Kobayashi, Opt. Lett. 21, 1683 (1991).
[CrossRef]

1990 (1)

1989 (1)

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[CrossRef]

1987 (1)

1986 (1)

1969 (1)

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Bouchène, M. A.

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

de Boeij, W. P.

W. P. de Boeij, M. S. Pshnichnikov, and D. A. Wiersma, Chem. Phys. Lett. 238, 1 (1995).

Débarre, A.

M. A. Bouchène, A. Débarre, J.-C. Keller, J.-L. Le Gouët, and P. Tchénio, J. Opt. Soc. Am. B 9, 281 (1992).
[CrossRef]

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[CrossRef]

Erni, D.

Grischkowsky, D.

Keller, J.-C.

M. A. Bouchène, A. Débarre, J.-C. Keller, J.-L. Le Gouët, and P. Tchénio, J. Opt. Soc. Am. B 9, 281 (1992).
[CrossRef]

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[CrossRef]

Kobayashi, T.

K. Minoshima, M. Taiji, and T. Kobayashi, Opt. Lett. 21, 1683 (1991).
[CrossRef]

Le Gouët, J.-L.

M. A. Bouchène, A. Débarre, J.-C. Keller, J.-L. Le Gouët, and P. Tchénio, J. Opt. Soc. Am. B 9, 281 (1992).
[CrossRef]

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[CrossRef]

Martinez, O. E.

Minoshima, K.

K. Minoshima, M. Taiji, and T. Kobayashi, Opt. Lett. 21, 1683 (1991).
[CrossRef]

Mogi, K.

Naganuma, K.

Pshnichnikov, M. S.

W. P. de Boeij, M. S. Pshnichnikov, and D. A. Wiersma, Chem. Phys. Lett. 238, 1 (1995).

Rebane, A.

Richard, A.

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[CrossRef]

Rothenberg, J. E.

Schwoerer, H.

Taiji, M.

K. Minoshima, M. Taiji, and T. Kobayashi, Opt. Lett. 21, 1683 (1991).
[CrossRef]

Tchénio, P.

M. A. Bouchène, A. Débarre, J.-C. Keller, J.-L. Le Gouët, and P. Tchénio, J. Opt. Soc. Am. B 9, 281 (1992).
[CrossRef]

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[CrossRef]

Treacy, E. B.

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Walmsley, I. A.

I. A. Walmsley, Opt. Photon. News 10(4), 29 (1999), and references therein.

Wiersma, D. A.

W. P. de Boeij, M. S. Pshnichnikov, and D. A. Wiersma, Chem. Phys. Lett. 238, 1 (1995).

Yamada, H.

Chem. Phys. Lett. (1)

W. P. de Boeij, M. S. Pshnichnikov, and D. A. Wiersma, Chem. Phys. Lett. 238, 1 (1995).

IEEE J. Quantum Electron. (1)

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

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

Opt. Commun. (1)

A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P. Tchénio, Opt. Commun. 73, 309 (1989).
[CrossRef]

Opt. Lett. (3)

Opt. Photon. News (1)

I. A. Walmsley, Opt. Photon. News 10(4), 29 (1999), and references therein.

Other (1)

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

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Figures (3)

Fig. 1
Fig. 1

Block diagram of the experimental setup.

Fig. 2
Fig. 2

(a) Composite interference pattern as detected on the photodiode array. (b) Real and (c) imaginary parts of the interference pattern Fourier transform. The positive frequency sidebands at K0 and K1 are digitally filtered out, and their inverse Fourier transforms are successively taken, providing the two analytic signals.

Fig. 3
Fig. 3

Experimental variations of (a) the phase and (b) the modulus of W¯sT as a function of time delay T. The solid curves in (a) represent the data fit by a parabola. Performing 2000 steps, the translation stage makes the optical path difference vary over 8 mm. With three recordings at each stage position, the data number amounts to 6000. However, vibrations corrupt the data collected during the translation stage motion, leading to the rejection of one of every three data. The remaining 4000 valid data are packed into 800 averages over 5 recordings, which are represented here by tiny rectangles.

Equations (7)

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λs=c/2ν1-ν0+Δν.
Wintx=˜*ν˜sν×exp2iπν+ν0T+L/c+iK0xdν+Wm0 exp2iπν1T+L/c+iK1x+c.c.,
WsT=˜ν2hνexp2iπν+ν0T+L/cdν,
WmT=Wm0 exp2iπν1T+L/c.
hν-ν0=expiπμν-ν02.
W¯sT=expiφ-iπT2/μטν1-ν0-T/μ2/μ,
μ=8.16×10-24 s2.

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