Abstract

We discuss our design, construction, and characterization of thin-film Gires–Tournois interferometers for cubic-phase correction of ultrashort (<10-fsec) laser pulses. We include in the theory of the group delay of Gires–Tournois interferometers the dispersion of the thin-film layer, an important effect in the broadband limit. We characterize and use specific broadband, high-efficiency, low-dispersion substrates for this application.

© 1989 Optical Society of America

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References

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  1. W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
    [CrossRef]
  2. E. B. Treacy, IEEE J. Quantum Electron. QE-5, 545 (1969).
  3. W. J. Tomlinson, W. H. Knox, J. Opt. Soc. Am. B 4, 1404 (1987).
    [CrossRef]
  4. R. L. Fork, C. H. Brito-Cruz, P. C. Becker, C. V. Shank, Opt. Lett. 12, 483 (1987).
    [CrossRef] [PubMed]
  5. F. Gires, P. Tournois, C. R. Acad. Sci. 258, 6112 (1964).
  6. M. A. Duguay, J. W. Hansen, Appl. Phys. Lett. 14, 14 (1969).
    [CrossRef]
  7. J. Heppner, J. Kuhl, Appl. Phys. Lett. 47, 453 (1985); J. Kuhl, J. Heppner, IEEE J. Quantum Electron. QE-22, 182 (1986).
    [CrossRef]
  8. W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, Opt. Lett. 13, 574 (1988).
    [CrossRef] [PubMed]
  9. W. Zhao, E. Bourkoff, Appl. Phys. Lett. 50, 1304 (1987).
    [CrossRef]

1988 (1)

1987 (3)

1985 (2)

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

J. Heppner, J. Kuhl, Appl. Phys. Lett. 47, 453 (1985); J. Kuhl, J. Heppner, IEEE J. Quantum Electron. QE-22, 182 (1986).
[CrossRef]

1969 (2)

M. A. Duguay, J. W. Hansen, Appl. Phys. Lett. 14, 14 (1969).
[CrossRef]

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 545 (1969).

1964 (1)

F. Gires, P. Tournois, C. R. Acad. Sci. 258, 6112 (1964).

Becker, P. C.

Bourkoff, E.

W. Zhao, E. Bourkoff, Appl. Phys. Lett. 50, 1304 (1987).
[CrossRef]

Brito-Cruz, C. H.

Downer, M. C.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

Duguay, M. A.

M. A. Duguay, J. W. Hansen, Appl. Phys. Lett. 14, 14 (1969).
[CrossRef]

Fork, R. L.

R. L. Fork, C. H. Brito-Cruz, P. C. Becker, C. V. Shank, Opt. Lett. 12, 483 (1987).
[CrossRef] [PubMed]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

Gires, F.

F. Gires, P. Tournois, C. R. Acad. Sci. 258, 6112 (1964).

Hansen, J. W.

M. A. Duguay, J. W. Hansen, Appl. Phys. Lett. 14, 14 (1969).
[CrossRef]

Heppner, J.

J. Heppner, J. Kuhl, Appl. Phys. Lett. 47, 453 (1985); J. Kuhl, J. Heppner, IEEE J. Quantum Electron. QE-22, 182 (1986).
[CrossRef]

Hirlimann, C. A.

Knox, W. H.

Kuhl, J.

J. Heppner, J. Kuhl, Appl. Phys. Lett. 47, 453 (1985); J. Kuhl, J. Heppner, IEEE J. Quantum Electron. QE-22, 182 (1986).
[CrossRef]

Li, K. D.

Pearson, N. M.

Shank, C. V.

R. L. Fork, C. H. Brito-Cruz, P. C. Becker, C. V. Shank, Opt. Lett. 12, 483 (1987).
[CrossRef] [PubMed]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

Stolen, R. H.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

Tomlinson, W. J.

Tournois, P.

F. Gires, P. Tournois, C. R. Acad. Sci. 258, 6112 (1964).

Treacy, E. B.

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 545 (1969).

Valdmanis, J. A.

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

Zhao, W.

W. Zhao, E. Bourkoff, Appl. Phys. Lett. 50, 1304 (1987).
[CrossRef]

Appl. Phys. Lett. (4)

M. A. Duguay, J. W. Hansen, Appl. Phys. Lett. 14, 14 (1969).
[CrossRef]

J. Heppner, J. Kuhl, Appl. Phys. Lett. 47, 453 (1985); J. Kuhl, J. Heppner, IEEE J. Quantum Electron. QE-22, 182 (1986).
[CrossRef]

W. Zhao, E. Bourkoff, Appl. Phys. Lett. 50, 1304 (1987).
[CrossRef]

W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, J. A. Valdmanis, Appl. Phys. Lett. 46, 1120 (1985).
[CrossRef]

C. R. Acad. Sci. (1)

F. Gires, P. Tournois, C. R. Acad. Sci. 258, 6112 (1964).

IEEE J. Quantum Electron. (1)

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 545 (1969).

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

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Figures (3)

Fig. 1
Fig. 1

Group-delay spectrum after one reflection off a thin-film Gires–Tournois interferometer consisting of a single layer of TiO2, 70.1 nm thick, on a broadband, high-reflectivity, low-dispersion substrate as shown in the inset.

Fig. 2
Fig. 2

(a) Top: the reflectance spectrum at 45° of the CPM laser corner mirror substrate shown in the inset. Bottom: its group-delay spectrum at 45° and with s polarization. (b) Top: the reflectance spectrum at 45° of the ER.2 mirror substrate shown in the inset. Bottom: its group-delay spectrum at 45° and with s polarization.

Fig. 3
Fig. 3

Group-delay spectrum for s polarization after reflecting off the same Gires–Tournois interferometer 12 times at 45° incidence. Curve a, the theoretical prediction with n = 2.4; curve b, the theoretical prediction with n = 1.2 + (1.41 × 10−31)ω2; curve c, the experimental measurement with the CPM laser corner mirror substrate; curve d, the experimental measurement with the ER.2 mirror substrate.

Equations (5)

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E ( t ) = E 0 * f ( t , t p ) exp ( i ω t ) ,
t 0 = 2 n d c 1 - sin 2 θ n 2 ,
Ψ exp ( i ω t ) = Ψ exp [ i ( ω t + Φ ) ] = - R + exp [ i ( φ - ω t 0 ) ] 1 - R exp [ i ( φ - ω t 0 ) ] exp ( i ω t ) ,
tan Φ = ( 1 - R ) sin ( φ - ω t 0 ) - 2 R + ( 1 + R ) cos ( φ - ω t 0 ) .
- d Φ d ω = ( 1 - R ) t 0 1 + R - 2 R cos ( φ - ω t 0 ) .

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