Abstract

The group delay of multilayer laser mirrors was measured by determining the spectral position of transmission maxima of a Fabry–Perot interferometer formed by the mirrors to be characterized. By optimizing the spacer thickness, we obtained an accuracy of the group-delay measurement of better than 0.23 fs. To our knowledge, this is the most precise direct measuring method reported.

© 1995 Optical Society of America

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References

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  1. W. Dietel, E. Döpel, K. Hehl, W. Rudolph, E. Schmidt, Opt. Commun. 50, 179 (1984).
    [CrossRef]
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    [CrossRef]
  3. Ch. Spielmann, P. F. Curley, T. Brabec, F. Krausz, IEEE J. Quantum Electron. 30, 1100 (1994).
    [CrossRef]
  4. M. Yamashita, M. Ishikawa, K. Torizuka, T. Sato, Opt. Lett. 11, 504 (1986).
    [CrossRef] [PubMed]
  5. J. Kuhl, J. Heppner, IEEE J. Quantum Electron. QE-22, 182 (1986).
    [CrossRef]
  6. R. Szipöcs, K. Ferencz, Ch. Spielmann, F. Krausz, Opt. Lett. 19, 201 (1994).
    [CrossRef] [PubMed]
  7. J. Hebling, E. J. Mayer, J. Kuhl, R. Szipöcs, Opt. Lett. 20, 921 (1995).
    [CrossRef]
  8. A. Stingl, M. Lenzner, Ch. Spielmann, F. Krausz, R. Szipöcs, Opt. Lett. 20, 602 (1995).
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  9. M. Beck, I. A. Wamsley, J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
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  10. J. Schwider, Appl. Opt. 31, 6107 (1992).
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  11. W. H. Knox, Appl. Phys. B 58, 225 (1994).
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  12. A. P. Kovács, K. Osvay, Z. Bor, R. Szipöcs, Opt. Lett. 20, 788 (1995).
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  13. S. H. C. Piotrowski McCall, J. A. Dobrowolski, G. G. Stepherd, Appl. Opt. 28, 2854 (1989).
    [CrossRef]

1995 (3)

1994 (3)

R. Szipöcs, K. Ferencz, Ch. Spielmann, F. Krausz, Opt. Lett. 19, 201 (1994).
[CrossRef] [PubMed]

W. H. Knox, Appl. Phys. B 58, 225 (1994).
[CrossRef]

Ch. Spielmann, P. F. Curley, T. Brabec, F. Krausz, IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

1992 (1)

1991 (1)

M. Beck, I. A. Wamsley, J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
[CrossRef]

1989 (1)

1986 (3)

M. Yamashita, M. Ishikawa, K. Torizuka, T. Sato, Opt. Lett. 11, 504 (1986).
[CrossRef] [PubMed]

J. Kuhl, J. Heppner, IEEE J. Quantum Electron. QE-22, 182 (1986).
[CrossRef]

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, T. Simos, IEEE J. Quantum Electron. QE-22, 186 (1986).
[CrossRef]

1984 (1)

W. Dietel, E. Döpel, K. Hehl, W. Rudolph, E. Schmidt, Opt. Commun. 50, 179 (1984).
[CrossRef]

Beck, M.

M. Beck, I. A. Wamsley, J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
[CrossRef]

Bor, Z.

Bourkoff, E.

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, T. Simos, IEEE J. Quantum Electron. QE-22, 186 (1986).
[CrossRef]

Brabec, T.

Ch. Spielmann, P. F. Curley, T. Brabec, F. Krausz, IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

Christodoulides, D. N.

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, T. Simos, IEEE J. Quantum Electron. QE-22, 186 (1986).
[CrossRef]

Curley, P. F.

Ch. Spielmann, P. F. Curley, T. Brabec, F. Krausz, IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

Dietel, W.

W. Dietel, E. Döpel, K. Hehl, W. Rudolph, E. Schmidt, Opt. Commun. 50, 179 (1984).
[CrossRef]

Dobrowolski, J. A.

Döpel, E.

W. Dietel, E. Döpel, K. Hehl, W. Rudolph, E. Schmidt, Opt. Commun. 50, 179 (1984).
[CrossRef]

Ferencz, K.

Hebling, J.

J. Hebling, E. J. Mayer, J. Kuhl, R. Szipöcs, Opt. Lett. 20, 921 (1995).
[CrossRef]

Hehl, K.

W. Dietel, E. Döpel, K. Hehl, W. Rudolph, E. Schmidt, Opt. Commun. 50, 179 (1984).
[CrossRef]

Heppner, J.

J. Kuhl, J. Heppner, IEEE J. Quantum Electron. QE-22, 182 (1986).
[CrossRef]

Ishikawa, M.

Joseph, R. I.

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, T. Simos, IEEE J. Quantum Electron. QE-22, 186 (1986).
[CrossRef]

Kafka, J. D.

M. Beck, I. A. Wamsley, J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
[CrossRef]

Knox, W. H.

W. H. Knox, Appl. Phys. B 58, 225 (1994).
[CrossRef]

Kovács, A. P.

Krausz, F.

Kuhl, J.

J. Hebling, E. J. Mayer, J. Kuhl, R. Szipöcs, Opt. Lett. 20, 921 (1995).
[CrossRef]

J. Kuhl, J. Heppner, IEEE J. Quantum Electron. QE-22, 182 (1986).
[CrossRef]

Lenzner, M.

Mayer, E. J.

J. Hebling, E. J. Mayer, J. Kuhl, R. Szipöcs, Opt. Lett. 20, 921 (1995).
[CrossRef]

Osvay, K.

Piotrowski McCall, S. H. C.

Rudolph, W.

W. Dietel, E. Döpel, K. Hehl, W. Rudolph, E. Schmidt, Opt. Commun. 50, 179 (1984).
[CrossRef]

Sato, T.

Schmidt, E.

W. Dietel, E. Döpel, K. Hehl, W. Rudolph, E. Schmidt, Opt. Commun. 50, 179 (1984).
[CrossRef]

Schwider, J.

Simos, T.

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, T. Simos, IEEE J. Quantum Electron. QE-22, 186 (1986).
[CrossRef]

Spielmann, Ch.

Stepherd, G. G.

Stingl, A.

Szipöcs, R.

Torizuka, K.

Wamsley, I. A.

M. Beck, I. A. Wamsley, J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
[CrossRef]

Yamashita, M.

Appl. Opt. (2)

Appl. Phys. B (1)

W. H. Knox, Appl. Phys. B 58, 225 (1994).
[CrossRef]

IEEE J. Quantum Electron. (4)

J. Kuhl, J. Heppner, IEEE J. Quantum Electron. QE-22, 182 (1986).
[CrossRef]

D. N. Christodoulides, E. Bourkoff, R. I. Joseph, T. Simos, IEEE J. Quantum Electron. QE-22, 186 (1986).
[CrossRef]

Ch. Spielmann, P. F. Curley, T. Brabec, F. Krausz, IEEE J. Quantum Electron. 30, 1100 (1994).
[CrossRef]

M. Beck, I. A. Wamsley, J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
[CrossRef]

Opt. Commun. (1)

W. Dietel, E. Döpel, K. Hehl, W. Rudolph, E. Schmidt, Opt. Commun. 50, 179 (1984).
[CrossRef]

Opt. Lett. (5)

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Figures (3)

Fig. 1
Fig. 1

Transmission of a FPI at different reflectivities.

Fig. 2
Fig. 2

Measured (dots) and designed (solid curves) values of (a) reflectivity and (b) group delay of an Ar+ sample mirror.

Fig. 3
Fig. 3

Measured (circles) and designed (dashed curve) GDD of an intracavity GDD-controlling OPO mirror.

Equations (8)

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δ ( ω ) = 2 [ h cos α c ω + ϕ ( ω ) ] = 2 π i ,
τ ( ω i , i - 1 ) = d ϕ d ω | ω i , i - 1 ϕ ( ω i ) - ϕ ( ω i - 1 ) ω i - ω i - 1 = - h cos α c + λ i λ i - 1 2 c ( λ i - λ i - 1 ) ,
T ( ω ) = ( 1 - R ) 2 ( 1 - R ) 2 + 4 R sin 2 [ δ ( ω ) / 2 ]
Δ τ n = d ϕ ( ω ) d ω | ω i , i - 1 - ϕ ( ω i ) - ϕ ( ω i - 1 ) ω i - ω i - 1 ,
Δ τ n = ( π - Δ ϕ ) 2 24 d 3 ϕ ( ω ) d ω 3 | ω i , i - 1 ( c h ) 2 ,
Δ τ m = 1 2 c ( λ i + λ i - 1 ) ( λ i - 1 - λ i ) - 2 λ i λ i - 1 ( λ i - 1 - λ i ) 2 Δ λ ,
Δ τ m 2 π ( π - Δ ϕ ) 2 1 - T L T L F h c ,
GDD = d τ ( ω ) d ω | ω i τ ( ω i + 1 , i ) - τ ( ω i , i - 1 ) ω i + 1 , i - ω i , i - 1 = 1 2 π c 2 × ( λ i + 1 λ i - 1 λ i - 1 - λ i + 1 ) ( λ i + 1 λ i λ i + 1 - λ i - λ i λ i - 1 λ i - λ i - 1 ) .

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