Abstract

We report direct measurements of the frequency dependence of the optical group delay for a number of optical components commonly used in femtosecond optics. We have investigated the group-delay errors that occur on reflection from metal and dielectric mirrors under various conditions and passage through devices that introduce angular dispersion. We obtain measurement accuracy of about ±1 fsec over the spectral range of 400–750 nm.

© 1988 Optical Society of America

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References

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  1. R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
    [CrossRef]
  2. J. A. Valdmanis, R. L. Fork, J. P. Gordon, Opt. Lett. 10, 131 (1985).
    [CrossRef] [PubMed]
  3. 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]
  4. R. L. Fork, C. H. Brito-Cruz, P. C. Becker, C. V. Shank, Opt. Lett. 12, 483 (1987).
    [CrossRef] [PubMed]
  5. W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, J. Opt. Soc. Am. A 4(13), P129 (1987).
    [CrossRef]
  6. A. A. Michelson, Light Waves and Their Uses (University of Chicago Press, Chicago, 1902).
  7. L. G. Cohen, J. Stone, Electron. Lett. 18, 564 (1982).
    [CrossRef]
  8. We used two identical Iconel–metal-coated glass plates that are step coated in 0.1 optical-density gradations. This ensures the precise compensation required for broadband operation and also allows precise balancing of the intensities emerging from the two beams. We have been able to obtain up to 50% fringe contrast with white light even with lossy elements in this manner.
  9. We find the center of the fringe pattern in a noise-insensitive manner by subtracting the dc value, squaring the result, and integrating. The 50% rise point represents the center of the packet. To compensate for long-term drift in the translation stage over the approximately 30-min interval of a complete scan, we return the tunable filter to the same reference wavelength after each new wavelength scan and check that the time center of the fringe pattern is unchanged. Small systematic errors are effectively canceled in this way. In addition, a He–Be reference interferometer beam is simultaneously read for accurate on-line length calibrations.
  10. W. H. Knox, N. M. Pearson, K. D. Li, C. Hirlimann, J. Opt. Soc. Am. B (to be submitted for publication).
  11. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 536.
  12. For measurements of extremely small group-delay errors, we use a multiple-bounce arrangement wherein the beam passes through two identical mirrors that are parallel. For the measurements in Fig. 1, a total of 12 reflections is used. We then plot the measured group delay divided by 12 to obtain the single-bounce contribution. The measurement accuracy is then a few femtoseconds divided by 12, or a few hundred attoseconds.
  13. A. M. Weiner, J. G. Fujimoto, E. P. Ippen, Opt. Lett. 10, 71 (1985).
    [CrossRef] [PubMed]
  14. S. De Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 553 (1984).
  15. J. P. Gordon, R. L. Fork, Opt. Lett. 9, 153 (1984).
    [CrossRef] [PubMed]
  16. E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
    [CrossRef]
  17. W. J. Tomlinson, W. H. Knox, J. Opt. Soc. Am. B 4, 1404 (1987).
    [CrossRef]
  18. The use of prisms to cancel grating errors was first suggested by J. D. Kafka, Spectra-Physics, 1250 West Middlefield Road, Mountain View, California 94042 (personal communication).

1987 (3)

1985 (3)

1984 (2)

J. P. Gordon, R. L. Fork, Opt. Lett. 9, 153 (1984).
[CrossRef] [PubMed]

S. De Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 553 (1984).

1982 (1)

L. G. Cohen, J. Stone, Electron. Lett. 18, 564 (1982).
[CrossRef]

1981 (1)

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

1969 (1)

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

Becker, P. C.

Brito-Cruz, C. H.

Cohen, L. G.

L. G. Cohen, J. Stone, Electron. Lett. 18, 564 (1982).
[CrossRef]

De Silvestri, S.

S. De Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 553 (1984).

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]

Fork, R. L.

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

J. A. Valdmanis, R. L. Fork, J. P. Gordon, Opt. Lett. 10, 131 (1985).
[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]

J. P. Gordon, R. L. Fork, Opt. Lett. 9, 153 (1984).
[CrossRef] [PubMed]

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Fujimoto, J. G.

Gordon, J. P.

Greene, B. I.

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Hirlimann, C.

W. H. Knox, N. M. Pearson, K. D. Li, C. Hirlimann, J. Opt. Soc. Am. B (to be submitted for publication).

Hirlimann, C. A.

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, J. Opt. Soc. Am. A 4(13), P129 (1987).
[CrossRef]

Ippen, E. P.

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 536.

Kafka, J. D.

The use of prisms to cancel grating errors was first suggested by J. D. Kafka, Spectra-Physics, 1250 West Middlefield Road, Mountain View, California 94042 (personal communication).

Knox, W. H.

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, J. Opt. Soc. Am. A 4(13), P129 (1987).
[CrossRef]

W. J. Tomlinson, W. H. Knox, J. Opt. Soc. Am. B 4, 1404 (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]

W. H. Knox, N. M. Pearson, K. D. Li, C. Hirlimann, J. Opt. Soc. Am. B (to be submitted for publication).

Laporta, P.

S. De Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 553 (1984).

Li, K. D.

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, J. Opt. Soc. Am. A 4(13), P129 (1987).
[CrossRef]

W. H. Knox, N. M. Pearson, K. D. Li, C. Hirlimann, J. Opt. Soc. Am. B (to be submitted for publication).

Michelson, A. A.

A. A. Michelson, Light Waves and Their Uses (University of Chicago Press, Chicago, 1902).

Pearson, N. M.

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, J. Opt. Soc. Am. A 4(13), P129 (1987).
[CrossRef]

W. H. Knox, N. M. Pearson, K. D. Li, C. Hirlimann, J. Opt. Soc. Am. B (to be submitted for publication).

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]

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[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]

Stone, J.

L. G. Cohen, J. Stone, Electron. Lett. 18, 564 (1982).
[CrossRef]

Svelto, O.

S. De Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 553 (1984).

Tomlinson, W. J.

Treacy, E. B.

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

Valdmanis, J. A.

J. A. Valdmanis, R. L. Fork, J. P. Gordon, Opt. Lett. 10, 131 (1985).
[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]

Weiner, A. M.

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 536.

Appl. Phys. Lett. (2)

R. L. Fork, B. I. Greene, C. V. Shank, Appl. Phys. Lett. 38, 671 (1981).
[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]

Electron. Lett. (1)

L. G. Cohen, J. Stone, Electron. Lett. 18, 564 (1982).
[CrossRef]

IEEE J. Quantum Electron. (2)

S. De Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 553 (1984).

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

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

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, J. Opt. Soc. Am. A 4(13), P129 (1987).
[CrossRef]

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

Opt. Lett. (4)

Other (7)

A. A. Michelson, Light Waves and Their Uses (University of Chicago Press, Chicago, 1902).

The use of prisms to cancel grating errors was first suggested by J. D. Kafka, Spectra-Physics, 1250 West Middlefield Road, Mountain View, California 94042 (personal communication).

We used two identical Iconel–metal-coated glass plates that are step coated in 0.1 optical-density gradations. This ensures the precise compensation required for broadband operation and also allows precise balancing of the intensities emerging from the two beams. We have been able to obtain up to 50% fringe contrast with white light even with lossy elements in this manner.

We find the center of the fringe pattern in a noise-insensitive manner by subtracting the dc value, squaring the result, and integrating. The 50% rise point represents the center of the packet. To compensate for long-term drift in the translation stage over the approximately 30-min interval of a complete scan, we return the tunable filter to the same reference wavelength after each new wavelength scan and check that the time center of the fringe pattern is unchanged. Small systematic errors are effectively canceled in this way. In addition, a He–Be reference interferometer beam is simultaneously read for accurate on-line length calibrations.

W. H. Knox, N. M. Pearson, K. D. Li, C. Hirlimann, J. Opt. Soc. Am. B (to be submitted for publication).

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 536.

For measurements of extremely small group-delay errors, we use a multiple-bounce arrangement wherein the beam passes through two identical mirrors that are parallel. For the measurements in Fig. 1, a total of 12 reflections is used. We then plot the measured group delay divided by 12 to obtain the single-bounce contribution. The measurement accuracy is then a few femtoseconds divided by 12, or a few hundred attoseconds.

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Figures (2)

Fig. 1
Fig. 1

Experimental arrangement and detected intensity as a function of delay time in the reference arm (a) for compensated interferometer and (b) after insertion of 1-mm glass slide into one arm. S, source; D, device under test; F, tunable filter; P, photomultiplier tube. The center of the fringe pattern moves by less than ±1 fsec for the compensated case as the wavelength is changed.

Fig. 2
Fig. 2

Group delay as a function of frequency for curves (a) ER.2 mirror, (b) ER.1 mirror, (c) AL.2 mirror, (d) pure gold mirror, (e) BD.1 broadband dielectric mirror, (f) 3% output coupler at normal incidence, (g) CPM laser corner mirror at 45° incidence angle for p polarization, (h) CPM laser corner mirror at 45° incidence angle for s polarization. In curves (j) and (k) results for flint Brewster prisms are shown, with curve (j) corresponding to less glass and curve (k) to more glass.

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