Abstract

A new method and apparatus for measuring the group delay in optical components and laser cavities are described. Cross-correlational fringes are fully recorded with a Michelson interferometer, in one of whose arms the optics to be measured are inserted. The path difference of the interferometer is calibrated to subwavelength accuracy, and the group delay is calculated from the phase of the Fourier transform of the measured fringe. The group delay for the entire visible-wavelength region is evaluated after a single measurement in approximately 10 min, using white light.

© 1990 Optical Society of America

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References

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  1. C. H. Brito Cruz, P. C. Becker, R. L. Fork, C. V. Shank, Opt. Lett. 13, 123 (1988).
    [CrossRef] [PubMed]
  2. W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, Opt. Lett. 13, 574 (1988).
    [CrossRef] [PubMed]
  3. W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), p. 118.
    [CrossRef]
  4. M. Tateda, N. Shibata, S. Seikai, IEEE J. Quantum Electron. QE-17, 404 (1981).
    [CrossRef]
  5. J. Stone, L. G. Cohen, Electron. Lett. 18, 716 (1982).
    [CrossRef]
  6. M. J. Downs, K. W. Raine, Precis. Eng. 1, 85 (1979).
    [CrossRef]
  7. A. Savitzky, M. J. E. Golay, Anal. Chem. 36, 1627 (1964).
    [CrossRef]
  8. A. M. Weiner, J. G. Fujimoto, E. P. Ippen, Opt. Lett. 10, 71 (1985).
    [CrossRef] [PubMed]
  9. R. L. Fork, O. E. Martinez, J. P. Gordon, Opt. Lett. 9, 150 (1984).
    [CrossRef] [PubMed]

1988 (2)

1985 (1)

1984 (1)

1982 (1)

J. Stone, L. G. Cohen, Electron. Lett. 18, 716 (1982).
[CrossRef]

1981 (1)

M. Tateda, N. Shibata, S. Seikai, IEEE J. Quantum Electron. QE-17, 404 (1981).
[CrossRef]

1979 (1)

M. J. Downs, K. W. Raine, Precis. Eng. 1, 85 (1979).
[CrossRef]

1964 (1)

A. Savitzky, M. J. E. Golay, Anal. Chem. 36, 1627 (1964).
[CrossRef]

Becker, P. C.

Brito Cruz, C. H.

Cohen, L. G.

J. Stone, L. G. Cohen, Electron. Lett. 18, 716 (1982).
[CrossRef]

Downs, M. J.

M. J. Downs, K. W. Raine, Precis. Eng. 1, 85 (1979).
[CrossRef]

Fork, R. L.

Fujimoto, J. G.

Golay, M. J. E.

A. Savitzky, M. J. E. Golay, Anal. Chem. 36, 1627 (1964).
[CrossRef]

Gordon, J. P.

Hirlimann, C. A.

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, Opt. Lett. 13, 574 (1988).
[CrossRef] [PubMed]

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), p. 118.
[CrossRef]

Ippen, E. P.

Knox, W. H.

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, Opt. Lett. 13, 574 (1988).
[CrossRef] [PubMed]

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), p. 118.
[CrossRef]

Li, K. D.

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, Opt. Lett. 13, 574 (1988).
[CrossRef] [PubMed]

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), p. 118.
[CrossRef]

Martinez, O. E.

Pearson, N. M.

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, Opt. Lett. 13, 574 (1988).
[CrossRef] [PubMed]

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), p. 118.
[CrossRef]

Raine, K. W.

M. J. Downs, K. W. Raine, Precis. Eng. 1, 85 (1979).
[CrossRef]

Savitzky, A.

A. Savitzky, M. J. E. Golay, Anal. Chem. 36, 1627 (1964).
[CrossRef]

Seikai, S.

M. Tateda, N. Shibata, S. Seikai, IEEE J. Quantum Electron. QE-17, 404 (1981).
[CrossRef]

Shank, C. V.

Shibata, N.

M. Tateda, N. Shibata, S. Seikai, IEEE J. Quantum Electron. QE-17, 404 (1981).
[CrossRef]

Stone, J.

J. Stone, L. G. Cohen, Electron. Lett. 18, 716 (1982).
[CrossRef]

Tateda, M.

M. Tateda, N. Shibata, S. Seikai, IEEE J. Quantum Electron. QE-17, 404 (1981).
[CrossRef]

Weiner, A. M.

Anal. Chem. (1)

A. Savitzky, M. J. E. Golay, Anal. Chem. 36, 1627 (1964).
[CrossRef]

Electron. Lett. (1)

J. Stone, L. G. Cohen, Electron. Lett. 18, 716 (1982).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Tateda, N. Shibata, S. Seikai, IEEE J. Quantum Electron. QE-17, 404 (1981).
[CrossRef]

Opt. Lett. (4)

Precis. Eng. (1)

M. J. Downs, K. W. Raine, Precis. Eng. 1, 85 (1979).
[CrossRef]

Other (1)

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, in Ultrafast Phenomena VI, T. Yajima, K. Yoshihara, C. B. Harris, S. Shionoya, eds. (Springer-Verlag, Berlin, 1988), p. 118.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the measurement apparatus. BS, cube beam splitter; PBS, polarization beam splitter; PMT, photomultiplier tube; SM, single mode; Pol., polarizer; AC amp, ac voltage amplifier. A He–Ne laser is used to calibrate the path difference of the interferometer with sub-wavelength accuracy. The fiber-transmitted white light from a Xe lamp has a beam divergence of less than 1 mrad, which permits measurement on components having a long optical path. (b) The measured correlation on a blank sample condition. The interferometric signals are averaged over 12 scans. (c) The apparatus inherent bias in group delay obtained from the Fourier transform of (b). This bias is subtracted from subsequent measurements on samples.

Fig. 2
Fig. 2

Curve a: the measured group delay of a general-purpose dielectric mirror. Curve b: in situ measured group delay of a dye-laser spherical mirror. The values have been divided by 4 to represent group delay for a single reflection. Spikes due to multilayer resonance are clearly observed in these results.

Fig. 3
Fig. 3

Group-delay measurements on a SF glass–Brewster prism pair with prism insertion x varied as a parameter. The insertion is defined as the prism base plane translation in the perpendicular direction, and a higher x value corresponds to a longer path in the glass. The measurements were taken on a prism pair mounted in a laser. Inset: GVD values as a function of x obtained from the slope of the group-delay curves; the slopes of the lines are calculated by using refractive-index data in the 1987 Ohara glass catalog.

Fig. 4
Fig. 4

Curve a: the measured group delay of 0.1 mM of Rhodamine 6G dissolved in ethylene glycol in a glass cell; the round-trip path length in the solution was 2.0 mm. Curve b: the group delay of 2-mm-thick pure ethylene glycol. Curve c: the group delay of Rhodamine 6G obtained after subtracting those of solvent and cell from the data shown in curve a; the filled circles represent simulated results of a conventional contour shift measurement, with a Lorentzian filter with a 10-nm bandwidth assumed.

Equations (2)

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S c ( τ ) = R E s ( t ) E t ( t τ ) d t .
τ s ( ω ) = d ϕ ( ω ) d ω τ bias ( ω ) + τ 0 .

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