Abstract

White-light interferograms provide a simple, accurate, and physically intuitive picture of what happens to broadband optical pulses on transmission through, or reflection from, common optical materials. Quantitative measurement of group delay are made with an accuracy of ±0.1 fs and with high spectral resolution. This measurement accuracy is applied to the determination of d2n/dλ2 and d3n/dλ3 of fused silica with an accuracy of ±5 × 10−5 μm−2 and ±1 × 10−3 μm−3, respectively. Further applications are found in the measurement of the dispersion of broadband mirrors and a multiple-quantum-well structure.

© 1996 Optical Society of America

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1994 (3)

1993 (2)

1991 (2)

M. Beck, I. A. Walmsley, and J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
[Crossref]

K. Naganuma and H. Yasaka, IEEE J. Quantum Electron. 27, 1280 (1991).
[Crossref]

1990 (3)

1989 (1)

1988 (1)

1987 (1)

1983 (1)

Asaki, M. T.

Beck, M.

M. Beck, I. A. Walmsley, and J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
[Crossref]

M. Beck and I. A. Walmsley, Opt. Lett. 15, 492 (1990).
[Crossref] [PubMed]

Becker, P. C.

Bor, Z.

A. P. Kovács, K. Osvay, Z. Bor, and R. Szipöcs, Opt. Lett. 20, 788 (1995).
[Crossref]

Z. Bor, K. Osvay, B. Rácz, and G. Szabó, Opt. Commun. 78, 109 (1990).
[Crossref]

Brabec, T.

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

P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Wintner, and A. J. Schmidt, Opt. Lett. 18, 54 (1993).
[Crossref] [PubMed]

Brito-Cruz, C. H.

Brovelli, L. R.

Chiu, T. H.

Curley, P. F.

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

P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Wintner, and A. J. Schmidt, Opt. Lett. 18, 54 (1993).
[Crossref] [PubMed]

Diels, J.-C.

W. Dietel, J. J. Fontaine, and J.-C. Diels, Opt. Lett. 8, 4 (1983).
[Crossref] [PubMed]

P. Pulaski and J.-C. Diels, in Conference on Lasers and Electro-Optics, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 153.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomenon: Fundamentals, Techniques and Applications on a Femtosecond Time Scale (Academic, Boston, Mass., 1995).

Dietel, W.

Fontaine, J. J.

Fork, R. L.

Furtak, T. E.

M. V. Klein and T. E. Furtak, Optics (Wiley, New York, 1986).

Garvey, D.

Hirlimann, C. A.

Huang, C.-P.

Kafka, J. D.

M. Beck, I. A. Walmsley, and J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
[Crossref]

Kapteyn, H. C.

Keller, U.

Klein, M. V.

M. V. Klein and T. E. Furtak, Optics (Wiley, New York, 1986).

Knox, W. H.

Kovács, A. P.

Krausz, F.

Kumar, V. N.

Li, K. D.

Mogi, K.

Murnane, M. M.

Naganuma, K.

K. Naganuma and H. Yasaka, IEEE J. Quantum Electron. 27, 1280 (1991).
[Crossref]

K. Naganuma, K. Mogi, and H. Yamada, Opt. Lett. 17, 393 (1990).
[Crossref]

Osvay, K.

A. P. Kovács, K. Osvay, Z. Bor, and R. Szipöcs, Opt. Lett. 20, 788 (1995).
[Crossref]

Z. Bor, K. Osvay, B. Rácz, and G. Szabó, Opt. Commun. 78, 109 (1990).
[Crossref]

Pearson, N. M.

Pulaski, P.

P. Pulaski and J.-C. Diels, in Conference on Lasers and Electro-Optics, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 153.

Rácz, B.

Z. Bor, K. Osvay, B. Rácz, and G. Szabó, Opt. Commun. 78, 109 (1990).
[Crossref]

Rao, D. N.

Rudolph, W.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomenon: Fundamentals, Techniques and Applications on a Femtosecond Time Scale (Academic, Boston, Mass., 1995).

Schmidt, A. J.

Shank, C. V.

Spielmann, C.

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

A. Stingl, C. Spielmann, F. Krausz, and R. Szipöcs, Opt. Lett. 19, 204 (1994).
[Crossref]

Spielmann, Ch.

Stingl, A.

Szabó, G.

Z. Bor, K. Osvay, B. Rácz, and G. Szabó, Opt. Commun. 78, 109 (1990).
[Crossref]

Szipöcs, R.

Taft, G.

Walmsley, I. A.

M. Beck, I. A. Walmsley, and J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
[Crossref]

M. Beck and I. A. Walmsley, Opt. Lett. 15, 492 (1990).
[Crossref] [PubMed]

Wintner, E.

Yamada, H.

Yasaka, H.

K. Naganuma and H. Yasaka, IEEE J. Quantum Electron. 27, 1280 (1991).
[Crossref]

Zhou, J.

IEEE J. Quantum Electron. (3)

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

K. Naganuma and H. Yasaka, IEEE J. Quantum Electron. 27, 1280 (1991).
[Crossref]

M. Beck, I. A. Walmsley, and J. D. Kafka, IEEE J. Quantum Electron. 27, 2074 (1991).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

Z. Bor, K. Osvay, B. Rácz, and G. Szabó, Opt. Commun. 78, 109 (1990).
[Crossref]

Opt. Lett. (11)

Other (5)

P. Pulaski and J.-C. Diels, in Conference on Lasers and Electro-Optics, Vol. 15 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 153.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomenon: Fundamentals, Techniques and Applications on a Femtosecond Time Scale (Academic, Boston, Mass., 1995).

Optics Guide 5 (Melles Griot, Irvine, Calif., 1990).

Newport Catalog (Newport Corporation, Irvine, Calif., 1994).

M. V. Klein and T. E. Furtak, Optics (Wiley, New York, 1986).

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Figures (9)

Fig. 1
Fig. 1

(a) Balanced Michelson interferometer consisting of a beam splitter (BS), mirrors (M1, M2), and a compensator plate (C). (b) The unbalanced Michelson interferometer is identical to that in (a) with the exception of an extra piece of glass (S) in one arm. D’s, detectors.

Fig. 2
Fig. 2

Experimental setup for recording white-light interferograms. White light and helium–neon laser fringes are measured simultaneously with detectors D1 and D2 and stored in a computer. We use the helium–neon fringes to determine by what distance mirror M2 is moved. Other abbreviations as in Fig. 1.

Fig. 3
Fig. 3

(a) Interferogram with a balanced interferometer. A numerical fit of the sampled data and a Lorentzian envelope are also plotted. (b) Curves (i) and (iii) are the amplitude and the phase, respectively, of the Fourier transform of the actual data, and curves (ii) and (iv) are the amplitude and the phase of the Fourier transform of the functional fit to the data.

Fig. 4
Fig. 4

(a) Interferogram with a microscope cover slide in one arm of the interferometer. (b) The result of the Fourier transform of these data in amplitude and phase. When a polynomial is fitted to the phase data, constants kl and kl can be determined. The fit is not shown because it is indistinguishable from the data.

Fig. 5
Fig. 5

Spectrally filtered interferograms recorded with a microscope cover slide in one arm of the interferometer. The white light is filtered before detection. The peak of the envelope for each interferogram is determined by the group delay at the center wavelength of each filter. From top to bottom, the center wavelengths of the filters are 750, 650, 600, 550, and 500 nm.

Fig. 6
Fig. 6

(a) Interferogram with d ≈ 4 mm of fused silica in one arm of the interferometer. (b) The result of the Fourier transform of these data. The constant and linear components of the spectral phase are subtracted, and the resulting curve is fitted with a third-order polynomial.

Fig. 7
Fig. 7

(a) Interferogram for which one mirror of the interferometer was replaced by a mirror with a multilayer dielectric coating. (b) Curve (i) is the normalized amplitude of the Fourier transform (the reflection spectrum), curve (ii) is the phase of the Fourier transform with the constant and linear contributions subtracted, and curve (iii) is a fifth-order polynomial fit to the phase.

Fig. 8
Fig. 8

Second and third derivatives of the spectral phase on reflection from a Newport UF.20 ultrafast mirror.

Fig. 9
Fig. 9

(a) Interferogram for which one mirror of the interferometer is replaced by a MQW structure. (b) Theoretical and experimental reflection amplitudes for the MQW. The experimentally measured amplitude is not normalized by the spectrum of the source. (c) First derivative of the phase shift on reflection as obtained from both the theory and the experiment.

Equations (21)

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I ( τ ) E ˜ 1 2 ( t τ ) + E ˜ 2 2 ( t ) + E ˜ 1 ( t τ ) E ˜ 2 * ( t ) × exp ( i ω l t ) + E ˜ 1 * ( t τ ) E ˜ 2 ( t ) exp ( i ω l τ ) ,
E ˜ ( ω ) = + E ˜ ( t ) exp ( i ω t ) d t , E ˜ ( t ) = 1 2 π + E ˜ ( ω ) exp ( i ω t ) d ω ,
2 E ˜ ( Ω + ω l ) = E ˜ ( Ω ) = + E ˜ ( t ) exp ( i Ω t ) d t , E ˜ ( t ) = 1 2 π + E ˜ ( Ω ) exp ( i Ω t ) d Ω .
A ˜ 1 + ( τ ) = E ˜ 1 * ( t τ ) E ˜ 2 ( t ) exp ( i ω l τ ) = A ˜ 1 + ( τ ) exp ( i ω l τ ) .
A ˜ 1 + ( ω ) = A ˜ 1 + ( τ ) exp ( i ω τ ) d τ = E ˜ 1 * ( ω ) E ˜ 2 ( ω )
A ˜ 1 + ( Ω ) = E ˜ 1 * ( Ω ) E ˜ 2 ( Ω ) .
A ˜ 1 + ( Ω ) = r ˜ 12 ( Ω ) E ˜ 1 * ( Ω ) E ˜ 2 ( Ω ) = r ˜ 12 ( Ω ) | E ˜ ( Ω ) | 2 ,
E ˜ 2 ( Ω ) = T ( Ω ) E ˜ 1 ( Ω ) exp { id [ k ( Ω ) Ω + ω l c ] } ,
A ˜ 2 + ( Ω ) = r ˜ 12 ( Ω ) | E ˜ ( Ω ) | 2 T ( Ω ) × exp { id [ k ( Ω ) Ω + ω l c ] } .
E ˜ 2 ( Ω ) T ( Ω ) E ˜ 1 ( Ω ) × exp { id [ k l + k l Ω + k l 2 Ω 2 + k l 6 Ω 3 + ] + i Ω + ω l c d } , E ˜ 2 ( Ω ) T ( Ω ) E ˜ 1 ( Ω ) × exp { id [ ω l c ( n l 1 ) + ( k l 1 c ) Ω + k l 2 Ω 2 + k l 6 Ω 3 + ] } .
k l = ( d k d ω ) l = [ n l + ω l ( d n d ω ) l ] 1 c = [ n l λ l ( d n d λ ) l ] 1 c
k l = ( d 2 k d ω 2 ) l = λ l 3 2 π c 2 ( d 2 n d λ 2 ) l
k l = ( d k d ω 3 ) l = λ 4 4 π 2 c 3 [ 3 ( d 2 n d λ 2 ) l + λ l ( d 3 n d λ 3 ) l ]
d v g d λ = ω 2 v g 2 2 π c d 2 k d ω 2 .
E ˜ 2 ( Ω ) E ˜ 1 ( Ω ) exp ( i ω l d c ) × exp { id [ k l + ( k l 1 c ) Ω ] } .
E ˜ 2 ( t ) = exp [ i ω l d ( n l 1 ) / c ] E ˜ 1 ( t Δ t )
Δ t = d ( k l 1 c ) = d c [ ( n l 1 ) λ l ( d n d λ ) l ] = d v g .
f ( x ) = g ( x ) h ( x ) ,
h ( x ) = cos { [ A exp ( x 2 / B ) + C ] x + D }
g ( x ) = E 1 + x 2 / F + G .
d 2 n d λ 2 = a 2 4 π c 2 λ l 2 d .

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