Abstract

We measure the second- and third-order dispersion coefficients, d 2 k/ dω 2 and d 3 k/dω3, of water for wavelengths from 0.45 to 1.3 μm using a Michelson white-light interferometer. In this interval, the second-order dispersion ranges from 0.068 to -0.1 fs2/μm, and the third-order dispersion ranges from 0.048 to 1.18 fs3/μm. We observe an oscillation in d 2 k/dω2 near 1.1 μm that is due to water absorption features near that wavelength. From the dispersion coefficients, derivatives of the index of refraction of water are calculated and compared with available equations. These measured values of d 2 n/dλ2 and d 3 n/dλ3 should be useful in the evaluation and improvement of existing equations for n(λ) in water.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. S. A. Diddams, H. K. Eaton, A. A. Zozulya, T. S. Clement, “Characterizing the nonlinear propagation of femtosecond pulses in bulk media,” IEEE J. Sel. Top. Quantum Electron. 4, 306–316 (1998).
    [CrossRef]
  4. S. Petit, O. Crégut, C. Hirlimann, “A tunable femtosecond pulses amplifier,” Opt. Commun. 124, 49–55 (1996).
    [CrossRef]
  5. A. Brodeur, F. A. Ilkov, S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129, 193–198 (1996).
    [CrossRef]
  6. K. Naganuma, K. Mogi, H. Yamada, “Group-delay measurement using the Fourier transform of an interferometric cross correlation generated by white light,” Opt. Lett. 15, 393–395 (1990).
    [CrossRef] [PubMed]
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    [CrossRef]
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  12. K. Naganuma, H. Yasaka, “Group delay and α-parameter measurement of 1.3 μm semiconductor traveling-wave optical amplifier using the interferometric method,” IEEE J. Quantum Electron. 27, 1280–1287 (1991).
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1998 (1)

S. A. Diddams, H. K. Eaton, A. A. Zozulya, T. S. Clement, “Characterizing the nonlinear propagation of femtosecond pulses in bulk media,” IEEE J. Sel. Top. Quantum Electron. 4, 306–316 (1998).
[CrossRef]

1997 (4)

1996 (3)

S. Diddams, J.-C. Diels, “Dispersion measurements with white light interferometry,” J. Opt. Soc. Am. B 13, 1120–1129 (1996).
[CrossRef]

S. Petit, O. Crégut, C. Hirlimann, “A tunable femtosecond pulses amplifier,” Opt. Commun. 124, 49–55 (1996).
[CrossRef]

A. Brodeur, F. A. Ilkov, S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129, 193–198 (1996).
[CrossRef]

1995 (2)

X. M. Zhao, J.-C. Diels, C. Y. Wang, J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599–612 (1995).
[CrossRef]

X. Quan, E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34, 3477–3480 (1995).
[CrossRef] [PubMed]

1994 (2)

K. Naganuma, Y. Sakai, “Interferometric measurement of wavelength dispersion on femtosecond laser cavities,” Opt. Lett. 19, 487–489 (1994).
[CrossRef] [PubMed]

W. H. Knox, “Dispersion measurements for femtosecond-pulse generation and applications,” Appl. Phys. B 58, 225–235 (1994).
[CrossRef]

1991 (1)

K. Naganuma, H. Yasaka, “Group delay and α-parameter measurement of 1.3 μm semiconductor traveling-wave optical amplifier using the interferometric method,” IEEE J. Quantum Electron. 27, 1280–1287 (1991).
[CrossRef]

1990 (4)

P. Schiebener, J. Straub, J. M. H. L. Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

M. Medhat, “Measurement of the refraction and dispersion of solids and liquids by the rings of equal chromatic order,” Optik (Stuttgart) 85, 73–77 (1990).

Z. Bor, K. Osvay, B. Rácz, G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

K. Naganuma, K. Mogi, H. Yamada, “Group-delay measurement using the Fourier transform of an interferometric cross correlation generated by white light,” Opt. Lett. 15, 393–395 (1990).
[CrossRef] [PubMed]

1988 (1)

1985 (2)

A. Brimontas, V. Vasilyauskas, A. Piskarskas, A. Stabinis, “Dispersion spreading of femtosecond light pulses in crystals, air and water,” Sov. J. Quantum Electron. 15, 787–790 (1985).
[CrossRef]

I. Thormählen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

1978 (1)

1977 (1)

G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
[CrossRef]

1974 (1)

1973 (1)

1972 (1)

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

1968 (1)

W. M. Irvine, J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

1963 (1)

J. G. Bayly, V. B. Kartha, W. H. Stevens, “The absorption spectra of liquid phase H2O, HDO, and D2O from 0.7 μm to 10 μm,” Infrared Phys. 3, 211–223 (1963).
[CrossRef]

1951 (1)

Bayly, J. G.

J. G. Bayly, V. B. Kartha, W. H. Stevens, “The absorption spectra of liquid phase H2O, HDO, and D2O from 0.7 μm to 10 μm,” Infrared Phys. 3, 211–223 (1963).
[CrossRef]

Birkhoff, R. D.

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Bor, Z.

Z. Bor, K. Osvay, B. Rácz, G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Brimontas, A.

A. Brimontas, V. Vasilyauskas, A. Piskarskas, A. Stabinis, “Dispersion spreading of femtosecond light pulses in crystals, air and water,” Sov. J. Quantum Electron. 15, 787–790 (1985).
[CrossRef]

Brodeur, A.

A. Brodeur, F. A. Ilkov, S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129, 193–198 (1996).
[CrossRef]

Chin, S. L.

A. Brodeur, F. A. Ilkov, S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129, 193–198 (1996).
[CrossRef]

Clement, T. S.

S. A. Diddams, H. K. Eaton, A. A. Zozulya, T. S. Clement, “Characterizing the nonlinear propagation of femtosecond pulses in bulk media,” IEEE J. Sel. Top. Quantum Electron. 4, 306–316 (1998).
[CrossRef]

Cook, K.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, C. R. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[CrossRef]

Crégut, O.

S. Petit, O. Crégut, C. Hirlimann, “A tunable femtosecond pulses amplifier,” Opt. Commun. 124, 49–55 (1996).
[CrossRef]

Curcio, J. A.

Diddams, S.

Diddams, S. A.

S. A. Diddams, H. K. Eaton, A. A. Zozulya, T. S. Clement, “Characterizing the nonlinear propagation of femtosecond pulses in bulk media,” IEEE J. Sel. Top. Quantum Electron. 4, 306–316 (1998).
[CrossRef]

Diels, J.-C.

S. Diddams, J.-C. Diels, “Dispersion measurements with white light interferometry,” J. Opt. Soc. Am. B 13, 1120–1129 (1996).
[CrossRef]

X. M. Zhao, J.-C. Diels, C. Y. Wang, J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599–612 (1995).
[CrossRef]

Eaton, H. K.

S. A. Diddams, H. K. Eaton, A. A. Zozulya, T. S. Clement, “Characterizing the nonlinear propagation of femtosecond pulses in bulk media,” IEEE J. Sel. Top. Quantum Electron. 4, 306–316 (1998).
[CrossRef]

Elizondo, J. M.

X. M. Zhao, J.-C. Diels, C. Y. Wang, J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599–612 (1995).
[CrossRef]

Feng, Q.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, C. R. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[CrossRef]

Fry, E. S.

Fuji, T.

Gallagher, J. S.

P. Schiebener, J. Straub, J. M. H. L. Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Grigull, U.

I. Thormählen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Hale, G. M.

Hamm, R. N.

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Hammer, D. X.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, C. R. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[CrossRef]

Hattori, T.

Hirlimann, C.

S. Petit, O. Crégut, C. Hirlimann, “A tunable femtosecond pulses amplifier,” Opt. Commun. 124, 49–55 (1996).
[CrossRef]

Hirlimann, C. A.

Huibers, P. D. T.

Ilkov, F. A.

A. Brodeur, F. A. Ilkov, S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129, 193–198 (1996).
[CrossRef]

Irvine, W. M.

W. M. Irvine, J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

Kartha, V. B.

J. G. Bayly, V. B. Kartha, W. H. Stevens, “The absorption spectra of liquid phase H2O, HDO, and D2O from 0.7 μm to 10 μm,” Infrared Phys. 3, 211–223 (1963).
[CrossRef]

Kawato, S.

Kennedy, P. K.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, C. R. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[CrossRef]

Kerr, G. D.

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Khashan, M. A.

Knox, W. H.

Li, K. D.

McNeil, G. T.

G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
[CrossRef]

Medhat, M.

M. Medhat, “Measurement of the refraction and dispersion of solids and liquids by the rings of equal chromatic order,” Optik (Stuttgart) 85, 73–77 (1990).

Mielenz, K. D.

Miyata, M.

Mogi, K.

Moloney, J. V.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, C. R. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[CrossRef]

Naganuma, K.

Nakatsuka, H.

Nassif, A. Y.

Newell, A. C.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, C. R. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[CrossRef]

Osvay, K.

Z. Bor, K. Osvay, B. Rácz, G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Painter, L. R.

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Palmer, K. F.

Pearson, N. M.

Petit, S.

S. Petit, O. Crégut, C. Hirlimann, “A tunable femtosecond pulses amplifier,” Opt. Commun. 124, 49–55 (1996).
[CrossRef]

Petty, C. C.

Piskarskas, A.

A. Brimontas, V. Vasilyauskas, A. Piskarskas, A. Stabinis, “Dispersion spreading of femtosecond light pulses in crystals, air and water,” Sov. J. Quantum Electron. 15, 787–790 (1985).
[CrossRef]

Pollack, J. B.

W. M. Irvine, J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

Quan, X.

Querry, M. R.

Rácz, B.

Z. Bor, K. Osvay, B. Rácz, G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Rockwell, B. A.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, C. R. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[CrossRef]

Sakai, Y.

Schiebener, P.

P. Schiebener, J. Straub, J. M. H. L. Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Sengers, J. M. H. L.

P. Schiebener, J. Straub, J. M. H. L. Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Stabinis, A.

A. Brimontas, V. Vasilyauskas, A. Piskarskas, A. Stabinis, “Dispersion spreading of femtosecond light pulses in crystals, air and water,” Sov. J. Quantum Electron. 15, 787–790 (1985).
[CrossRef]

Stevens, W. H.

J. G. Bayly, V. B. Kartha, W. H. Stevens, “The absorption spectra of liquid phase H2O, HDO, and D2O from 0.7 μm to 10 μm,” Infrared Phys. 3, 211–223 (1963).
[CrossRef]

Straub, J.

P. Schiebener, J. Straub, J. M. H. L. Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

I. Thormählen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Szabó, G.

Z. Bor, K. Osvay, B. Rácz, G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Thompson, C. R.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, C. R. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[CrossRef]

Thormählen, I.

I. Thormählen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

Vasilyauskas, V.

A. Brimontas, V. Vasilyauskas, A. Piskarskas, A. Stabinis, “Dispersion spreading of femtosecond light pulses in crystals, air and water,” Sov. J. Quantum Electron. 15, 787–790 (1985).
[CrossRef]

Wang, C. Y.

X. M. Zhao, J.-C. Diels, C. Y. Wang, J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599–612 (1995).
[CrossRef]

Williams, D.

Williams, M. W.

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Wright, E. M.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, C. R. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[CrossRef]

Yamada, H.

Yasaka, H.

K. Naganuma, H. Yasaka, “Group delay and α-parameter measurement of 1.3 μm semiconductor traveling-wave optical amplifier using the interferometric method,” IEEE J. Quantum Electron. 27, 1280–1287 (1991).
[CrossRef]

Zhao, X. M.

X. M. Zhao, J.-C. Diels, C. Y. Wang, J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599–612 (1995).
[CrossRef]

Zozulya, A. A.

S. A. Diddams, H. K. Eaton, A. A. Zozulya, T. S. Clement, “Characterizing the nonlinear propagation of femtosecond pulses in bulk media,” IEEE J. Sel. Top. Quantum Electron. 4, 306–316 (1998).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. B (1)

W. H. Knox, “Dispersion measurements for femtosecond-pulse generation and applications,” Appl. Phys. B 58, 225–235 (1994).
[CrossRef]

Icarus (1)

W. M. Irvine, J. B. Pollack, “Infrared optical properties of water and ice spheres,” Icarus 8, 324–360 (1968).
[CrossRef]

IEEE J. Quantum Electron. (3)

X. M. Zhao, J.-C. Diels, C. Y. Wang, J. M. Elizondo, “Femtosecond ultraviolet laser pulse induced lightning discharges in gases,” IEEE J. Quantum Electron. 31, 599–612 (1995).
[CrossRef]

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, C. R. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[CrossRef]

K. Naganuma, H. Yasaka, “Group delay and α-parameter measurement of 1.3 μm semiconductor traveling-wave optical amplifier using the interferometric method,” IEEE J. Quantum Electron. 27, 1280–1287 (1991).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

S. A. Diddams, H. K. Eaton, A. A. Zozulya, T. S. Clement, “Characterizing the nonlinear propagation of femtosecond pulses in bulk media,” IEEE J. Sel. Top. Quantum Electron. 4, 306–316 (1998).
[CrossRef]

Infrared Phys. (1)

J. G. Bayly, V. B. Kartha, W. H. Stevens, “The absorption spectra of liquid phase H2O, HDO, and D2O from 0.7 μm to 10 μm,” Infrared Phys. 3, 211–223 (1963).
[CrossRef]

J. Opt. Soc. Am. (2)

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

J. Phys. Chem. Ref. Data (2)

I. Thormählen, J. Straub, U. Grigull, “Refractive index of water and its dependence on wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 14, 933–945 (1985).
[CrossRef]

P. Schiebener, J. Straub, J. M. H. L. Sengers, J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature, and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[CrossRef]

Opt. Commun. (3)

S. Petit, O. Crégut, C. Hirlimann, “A tunable femtosecond pulses amplifier,” Opt. Commun. 124, 49–55 (1996).
[CrossRef]

A. Brodeur, F. A. Ilkov, S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129, 193–198 (1996).
[CrossRef]

Z. Bor, K. Osvay, B. Rácz, G. Szabó, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Opt. Eng. (1)

G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
[CrossRef]

Opt. Lett. (3)

Optik (Stuttgart) (1)

M. Medhat, “Measurement of the refraction and dispersion of solids and liquids by the rings of equal chromatic order,” Optik (Stuttgart) 85, 73–77 (1990).

Phys. Rev. A (1)

G. D. Kerr, R. N. Hamm, M. W. Williams, R. D. Birkhoff, L. R. Painter, “Optical and dielectric properties of water in the vacuum ultraviolet,” Phys. Rev. A 5, 2523 (1972).
[CrossRef]

Sov. J. Quantum Electron. (1)

A. Brimontas, V. Vasilyauskas, A. Piskarskas, A. Stabinis, “Dispersion spreading of femtosecond light pulses in crystals, air and water,” Sov. J. Quantum Electron. 15, 787–790 (1985).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Michelson white-light interferometer setup: BS, beam splitter; C, compensator; WLD, white-light detector; PD, photodiode detector; M1, M2, and M, mirrors; L, lens; SC, sample cell. The solid line represents white light from the halogen bulb, and the dashed line represents light from the He–Ne laser used for calibration of the time delay.

Fig. 2
Fig. 2

White-light interferograms (a) without any sample and (b) with water held in the glass sample cell. A Si photodiode was used for detection. Note the difference in time scales for the different scans. The time zero was arbitrarily set at the peak of each interferogram, and for clarity only a portion of each interferogram is shown.

Fig. 3
Fig. 3

Spectral amplitude (solid curve) and phase (dotted curve) of the Fourier transforms of interferograms shown in Fig. 2.: (a) without any sample and (b) with water held in the glass sample cell. Note the change in curvature of the phase brought about by inserting the water sample.

Fig. 4
Fig. 4

Measured values of (a) the second-order dispersion k″ and (b) the third-order dispersion k‴ for Fisher high-performance liquid chromatography-grade water as a function of angular frequency ω.

Fig. 5
Fig. 5

Index of refraction n(λ) for water calculated from Eq. (10), Quan and Fry23; Eq. (11), McNeil17; Eq. (12), Mielenz18; and accepted values from Irvine and Pollack.25

Fig. 6
Fig. 6

Comparison of measured values for the (a) second derivative of the index of refraction d 2 n/dλ2 and (b) third derivative of the index of refraction d 3 n/dλ3 for water to values calculated from Eq. (10), Quan and Fry23; Eq. (11), McNeil17; and Eq. (12), Mielenz.18

Fig. 7
Fig. 7

Δ2, the difference between measured and calculated values of d 2 n/dλ2 for water from (a) Eq. (10), Quan and Fry23; (b) Eq. (11), McNeil17; and (c) Eq. (12), Mielenz.18 Dark bars represent the stated range of validity for each equation, and light bars represent an extension beyond the original wavelength range.

Fig. 8
Fig. 8

Δ3, the difference between measured and calculated values of d 3 n/dλ3 for water from (a) Eq. (10), Quan and Fry23; (b) Eq. (11), McNeil17; and (c) Eq. (12), Mielenz.18 Dark bars represent the stated range of validity for each equation, and light bars represent an extension beyond the original wavelength range.

Tables (1)

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Table 1 Second- and Third-Order Dispersion Coefficients and Derivatives of the Index of Refraction Measured with White-Light Interferometry

Equations (12)

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E 1 t = 1 t exp - i ω 0 t - i ϕ 1 t ,
E 2 t - τ = 2 t - τ exp - i ω 0 × t - τ - i ϕ 2 t - τ ,
I τ     | E 1 t | 2 + | E 2 t - τ | 2 + E 1 * t E 2 t - τ + E 1 t E 2 * t - τ ,
I int τ = E 1 * t E 2 t - τ + c . c . = 1 t 2 t - τ exp i ω 0 τ + i ϕ 1 t - i ϕ 2 t - τ + c . c ,
I int ω = I int τ = E 1 * ω E 2 ω + c . c .
I int ω = | E 1 ω | 2 exp ik ω d .
Φ Ω = k Ω d k 0 d + k 0 Ω d + k 0 2   Ω 2 d + k 0 6   Ω 3 d + ,
d 2 n d λ 2 | λ 0 = 2 π c 2 λ 0 3   k 0 ,
d 3 n d λ 3 λ 0 = - 2 π c 2 λ 0 4 3 k 0 + 2 π c λ 0   k 0 .
n = 1.313242 + 15.7834 λ - 4382 λ 2 + 1.1455 × 10 6 λ 3
n = 1.3237 - 3.2 × 10 7 λ 4 + 3300 λ 2
n 2 = 1.7604457   +   4.03368   ×   10 - 3   λ - 1.54182   × 10 - 2   λ 2 + 6.44277 × 10 - 3 λ 2 - 1.49119 × 10 - 2

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