Abstract

We report on a technique for measuring the refractive indices of nonabsorbing media over a broad spectral range from 0.5 to 5 μm. White-light interferometry based on a double-interferometer system consisting of a fixed Mach-Zehnder interferometer and a Fourier-transform spectrometer is used for direct measurement of the absolute rotation-dependent phase shift induced by an optical element. Refractive index n(λ) over the whole investigated spectral range is thus obtained directly to an accuracy of 10-4 without the need for any specific assumption about dispersion. Results for synthetic fused silica are presented and discussed.

© 2003 Optical Society of America

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References

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  1. C. Sainz, P. Jourdain, R. Escalona, J. Calatrani, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
    [CrossRef]
  2. H. Delbarre, C. Przygodzki, M. Tassou, D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
    [CrossRef]
  3. P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193, 1–7 (2001).
    [CrossRef]
  4. W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, “Interferometric measurements of femtosecond group delay in optical components,” Opt. Lett. 13, 574–576 (1988).
    [CrossRef] [PubMed]
  5. K. D. Li, W. H. Knox, N. M. Pearson, “Broadband cubic-phase compensation with resonant Gires-Turnois interferometers,” Opt. Lett. 14, 450–452 (1989).
    [CrossRef] [PubMed]
  6. M. Beck, I. A. Walmsley, “Measurement of group delay with high temporal and spectral resolution,” Opt. Lett. 15, 492–494 (1990).
    [CrossRef] [PubMed]
  7. K. Naganuma, K. Mogi, H. Yamada, “Group-delay measurements using the Fourier transform of an interferometric cross correlation generated by white light,” Opt. Lett 15, 393–395 (1990).
    [CrossRef] [PubMed]
  8. V. N. Kumar, D. N. Rao, “Using interference in the frequency domain for precise determination of thickness and refractive indices of normal dispersive materials,” J. Opt. Soc. Am. B 12, 1559–1563 (2995).
    [CrossRef]
  9. S. Diddams, J. C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. B 13, 1120–1128 (1996).
  10. I. Abdulhalim, “Spectroscopic interference microscopy technique for measurement of layer parameters,” Meas. Sci. Technol. 12, 1996–2001 (2001).
    [CrossRef]
  11. K. Betzler, A. Groene, N. Schmidt, P. Voigt, “Interferometric measurements of refractive indices,” Rev. Sci. Instrum. 59, 652–653 (1988).
    [CrossRef]
  12. S. A. Alexandrov, I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
    [CrossRef]
  13. S. De Nicola, P. Ferraro, A. Finzio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
    [CrossRef]
  14. E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).
  15. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965).
    [CrossRef]

2995 (1)

2002 (1)

S. De Nicola, P. Ferraro, A. Finzio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

2001 (2)

I. Abdulhalim, “Spectroscopic interference microscopy technique for measurement of layer parameters,” Meas. Sci. Technol. 12, 1996–2001 (2001).
[CrossRef]

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193, 1–7 (2001).
[CrossRef]

2000 (2)

H. Delbarre, C. Przygodzki, M. Tassou, D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

S. A. Alexandrov, I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

1996 (1)

S. Diddams, J. C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. B 13, 1120–1128 (1996).

1994 (1)

C. Sainz, P. Jourdain, R. Escalona, J. Calatrani, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

1990 (2)

M. Beck, I. A. Walmsley, “Measurement of group delay with high temporal and spectral resolution,” Opt. Lett. 15, 492–494 (1990).
[CrossRef] [PubMed]

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

1989 (1)

1988 (2)

K. Betzler, A. Groene, N. Schmidt, P. Voigt, “Interferometric measurements of refractive indices,” Rev. Sci. Instrum. 59, 652–653 (1988).
[CrossRef]

W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, “Interferometric measurements of femtosecond group delay in optical components,” Opt. Lett. 13, 574–576 (1988).
[CrossRef] [PubMed]

1965 (1)

Abdulhalim, I.

I. Abdulhalim, “Spectroscopic interference microscopy technique for measurement of layer parameters,” Meas. Sci. Technol. 12, 1996–2001 (2001).
[CrossRef]

Alexandrov, S. A.

S. A. Alexandrov, I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

Beck, M.

Betzler, K.

K. Betzler, A. Groene, N. Schmidt, P. Voigt, “Interferometric measurements of refractive indices,” Rev. Sci. Instrum. 59, 652–653 (1988).
[CrossRef]

Boucher, D.

H. Delbarre, C. Przygodzki, M. Tassou, D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

Calatrani, J.

C. Sainz, P. Jourdain, R. Escalona, J. Calatrani, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

Chernyh, I. V.

S. A. Alexandrov, I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

De Natale, P.

S. De Nicola, P. Ferraro, A. Finzio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

De Nicola, S.

S. De Nicola, P. Ferraro, A. Finzio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Delbarre, H.

H. Delbarre, C. Przygodzki, M. Tassou, D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

Diddams, S.

S. Diddams, J. C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. B 13, 1120–1128 (1996).

Diels, J. C.

S. Diddams, J. C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. B 13, 1120–1128 (1996).

Escalona, R.

C. Sainz, P. Jourdain, R. Escalona, J. Calatrani, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

Ferraro, P.

S. De Nicola, P. Ferraro, A. Finzio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Finzio, A.

S. De Nicola, P. Ferraro, A. Finzio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Grilli, S.

S. De Nicola, P. Ferraro, A. Finzio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Groene, A.

K. Betzler, A. Groene, N. Schmidt, P. Voigt, “Interferometric measurements of refractive indices,” Rev. Sci. Instrum. 59, 652–653 (1988).
[CrossRef]

Hirlimann, C. A.

Hlubina, P.

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193, 1–7 (2001).
[CrossRef]

Jourdain, P.

C. Sainz, P. Jourdain, R. Escalona, J. Calatrani, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

Knox, W. H.

Kumar, V. N.

Li, K. D.

Malitson, I. H.

Mogi, K.

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

Naganuma, K.

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

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).

Pearson, N. M.

Pierattini, G.

S. De Nicola, P. Ferraro, A. Finzio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Przygodzki, C.

H. Delbarre, C. Przygodzki, M. Tassou, D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

Rao, D. N.

Sainz, C.

C. Sainz, P. Jourdain, R. Escalona, J. Calatrani, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

Schmidt, N.

K. Betzler, A. Groene, N. Schmidt, P. Voigt, “Interferometric measurements of refractive indices,” Rev. Sci. Instrum. 59, 652–653 (1988).
[CrossRef]

Tassou, M.

H. Delbarre, C. Przygodzki, M. Tassou, D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

Voigt, P.

K. Betzler, A. Groene, N. Schmidt, P. Voigt, “Interferometric measurements of refractive indices,” Rev. Sci. Instrum. 59, 652–653 (1988).
[CrossRef]

Walmsley, I. A.

Yamada, H.

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

Appl. Phys. B (1)

H. Delbarre, C. Przygodzki, M. Tassou, D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45–51 (2000).
[CrossRef]

J. Opt. Soc. Am. (2)

S. Diddams, J. C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. B 13, 1120–1128 (1996).

I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965).
[CrossRef]

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

Meas. Sci. Technol. (1)

I. Abdulhalim, “Spectroscopic interference microscopy technique for measurement of layer parameters,” Meas. Sci. Technol. 12, 1996–2001 (2001).
[CrossRef]

Opt. Commun. (3)

C. Sainz, P. Jourdain, R. Escalona, J. Calatrani, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

P. Hlubina, “White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica,” Opt. Commun. 193, 1–7 (2001).
[CrossRef]

S. De Nicola, P. Ferraro, A. Finzio, P. De Natale, S. Grilli, G. Pierattini, “A Mach-Zehnder interferometric system for measuring the refractive indices of uniaxial crystals,” Opt. Commun. 202, 9–15 (2002).
[CrossRef]

Opt. Eng. (1)

S. A. Alexandrov, I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

Opt. Lett (1)

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

Opt. Lett. (3)

Rev. Sci. Instrum. (1)

K. Betzler, A. Groene, N. Schmidt, P. Voigt, “Interferometric measurements of refractive indices,” Rev. Sci. Instrum. 59, 652–653 (1988).
[CrossRef]

Other (1)

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: NS, high-resolution nanometer stage; QTH, halogen lamp; BS1, BS2, beam splitters; RS, rotation stage; D, detector.

Fig. 2
Fig. 2

(a) Detected interferogram, showing typical three-peaks structure given by the autocorrelation (central peak) and the cross-correlation (side peaks) signals. (b) Discrepancy between the measured and the calculated absolute phase delay when the OPD between the two arms of the MZI is changed by 100 ± 0.5 nm.

Fig. 3
Fig. 3

(a) Measured relative phase shifts for a SiO2 slab, 1238 ± 1 μm thick, at several angles of incidence from 0° to 10° in steps of 1°. (b) Absolute angular-dependent phase shifts at two wavelengths (squares) and fitted to Eq. (2) (solid curves).

Fig. 4
Fig. 4

(a) Experimentally determined refractive-index dispersion of SiO2 compared to that calculated by the three-term Sellmeier formula and one reported in the literature14 (filled squares). (b) Difference between the experimentally determined refractive index and that calculated by the Sellmeier formula.

Equations (2)

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φλ=2πλOPD=2πλdnλ-1+L,
Δφ=φθ-φθ0=2πλ dnλ2-sin2 θ1/2-cos θ-nλ2-sin2 θ01/2+cos θ0.

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