Abstract

We report a simple method of measuring the absolute values of the phase refractive index of an optical material of a flat plate shape over a wide spectral range at a single measurement run. A white-light interferometric technique with angle rotation of the optical plate sample located in one of the interfer ometer arms was used in this method. The validity of this method was proved by measuring the absolute phase refractive indices of flat plate samples of fused silica and BK7, and by comparing them with calculated values from their well-known Sellmeier dispersion formulas. The accuracy of this refractive index measurement method was within 0.002, which can be further improved by enhancing the angle measurement accuracy of the angle rotating stage used in this method.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2009 (2)

D. S. Park, B. H. O, S. G. Park, E. H. Lee, S. G. Lee, “Simultaneous measurement of thickness and refractive index of transparent material using a collimated beam having a finite radius,” Hankook Kwanghak Hoeji (Korean) 20, 29–33 (2009).
[CrossRef]

S. H. Lee, S. H. Kim, K. H. Kim, M. H. Lee, E.-H. Lee, “A novel method for measuring continuous dispersion spectrum of electro-optic coefficients of nonlinear materials,” Opt. Express 17, 9828–9833 (2009).
[CrossRef] [PubMed]

2008 (3)

2007 (2)

2006 (1)

H. J. Choi, B. J. Kim, H. H. Lim, M. Cha, “Measurement of the refractive indices of glass and anisotropic crystal by using a Michelson interferometer,” J. Korean Phys. Soc. 53, 489–494 (2006).

2005 (2)

W. Liang, Y. Huang, Y. Xu, R. K. Lee, A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86, 1–3 (2005).
[CrossRef]

I. Del Villar, I. R. Matias, F. J. Arregui, “Enhancement of sensitivity in long-period fiber gratings with deposition of low-refractive-index materials,” Opt. Lett. 30, 2363–2365 (2005).
[CrossRef] [PubMed]

2003 (1)

2002 (3)

H. Maruyama, S. Inoue, T. Mitsuyama, M. Ohmi, M. Haruna, “Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness,” Appl. Opt. 41, 1315–1322 (2002).
[CrossRef] [PubMed]

D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
[CrossRef]

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

2000 (1)

1999 (1)

1998 (1)

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

1997 (3)

G. H. Meeten, “Refractive index errors in the critical-angle and the Brewster-angle methods applied to absorbing and heterogeneous materials,” Meas. Sci. Technol. 8, 728–733 (1997).
[CrossRef]

J. Rheims, J. Köser, T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

J. F. H. Nicholls, B. Henderson, B. H. T. Chai, “Accurate determination of the indices of refraction of nonlinear optical crystals,” Appl. Opt. 36, 8587–8594 (1997).
[CrossRef]

1996 (1)

J. C. Martínez-Antón, E. Bemabeu, “Simultaneous determination of film thickness and refractive index by interferential spectrogoniometry,” Opt. Commun. 132, 321–328 (1996).
[CrossRef]

1995 (1)

1994 (1)

G. Ghosh, M. Endo, T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

1992 (1)

W. V. Sorin, D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photonics Technol. Lett. 4, 105–107 (1992).
[CrossRef]

1988 (2)

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

D. J. Gettemy, W. C. Harker, G. Lindholm, N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24, 2231–2237 (1988).
[CrossRef]

1979 (1)

M. Debenham, G. D. Dew, D. E. Putland, “An improved recording refractometer for optical glasses in the wavelength range 300 to 2600 nm,” Opt. Acta 26, 1487–1503 (1979).
[CrossRef]

1973 (1)

1966 (1)

Arregui, F. J.

Barnes, N. P.

D. J. Gettemy, W. C. Harker, G. Lindholm, N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24, 2231–2237 (1988).
[CrossRef]

Beaumont, A.

Bemabeu, E.

J. C. Martínez-Antón, E. Bemabeu, “Simultaneous determination of film thickness and refractive index by interferential spectrogoniometry,” Opt. Commun. 132, 321–328 (1996).
[CrossRef]

Betzler, K.

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

Bhattacharyya, D.

D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
[CrossRef]

Bouma, B. E.

Brezinski, M. E.

Cha, M.

H. J. Choi, H. H. Lim, B. J. Kim, M. Cha, “Measurement of the birefringence in bulk optical media by using interferometric methods,” J. Korean Phys. Soc. 53, 3197–3200 (2008).
[CrossRef]

H. J. Choi, B. J. Kim, H. H. Lim, M. Cha, “Measurement of the refractive indices of glass and anisotropic crystal by using a Michelson interferometer,” J. Korean Phys. Soc. 53, 489–494 (2006).

Chai, B. H. T.

Choi, H. J.

H. J. Choi, H. H. Lim, B. J. Kim, M. Cha, “Measurement of the birefringence in bulk optical media by using interferometric methods,” J. Korean Phys. Soc. 53, 3197–3200 (2008).
[CrossRef]

H. J. Choi, B. J. Kim, H. H. Lim, M. Cha, “Measurement of the refractive indices of glass and anisotropic crystal by using a Michelson interferometer,” J. Korean Phys. Soc. 53, 489–494 (2006).

Coppola, G.

De Nicola, S.

Debenham, M.

M. Debenham, G. D. Dew, D. E. Putland, “An improved recording refractometer for optical glasses in the wavelength range 300 to 2600 nm,” Opt. Acta 26, 1487–1503 (1979).
[CrossRef]

Del Villar, I.

Dew, G. D.

M. Debenham, G. D. Dew, D. E. Putland, “An improved recording refractometer for optical glasses in the wavelength range 300 to 2600 nm,” Opt. Acta 26, 1487–1503 (1979).
[CrossRef]

Dutta, B. K.

D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
[CrossRef]

Endo, M.

G. Ghosh, M. Endo, T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

Fehri, M. F.

Ferraro, P.

Flavin, D. A.

Fujimoto, J. G.

Fukano, T.

Gauvreau, B.

Gettemy, D. J.

D. J. Gettemy, W. C. Harker, G. Lindholm, N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24, 2231–2237 (1988).
[CrossRef]

Ghosh, G.

G. Ghosh, M. Endo, T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

Ghosh, P. N.

D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
[CrossRef]

Gray, D. F.

W. V. Sorin, D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photonics Technol. Lett. 4, 105–107 (1992).
[CrossRef]

Gröne, A.

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

Han, Y.

Harker, W. C.

D. J. Gettemy, W. C. Harker, G. Lindholm, N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24, 2231–2237 (1988).
[CrossRef]

Hart, C.

Haruna, M.

Hassani, A.

Hee, M. R.

Henderson, B.

Herzinger, C. M.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

Huang, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86, 1–3 (2005).
[CrossRef]

Inoue, S.

Iodice, M.

Iwasaki, T.

G. Ghosh, M. Endo, T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

Johs, B.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

Kabashin, A.

Kim, B. J.

H. J. Choi, H. H. Lim, B. J. Kim, M. Cha, “Measurement of the birefringence in bulk optical media by using interferometric methods,” J. Korean Phys. Soc. 53, 3197–3200 (2008).
[CrossRef]

H. J. Choi, B. J. Kim, H. H. Lim, M. Cha, “Measurement of the refractive indices of glass and anisotropic crystal by using a Michelson interferometer,” J. Korean Phys. Soc. 53, 489–494 (2006).

Kim, D. Y.

Kim, K. H.

Kim, S. H.

Köser, J.

J. Rheims, J. Köser, T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Lee, E. H.

D. S. Park, B. H. O, S. G. Park, E. H. Lee, S. G. Lee, “Simultaneous measurement of thickness and refractive index of transparent material using a collimated beam having a finite radius,” Hankook Kwanghak Hoeji (Korean) 20, 29–33 (2009).
[CrossRef]

Lee, E.-H.

Lee, J. Y.

Lee, M. H.

Lee, R. K.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86, 1–3 (2005).
[CrossRef]

Lee, S. G.

D. S. Park, B. H. O, S. G. Park, E. H. Lee, S. G. Lee, “Simultaneous measurement of thickness and refractive index of transparent material using a collimated beam having a finite radius,” Hankook Kwanghak Hoeji (Korean) 20, 29–33 (2009).
[CrossRef]

Lee, S. H.

Li, Y.

Liang, W.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86, 1–3 (2005).
[CrossRef]

Lim, H. H.

H. J. Choi, H. H. Lim, B. J. Kim, M. Cha, “Measurement of the birefringence in bulk optical media by using interferometric methods,” J. Korean Phys. Soc. 53, 3197–3200 (2008).
[CrossRef]

H. J. Choi, B. J. Kim, H. H. Lim, M. Cha, “Measurement of the refractive indices of glass and anisotropic crystal by using a Michelson interferometer,” J. Korean Phys. Soc. 53, 489–494 (2006).

Lindholm, G.

D. J. Gettemy, W. C. Harker, G. Lindholm, N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24, 2231–2237 (1988).
[CrossRef]

Martínez-Antón, J. C.

J. C. Martínez-Antón, E. Bemabeu, “Simultaneous determination of film thickness and refractive index by interferential spectrogoniometry,” Opt. Commun. 132, 321–328 (1996).
[CrossRef]

Maruyama, H.

Matias, I. R.

McGahan, W. A.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

Meeten, G. H.

G. H. Meeten, “Refractive index errors in the critical-angle and the Brewster-angle methods applied to absorbing and heterogeneous materials,” Meas. Sci. Technol. 8, 728–733 (1997).
[CrossRef]

Mitsuyama, T.

Murphy, D. F.

Nicholls, J. F. H.

O, B. H.

D. S. Park, B. H. O, S. G. Park, E. H. Lee, S. G. Lee, “Simultaneous measurement of thickness and refractive index of transparent material using a collimated beam having a finite radius,” Hankook Kwanghak Hoeji (Korean) 20, 29–33 (2009).
[CrossRef]

Ohmi, M.

Park, D. S.

D. S. Park, B. H. O, S. G. Park, E. H. Lee, S. G. Lee, “Simultaneous measurement of thickness and refractive index of transparent material using a collimated beam having a finite radius,” Hankook Kwanghak Hoeji (Korean) 20, 29–33 (2009).
[CrossRef]

Park, S. G.

D. S. Park, B. H. O, S. G. Park, E. H. Lee, S. G. Lee, “Simultaneous measurement of thickness and refractive index of transparent material using a collimated beam having a finite radius,” Hankook Kwanghak Hoeji (Korean) 20, 29–33 (2009).
[CrossRef]

Paulson, W.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

Putland, D. E.

M. Debenham, G. D. Dew, D. E. Putland, “An improved recording refractometer for optical glasses in the wavelength range 300 to 2600 nm,” Opt. Acta 26, 1487–1503 (1979).
[CrossRef]

Ray, A.

D. Bhattacharyya, A. Ray, B. K. Dutta, P. N. Ghosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93–96 (2002).
[CrossRef]

Rheims, J.

J. Rheims, J. Köser, T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Schmidt, N.

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

Shumate, M. S.

Singh, S.

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

Skorobogatiy, M.

Sorin, W. V.

W. V. Sorin, D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photonics Technol. Lett. 4, 105–107 (1992).
[CrossRef]

Southern, J. F.

Tearney, G. J.

Tedaldi, M.

Tomlins, P. H.

Torge, R.

Tsai, H.-L.

Ulrich, R.

Voigt, P.

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

Wei, T.

Woollam, J. A.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83, 3323–3336 (1998).
[CrossRef]

Woolliams, P.

Wriedt, T.

J. Rheims, J. Köser, T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8, 601–605 (1997).
[CrossRef]

Xiao, H.

Xu, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86, 1–3 (2005).
[CrossRef]

Yamaguchi, I.

Yariv, A.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86, 1–3 (2005).
[CrossRef]

Appl. Opt. (8)

M. S. Shumate, “Interferometric measurement of large indices of refraction,” Appl. Opt. 5, 327–331 (1966).
[CrossRef] [PubMed]

R. Ulrich, R. Torge, “Measurement of thin film parameters with a prism coupler,” Appl. Opt. 12, 2901–2908 (1973).
[CrossRef] [PubMed]

T. Fukano, I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065–4073 (1999).
[CrossRef]

D. F. Murphy, D. A. Flavin, “Dispersion-insensitive measurement of thickness and group refractive index by low- coherence interferometry,” Appl. Opt. 39, 4607–4615 (2000).
[CrossRef]

J. F. H. Nicholls, B. Henderson, B. H. T. Chai, “Accurate determination of the indices of refraction of nonlinear optical crystals,” Appl. Opt. 36, 8587–8594 (1997).
[CrossRef]

H. Maruyama, S. Inoue, T. Mitsuyama, M. Ohmi, M. Haruna, “Low-coherence interferometer system for the simultaneous measurement of refractive index and thickness,” Appl. Opt. 41, 1315–1322 (2002).
[CrossRef] [PubMed]

G. Coppola, P. Ferraro, M. Iodice, S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer,” Appl. Opt. 42, 3882–3887 (2003).
[CrossRef] [PubMed]

J. Y. Lee, D. Y. Kim, “Spectrum-sliced Fourier-domain low-coherence interferometry for measuring the chromatic dispersion of an optical fiber,” Appl. Opt. 46, 7289–7296 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

W. Liang, Y. Huang, Y. Xu, R. K. Lee, A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86, 1–3 (2005).
[CrossRef]

Hankook Kwanghak Hoeji (Korean) (1)

D. S. Park, B. H. O, S. G. Park, E. H. Lee, S. G. Lee, “Simultaneous measurement of thickness and refractive index of transparent material using a collimated beam having a finite radius,” Hankook Kwanghak Hoeji (Korean) 20, 29–33 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

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Figures (5)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Optical path length illustration along the sample at a rotated sample angle θ.

Fig. 3
Fig. 3

(a) Measured and (b) normalized interference patterns.

Fig. 4
Fig. 4

Relative phase change curves at two different angles.

Fig. 5
Fig. 5

Measured dispersion curves of the fused silica and BK7 glasses compared with the calculated ones from the Sellmeier formulas.

Equations (11)

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I ( λ ) = | E A ( λ ) + E B ( λ ) | 2 = | E 0 2 ( λ ) | ( 1 + a 2 ) + 2 a | E 0 2 ( λ ) | cos { ϕ ( λ ) } ,
ϕ ( λ , θ ) = ϕ f ( λ ) + 2 π λ { O P L R . A . ( λ ) O P L S . A . ( λ , θ ) } .
O P L S . A . ( λ , θ ) = n 0 ( λ ) L n 0 ( λ ) D ( λ , θ ) + n ( λ ) d ( λ , θ ) .
cos θ = 1 n 0 2 ( λ ) sin 2 θ n 2 ( λ ) = n 2 ( λ ) n 0 2 ( λ ) sin 2 θ n ( λ ) .
d = d cos θ = n ( λ ) n 2 ( λ ) n 0 2 ( λ ) sin 2 θ d ,
D = d cos ( θ θ ) = d ( cos θ + n 0 ( λ ) sin 2 θ n 2 ( λ ) n 0 2 ( λ ) sin 2 θ ) .
O P L S . A . ( λ , θ ) = n 0 ( λ ) L + d [ n 0 ( λ ) cos θ + n 2 ( λ ) n 0 2 ( λ ) sin 2 θ ] .
Δ O P L S . A . ( λ , θ ) = O P L S . A . ( λ , θ 2 ) O P L S . A . ( λ , θ 1 ) = d [ n 0 ( λ ) cos θ 1 n 0 ( λ ) cos θ 2 n 2 ( λ ) n 0 2 ( λ ) sin 2 θ 1 + n 2 ( λ ) n 0 2 ( λ ) sin 2 θ 2 ] .
ψ ( λ ) ϕ ( λ ) = 2 π λ Δ O P L S . A . ( λ , θ ) .
n ( λ ) = ( n 0 2 ( λ ) sin 2 θ 1 n 0 2 ( λ ) sin 2 θ 2 A 2 2 A ) 2 + n 0 2 ( λ ) sin 2 θ 1 ,
A = λ 2 π d [ ψ ( λ ) ϕ ( λ ) ] n 0 ( λ ) cos θ 1 + n 0 ( λ ) cos θ 2 .

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