Abstract

We developed an accurate and efficient method for measuring the refractive indices of a transparent plate by analyzing the transmitted intensity versus angle of incidence. By using two different wavelengths, we resolved the 2π-ambiguity inherent to the phase measurement involving a thick medium, leading to independent determination of the absolute index of refraction and the thickness with a relative uncertainty of 10−5. The validity and the accuracy of our method were confirmed with a standard reference material. Furthermore, our method is insensitive to environmental perturbations, and simple to implement, compared to the conventional index measurement methods providing similar accuracy.

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References

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  1. R. W. Boyd, Nonlinear Optics 2nd ed. (Academic Press, 2003).
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).
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  4. D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24(11), 2231–2237 (1988).
    [CrossRef]
  5. Schott North America, Inc., “Optical glass,” http://www.us.schott.com/advanced_optics/english/ our_products/materials/optical_ glass.html .
  6. G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
    [CrossRef]
  7. C. O. Atago, LTD., http://www.atago.net .
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    [CrossRef] [PubMed]
  9. 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(7), 728–733 (1997).
    [CrossRef]
  10. Metricon Corp, http://www.metricon.com .
  11. M. S. Shumate, “Interferometric measurement of large indices of refraction,” Appl. Opt. 5(2), 327–331 (1966).
    [CrossRef] [PubMed]
  12. G. D. Gillen and S. Guha, “Refractive-index measurements of zinc germanium diphosphide at 300 and 77 K by use of a modified Michelson interferometer,” Appl. Opt. 43(10), 2054–2058 (2004).
    [CrossRef] [PubMed]
  13. J. C. Brasunas and G. M. Curshman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34(7), 2126–2130 (1995).
    [CrossRef]
  14. G. D. Gillen and S. Guha, “Use of Michelson and Fabry-Perot interferometry for independent determination of the refractive index and physical thickness of wafers,” Appl. Opt. 44(3), 344–347 (2005).
    [CrossRef] [PubMed]
  15. G. Coppola, P. Ferraro, M. Iodice, and 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(19), 3882–3887 (2003).
    [CrossRef] [PubMed]
  16. F. L. Pedrotti, and L. S. Pedrotti, Introduction to Optics 2nd ed. (Prentice Hall, 1996).
  17. J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the helium-neon laser at 633 nm,” Metrologia 46(1), 11–18 (2009).
    [CrossRef]
  18. J. A. Stone, and J. H. Zimmerman, “Index of refraction of air,” http://emtoolbox.nist.gov/Wavelength/ Edlen.asp .
  19. National Institute of Standards and Technology, Certificate of Standard Reference Material® 1822a, 24 January 2007, http://www.nist.gov
  20. Korea Research Institute of Standards and Science, Test Report, Certificate No. 0901–00920–001, 12 August 2009.

2009 (1)

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the helium-neon laser at 633 nm,” Metrologia 46(1), 11–18 (2009).
[CrossRef]

2005 (1)

2004 (1)

2003 (1)

1997 (1)

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(7), 728–733 (1997).
[CrossRef]

1995 (1)

J. C. Brasunas and G. M. Curshman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34(7), 2126–2130 (1995).
[CrossRef]

1988 (1)

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24(11), 2231–2237 (1988).
[CrossRef]

1984 (1)

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

1983 (1)

1966 (1)

Awai, I.

Barnes, N. P.

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24(11), 2231–2237 (1988).
[CrossRef]

Brasunas, J. C.

J. C. Brasunas and G. M. Curshman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34(7), 2126–2130 (1995).
[CrossRef]

Coppola, G.

Curshman, G. M.

J. C. Brasunas and G. M. Curshman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34(7), 2126–2130 (1995).
[CrossRef]

De Nicola, S.

Decker, J. E.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the helium-neon laser at 633 nm,” Metrologia 46(1), 11–18 (2009).
[CrossRef]

Edwards, G. J.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

Ferraro, P.

Gettemy, D. J.

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24(11), 2231–2237 (1988).
[CrossRef]

Gill, P.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the helium-neon laser at 633 nm,” Metrologia 46(1), 11–18 (2009).
[CrossRef]

Gillen, G. D.

Guha, S.

Harker, W. C.

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24(11), 2231–2237 (1988).
[CrossRef]

Ikenoue, J.

Iodice, M.

Juncar, P.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the helium-neon laser at 633 nm,” Metrologia 46(1), 11–18 (2009).
[CrossRef]

Lawrence, M.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

Lewis, A.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the helium-neon laser at 633 nm,” Metrologia 46(1), 11–18 (2009).
[CrossRef]

Lindholm, G.

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24(11), 2231–2237 (1988).
[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(7), 728–733 (1997).
[CrossRef]

Onodera, H.

Rovera, G. D.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the helium-neon laser at 633 nm,” Metrologia 46(1), 11–18 (2009).
[CrossRef]

Shumate, M. S.

Stone, J. A.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the helium-neon laser at 633 nm,” Metrologia 46(1), 11–18 (2009).
[CrossRef]

Viliesid, M.

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the helium-neon laser at 633 nm,” Metrologia 46(1), 11–18 (2009).
[CrossRef]

Appl. Opt. (5)

IEEE J. Quantum Electron. (1)

D. J. Gettemy, W. C. Harker, G. Lindholm, and N. P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24(11), 2231–2237 (1988).
[CrossRef]

Meas. Sci. Technol. (1)

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(7), 728–733 (1997).
[CrossRef]

Metrologia (1)

J. A. Stone, J. E. Decker, P. Gill, P. Juncar, A. Lewis, G. D. Rovera, and M. Viliesid, “Advice from the CCL on the use of unstabilized lasers as standards of wavelength: the helium-neon laser at 633 nm,” Metrologia 46(1), 11–18 (2009).
[CrossRef]

Opt. Eng. (1)

J. C. Brasunas and G. M. Curshman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34(7), 2126–2130 (1995).
[CrossRef]

Opt. Quantum Electron. (1)

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16(4), 373–375 (1984).
[CrossRef]

Other (10)

C. O. Atago, LTD., http://www.atago.net .

Metricon Corp, http://www.metricon.com .

F. L. Pedrotti, and L. S. Pedrotti, Introduction to Optics 2nd ed. (Prentice Hall, 1996).

Schott North America, Inc., “Optical glass,” http://www.us.schott.com/advanced_optics/english/ our_products/materials/optical_ glass.html .

R. W. Boyd, Nonlinear Optics 2nd ed. (Academic Press, 2003).

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, 1997).

J. A. Stone, and J. H. Zimmerman, “Index of refraction of air,” http://emtoolbox.nist.gov/Wavelength/ Edlen.asp .

National Institute of Standards and Technology, Certificate of Standard Reference Material® 1822a, 24 January 2007, http://www.nist.gov

Korea Research Institute of Standards and Science, Test Report, Certificate No. 0901–00920–001, 12 August 2009.

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagram of dual wavelength experimental setup. Inset describes multiply reflected/transmitted waves at angle of incidence θ.

Fig. 2.
Fig. 2.

Transmitted intensity versus angle of incidence for λ = 1529 nm.

Fig. 3.
Fig. 3.

Contour plots of 1/S versus (n, d) for DFB laser (1529 nm) (a) and for He-Ne laser (633 nm) (b). Because contours are too narrow to view, the projections are shown for one peak in (a). The vertical arrows indicate the peaks with an identical thickness.

Tables (1)

Tables Icon

Table 1. Uncertainties in measured parameters.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ϕ ( θ ) = 4 πd λ n 2 n a 2 sin 2 θ ,
I ( θ ) = I 0 [ 1 R ( θ ) ] 2 R 2 ( θ ) + 1 2 R ( θ ) cos ϕ ( θ ) ,
θ m = sin 1 1 n a n 2 ( λm 2 d ) 2 .
S = i θ exp , i θ cal , i 2 ,

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