Abstract

We developed an efficient method for measuring the principal refractive indices and thickness of an optically anisotropic wafer that involves the analysis of Fabry–Perot interference fringes. Utilizing the birefringence of the medium, the 2π phase ambiguity was readily resolved in single-wavelength measurements of the birefringent medium index. Although the accuracy of the index measurements is limited due to the innate ambiguity, our analysis method overcame this limit and could determine the principal refractive indices and thickness with an uncertainty of 105. Our method was validated against measurements of a lithium niobate wafer for which the values of the indices are precisely known.

© 2014 Optical Society of America

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References

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  1. IDEX Optics & Photonics, https://marketplace.idexop.com/Frontend/PDFs/Material-Properties.pdf .
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1989), pp. 7–12.
  3. R. W. Boyd, in Nonlinear Optics, 2nd ed. (Academic, 2003), pp. 79–88.
  4. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer-Verlag, 1999), Chap. 3.
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    [CrossRef]
  6. D. J. Gettemy, W. C. Harker, G. Lindholm, and P. Barnes, “Some optical properties of KTP, LiIO3, and LiNbO3,” IEEE J. Quantum Electron. 24, 2231–2237 (1988).
    [CrossRef]
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    [CrossRef]
  8. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
    [CrossRef]
  9. G. J. Edwards and M. Lawrence, “A temperature dependent dispersion for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
    [CrossRef]
  10. D. F. Nelson and R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
    [CrossRef]
  11. H. J. Choi, H. H. Lim, H. S. Moon, T. B. Eom, J. J. Ju, and M. Cha, “Measurement of refractive index and thickness of transparent plate by dual-wavelength interference,” Opt. Express 18, 9429–9434 (2010).
    [CrossRef]
  12. F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, 1996), pp. 213–214.
  13. M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119 (2005).
    [CrossRef]
  14. J. A. Stone and J. H. Zimmerman, “Index of refraction of air,” http://emtoolbox.nist.gov/Wavelength/Edlen.asp .

2010 (1)

2005 (1)

M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119 (2005).
[CrossRef]

2003 (1)

1997 (1)

1988 (1)

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

1984 (1)

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

1974 (1)

D. F. Nelson and R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

1965 (1)

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1989), pp. 7–12.

Barnes, P.

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

Blau, P.

Bond, W. L.

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[CrossRef]

Boyd, R. W.

R. W. Boyd, in Nonlinear Optics, 2nd ed. (Academic, 2003), pp. 79–88.

Bruner, A.

Cha, M.

Choi, H. J.

Comoretto, D.

M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119 (2005).
[CrossRef]

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer-Verlag, 1999), Chap. 3.

Edwards, G. J.

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

Eger, D.

Eom, T. B.

Galli, M.

M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119 (2005).
[CrossRef]

Gettemy, D. J.

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

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer-Verlag, 1999), Chap. 3.

Harker, W. C.

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

Ju, J. J.

Jundt, D. H.

Katz, M.

Lawrence, M.

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

Lim, H. H.

Lindholm, G.

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

Marabelli, F.

M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119 (2005).
[CrossRef]

Mikulyak, R. M.

D. F. Nelson and R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

Moon, H. S.

Nelson, D. F.

D. F. Nelson and R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer-Verlag, 1999), Chap. 3.

Oron, M. B.

Pedrotti, F. L.

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, 1996), pp. 213–214.

Pedrotti, L. S.

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, 1996), pp. 213–214.

Appl. Phys. Lett. (1)

M. Galli, F. Marabelli, and D. Comoretto, “Interferometric determination of the anisotropic index dispersion of poly-(p-phenylene-vinylene),” Appl. Phys. Lett. 86, 201119 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Appl. Phys. (2)

D. F. Nelson and R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

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

Other (6)

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, 1996), pp. 213–214.

IDEX Optics & Photonics, https://marketplace.idexop.com/Frontend/PDFs/Material-Properties.pdf .

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1989), pp. 7–12.

R. W. Boyd, in Nonlinear Optics, 2nd ed. (Academic, 2003), pp. 79–88.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 3rd ed. (Springer-Verlag, 1999), Chap. 3.

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

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagrams of experimental configurations for measuring (a) ne and (b) no.

Fig. 2.
Fig. 2.

Transmission versus angle of incidence for no (top) and ne (bottom).

Fig. 3.
Fig. 3.

Contour plots of 1/S for (a) ordinary (top) and extraordinary (bottom) polarization and (b) magnified plots of the circled peaks.

Fig. 4.
Fig. 4.

Fitting of projections of Fig. 3(b) to Lorentzian functions (solid lines) for extraordinary (top) and ordinary (bottom) polarizations.

Tables (1)

Tables Icon

Table 1. Refractive Indices and Thickness; λ=1529.2nm, T=22°C

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