Abstract

A new method to correlate prism and substrate refractive indices is presented and applied to the determination of rutile refractive indices, both ordinary and extraordinary, at different wavelengths in the visible and the near infrared. The method exploits radiation modes and, when the sample structure allows it, hybrid modes. An accuracy of approximately 2 × 10-4 was achieved without the need of any specific preparation of the samples. The method exhibits a good versatility since it can be exploited for the determination of the refractive index of a coupling prism when the substrate index is known and vice versa.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. K. Tien, R. Ulrich, “Theory of prism–film coupler and thin-film light guides,” J. Opt. Soc. Am. 60, 1325–1337 (1970).
    [CrossRef]
  2. K. S. Chiang, “Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. LT-3, 385–391 (1985).
    [CrossRef]
  3. X. Mu, X. Yue, J. Chen, J. Wang, Z. Shao, “Planar waveguide refractive index distribution functions determined precisely from mode indices,” Appl. Opt. 33, 3227–3230 (1994).
    [CrossRef] [PubMed]
  4. J. R. Devore, “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am. 41, 416–419 (1951).
    [CrossRef]
  5. W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
    [CrossRef]
  6. M. R. Shenoy, R. M. De La Rue, “On the refractive index of rutile,” IEE Proc. J 139, 163–165 (1992).
  7. J. Rams, A. Tejeda, J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys. 82, 994–997 (1997).
    [CrossRef]
  8. S. K. Sheem, W. K. Burns, A. F. Milton, “Leaky-mode propagation in Ti-diffused LiNbO3 and LiTaO3 waveguides,” Opt. Lett. 3, 76–78 (1978).
    [CrossRef]
  9. G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–374 (1984).
    [CrossRef]
  10. U. Schlarb, K. Betzler, “Refractive indices of lithium niobate as a function of temperature, wavelength, and composition: a generalized fit,” Phys. Rev. B 48, 15613–15620 (1993).
    [CrossRef]

1997 (1)

J. Rams, A. Tejeda, J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys. 82, 994–997 (1997).
[CrossRef]

1994 (1)

1993 (1)

U. Schlarb, K. Betzler, “Refractive indices of lithium niobate as a function of temperature, wavelength, and composition: a generalized fit,” Phys. Rev. B 48, 15613–15620 (1993).
[CrossRef]

1992 (1)

M. R. Shenoy, R. M. De La Rue, “On the refractive index of rutile,” IEE Proc. J 139, 163–165 (1992).

1985 (1)

K. S. Chiang, “Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. LT-3, 385–391 (1985).
[CrossRef]

1984 (1)

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–374 (1984).
[CrossRef]

1978 (1)

1970 (1)

1965 (1)

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

1951 (1)

Betzler, K.

U. Schlarb, K. Betzler, “Refractive indices of lithium niobate as a function of temperature, wavelength, and composition: a generalized fit,” Phys. Rev. B 48, 15613–15620 (1993).
[CrossRef]

Bond, W. L.

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

Burns, W. K.

Cabrera, J. M.

J. Rams, A. Tejeda, J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys. 82, 994–997 (1997).
[CrossRef]

Chen, J.

Chiang, K. S.

K. S. Chiang, “Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. LT-3, 385–391 (1985).
[CrossRef]

De La Rue, R. M.

M. R. Shenoy, R. M. De La Rue, “On the refractive index of rutile,” IEE Proc. J 139, 163–165 (1992).

Devore, J. R.

Edwards, G. J.

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–374 (1984).
[CrossRef]

Lawrence, M.

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–374 (1984).
[CrossRef]

Milton, A. F.

Mu, X.

Rams, J.

J. Rams, A. Tejeda, J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys. 82, 994–997 (1997).
[CrossRef]

Schlarb, U.

U. Schlarb, K. Betzler, “Refractive indices of lithium niobate as a function of temperature, wavelength, and composition: a generalized fit,” Phys. Rev. B 48, 15613–15620 (1993).
[CrossRef]

Shao, Z.

Sheem, S. K.

Shenoy, M. R.

M. R. Shenoy, R. M. De La Rue, “On the refractive index of rutile,” IEE Proc. J 139, 163–165 (1992).

Tejeda, A.

J. Rams, A. Tejeda, J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys. 82, 994–997 (1997).
[CrossRef]

Tien, P. K.

Ulrich, R.

Wang, J.

Yue, X.

Appl. Opt. (1)

IEE Proc. J (1)

M. R. Shenoy, R. M. De La Rue, “On the refractive index of rutile,” IEE Proc. J 139, 163–165 (1992).

J. Appl. Phys. (1)

J. Rams, A. Tejeda, J. M. Cabrera, “Refractive indices of rutile as a function of temperature and wavelength,” J. Appl. Phys. 82, 994–997 (1997).
[CrossRef]

J. Appl. Phys. (1)

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

J. Lightwave Technol. (1)

K. S. Chiang, “Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. LT-3, 385–391 (1985).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Quantum Electron. (1)

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–374 (1984).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

U. Schlarb, K. Betzler, “Refractive indices of lithium niobate as a function of temperature, wavelength, and composition: a generalized fit,” Phys. Rev. B 48, 15613–15620 (1993).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Scheme of the measurement principle: the coupling angle α and the output angle ψ of a radiation mode are related by means of n s and n p .

Fig. 2
Fig. 2

Experimental setup for the measurements of the coupling angle α and of the radiation modes output angle ψ. M1 and M2, mirrors; β1 and β2, mirror rotation angles; pm, powermeter; ph, pinhole; and bs, beam splitter.

Tables (4)

Tables Icon

Table 2 Ordinary and Extraordinary Refractive Indices of LiNbO3 Used in These Experiments and Determined by Means of Minimum Deviation Measurements

Tables Icon

Table 3 Coupling Angle α and Output Angle ψ at λ = 0.532 µma

Tables Icon

Table 4 Rutile Refractive Indices, Obtained with the Method Here Proposed, Compared with The Other Valuesa

Equations (7)

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

n eff = sin   α   cos   ε + n p 2 - sin 2   α 1 / 2   sin   ε ,
n eff = n s   cos   θ ,
n s   sin   θ = n 0   sin   ψ ,
σ 1 n p = n p ψ   δ ψ = 2 × 10 - 4 ,
σ 1 n s = n s ψ   δ ψ = 9 × 10 - 5 .
σ 2 n p = n p α   δ α = 4 × 10 - 5 ,
σ 2 n s = n s α   δ α = 5 × 10 - 5 .

Metrics