Abstract

A modified interferometric technique is shown to be able to determine even the small values of electro-optic (EO) coefficients with good accuracy. The experimental setup is a Michelson interferometer that includes an EO modulator in one arm and the crystal under study in the other arm. The method is based on the measurement of the reference modulator phase shift to compensate the phase shift induced by a dc field in the crystal under study. An original technique of detection ensures a better sensitivity since a refractive-index change of 10-7 and an optical path-length variation of λ/1000 can be achieved. The relative sign of EO coefficients, the change of the sample dimensions owing to the piezoelectric effect, and the influence of the temperature are successively discussed. The technique was applied to determine some EO coefficients of a standard lithium niobate crystal and all components of the EO tensor in a β-barium borate crystal.

© 2000 Optical Society of America

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References

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  1. F. Agullo-Lopez, J. M. Cabrera, and F. Agullo-Rueda, Electro-optics (Academic, London, 1994).
  2. J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
    [CrossRef]
  3. Y. Fujii and T. Sakudo, “Interferometric determination of the quadratic electro-optic coefficients in SrTiO3,” J. Appl. Phys. 41, 4118–4120 (1970).
    [CrossRef]
  4. K. Onuki, N. Uchida, and T. Saku, “Interferometric method for measuring electro-optic coefficients in crystals,” J. Opt. Soc. Am. B 62, 1030–1032 (1972).
    [CrossRef]
  5. H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun. 86, 509–512 (1991).
    [CrossRef]
  6. J. P. Salvestrini, M. D. Fontana, B. Wyncke, and F. Brehat, “Comparative measurements of the frequency dependence of electrooptical and dielectric coefficients in inorganic crystals,” Nonlinear Opt. 17, 271–280 (1997).
  7. M. Aillerie, M. D. Fontana, F. Abdi, C. Carabatos-Nedelec, N. Theofanous, and G. Alexakis, “Influence of temperature dependent spontaneous birefringence in the electro-optic measurements of LiNbO3,” J. Appl. Phys. 65, 2406–2408 (1989).
    [CrossRef]
  8. K. F. Hulme, P. H. Davis, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C 2, 855–857 (1969).
    [CrossRef]
  9. J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
    [CrossRef]
  10. U. Schlarb and 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]
  11. Numeral Data and Functional Relationships in Sciences and Technology, Group III, Landolt-Bornstein, K.-H. Hellwedge, ed. (Springer-Verlag, New York, 1979), Vol. 11.
  12. N. G. Theofanous, M. Aillerie, M. D. Fontana, and G. E. Alexakis, “A frequency doubling electrooptic modulation sys-tem for Pockels effect measurements: application in LiNbO3,” Rev. Sci. Instrum. 68, 2138–2143 (1997).
    [CrossRef]
  13. C. T. Chen, B. Wu, A. Jiang, and G. You, “A new type of ultraviolet SHG crystal: β-BBO,” Sci. Sin. Ser. B 18, 235–243 (1985).
  14. C. T. Chen, “Chinese lab grows new nonlinear optical borate crystals,” Laser Focus World, 129–137 (1989).
  15. L. Bohaty and J. Liebertz, “Electro-optic and electrostrictive properties of the low-temperature phase of barium metaborate BaB2O4,” Z. Kristallogr. 192, 91–95 (1990).
    [CrossRef]
  16. K. Polgár and A. Pétér, “Growth and characterization of alpha, and beta-barium metaborate single crystals,” J. Cryst. Growth 134, 209–215 (1991).
  17. J. Liebertz and S. Stähr, “Zur Tieftemperaturephase von BaB2O4,” Z. Kristallogr. 165, 91–95 (1983).
    [CrossRef]
  18. D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
    [CrossRef]
  19. R. Guo and A. S. Bhalla, “Pyroelectric, piezoelectric and dielectric properties of β-BaB2O4 single crystal,” J. Appl. Phys. 66, 6186–6188 (1989).
    [CrossRef]

1998 (1)

J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
[CrossRef]

1997 (2)

J. P. Salvestrini, M. D. Fontana, B. Wyncke, and F. Brehat, “Comparative measurements of the frequency dependence of electrooptical and dielectric coefficients in inorganic crystals,” Nonlinear Opt. 17, 271–280 (1997).

N. G. Theofanous, M. Aillerie, M. D. Fontana, and G. E. Alexakis, “A frequency doubling electrooptic modulation sys-tem for Pockels effect measurements: application in LiNbO3,” Rev. Sci. Instrum. 68, 2138–2143 (1997).
[CrossRef]

1993 (1)

U. Schlarb and 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]

1991 (2)

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun. 86, 509–512 (1991).
[CrossRef]

K. Polgár and A. Pétér, “Growth and characterization of alpha, and beta-barium metaborate single crystals,” J. Cryst. Growth 134, 209–215 (1991).

1990 (1)

L. Bohaty and J. Liebertz, “Electro-optic and electrostrictive properties of the low-temperature phase of barium metaborate BaB2O4,” Z. Kristallogr. 192, 91–95 (1990).
[CrossRef]

1989 (2)

R. Guo and A. S. Bhalla, “Pyroelectric, piezoelectric and dielectric properties of β-BaB2O4 single crystal,” J. Appl. Phys. 66, 6186–6188 (1989).
[CrossRef]

M. Aillerie, M. D. Fontana, F. Abdi, C. Carabatos-Nedelec, N. Theofanous, and G. Alexakis, “Influence of temperature dependent spontaneous birefringence in the electro-optic measurements of LiNbO3,” J. Appl. Phys. 65, 2406–2408 (1989).
[CrossRef]

1987 (1)

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

1985 (1)

C. T. Chen, B. Wu, A. Jiang, and G. You, “A new type of ultraviolet SHG crystal: β-BBO,” Sci. Sin. Ser. B 18, 235–243 (1985).

1983 (1)

J. Liebertz and S. Stähr, “Zur Tieftemperaturephase von BaB2O4,” Z. Kristallogr. 165, 91–95 (1983).
[CrossRef]

1972 (1)

K. Onuki, N. Uchida, and T. Saku, “Interferometric method for measuring electro-optic coefficients in crystals,” J. Opt. Soc. Am. B 62, 1030–1032 (1972).
[CrossRef]

1970 (1)

Y. Fujii and T. Sakudo, “Interferometric determination of the quadratic electro-optic coefficients in SrTiO3,” J. Appl. Phys. 41, 4118–4120 (1970).
[CrossRef]

1969 (1)

K. F. Hulme, P. H. Davis, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C 2, 855–857 (1969).
[CrossRef]

1967 (1)

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

Abdi, F.

M. Aillerie, M. D. Fontana, F. Abdi, C. Carabatos-Nedelec, N. Theofanous, and G. Alexakis, “Influence of temperature dependent spontaneous birefringence in the electro-optic measurements of LiNbO3,” J. Appl. Phys. 65, 2406–2408 (1989).
[CrossRef]

Aillerie, M.

N. G. Theofanous, M. Aillerie, M. D. Fontana, and G. E. Alexakis, “A frequency doubling electrooptic modulation sys-tem for Pockels effect measurements: application in LiNbO3,” Rev. Sci. Instrum. 68, 2138–2143 (1997).
[CrossRef]

M. Aillerie, M. D. Fontana, F. Abdi, C. Carabatos-Nedelec, N. Theofanous, and G. Alexakis, “Influence of temperature dependent spontaneous birefringence in the electro-optic measurements of LiNbO3,” J. Appl. Phys. 65, 2406–2408 (1989).
[CrossRef]

Alexakis, G.

M. Aillerie, M. D. Fontana, F. Abdi, C. Carabatos-Nedelec, N. Theofanous, and G. Alexakis, “Influence of temperature dependent spontaneous birefringence in the electro-optic measurements of LiNbO3,” J. Appl. Phys. 65, 2406–2408 (1989).
[CrossRef]

Alexakis, G. E.

N. G. Theofanous, M. Aillerie, M. D. Fontana, and G. E. Alexakis, “A frequency doubling electrooptic modulation sys-tem for Pockels effect measurements: application in LiNbO3,” Rev. Sci. Instrum. 68, 2138–2143 (1997).
[CrossRef]

Betzler, K.

U. Schlarb and 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]

Bhalla, A. S.

R. Guo and A. S. Bhalla, “Pyroelectric, piezoelectric and dielectric properties of β-BaB2O4 single crystal,” J. Appl. Phys. 66, 6186–6188 (1989).
[CrossRef]

Bohaty, L.

L. Bohaty and J. Liebertz, “Electro-optic and electrostrictive properties of the low-temperature phase of barium metaborate BaB2O4,” Z. Kristallogr. 192, 91–95 (1990).
[CrossRef]

Brehat, F.

J. P. Salvestrini, M. D. Fontana, B. Wyncke, and F. Brehat, “Comparative measurements of the frequency dependence of electrooptical and dielectric coefficients in inorganic crystals,” Nonlinear Opt. 17, 271–280 (1997).

Cabañes, A. García

J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
[CrossRef]

Cabrera, J. M.

J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
[CrossRef]

Carabatos-Nedelec, C.

M. Aillerie, M. D. Fontana, F. Abdi, C. Carabatos-Nedelec, N. Theofanous, and G. Alexakis, “Influence of temperature dependent spontaneous birefringence in the electro-optic measurements of LiNbO3,” J. Appl. Phys. 65, 2406–2408 (1989).
[CrossRef]

Chen, C. T.

C. T. Chen, B. Wu, A. Jiang, and G. You, “A new type of ultraviolet SHG crystal: β-BBO,” Sci. Sin. Ser. B 18, 235–243 (1985).

Chen, D.

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

Cound, V. M.

K. F. Hulme, P. H. Davis, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C 2, 855–857 (1969).
[CrossRef]

Davis, L.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Davis, P. H.

K. F. Hulme, P. H. Davis, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C 2, 855–857 (1969).
[CrossRef]

de Toro, J. A.

J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
[CrossRef]

Eimerl, D.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Fontana, M. D.

J. P. Salvestrini, M. D. Fontana, B. Wyncke, and F. Brehat, “Comparative measurements of the frequency dependence of electrooptical and dielectric coefficients in inorganic crystals,” Nonlinear Opt. 17, 271–280 (1997).

N. G. Theofanous, M. Aillerie, M. D. Fontana, and G. E. Alexakis, “A frequency doubling electrooptic modulation sys-tem for Pockels effect measurements: application in LiNbO3,” Rev. Sci. Instrum. 68, 2138–2143 (1997).
[CrossRef]

M. Aillerie, M. D. Fontana, F. Abdi, C. Carabatos-Nedelec, N. Theofanous, and G. Alexakis, “Influence of temperature dependent spontaneous birefringence in the electro-optic measurements of LiNbO3,” J. Appl. Phys. 65, 2406–2408 (1989).
[CrossRef]

Fujii, Y.

Y. Fujii and T. Sakudo, “Interferometric determination of the quadratic electro-optic coefficients in SrTiO3,” J. Appl. Phys. 41, 4118–4120 (1970).
[CrossRef]

Graham, E. K.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Guo, R.

R. Guo and A. S. Bhalla, “Pyroelectric, piezoelectric and dielectric properties of β-BaB2O4 single crystal,” J. Appl. Phys. 66, 6186–6188 (1989).
[CrossRef]

He, X. H.

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun. 86, 509–512 (1991).
[CrossRef]

Hulme, K. F.

K. F. Hulme, P. H. Davis, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C 2, 855–857 (1969).
[CrossRef]

Jiang, A.

C. T. Chen, B. Wu, A. Jiang, and G. You, “A new type of ultraviolet SHG crystal: β-BBO,” Sci. Sin. Ser. B 18, 235–243 (1985).

Liebertz, J.

L. Bohaty and J. Liebertz, “Electro-optic and electrostrictive properties of the low-temperature phase of barium metaborate BaB2O4,” Z. Kristallogr. 192, 91–95 (1990).
[CrossRef]

J. Liebertz and S. Stähr, “Zur Tieftemperaturephase von BaB2O4,” Z. Kristallogr. 165, 91–95 (1983).
[CrossRef]

Onuki, K.

K. Onuki, N. Uchida, and T. Saku, “Interferometric method for measuring electro-optic coefficients in crystals,” J. Opt. Soc. Am. B 62, 1030–1032 (1972).
[CrossRef]

Otto, G. N.

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

Pétér, A.

K. Polgár and A. Pétér, “Growth and characterization of alpha, and beta-barium metaborate single crystals,” J. Cryst. Growth 134, 209–215 (1991).

Polgár, K.

K. Polgár and A. Pétér, “Growth and characterization of alpha, and beta-barium metaborate single crystals,” J. Cryst. Growth 134, 209–215 (1991).

Saku, T.

K. Onuki, N. Uchida, and T. Saku, “Interferometric method for measuring electro-optic coefficients in crystals,” J. Opt. Soc. Am. B 62, 1030–1032 (1972).
[CrossRef]

Sakudo, T.

Y. Fujii and T. Sakudo, “Interferometric determination of the quadratic electro-optic coefficients in SrTiO3,” J. Appl. Phys. 41, 4118–4120 (1970).
[CrossRef]

Salvestrini, J. P.

J. P. Salvestrini, M. D. Fontana, B. Wyncke, and F. Brehat, “Comparative measurements of the frequency dependence of electrooptical and dielectric coefficients in inorganic crystals,” Nonlinear Opt. 17, 271–280 (1997).

Schlarb, U.

U. Schlarb and 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]

Serrano, M. D.

J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
[CrossRef]

Shih, Y. H.

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun. 86, 509–512 (1991).
[CrossRef]

Stähr, S.

J. Liebertz and S. Stähr, “Zur Tieftemperaturephase von BaB2O4,” Z. Kristallogr. 165, 91–95 (1983).
[CrossRef]

Tang, S. H.

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun. 86, 509–512 (1991).
[CrossRef]

Theofanous, N.

M. Aillerie, M. D. Fontana, F. Abdi, C. Carabatos-Nedelec, N. Theofanous, and G. Alexakis, “Influence of temperature dependent spontaneous birefringence in the electro-optic measurements of LiNbO3,” J. Appl. Phys. 65, 2406–2408 (1989).
[CrossRef]

Theofanous, N. G.

N. G. Theofanous, M. Aillerie, M. D. Fontana, and G. E. Alexakis, “A frequency doubling electrooptic modulation sys-tem for Pockels effect measurements: application in LiNbO3,” Rev. Sci. Instrum. 68, 2138–2143 (1997).
[CrossRef]

Uchida, N.

K. Onuki, N. Uchida, and T. Saku, “Interferometric method for measuring electro-optic coefficients in crystals,” J. Opt. Soc. Am. B 62, 1030–1032 (1972).
[CrossRef]

Velsko, S.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Wu, B.

C. T. Chen, B. Wu, A. Jiang, and G. You, “A new type of ultraviolet SHG crystal: β-BBO,” Sci. Sin. Ser. B 18, 235–243 (1985).

Wyncke, B.

J. P. Salvestrini, M. D. Fontana, B. Wyncke, and F. Brehat, “Comparative measurements of the frequency dependence of electrooptical and dielectric coefficients in inorganic crystals,” Nonlinear Opt. 17, 271–280 (1997).

You, G.

C. T. Chen, B. Wu, A. Jiang, and G. You, “A new type of ultraviolet SHG crystal: β-BBO,” Sci. Sin. Ser. B 18, 235–243 (1985).

Zalkin, A.

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Zhang, H. Y.

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun. 86, 509–512 (1991).
[CrossRef]

Zook, J. D.

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

Appl. Phys. Lett. (1)

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

J. Appl. Phys. (4)

Y. Fujii and T. Sakudo, “Interferometric determination of the quadratic electro-optic coefficients in SrTiO3,” J. Appl. Phys. 41, 4118–4120 (1970).
[CrossRef]

M. Aillerie, M. D. Fontana, F. Abdi, C. Carabatos-Nedelec, N. Theofanous, and G. Alexakis, “Influence of temperature dependent spontaneous birefringence in the electro-optic measurements of LiNbO3,” J. Appl. Phys. 65, 2406–2408 (1989).
[CrossRef]

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

R. Guo and A. S. Bhalla, “Pyroelectric, piezoelectric and dielectric properties of β-BaB2O4 single crystal,” J. Appl. Phys. 66, 6186–6188 (1989).
[CrossRef]

J. Cryst. Growth (1)

K. Polgár and A. Pétér, “Growth and characterization of alpha, and beta-barium metaborate single crystals,” J. Cryst. Growth 134, 209–215 (1991).

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

K. Onuki, N. Uchida, and T. Saku, “Interferometric method for measuring electro-optic coefficients in crystals,” J. Opt. Soc. Am. B 62, 1030–1032 (1972).
[CrossRef]

J. Phys. C (1)

K. F. Hulme, P. H. Davis, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C 2, 855–857 (1969).
[CrossRef]

Nonlinear Opt. (1)

J. P. Salvestrini, M. D. Fontana, B. Wyncke, and F. Brehat, “Comparative measurements of the frequency dependence of electrooptical and dielectric coefficients in inorganic crystals,” Nonlinear Opt. 17, 271–280 (1997).

Opt. Commun. (2)

J. A. de Toro, M. D. Serrano, A. García Cabañes, and J. M. Cabrera, “Accurate interferometric measurement of electro-optic coefficients: application to quasi-stoichiometric LiNbO3,” Opt. Commun. 154, 23–27 (1998).
[CrossRef]

H. Y. Zhang, X. H. He, Y. H. Shih, and S. H. Tang, “A new method for measuring the electro-optic coefficients with higher sensitivity and higher accuracy,” Opt. Commun. 86, 509–512 (1991).
[CrossRef]

Phys. Rev. B (1)

U. Schlarb and 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]

Rev. Sci. Instrum. (1)

N. G. Theofanous, M. Aillerie, M. D. Fontana, and G. E. Alexakis, “A frequency doubling electrooptic modulation sys-tem for Pockels effect measurements: application in LiNbO3,” Rev. Sci. Instrum. 68, 2138–2143 (1997).
[CrossRef]

Sci. Sin. Ser. B (1)

C. T. Chen, B. Wu, A. Jiang, and G. You, “A new type of ultraviolet SHG crystal: β-BBO,” Sci. Sin. Ser. B 18, 235–243 (1985).

Z. Kristallogr. (2)

J. Liebertz and S. Stähr, “Zur Tieftemperaturephase von BaB2O4,” Z. Kristallogr. 165, 91–95 (1983).
[CrossRef]

L. Bohaty and J. Liebertz, “Electro-optic and electrostrictive properties of the low-temperature phase of barium metaborate BaB2O4,” Z. Kristallogr. 192, 91–95 (1990).
[CrossRef]

Other (3)

C. T. Chen, “Chinese lab grows new nonlinear optical borate crystals,” Laser Focus World, 129–137 (1989).

F. Agullo-Lopez, J. M. Cabrera, and F. Agullo-Rueda, Electro-optics (Academic, London, 1994).

Numeral Data and Functional Relationships in Sciences and Technology, Group III, Landolt-Bornstein, K.-H. Hellwedge, ed. (Springer-Verlag, New York, 1979), Vol. 11.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the experimental interferometer setup. (Insert, left part) Picture of the interference pattern obtained in a BBO single crystal. (Insert, right part) Intensity profile of six dark and five clear fringes obtained by translation or a vertical slit and a photodetector along the interference pattern.

Fig. 2
Fig. 2

Recorded (top) and simulated (bottom) input and output signals. The signals on the left side are recorded when the slit is exactly on a fringe at extreme intensities (double-frequency signal), whereas the signals on the right side are obtained when the interference pattern is shifted. In each scope the upper signal refers to the electric voltage applied to the modulator, and the lower signal is the optical output on the photodiode.

Fig. 3
Fig. 3

Drift of the modulator compensating voltage as a function of time.

Fig. 4
Fig. 4

Example of the plot obtained by measurement of the EO coefficient r33 of LiNbO3. The squares refer to the voltage applied to the modulator to adjust the optical path length up to a dark fringe. The circles concern the voltage applied to compensate the effect of the applied electric field on the sample studied. V is the voltage applied to the crystal.

Fig. 5
Fig. 5

X-cut plane of the BBO crystal (sample 3) used in the measurements of the EO coefficient r51.

Fig. 6
Fig. 6

Example of the plot obtained to determine the EO coefficient r13 of BBO. The experimental data were recorded on a sample with dimensions e=2.3 mm along axis 3, and L=4.69 mm along axis 1.

Tables (2)

Tables Icon

Table 1 Electro-Optic Results Obtained in LiNbO3a

Tables Icon

Table 2 Electro-Optic Results Obtained in BBOa

Equations (17)

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

Δδ=2Δ(niLj)=2Lj[-12ni3ri,k+(ni-1)dk,j]Ek,
ri,k=ri,k*+pi,k=-ekni3LjVkCmΔVm+2(nj-1)ni3dk,j,
Cm=λ2Vπ/2.
1n02-r22E2+r13E3x12+1n02+r22E2+r13E3x22+1ne2+r33E3x32+2r51E2x2x3+2r51E1x1x3-2r22E1x1x2=1.
X=x1,
Y=22(x2-x3),
Z=22(x2+x3).
2πλ2[(nm+Δnm-1)Lm-(nc+Δnc-1)Lc],
Δnm=-12rmnm3(Edm+Eam cos ωt),
Icos2(A+B+C cos ωt),
cos2(C cos ωt)1-C22-C22cos 2ωt,
sin2(C cos ωt)C22+C22cos 2ωt,
12[1±sin(2C cos ωt)]12±C cos ωt.
I12[1±(1-22)cos(2C cos ωt)-2 sin(2C cos ωt)],
s2(r*)=sA2(r*)+sB2(r*),
sA2(r*)=i=1x(ri*-r*¯)2,
sB2(r*)=r*L2s2(L)+r*e2s2(e)+r*n2s2(n),+r*V2s2(V)+r*Cm2s2(Cm)+r*Vm2s2(Vm),

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