Abstract

We show that a Z-transform-based time-response analysis of the electro-optical response of a crystal to a step voltage with a short rise time allows one to obtain the dispersion of the electro-optical coefficients over a wide frequency range. We describe the method employed and present the results obtained for the main electro-optic coefficients (r 22, r 61, and r c) of a standard LiNbO3 crystal. We also show that this method is able to provide even small values of the electro-optic coefficients as well as the dispersion within a wide frequency range, which is limited only by the rise time of the step voltage.

© 2003 Optical Society of America

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References

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  1. A. Yariv, P. Yeh, “Physical properties of electro-optic coefficient,” in Optical Waves in Crystals, (Wiley, New York, 1984) pp. 264–266.
  2. J. P. Salvestrini, M. D. Fontana, B. Wyncke, F. Brehat, “Comparative measurements of the frequency dependence of electro-optical and dielectric coefficients in inorganic crystals,” Nonlinear Opt. 17, 271–280 (1997).
  3. P. C. Amundsen, G. Wang, “Low-loss LiNbO3Q-switches: compensation of acoustically-induced refractive index variations,” IEEE J. Quantum Electron. 23, 2252–2257 (1987).
    [CrossRef]
  4. M. Aillerie, M. D. Fontana, N. Théofanous, “Measurement of electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
    [CrossRef]
  5. R. Spreiter, Ch. Bosshard, F. Pan, P. Gûnter, “High-frequency response and acoustic phonon contribution of the linear electro-optic effect in DAST,” Opt. Lett. 22, 564–566 (1997).
    [CrossRef] [PubMed]
  6. M. Aillerie, M. D. Fontana, F. Abdi, C. Carabatos-Nedelec, N. Théofanous, G. E. Alexakis, “Influence of the temperature-dependent spontaneous birefringence in the electro-optic measurements of LiNbO3,” J. App. Phys. 65, 2406–2408 (1989).
    [CrossRef]
  7. L. Guilbert, J. P. Salvestrini, M. D. Fontana, H. Hassan, “Combined effects due to phase, intensity, and contrast in electro-optic modulation: application to ferroelectric materials,” IEEE J. Quantum. Electron. 35, 273–280 (1999).
    [CrossRef]
  8. A. Chirakadze, S. Machavariani, A. Natsvlishvili, B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216–1218 (1990).
    [CrossRef]
  9. F. Abdi, M. Aillerie, P. Bourson, M. D. Fontana, K. Polgar, “Electro-optic properties in pure LiNbO3 crystals from the congruent to the stoichiometric composition,” J. Appl. Phys. 84, 2251–2254 (1998).
    [CrossRef]
  10. M. Aillerie, F. Abdi, M. D. Fontana, N. Théofanous, E. Abarkan, “Accurate measurements of the electro-optic coefficients and birefringence changes using an external modulation signal,” Rev. Sci. Instrum. 70, 1627–1634 (2000).
    [CrossRef]
  11. E. H. Turner, “High frequency electro-optic coefficients of lithium niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
    [CrossRef]
  12. A. W. Warner, M. Onoe, G. A. Coquin, “Determination of elastic and piezoelectric constants for crystals in class (3m),” J. Acoust. Soc. Am. 46, 1223–1231 (1966).
  13. R. W. Dixon, M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
    [CrossRef]
  14. C. A. Ebbers, “Linear electro-optic effect in β-BaB2O4,” Appl. Phys. Lett. 52, 1948–1949 (1988).
    [CrossRef]
  15. J. Zaccaro, J. P. Salvestrini, A. Ibanez, P. Ney, M. D. Fontana, “Electric-field frequency dependence of Pockels coefficients in 2-amino-5-nitropyridium dihydrogen phosphate organic-inorganic crystals,” J. Opt. Soc. Am. B 17, 427–432 (2000).
    [CrossRef]

2000 (3)

M. Aillerie, F. Abdi, M. D. Fontana, N. Théofanous, E. Abarkan, “Accurate measurements of the electro-optic coefficients and birefringence changes using an external modulation signal,” Rev. Sci. Instrum. 70, 1627–1634 (2000).
[CrossRef]

M. Aillerie, M. D. Fontana, N. Théofanous, “Measurement of electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[CrossRef]

J. Zaccaro, J. P. Salvestrini, A. Ibanez, P. Ney, M. D. Fontana, “Electric-field frequency dependence of Pockels coefficients in 2-amino-5-nitropyridium dihydrogen phosphate organic-inorganic crystals,” J. Opt. Soc. Am. B 17, 427–432 (2000).
[CrossRef]

1999 (1)

L. Guilbert, J. P. Salvestrini, M. D. Fontana, H. Hassan, “Combined effects due to phase, intensity, and contrast in electro-optic modulation: application to ferroelectric materials,” IEEE J. Quantum. Electron. 35, 273–280 (1999).
[CrossRef]

1998 (1)

F. Abdi, M. Aillerie, P. Bourson, M. D. Fontana, K. Polgar, “Electro-optic properties in pure LiNbO3 crystals from the congruent to the stoichiometric composition,” J. Appl. Phys. 84, 2251–2254 (1998).
[CrossRef]

1997 (2)

R. Spreiter, Ch. Bosshard, F. Pan, P. Gûnter, “High-frequency response and acoustic phonon contribution of the linear electro-optic effect in DAST,” Opt. Lett. 22, 564–566 (1997).
[CrossRef] [PubMed]

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

1990 (1)

A. Chirakadze, S. Machavariani, A. Natsvlishvili, B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216–1218 (1990).
[CrossRef]

1989 (1)

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

1988 (1)

C. A. Ebbers, “Linear electro-optic effect in β-BaB2O4,” Appl. Phys. Lett. 52, 1948–1949 (1988).
[CrossRef]

1987 (1)

P. C. Amundsen, G. Wang, “Low-loss LiNbO3Q-switches: compensation of acoustically-induced refractive index variations,” IEEE J. Quantum Electron. 23, 2252–2257 (1987).
[CrossRef]

1966 (3)

E. H. Turner, “High frequency electro-optic coefficients of lithium niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
[CrossRef]

A. W. Warner, M. Onoe, G. A. Coquin, “Determination of elastic and piezoelectric constants for crystals in class (3m),” J. Acoust. Soc. Am. 46, 1223–1231 (1966).

R. W. Dixon, M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[CrossRef]

Abarkan, E.

M. Aillerie, F. Abdi, M. D. Fontana, N. Théofanous, E. Abarkan, “Accurate measurements of the electro-optic coefficients and birefringence changes using an external modulation signal,” Rev. Sci. Instrum. 70, 1627–1634 (2000).
[CrossRef]

Abdi, F.

M. Aillerie, F. Abdi, M. D. Fontana, N. Théofanous, E. Abarkan, “Accurate measurements of the electro-optic coefficients and birefringence changes using an external modulation signal,” Rev. Sci. Instrum. 70, 1627–1634 (2000).
[CrossRef]

F. Abdi, M. Aillerie, P. Bourson, M. D. Fontana, K. Polgar, “Electro-optic properties in pure LiNbO3 crystals from the congruent to the stoichiometric composition,” J. Appl. Phys. 84, 2251–2254 (1998).
[CrossRef]

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

Aillerie, M.

M. Aillerie, M. D. Fontana, N. Théofanous, “Measurement of electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[CrossRef]

M. Aillerie, F. Abdi, M. D. Fontana, N. Théofanous, E. Abarkan, “Accurate measurements of the electro-optic coefficients and birefringence changes using an external modulation signal,” Rev. Sci. Instrum. 70, 1627–1634 (2000).
[CrossRef]

F. Abdi, M. Aillerie, P. Bourson, M. D. Fontana, K. Polgar, “Electro-optic properties in pure LiNbO3 crystals from the congruent to the stoichiometric composition,” J. Appl. Phys. 84, 2251–2254 (1998).
[CrossRef]

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

Alexakis, G. E.

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

Amundsen, P. C.

P. C. Amundsen, G. Wang, “Low-loss LiNbO3Q-switches: compensation of acoustically-induced refractive index variations,” IEEE J. Quantum Electron. 23, 2252–2257 (1987).
[CrossRef]

Bosshard, Ch.

Bourson, P.

F. Abdi, M. Aillerie, P. Bourson, M. D. Fontana, K. Polgar, “Electro-optic properties in pure LiNbO3 crystals from the congruent to the stoichiometric composition,” J. Appl. Phys. 84, 2251–2254 (1998).
[CrossRef]

Brehat, F.

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

Carabatos-Nedelec, C.

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

Chirakadze, A.

A. Chirakadze, S. Machavariani, A. Natsvlishvili, B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216–1218 (1990).
[CrossRef]

Cohen, M. G.

R. W. Dixon, M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[CrossRef]

Coquin, G. A.

A. W. Warner, M. Onoe, G. A. Coquin, “Determination of elastic and piezoelectric constants for crystals in class (3m),” J. Acoust. Soc. Am. 46, 1223–1231 (1966).

Dixon, R. W.

R. W. Dixon, M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[CrossRef]

Ebbers, C. A.

C. A. Ebbers, “Linear electro-optic effect in β-BaB2O4,” Appl. Phys. Lett. 52, 1948–1949 (1988).
[CrossRef]

Fontana, M. D.

M. Aillerie, F. Abdi, M. D. Fontana, N. Théofanous, E. Abarkan, “Accurate measurements of the electro-optic coefficients and birefringence changes using an external modulation signal,” Rev. Sci. Instrum. 70, 1627–1634 (2000).
[CrossRef]

J. Zaccaro, J. P. Salvestrini, A. Ibanez, P. Ney, M. D. Fontana, “Electric-field frequency dependence of Pockels coefficients in 2-amino-5-nitropyridium dihydrogen phosphate organic-inorganic crystals,” J. Opt. Soc. Am. B 17, 427–432 (2000).
[CrossRef]

M. Aillerie, M. D. Fontana, N. Théofanous, “Measurement of electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[CrossRef]

L. Guilbert, J. P. Salvestrini, M. D. Fontana, H. Hassan, “Combined effects due to phase, intensity, and contrast in electro-optic modulation: application to ferroelectric materials,” IEEE J. Quantum. Electron. 35, 273–280 (1999).
[CrossRef]

F. Abdi, M. Aillerie, P. Bourson, M. D. Fontana, K. Polgar, “Electro-optic properties in pure LiNbO3 crystals from the congruent to the stoichiometric composition,” J. Appl. Phys. 84, 2251–2254 (1998).
[CrossRef]

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

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

Guilbert, L.

L. Guilbert, J. P. Salvestrini, M. D. Fontana, H. Hassan, “Combined effects due to phase, intensity, and contrast in electro-optic modulation: application to ferroelectric materials,” IEEE J. Quantum. Electron. 35, 273–280 (1999).
[CrossRef]

Gûnter, P.

Hassan, H.

L. Guilbert, J. P. Salvestrini, M. D. Fontana, H. Hassan, “Combined effects due to phase, intensity, and contrast in electro-optic modulation: application to ferroelectric materials,” IEEE J. Quantum. Electron. 35, 273–280 (1999).
[CrossRef]

Hvitia, B.

A. Chirakadze, S. Machavariani, A. Natsvlishvili, B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216–1218 (1990).
[CrossRef]

Ibanez, A.

Machavariani, S.

A. Chirakadze, S. Machavariani, A. Natsvlishvili, B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216–1218 (1990).
[CrossRef]

Natsvlishvili, A.

A. Chirakadze, S. Machavariani, A. Natsvlishvili, B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216–1218 (1990).
[CrossRef]

Ney, P.

Onoe, M.

A. W. Warner, M. Onoe, G. A. Coquin, “Determination of elastic and piezoelectric constants for crystals in class (3m),” J. Acoust. Soc. Am. 46, 1223–1231 (1966).

Pan, F.

Polgar, K.

F. Abdi, M. Aillerie, P. Bourson, M. D. Fontana, K. Polgar, “Electro-optic properties in pure LiNbO3 crystals from the congruent to the stoichiometric composition,” J. Appl. Phys. 84, 2251–2254 (1998).
[CrossRef]

Salvestrini, J. P.

J. Zaccaro, J. P. Salvestrini, A. Ibanez, P. Ney, M. D. Fontana, “Electric-field frequency dependence of Pockels coefficients in 2-amino-5-nitropyridium dihydrogen phosphate organic-inorganic crystals,” J. Opt. Soc. Am. B 17, 427–432 (2000).
[CrossRef]

L. Guilbert, J. P. Salvestrini, M. D. Fontana, H. Hassan, “Combined effects due to phase, intensity, and contrast in electro-optic modulation: application to ferroelectric materials,” IEEE J. Quantum. Electron. 35, 273–280 (1999).
[CrossRef]

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

Spreiter, R.

Théofanous, N.

M. Aillerie, M. D. Fontana, N. Théofanous, “Measurement of electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[CrossRef]

M. Aillerie, F. Abdi, M. D. Fontana, N. Théofanous, E. Abarkan, “Accurate measurements of the electro-optic coefficients and birefringence changes using an external modulation signal,” Rev. Sci. Instrum. 70, 1627–1634 (2000).
[CrossRef]

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

Turner, E. H.

E. H. Turner, “High frequency electro-optic coefficients of lithium niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
[CrossRef]

Wang, G.

P. C. Amundsen, G. Wang, “Low-loss LiNbO3Q-switches: compensation of acoustically-induced refractive index variations,” IEEE J. Quantum Electron. 23, 2252–2257 (1987).
[CrossRef]

Warner, A. W.

A. W. Warner, M. Onoe, G. A. Coquin, “Determination of elastic and piezoelectric constants for crystals in class (3m),” J. Acoust. Soc. Am. 46, 1223–1231 (1966).

Wyncke, B.

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

Yariv, A.

A. Yariv, P. Yeh, “Physical properties of electro-optic coefficient,” in Optical Waves in Crystals, (Wiley, New York, 1984) pp. 264–266.

Yeh, P.

A. Yariv, P. Yeh, “Physical properties of electro-optic coefficient,” in Optical Waves in Crystals, (Wiley, New York, 1984) pp. 264–266.

Zaccaro, J.

Appl. Phys. B (1)

M. Aillerie, M. D. Fontana, N. Théofanous, “Measurement of electro-optic coefficients: description and comparison of the experimental techniques,” Appl. Phys. B 70, 317–334 (2000).
[CrossRef]

Appl. Phys. Lett. (3)

E. H. Turner, “High frequency electro-optic coefficients of lithium niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
[CrossRef]

R. W. Dixon, M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[CrossRef]

C. A. Ebbers, “Linear electro-optic effect in β-BaB2O4,” Appl. Phys. Lett. 52, 1948–1949 (1988).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. C. Amundsen, G. Wang, “Low-loss LiNbO3Q-switches: compensation of acoustically-induced refractive index variations,” IEEE J. Quantum Electron. 23, 2252–2257 (1987).
[CrossRef]

IEEE J. Quantum. Electron. (1)

L. Guilbert, J. P. Salvestrini, M. D. Fontana, H. Hassan, “Combined effects due to phase, intensity, and contrast in electro-optic modulation: application to ferroelectric materials,” IEEE J. Quantum. Electron. 35, 273–280 (1999).
[CrossRef]

J. Acoust. Soc. Am. (1)

A. W. Warner, M. Onoe, G. A. Coquin, “Determination of elastic and piezoelectric constants for crystals in class (3m),” J. Acoust. Soc. Am. 46, 1223–1231 (1966).

J. App. Phys. (1)

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

J. Appl. Phys. (1)

F. Abdi, M. Aillerie, P. Bourson, M. D. Fontana, K. Polgar, “Electro-optic properties in pure LiNbO3 crystals from the congruent to the stoichiometric composition,” J. Appl. Phys. 84, 2251–2254 (1998).
[CrossRef]

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

J. Phys. D (1)

A. Chirakadze, S. Machavariani, A. Natsvlishvili, B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216–1218 (1990).
[CrossRef]

Nonlinear Opt. (1)

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

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

M. Aillerie, F. Abdi, M. D. Fontana, N. Théofanous, E. Abarkan, “Accurate measurements of the electro-optic coefficients and birefringence changes using an external modulation signal,” Rev. Sci. Instrum. 70, 1627–1634 (2000).
[CrossRef]

Other (1)

A. Yariv, P. Yeh, “Physical properties of electro-optic coefficient,” in Optical Waves in Crystals, (Wiley, New York, 1984) pp. 264–266.

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Figures (10)

Fig. 1
Fig. 1

(a) Sénarmont arrangement used for EO measurements. (b) Optical transmission function versus the angle of the analyzer β. The point M 0 is the minimum transmission point for which the output optical signal has a frequency twice as big as the frequency of the applied electric field. M 1 is the 50% transmission point yielding the linear replica of the ac voltage.

Fig. 2
Fig. 2

Calculus sequences for obtaining the frequency response of the EO coefficients. The applied voltage has a step form.

Fig. 3
Fig. 3

(a) Schematic diagram of the experimental setup for measuring EO time response. (b) Equivalent circuit of the electrical part of the experimental setup: (1) pulse generator, (2) electric cable, (3) shunt terminator, and (4) crystal.

Fig. 4
Fig. 4

Phase shift Γ (involving the EO coefficient r c ) induced by a dc voltage applied along the z axis for a light beam propagating along the x axis.

Fig. 5
Fig. 5

Frequency dispersion of the EO coefficient r 22 obtained via the MDM measurements in LiNbO3.

Fig. 6
Fig. 6

(a) Time response of the optical detector and of the applied step voltage. (b) The deduced response Δi(ν) of the detection system and the ideal response Δi R (ν).

Fig. 7
Fig. 7

Plots versus time of the applied voltage and the optical signal for the configuration involving the EO coefficient r 22.

Fig. 8
Fig. 8

Time dependence at different time scales of the optical signal for the configuration involving the EO coefficient r 22 of LiNbO3. For time periods shorter than 1 ns, the solid curves are replaced by dotted curves and are only guidelines for the eyes.

Fig. 9
Fig. 9

Comparison in the frequency dispersion of the EO coefficient r 22 of LiNbO3 between (a) direct values obtained by measurements within the MDM and (b) values derived from the TRM.

Fig. 10
Fig. 10

Deduced phase shift (by use of the Z transformation) between the applied step voltage and the optical response, corresponding to the difference of the arguments of Δi(ν) and ΔV(ν). The sign of the EO coefficient is positive if the phase is zero and negative if the phase is equal to 180 deg.

Tables (3)

Tables Icon

Table 1 Description of the Electro-Optical Configurations Used in Our Experiments on Lithium Niobate Crystalsa

Tables Icon

Table 2 Absolute Values of EO Coefficients at Constant Stress (rT ) and at Constant Strain (rS ) in LiNbO3 Obtained at 633 nm and at Room Temperature by Various Techniquesa

Tables Icon

Table 3 Comparison between the Difference |rT - rS| Derived from our Measurements and the Product of p × d in LiNbO3 a

Equations (12)

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

T=1-γ sinΓ-2β2,
ΓE=2πLλΔnE,
ΔnE=Δn0-12neff3reffE.
Δβ=ΔΓ2=πL2λn3reffE.
reffν=2λDπneff3I0LippνVppν.
Δit=πneff3LI02λDrefft  ΔVt,
reffν=2λDπneff3I0LΔiνΔVν.
tn=nΔτ.
Δiνm=n=0N-1Z-nΔitn, ΔVνm=n=0N-1Z-nΔVtn,
Z=exp-2iπmN.
hν=ΔiνΔiRν,
reffν=2λdπneff3I0LΔiνΔVνhν.

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