Abstract

An experimental investigation of the electric field in the bulk of a Bi12SiO20 crystal is carried out, and a two-region model is developed that can account for the buildup of screening charges near the electrodes. In light of our results, a simple method is proposed for the determination of the effective electro-optic coefficients based on applying a sufficiently high-frequency square-wave voltage to prevent screening charge buildup. A demonstration of this method for Bi12SiO20 leads to a value of 4.4 pm/V for the stress-free (unclamped) coefficient, and a subsequent consideration of piezoelastic contributions allows the strain-free (clamped) coefficient to be estimated at 3.7 pm/V.

© 1995 Optical Society of America

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  1. A. Marrakchi, J. P. Huignard, and P. Günter, “Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20,” Appl. Phys. 24, 131–138 (1981).
    [Crossref]
  2. J. E. Millerd, E. M. Garmire, and M. B. Klein, “Investigation of photorefractive self-pumped phase-conjugate mirrors in the presence of loss and high modulation,” J. Opt. Soc. Am. B 9, 1499–1506 (1992).
    [Crossref]
  3. M. B. Klein, S. W. McCahon, T. F. Boggess, and G. C. Valley, “High-accuracy, high-reflectivity phase conjugation at 1.06 mm by four-wave mixing in photorefractive gallium arsenide,” J. Opt. Soc. Am. B 5, 2467–2472 (1988).
    [Crossref]
  4. Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiment,” J. Appl. Phys. 58, 45–57 (1985).
    [Crossref]
  5. A. Grunnet-Jepsen, C. H. Kwak, I. Richter, and L. Solymar, “Fundamental space-charge fields for applied alternating electric fields in photorefractive materials,” J. Opt. Soc. Am. B 11, 124–131 (1994).
    [Crossref]
  6. S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “Running holograms in photorefractive Bi12SiO20crystals,” Opt. Commun. 44, 19–23 (1982).
    [Crossref]
  7. S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an alternating electric field,” Opt. Commun. 53, 292–295 (1985).
    [Crossref]
  8. D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
    [Crossref]
  9. C. J. Raymond, “Electric fields in photorefractive materials,” M.Sc. thesis (Department of Engineering Science, Oxford University, Oxford, UK, 1992).
  10. M. Ziari, W. H. Steier, P. M. Ranon, M. B. Klein, and S. Trivedi, “Enhancement of the photorefractive gain at 1.3–1.5 mm in CdTe using alternating electric fields,” J. Opt. Soc. Am. B 9, 1461–1466 (1992).
    [Crossref]
  11. J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245–2252 (1990).
    [Crossref]
  12. M. Henry, S. Mallick, D. Rouède, L. E. Celaya, and A. Garcia Weidner, “Propagation of light in an optically active electro-optic crystal of Bi12SiO20: measurement of the electro-optic coefficient,” J. Appl. Phys. 59, 2650–2654 (1986).
    [Crossref]
  13. T. J. Tayag, T. E. Batchman, and J. J. Sluss, “Direct measurement of electrogyratory effect in bismuth silicon oxide,” Appl. Opt. 31, 625–629 (1992).
    [Crossref] [PubMed]
  14. F. Vachss and L. Hesselink, “Measurement of the electro-gyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
    [Crossref]
  15. H. Rajbenbach, J. M. Verdiell, and J. P. Huignard, “Visualization of electrical domains in semi-insulating GaAs:Cr and potential use for variable grating mode operation,” Appl. Phys. Lett. 53, 541–543 (1988).
    [Crossref]
  16. A. R. Tanguay, “The Czochralski growth and optical properties of bismuth silicon oxide,” Ph.D. dissertation (Yale University, New Haven, Conn., 1977).
  17. R. Waser, “Bulk conductivity and defect chemistry of acceptor-doped strontium titanate in the quenched state,” J. Am. Ceram. Soc. 74, 1934–1940 (1991).
    [Crossref]
  18. P. Asthana, “Volume holographic techniques for highly multiplexed interconnection applications,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1991).
  19. M. Ziari and W. H. Steier, “Optical switching in cadmium telluride using a light-induced electrode nonlinearity,” Appl. Opt. 32, 5711–5723 (1993).
    [Crossref] [PubMed]
  20. S. M. Sze, Semiconductor Devices (Wiley, New York, 1985).
  21. A. Grunnet-Jepsen and L. Solymar, “Investigation of the internal electric field in Bi12SiO20under applied alternating electric fields,” presented at 1994 Annual Meeting of the Optical Society of America, Dallas, Texas, 1994.
  22. D. F. Nelson, Electric, Optic, and Acoustic Interactions in Dielectrics (Wiley, New York, 1979).
  23. P. Günter and M. Zgonik, “Clamped–unclamped electro-optic coefficient dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
    [Crossref]
  24. I. P. Kaminow, An Introduction to Electrooptic Devices (Academic, New York, 1974).
  25. J. F. Nye, Physical Properties of Crystals (Oxford U. Press, New York, 1985).
  26. S. Shandarov, “The influence of piezoelectric effect on photorefractive gratings in electro-optic crystals,” Appl. Phys. A 55, 91–96 (1992).
    [Crossref]
  27. G. Pauliat, P. Mathey, and G. Roosen, “Influence of piezoelectricity on the photorefractive effect,” J. Opt. Soc. Am. B 8, 1942–1946 (1991).
    [Crossref]
  28. R. O’B. Carpenter, “The electro-optic effect in uniaxial crystals of the dihydrogen phosphate type. III. Measurement of coefficients,” J. Opt. Soc. Am. 40, 225–229 (1950).
    [Crossref]
  29. A. R. Johnston, “The strain-free electro-optic effect in single-crystal barium titanate,” Appl. Phys. Lett. 7, 195–198 (1965).
    [Crossref]
  30. A. Yariv, Optical Electronics, 4th ed. (Saunders, New York, 1991).
  31. P. Pellat-Finet, “Measurement of the electro-optic coefficient of BSO crystals,” Opt. Commun. 50, 275–280 (1984).
    [Crossref]
  32. P. Bayvel, M. McCall, and R. V. Wright, “Continuous method for measuring the electro-optic coefficient in Bi12SiO20and Bi12GeO20,” Opt. Lett. 13, 27–29 (1988).
    [Crossref] [PubMed]
  33. W. H. Steier, J. Kumar, and M. Ziari, “Infrared power limiting and self-switching in CdTe,” Appl. Phys. Lett. 53, 840–841 (1988).
    [Crossref]
  34. B. Jean, G. Couturier, and P. Joffre, “Electro-optic measurements in a semiconductor: the case of CdIn2Te4,” J. Appl. Phys. 75, 3579–3585 (1994).
    [Crossref]
  35. Ph. Lemaire and M. Georges, “Electro-optic coefficient measurement: correction of the electric-field inhomogeneities in the transverse configuration,” Opt. Lett. 17, 1411–1413 (1992).
    [Crossref]
  36. V. N. Astratov, A. V. Il’inskii, and V. A. Kiselev, “Stratification of the space-charge in the case of a screening of a field in crystals,” Sov. Phys. Solid State 26, 1720–1725 (1984).
  37. V. V. Bryksin, L. I. Korovin, and Yu. I. Kuz’min, “Role of injection currents in the evolution of a photoinduced charge in photorefractive crystal,” Sov. Phys. Solid State 29, 757–761 (1987).
  38. S. Shandarov, V. V. Shepelevich, and N. D. Khatkov, “Variation of the permittivity tensor in cubic photorefractive piezoelectric crystals under the influence of the electric field of a holographic grating,” Opt. Spectrosc. (USSR) 70, 627–630 (1991).
  39. R. E. Aldrich, S. L. Hou, and M. L. Harvill, “Electrical and optical properties of Bi12SiO20,” J. Appl. Phys. 44, 493–494 (1971).
    [Crossref]

1994 (2)

A. Grunnet-Jepsen, C. H. Kwak, I. Richter, and L. Solymar, “Fundamental space-charge fields for applied alternating electric fields in photorefractive materials,” J. Opt. Soc. Am. B 11, 124–131 (1994).
[Crossref]

B. Jean, G. Couturier, and P. Joffre, “Electro-optic measurements in a semiconductor: the case of CdIn2Te4,” J. Appl. Phys. 75, 3579–3585 (1994).
[Crossref]

1993 (1)

1992 (5)

1991 (5)

R. Waser, “Bulk conductivity and defect chemistry of acceptor-doped strontium titanate in the quenched state,” J. Am. Ceram. Soc. 74, 1934–1940 (1991).
[Crossref]

S. Shandarov, V. V. Shepelevich, and N. D. Khatkov, “Variation of the permittivity tensor in cubic photorefractive piezoelectric crystals under the influence of the electric field of a holographic grating,” Opt. Spectrosc. (USSR) 70, 627–630 (1991).

D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
[Crossref]

G. Pauliat, P. Mathey, and G. Roosen, “Influence of piezoelectricity on the photorefractive effect,” J. Opt. Soc. Am. B 8, 1942–1946 (1991).
[Crossref]

P. Günter and M. Zgonik, “Clamped–unclamped electro-optic coefficient dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
[Crossref]

1990 (1)

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245–2252 (1990).
[Crossref]

1988 (4)

M. B. Klein, S. W. McCahon, T. F. Boggess, and G. C. Valley, “High-accuracy, high-reflectivity phase conjugation at 1.06 mm by four-wave mixing in photorefractive gallium arsenide,” J. Opt. Soc. Am. B 5, 2467–2472 (1988).
[Crossref]

H. Rajbenbach, J. M. Verdiell, and J. P. Huignard, “Visualization of electrical domains in semi-insulating GaAs:Cr and potential use for variable grating mode operation,” Appl. Phys. Lett. 53, 541–543 (1988).
[Crossref]

P. Bayvel, M. McCall, and R. V. Wright, “Continuous method for measuring the electro-optic coefficient in Bi12SiO20and Bi12GeO20,” Opt. Lett. 13, 27–29 (1988).
[Crossref] [PubMed]

W. H. Steier, J. Kumar, and M. Ziari, “Infrared power limiting and self-switching in CdTe,” Appl. Phys. Lett. 53, 840–841 (1988).
[Crossref]

1987 (2)

V. V. Bryksin, L. I. Korovin, and Yu. I. Kuz’min, “Role of injection currents in the evolution of a photoinduced charge in photorefractive crystal,” Sov. Phys. Solid State 29, 757–761 (1987).

F. Vachss and L. Hesselink, “Measurement of the electro-gyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
[Crossref]

1986 (1)

M. Henry, S. Mallick, D. Rouède, L. E. Celaya, and A. Garcia Weidner, “Propagation of light in an optically active electro-optic crystal of Bi12SiO20: measurement of the electro-optic coefficient,” J. Appl. Phys. 59, 2650–2654 (1986).
[Crossref]

1985 (2)

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[Crossref]

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiment,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

1984 (2)

P. Pellat-Finet, “Measurement of the electro-optic coefficient of BSO crystals,” Opt. Commun. 50, 275–280 (1984).
[Crossref]

V. N. Astratov, A. V. Il’inskii, and V. A. Kiselev, “Stratification of the space-charge in the case of a screening of a field in crystals,” Sov. Phys. Solid State 26, 1720–1725 (1984).

1982 (1)

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “Running holograms in photorefractive Bi12SiO20crystals,” Opt. Commun. 44, 19–23 (1982).
[Crossref]

1981 (1)

A. Marrakchi, J. P. Huignard, and P. Günter, “Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

1971 (1)

R. E. Aldrich, S. L. Hou, and M. L. Harvill, “Electrical and optical properties of Bi12SiO20,” J. Appl. Phys. 44, 493–494 (1971).
[Crossref]

1965 (1)

A. R. Johnston, “The strain-free electro-optic effect in single-crystal barium titanate,” Appl. Phys. Lett. 7, 195–198 (1965).
[Crossref]

1950 (1)

Aldrich, R. E.

R. E. Aldrich, S. L. Hou, and M. L. Harvill, “Electrical and optical properties of Bi12SiO20,” J. Appl. Phys. 44, 493–494 (1971).
[Crossref]

Asthana, P.

P. Asthana, “Volume holographic techniques for highly multiplexed interconnection applications,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1991).

Astratov, V. N.

V. N. Astratov, A. V. Il’inskii, and V. A. Kiselev, “Stratification of the space-charge in the case of a screening of a field in crystals,” Sov. Phys. Solid State 26, 1720–1725 (1984).

Batchman, T. E.

Bayvel, P.

Boggess, T. F.

Bryksin, V. V.

V. V. Bryksin, L. I. Korovin, and Yu. I. Kuz’min, “Role of injection currents in the evolution of a photoinduced charge in photorefractive crystal,” Sov. Phys. Solid State 29, 757–761 (1987).

Carpenter, R. O’B.

Celaya, L. E.

M. Henry, S. Mallick, D. Rouède, L. E. Celaya, and A. Garcia Weidner, “Propagation of light in an optically active electro-optic crystal of Bi12SiO20: measurement of the electro-optic coefficient,” J. Appl. Phys. 59, 2650–2654 (1986).
[Crossref]

Couturier, G.

B. Jean, G. Couturier, and P. Joffre, “Electro-optic measurements in a semiconductor: the case of CdIn2Te4,” J. Appl. Phys. 75, 3579–3585 (1994).
[Crossref]

Garcia Weidner, A.

M. Henry, S. Mallick, D. Rouède, L. E. Celaya, and A. Garcia Weidner, “Propagation of light in an optically active electro-optic crystal of Bi12SiO20: measurement of the electro-optic coefficient,” J. Appl. Phys. 59, 2650–2654 (1986).
[Crossref]

Garmire, E. M.

Georges, M.

Grunnet-Jepsen, A.

A. Grunnet-Jepsen, C. H. Kwak, I. Richter, and L. Solymar, “Fundamental space-charge fields for applied alternating electric fields in photorefractive materials,” J. Opt. Soc. Am. B 11, 124–131 (1994).
[Crossref]

A. Grunnet-Jepsen and L. Solymar, “Investigation of the internal electric field in Bi12SiO20under applied alternating electric fields,” presented at 1994 Annual Meeting of the Optical Society of America, Dallas, Texas, 1994.

Günter, P.

P. Günter and M. Zgonik, “Clamped–unclamped electro-optic coefficient dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
[Crossref]

A. Marrakchi, J. P. Huignard, and P. Günter, “Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

Harvill, M. L.

R. E. Aldrich, S. L. Hou, and M. L. Harvill, “Electrical and optical properties of Bi12SiO20,” J. Appl. Phys. 44, 493–494 (1971).
[Crossref]

Henry, M.

M. Henry, S. Mallick, D. Rouède, L. E. Celaya, and A. Garcia Weidner, “Propagation of light in an optically active electro-optic crystal of Bi12SiO20: measurement of the electro-optic coefficient,” J. Appl. Phys. 59, 2650–2654 (1986).
[Crossref]

Hesselink, L.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245–2252 (1990).
[Crossref]

F. Vachss and L. Hesselink, “Measurement of the electro-gyratory and electro-optic effects in BSO and BGO,” Opt. Commun. 62, 159–165 (1987).
[Crossref]

Hou, S. L.

R. E. Aldrich, S. L. Hou, and M. L. Harvill, “Electrical and optical properties of Bi12SiO20,” J. Appl. Phys. 44, 493–494 (1971).
[Crossref]

Huignard, J. P.

H. Rajbenbach, J. M. Verdiell, and J. P. Huignard, “Visualization of electrical domains in semi-insulating GaAs:Cr and potential use for variable grating mode operation,” Appl. Phys. Lett. 53, 541–543 (1988).
[Crossref]

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiment,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

A. Marrakchi, J. P. Huignard, and P. Günter, “Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

Il’inskii, A. V.

V. N. Astratov, A. V. Il’inskii, and V. A. Kiselev, “Stratification of the space-charge in the case of a screening of a field in crystals,” Sov. Phys. Solid State 26, 1720–1725 (1984).

Jean, B.

B. Jean, G. Couturier, and P. Joffre, “Electro-optic measurements in a semiconductor: the case of CdIn2Te4,” J. Appl. Phys. 75, 3579–3585 (1994).
[Crossref]

Joffre, P.

B. Jean, G. Couturier, and P. Joffre, “Electro-optic measurements in a semiconductor: the case of CdIn2Te4,” J. Appl. Phys. 75, 3579–3585 (1994).
[Crossref]

Johnston, A. R.

A. R. Johnston, “The strain-free electro-optic effect in single-crystal barium titanate,” Appl. Phys. Lett. 7, 195–198 (1965).
[Crossref]

Kaminow, I. P.

I. P. Kaminow, An Introduction to Electrooptic Devices (Academic, New York, 1974).

Khatkov, N. D.

S. Shandarov, V. V. Shepelevich, and N. D. Khatkov, “Variation of the permittivity tensor in cubic photorefractive piezoelectric crystals under the influence of the electric field of a holographic grating,” Opt. Spectrosc. (USSR) 70, 627–630 (1991).

Kiselev, V. A.

V. N. Astratov, A. V. Il’inskii, and V. A. Kiselev, “Stratification of the space-charge in the case of a screening of a field in crystals,” Sov. Phys. Solid State 26, 1720–1725 (1984).

Klein, M. B.

Korovin, L. I.

V. V. Bryksin, L. I. Korovin, and Yu. I. Kuz’min, “Role of injection currents in the evolution of a photoinduced charge in photorefractive crystal,” Sov. Phys. Solid State 29, 757–761 (1987).

Kulikov, V. V.

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “Running holograms in photorefractive Bi12SiO20crystals,” Opt. Commun. 44, 19–23 (1982).
[Crossref]

Kumar, J.

W. H. Steier, J. Kumar, and M. Ziari, “Infrared power limiting and self-switching in CdTe,” Appl. Phys. Lett. 53, 840–841 (1988).
[Crossref]

Kuz’min, Yu. I.

V. V. Bryksin, L. I. Korovin, and Yu. I. Kuz’min, “Role of injection currents in the evolution of a photoinduced charge in photorefractive crystal,” Sov. Phys. Solid State 29, 757–761 (1987).

Kwak, C. H.

Lemaire, Ph.

Mallick, S.

M. Henry, S. Mallick, D. Rouède, L. E. Celaya, and A. Garcia Weidner, “Propagation of light in an optically active electro-optic crystal of Bi12SiO20: measurement of the electro-optic coefficient,” J. Appl. Phys. 59, 2650–2654 (1986).
[Crossref]

Marrakchi, A.

A. Marrakchi, J. P. Huignard, and P. Günter, “Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20,” Appl. Phys. 24, 131–138 (1981).
[Crossref]

Mathey, P.

McCahon, S. W.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245–2252 (1990).
[Crossref]

M. B. Klein, S. W. McCahon, T. F. Boggess, and G. C. Valley, “High-accuracy, high-reflectivity phase conjugation at 1.06 mm by four-wave mixing in photorefractive gallium arsenide,” J. Opt. Soc. Am. B 5, 2467–2472 (1988).
[Crossref]

McCall, M.

Millerd, J. E.

Nelson, D. F.

D. F. Nelson, Electric, Optic, and Acoustic Interactions in Dielectrics (Wiley, New York, 1979).

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford U. Press, New York, 1985).

Pauliat, G.

Pellat-Finet, P.

P. Pellat-Finet, “Measurement of the electro-optic coefficient of BSO crystals,” Opt. Commun. 50, 275–280 (1984).
[Crossref]

Petrov, M. P.

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[Crossref]

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “Running holograms in photorefractive Bi12SiO20crystals,” Opt. Commun. 44, 19–23 (1982).
[Crossref]

Rajbenbach, H.

H. Rajbenbach, J. M. Verdiell, and J. P. Huignard, “Visualization of electrical domains in semi-insulating GaAs:Cr and potential use for variable grating mode operation,” Appl. Phys. Lett. 53, 541–543 (1988).
[Crossref]

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiment,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

Ranon, P. M.

Raymond, C. J.

C. J. Raymond, “Electric fields in photorefractive materials,” M.Sc. thesis (Department of Engineering Science, Oxford University, Oxford, UK, 1992).

Réfrégier, Ph.

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiment,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

Richter, I.

Roosen, G.

Rouède, D.

M. Henry, S. Mallick, D. Rouède, L. E. Celaya, and A. Garcia Weidner, “Propagation of light in an optically active electro-optic crystal of Bi12SiO20: measurement of the electro-optic coefficient,” J. Appl. Phys. 59, 2650–2654 (1986).
[Crossref]

Rytz, D.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245–2252 (1990).
[Crossref]

Shandarov, S.

S. Shandarov, “The influence of piezoelectric effect on photorefractive gratings in electro-optic crystals,” Appl. Phys. A 55, 91–96 (1992).
[Crossref]

S. Shandarov, V. V. Shepelevich, and N. D. Khatkov, “Variation of the permittivity tensor in cubic photorefractive piezoelectric crystals under the influence of the electric field of a holographic grating,” Opt. Spectrosc. (USSR) 70, 627–630 (1991).

Shepelevich, V. V.

S. Shandarov, V. V. Shepelevich, and N. D. Khatkov, “Variation of the permittivity tensor in cubic photorefractive piezoelectric crystals under the influence of the electric field of a holographic grating,” Opt. Spectrosc. (USSR) 70, 627–630 (1991).

Sluss, J. J.

Solymar, L.

A. Grunnet-Jepsen, C. H. Kwak, I. Richter, and L. Solymar, “Fundamental space-charge fields for applied alternating electric fields in photorefractive materials,” J. Opt. Soc. Am. B 11, 124–131 (1994).
[Crossref]

D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
[Crossref]

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiment,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

A. Grunnet-Jepsen and L. Solymar, “Investigation of the internal electric field in Bi12SiO20under applied alternating electric fields,” presented at 1994 Annual Meeting of the Optical Society of America, Dallas, Texas, 1994.

Steier, W. H.

Stepanov, S. I.

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[Crossref]

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “Running holograms in photorefractive Bi12SiO20crystals,” Opt. Commun. 44, 19–23 (1982).
[Crossref]

Sze, S. M.

S. M. Sze, Semiconductor Devices (Wiley, New York, 1985).

Tanguay, A. R.

A. R. Tanguay, “The Czochralski growth and optical properties of bismuth silicon oxide,” Ph.D. dissertation (Yale University, New Haven, Conn., 1977).

Tayag, T. J.

Trivedi, S.

Vachss, F.

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[Crossref]

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[Crossref]

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[Crossref]

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D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
[Crossref]

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J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245–2252 (1990).
[Crossref]

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[Crossref]

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Appl. Opt. (2)

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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R. Waser, “Bulk conductivity and defect chemistry of acceptor-doped strontium titanate in the quenched state,” J. Am. Ceram. Soc. 74, 1934–1940 (1991).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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Figures (8)

Fig. 1
Fig. 1

Experimental arrangement for measurement of the product of the internal electric field and the effective electro-optic coefficient.

Fig. 2
Fig. 2

Typical experimental result for the transmission of light (solid curve, left-hand axis) as a function of time for an ac square-wave applied voltage of 6-kV amplitude and 0.05-Hz frequency (dashed curve, right-hand axis). The incident light has a wavelength of 632.8 nm and an intensity of 1 mW/cm2.

Fig. 3
Fig. 3

Modulus of the internal electric field as a function of time for an ac square-wave applied voltage of 6-kV/cm amplitude and 0.05-Hz frequency and with a dc bias of 0.27 kV/cm to compensate for the intrinsic birefringence. The wavelength used was 632.8 nm, at which the refractive index of BSO is n = 2.52, the optical activity is ρ = 21.2 deg/mm, and the effective electro-optic coefficient is reff = 4.35 pm/V. The intensity of the incident light was 1 mW/cm2.

Fig. 4
Fig. 4

Same as Fig. 3 but for a wavelength of 514 nm, an intensity of 5 mW/cm2, and applied field frequencies of (a) 10 Hz, (b) 50 Hz, and (c) 100 Hz. At this wavelength reff = 4.3 pm/V, n = 2.62, and ρ = 39 deg/mm.

Fig. 5
Fig. 5

(a) Photorefractive material divided into two separate regions, (b) its equivalent electrical circuit.

Fig. 6
Fig. 6

Theoretical prediction of the modulus of an internal field for the parameters in Fig. 4.

Fig. 7
Fig. 7

Reciprocal time constant as a function of the intensity of incident 514-nm light.

Fig. 8
Fig. 8

Same as Fig. 3 but with an applied field frequency of 20 Hz. The electro-optic coefficient was chosen so that the internal field was V0/d (=6 kV/cm), as illustrated. This gives reff = 4.35 pm/V.

Equations (22)

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

T = I 0 I min I max I min .
T = ( q 2 q 3 sin μ 3 cos μ 2 cos μ 3 sin μ 2 ) 2 + [ q 1 q 3 sin μ 3 sin ( μ 2 + 2 ϕ ) ] 2 ,
q 1 = ½ n 2 r eff E 0 , q 2 = ρ λ π n , μ 1 = ½ π λ n 3 r eff E 0 L , μ 2 = ρ L ,
E = β ( V 0 / d ) ,
1 d 0 d β d x = 1 .
E max = ( 2 β ) ( V 0 / d ) .
J tot = J 0 + 0 s E t ,
J 0 = e μ n E ,
E a d a + E b d b = V 0 ( t ) ,
n = s I N D τ r ,
V a R a + C a d V a d t = V b R b + C b d V b d t ,
d V a d t + R a + R b R a R b ( C a + C b ) V a = V 0 ( t ) R b ( C a + C b ) + C b C a + C b d V 0 d t ,
R x = d x e s N D μ x I x τ r x , C x = 0 s d x .
E a ( t ) = 1 μ a τ r a I a d a μ a τ r a I a + d b μ b τ r b I b V 0 .
E b ( t ) = B τ f [ 1 exp ( ± T 0 2 τ f ) sinh ( T 0 2 τ f ) exp ( t τ f ) 1 ] ,
E a ( t ) = ± V 0 d b E b ( t ) d a ,
B = V 0 d b C b R a , τ f = C b R a R b R a + R b ,
d b = s 0 β ( 1 β ) R tot A τ f ,
μ a I a τ r a μ b I b τ r b = ξ η ,
Δ η i j = r ijk E k + s ijkl E k E l + ,
r ijk T = r ijk S + P ijmn E d kmn ,
r 41 T r 41 S = p 2323 e 123 c 2323 .

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