Abstract

We present and analyze the room temperature (T=23.5 °C) time behavior of the transmitted intensities of polarized light passing through an unclamped (100)-type single crystal of barium titanate (BaTiO3) when subject to a time-dependent, externally applied electric field. To the authors’ knowledge, this is the first reported observation and analysis of such time-resolved optical transients. According to a previous [ J. Opt. Soc. Am. A 22, 377 ( 2005)] observation by the authors, this original optical technique can, in principle, be used on 18 out of 20 noncentrosymmetric crystal point groups where the first-order (Pockels) and second-order (Kerr) electro-optic effects coexist. Because of its nondestructive nature, this novel optical method would be a useful tool in other fields of condensed-matter physics in which time-behavior observation and characterization of certain physical parameters of crystals are important.

© 2005 Optical Society of America

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  14. F. Jona, G. Shirane, Ferroelectric Crystals (Pergamon, New York, 1962). (Reprint, Dover, New York, 1993).
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  17. J. C. Burfoot, G. W. Taylor, Polar Dielectrics and Their Applications (MacMillan, London, 1979).
  18. L. O. Chua, C. A. Desoer, E. S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York, 1987).
  19. D. J. Griffiths, Introduction to Electrodynamics, 3rd ed. (Prentice Hall, Englewood Cliffs, N.J., 1999).
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  25. A. S. Sonin, V. É. Perfilova, “Electrooptical properties of barium titanate in the paraelectric phase,” Sov. Phys. Crystallogr. 14, 419–420 (1969).
  26. K. H. Hellwege, Landolt-Börnstein, New Series III/2 (Springer-Verlag, Berlin, 1969).
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    [CrossRef]
  34. W. Känzig, “Space charge layer near the surface of a ferroelectric,” Phys. Rev. 98, 549–550 (1955).
    [CrossRef]
  35. S. Triebwasser, “Space charge fields in BaTiO3,” Phys. Rev. 118, 100–105 (1960).
    [CrossRef]
  36. A. Branwood, O. H. Hughes, J. D. Hurd, R. H. Tredgold, “Evidence for space charge conduction in barium titanate single crystals,” Proc. Phys. Soc. London 79, 1161–1165 (1962).
    [CrossRef]
  37. M. V. Klassen-Neklyudova, Mechanical Twinning of Crystals (Kluwer-Consultants Bureau, Norwell, Mass., 1964).
    [CrossRef]
  38. E. K. H. Salje, Phase Transitions in Ferroelastic and Co-elastic Crystals (Cambridge U. Press, Cambridge, UK, 1990).
  39. V. S. Boyko, R. I. Garber, A. M. Kossevich, Reversible Crystal Plasticity (AIP Press, New York, 1994).
  40. R. R. Newton, A. J. Ahearn, K. G. McKay, “Observation of the ferro-electric Barkhausen effect in barium titanate,” Phys. Rev. 75, 103–106 (1949).
    [CrossRef]
  41. A. G. Chynoweth, “Barkhausen pulses in barium titanate,” Phys. Rev. 110, 1316–1332 (1958).
    [CrossRef]
  42. R. C. Miller, “Some experiments on the motion of 180° domain walls in BaTiO3,” Phys. Rev. 111, 736–739 (1958).
    [CrossRef]
  43. A. G. Chynoweth, “Effect of space charge fields on polarization reversal and the generation of Barkhausen pulses in barium titanate,” J. Appl. Phys. 30, 280–285 (1959).
    [CrossRef]
  44. V. M. Rudyak, “The Barkhausen effect,” Sov. Phys. Usp. 13, 461–479 (1971).
    [CrossRef]
  45. V. M. Rudyak, A. Yu. Kudzin, T. V. Panchenko, “Barkhausen jumps and stabilization of the spontaneous polarization of single crystals of BaTiO3,” Sov. Phys. Solid State 14, 2112–2113 (1973).
  46. S. A. Flerova, Yu. I. Samchenko, V. M. Gorbenko, “Light emission during pulsed repolarization of deformed BaTiO3 crystals,” Sov. Phys. Solid State 23, 1624–1625 (1981).
  47. V. V. Belov, O. Yu. Serdobol’skaya, “Emission of sound associated with polarization reversal in a ferroelectric crystal,” Sov. Phys. Solid State 26, 868–870 (1984).

2005 (1)

1996 (1)

S. R. Gilbert, L. A. Wills, B. W. Wessels, J. L. Schindler, J. A. Thomas, C. R. Kanewurf, “Electrical transport properties of epitaxial BaTiO3thin films,” J. Appl. Phys. 80, 969–977 (1996).
[CrossRef]

1984 (1)

V. V. Belov, O. Yu. Serdobol’skaya, “Emission of sound associated with polarization reversal in a ferroelectric crystal,” Sov. Phys. Solid State 26, 868–870 (1984).

1981 (1)

S. A. Flerova, Yu. I. Samchenko, V. M. Gorbenko, “Light emission during pulsed repolarization of deformed BaTiO3 crystals,” Sov. Phys. Solid State 23, 1624–1625 (1981).

1979 (1)

J. P. Boyeaux, F. M. Michael-Calendini, “Small polaron interpretation of BaTiO3transport properties from drift mobility measurements,” J. Phys. C 12, 545–556 (1979).
[CrossRef]

1973 (1)

V. M. Rudyak, A. Yu. Kudzin, T. V. Panchenko, “Barkhausen jumps and stabilization of the spontaneous polarization of single crystals of BaTiO3,” Sov. Phys. Solid State 14, 2112–2113 (1973).

1971 (1)

V. M. Rudyak, “The Barkhausen effect,” Sov. Phys. Usp. 13, 461–479 (1971).
[CrossRef]

1970 (1)

F.-S. Chen, “Modulators for optical communications,” Proc. IEEE 58, 1440–1457 (1970).
[CrossRef]

1969 (1)

A. S. Sonin, V. É. Perfilova, “Electrooptical properties of barium titanate in the paraelectric phase,” Sov. Phys. Crystallogr. 14, 419–420 (1969).

1966 (1)

V. É. Perfilova, A. S. Sonin, “The electrooptic properties of single crystals of barium titanate,” Sov. Phys. Solid State 8, 82–84 (1966).

1965 (1)

1964 (1)

1962 (1)

A. Branwood, O. H. Hughes, J. D. Hurd, R. H. Tredgold, “Evidence for space charge conduction in barium titanate single crystals,” Proc. Phys. Soc. London 79, 1161–1165 (1962).
[CrossRef]

1960 (1)

S. Triebwasser, “Space charge fields in BaTiO3,” Phys. Rev. 118, 100–105 (1960).
[CrossRef]

1959 (1)

A. G. Chynoweth, “Effect of space charge fields on polarization reversal and the generation of Barkhausen pulses in barium titanate,” J. Appl. Phys. 30, 280–285 (1959).
[CrossRef]

1958 (3)

A. G. Chynoweth, “Barkhausen pulses in barium titanate,” Phys. Rev. 110, 1316–1332 (1958).
[CrossRef]

R. C. Miller, “Some experiments on the motion of 180° domain walls in BaTiO3,” Phys. Rev. 111, 736–739 (1958).
[CrossRef]

D. Mayerhofer, “Transition to the ferroelectric state in barium titanate,” Phys. Rev. 112, 413–423 (1958).
[CrossRef]

1955 (1)

W. Känzig, “Space charge layer near the surface of a ferroelectric,” Phys. Rev. 98, 549–550 (1955).
[CrossRef]

1954 (1)

M. E. Drougard, D. R. Young, “Domain clamping effect in barium titanate single crystals,” Phys. Rev. 94, 1561–1564 (1954).
[CrossRef]

1949 (1)

R. R. Newton, A. J. Ahearn, K. G. McKay, “Observation of the ferro-electric Barkhausen effect in barium titanate,” Phys. Rev. 75, 103–106 (1949).
[CrossRef]

Ahearn, A. J.

R. R. Newton, A. J. Ahearn, K. G. McKay, “Observation of the ferro-electric Barkhausen effect in barium titanate,” Phys. Rev. 75, 103–106 (1949).
[CrossRef]

Belov, V. V.

V. V. Belov, O. Yu. Serdobol’skaya, “Emission of sound associated with polarization reversal in a ferroelectric crystal,” Sov. Phys. Solid State 26, 868–870 (1984).

Bhattacharya, K.

E. Burcsu, G. Ravichandran, K. Bhattacharya, “Electro-mechanical behaviour of 90-degree domain motion in barium titanate single crystals,” in Smart Structures and Materials 2001: Active Materials: Behavior and Mechanics, C. S. Lynch, ed., Proc. SPIE4333, 121–130 (2001).
[CrossRef]

Boyeaux, J. P.

J. P. Boyeaux, F. M. Michael-Calendini, “Small polaron interpretation of BaTiO3transport properties from drift mobility measurements,” J. Phys. C 12, 545–556 (1979).
[CrossRef]

Boyko, V. S.

V. S. Boyko, R. I. Garber, A. M. Kossevich, Reversible Crystal Plasticity (AIP Press, New York, 1994).

Branwood, A.

A. Branwood, O. H. Hughes, J. D. Hurd, R. H. Tredgold, “Evidence for space charge conduction in barium titanate single crystals,” Proc. Phys. Soc. London 79, 1161–1165 (1962).
[CrossRef]

Burcsu, E.

E. Burcsu, G. Ravichandran, K. Bhattacharya, “Electro-mechanical behaviour of 90-degree domain motion in barium titanate single crystals,” in Smart Structures and Materials 2001: Active Materials: Behavior and Mechanics, C. S. Lynch, ed., Proc. SPIE4333, 121–130 (2001).
[CrossRef]

Burfoot, J. C.

J. C. Burfoot, G. W. Taylor, Polar Dielectrics and Their Applications (MacMillan, London, 1979).

J. C. Burfoot, Ferroelectrics—An Introduction to the Physical Principles (Van Nostrand, London, 1967).

Chen, F.-S.

F.-S. Chen, “Modulators for optical communications,” Proc. IEEE 58, 1440–1457 (1970).
[CrossRef]

Cholet, P.

Chua, L. O.

L. O. Chua, C. A. Desoer, E. S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York, 1987).

Chynoweth, A. G.

A. G. Chynoweth, “Effect of space charge fields on polarization reversal and the generation of Barkhausen pulses in barium titanate,” J. Appl. Phys. 30, 280–285 (1959).
[CrossRef]

A. G. Chynoweth, “Barkhausen pulses in barium titanate,” Phys. Rev. 110, 1316–1332 (1958).
[CrossRef]

Davis, C. C.

C. C. Davis, Lasers and Electro-Optics (Cambridge U. Press, Cambridge, UK, 1996).

Desoer, C. A.

L. O. Chua, C. A. Desoer, E. S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York, 1987).

Drougard, M. E.

M. E. Drougard, D. R. Young, “Domain clamping effect in barium titanate single crystals,” Phys. Rev. 94, 1561–1564 (1954).
[CrossRef]

Flerova, S. A.

S. A. Flerova, Yu. I. Samchenko, V. M. Gorbenko, “Light emission during pulsed repolarization of deformed BaTiO3 crystals,” Sov. Phys. Solid State 23, 1624–1625 (1981).

Fowles, G.

G. Fowles, Introduction to Modern Optics, 2nd ed. (Dover, New York, 1989).

Furtak, T. E.

M. V. Klein, T. E. Furtak, Optics, 2nd ed. (Wiley, Hoboken, N.J., 1986).

Garber, R. I.

V. S. Boyko, R. I. Garber, A. M. Kossevich, Reversible Crystal Plasticity (AIP Press, New York, 1994).

Gilbert, S. R.

S. R. Gilbert, L. A. Wills, B. W. Wessels, J. L. Schindler, J. A. Thomas, C. R. Kanewurf, “Electrical transport properties of epitaxial BaTiO3thin films,” J. Appl. Phys. 80, 969–977 (1996).
[CrossRef]

Glass, A. M.

M. E. Lines, A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Clarendon, Oxford, UK, 1977).

Gorbenko, V. M.

S. A. Flerova, Yu. I. Samchenko, V. M. Gorbenko, “Light emission during pulsed repolarization of deformed BaTiO3 crystals,” Sov. Phys. Solid State 23, 1624–1625 (1981).

Griffiths, D. J.

D. J. Griffiths, Introduction to Electrodynamics, 3rd ed. (Prentice Hall, Englewood Cliffs, N.J., 1999).

Guenther, R. D.

R. D. Guenther, Modern Optics (Wiley, Hoboken, N.J., 1990).

Haas, W.

Hecht, E.

E. Hecht, Optics, 4th ed. (Pearson Addison-Wesley, Boston, Mass., 2001).

Hellwege, K. H.

K. H. Hellwege, Landolt-Börnstein, New Series III/2 (Springer-Verlag, Berlin, 1969).

Hughes, O. H.

A. Branwood, O. H. Hughes, J. D. Hurd, R. H. Tredgold, “Evidence for space charge conduction in barium titanate single crystals,” Proc. Phys. Soc. London 79, 1161–1165 (1962).
[CrossRef]

Hurd, J. D.

A. Branwood, O. H. Hughes, J. D. Hurd, R. H. Tredgold, “Evidence for space charge conduction in barium titanate single crystals,” Proc. Phys. Soc. London 79, 1161–1165 (1962).
[CrossRef]

Iizuka, K.

K. Iizuka, Elements of Photonics (Wiley, Hoboken, N.J., 2002).

Johannes, R.

Johnston, A. R.

Jona, F.

F. Jona, G. Shirane, Ferroelectric Crystals (Pergamon, New York, 1962). (Reprint, Dover, New York, 1993).

Kaminow, I. P.

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

Kanewurf, C. R.

S. R. Gilbert, L. A. Wills, B. W. Wessels, J. L. Schindler, J. A. Thomas, C. R. Kanewurf, “Electrical transport properties of epitaxial BaTiO3thin films,” J. Appl. Phys. 80, 969–977 (1996).
[CrossRef]

Känzig, W.

W. Känzig, “Space charge layer near the surface of a ferroelectric,” Phys. Rev. 98, 549–550 (1955).
[CrossRef]

Klassen-Neklyudova, M. V.

M. V. Klassen-Neklyudova, Mechanical Twinning of Crystals (Kluwer-Consultants Bureau, Norwell, Mass., 1964).
[CrossRef]

Klein, M. V.

M. V. Klein, T. E. Furtak, Optics, 2nd ed. (Wiley, Hoboken, N.J., 1986).

Kossevich, A. M.

V. S. Boyko, R. I. Garber, A. M. Kossevich, Reversible Crystal Plasticity (AIP Press, New York, 1994).

Kudzin, A. Yu.

V. M. Rudyak, A. Yu. Kudzin, T. V. Panchenko, “Barkhausen jumps and stabilization of the spontaneous polarization of single crystals of BaTiO3,” Sov. Phys. Solid State 14, 2112–2113 (1973).

Kuh, E. S.

L. O. Chua, C. A. Desoer, E. S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York, 1987).

Lines, M. E.

M. E. Lines, A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Clarendon, Oxford, UK, 1977).

Mayerhofer, D.

D. Mayerhofer, “Transition to the ferroelectric state in barium titanate,” Phys. Rev. 112, 413–423 (1958).
[CrossRef]

McKay, K. G.

R. R. Newton, A. J. Ahearn, K. G. McKay, “Observation of the ferro-electric Barkhausen effect in barium titanate,” Phys. Rev. 75, 103–106 (1949).
[CrossRef]

Melnichuk, M.

Michael-Calendini, F. M.

J. P. Boyeaux, F. M. Michael-Calendini, “Small polaron interpretation of BaTiO3transport properties from drift mobility measurements,” J. Phys. C 12, 545–556 (1979).
[CrossRef]

Miller, R. C.

R. C. Miller, “Some experiments on the motion of 180° domain walls in BaTiO3,” Phys. Rev. 111, 736–739 (1958).
[CrossRef]

Newton, R. R.

R. R. Newton, A. J. Ahearn, K. G. McKay, “Observation of the ferro-electric Barkhausen effect in barium titanate,” Phys. Rev. 75, 103–106 (1949).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford U. Press, New York, 2001).

Panchenko, T. V.

V. M. Rudyak, A. Yu. Kudzin, T. V. Panchenko, “Barkhausen jumps and stabilization of the spontaneous polarization of single crystals of BaTiO3,” Sov. Phys. Solid State 14, 2112–2113 (1973).

Perfilova, V. É.

A. S. Sonin, V. É. Perfilova, “Electrooptical properties of barium titanate in the paraelectric phase,” Sov. Phys. Crystallogr. 14, 419–420 (1969).

V. É. Perfilova, A. S. Sonin, “The electrooptic properties of single crystals of barium titanate,” Sov. Phys. Solid State 8, 82–84 (1966).

Ravichandran, G.

E. Burcsu, G. Ravichandran, K. Bhattacharya, “Electro-mechanical behaviour of 90-degree domain motion in barium titanate single crystals,” in Smart Structures and Materials 2001: Active Materials: Behavior and Mechanics, C. S. Lynch, ed., Proc. SPIE4333, 121–130 (2001).
[CrossRef]

Rudyak, V. M.

V. M. Rudyak, A. Yu. Kudzin, T. V. Panchenko, “Barkhausen jumps and stabilization of the spontaneous polarization of single crystals of BaTiO3,” Sov. Phys. Solid State 14, 2112–2113 (1973).

V. M. Rudyak, “The Barkhausen effect,” Sov. Phys. Usp. 13, 461–479 (1971).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, Hoboken, N.J., 1991).
[CrossRef]

Salje, E. K. H.

E. K. H. Salje, Phase Transitions in Ferroelastic and Co-elastic Crystals (Cambridge U. Press, Cambridge, UK, 1990).

Samchenko, Yu. I.

S. A. Flerova, Yu. I. Samchenko, V. M. Gorbenko, “Light emission during pulsed repolarization of deformed BaTiO3 crystals,” Sov. Phys. Solid State 23, 1624–1625 (1981).

Schindler, J. L.

S. R. Gilbert, L. A. Wills, B. W. Wessels, J. L. Schindler, J. A. Thomas, C. R. Kanewurf, “Electrical transport properties of epitaxial BaTiO3thin films,” J. Appl. Phys. 80, 969–977 (1996).
[CrossRef]

Serdobol’skaya, O. Yu.

V. V. Belov, O. Yu. Serdobol’skaya, “Emission of sound associated with polarization reversal in a ferroelectric crystal,” Sov. Phys. Solid State 26, 868–870 (1984).

Shirane, G.

F. Jona, G. Shirane, Ferroelectric Crystals (Pergamon, New York, 1962). (Reprint, Dover, New York, 1993).

Sonin, A. S.

A. S. Sonin, V. É. Perfilova, “Electrooptical properties of barium titanate in the paraelectric phase,” Sov. Phys. Crystallogr. 14, 419–420 (1969).

V. É. Perfilova, A. S. Sonin, “The electrooptic properties of single crystals of barium titanate,” Sov. Phys. Solid State 8, 82–84 (1966).

Sutherland, R. L.

R. L. Sutherland, Handbook of Nonlinear Optics, 2nd ed. (Marcel Dekker, New York, 2003).

Taylor, G. W.

J. C. Burfoot, G. W. Taylor, Polar Dielectrics and Their Applications (MacMillan, London, 1979).

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, Hoboken, N.J., 1991).
[CrossRef]

Thomas, J. A.

S. R. Gilbert, L. A. Wills, B. W. Wessels, J. L. Schindler, J. A. Thomas, C. R. Kanewurf, “Electrical transport properties of epitaxial BaTiO3thin films,” J. Appl. Phys. 80, 969–977 (1996).
[CrossRef]

Tredgold, R. H.

A. Branwood, O. H. Hughes, J. D. Hurd, R. H. Tredgold, “Evidence for space charge conduction in barium titanate single crystals,” Proc. Phys. Soc. London 79, 1161–1165 (1962).
[CrossRef]

Triebwasser, S.

S. Triebwasser, “Space charge fields in BaTiO3,” Phys. Rev. 118, 100–105 (1960).
[CrossRef]

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC Press, Boca Raton, Fla., 2003).

Weingart, J. M.

Wessels, B. W.

S. R. Gilbert, L. A. Wills, B. W. Wessels, J. L. Schindler, J. A. Thomas, C. R. Kanewurf, “Electrical transport properties of epitaxial BaTiO3thin films,” J. Appl. Phys. 80, 969–977 (1996).
[CrossRef]

Wills, L. A.

S. R. Gilbert, L. A. Wills, B. W. Wessels, J. L. Schindler, J. A. Thomas, C. R. Kanewurf, “Electrical transport properties of epitaxial BaTiO3thin films,” J. Appl. Phys. 80, 969–977 (1996).
[CrossRef]

Wood, L. T.

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, New York, 1997).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, Hoboken, N.J., 2003).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, Hoboken, N.J., 2003).

Young, D. R.

M. E. Drougard, D. R. Young, “Domain clamping effect in barium titanate single crystals,” Phys. Rev. 94, 1561–1564 (1954).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (2)

S. R. Gilbert, L. A. Wills, B. W. Wessels, J. L. Schindler, J. A. Thomas, C. R. Kanewurf, “Electrical transport properties of epitaxial BaTiO3thin films,” J. Appl. Phys. 80, 969–977 (1996).
[CrossRef]

A. G. Chynoweth, “Effect of space charge fields on polarization reversal and the generation of Barkhausen pulses in barium titanate,” J. Appl. Phys. 30, 280–285 (1959).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Phys. C (1)

J. P. Boyeaux, F. M. Michael-Calendini, “Small polaron interpretation of BaTiO3transport properties from drift mobility measurements,” J. Phys. C 12, 545–556 (1979).
[CrossRef]

Phys. Rev. (7)

D. Mayerhofer, “Transition to the ferroelectric state in barium titanate,” Phys. Rev. 112, 413–423 (1958).
[CrossRef]

W. Känzig, “Space charge layer near the surface of a ferroelectric,” Phys. Rev. 98, 549–550 (1955).
[CrossRef]

S. Triebwasser, “Space charge fields in BaTiO3,” Phys. Rev. 118, 100–105 (1960).
[CrossRef]

M. E. Drougard, D. R. Young, “Domain clamping effect in barium titanate single crystals,” Phys. Rev. 94, 1561–1564 (1954).
[CrossRef]

R. R. Newton, A. J. Ahearn, K. G. McKay, “Observation of the ferro-electric Barkhausen effect in barium titanate,” Phys. Rev. 75, 103–106 (1949).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Simple schematic of the optical amplitude modulation system. The modulated optical intensities Iy′ and Iz′ are polarized along the axes y′ and z′, respectively.

Fig. 2
Fig. 2

Time-behavior plot of the two modulated orthogonal intensities Iy′, Iz′ and the monitoring intensity Im for the first experimental trial. Iy′ and Iz′ are polarized along the axes y′ and z′, respectively. The Cartesian system of coordinates (x,y′,z′) is rotated counterclockwise by an angle θ=15° relative to the Cartesian coordinate system (x,y,z). The applied electric field (E1) across the BaTiO3 sample was switched in a steplike fashion approximately every 50 s for 500 s. The values in volts of the electric field taken in chronological order were 0, +400, −400, 0, +600, −600, 0, +200, −200, 0.

Fig. 3
Fig. 3

Same as Fig. 2 but for the second experimental trial. The values in volts of the electric field taken in chronological order were: 0, −400, +400, 0, −600, +600, −600, 0, +200, 0. In this case the −400-V field on the sample was kept on for ≈20 s only.

Fig. 4
Fig. 4

Schematic of the experimental setup; the y axis points out of the paper. The setup contains the following elements: laser, BaTiO3 crystal, 45°-linear polarizer (PO), Wollaston prism (WP), beam splitters (BS1, BS2, BS3), intensity detectors (D1, D2, D3), convergent lenses (L1, L2, L3), CCD camera (CCD), digital camera (DC), computer system (CS), incandescent lamp (IC), power supply (PS), millimeter ruler (R), screen (S), and a pair of gold wires (GW).

Fig. 5
Fig. 5

Schematic of the electric circuit; only the solid line represents real electric cable. The circuit comprises the following elements: power supply (PS), toggle switch (TS), equivalent resistance of wire circuit (R), BaTiO3 capacitor (C) with its internal resistance (RC), and the equivalent resistance of the ambient medium (Ra).

Fig. 6
Fig. 6

Plot of the curve-fitted intensities corresponding to the excitation transients when the applied electric field had just been changed from (a) 0 V/mm to +400 V/mm during the first experimental trial and (b) 0 V/mm to −400 V/mm during the second experimental trial. The interval between the plotted graph values is of ten data points for each case.

Fig. 7
Fig. 7

Plot of the curve-fitted intensities corresponding to the switching transients when the applied electric field had just been changed from (a) +200 V/mm to −200 V/mm during the first experimental trial, (b) −400 V/mm to +400 V/mm during the second experimental trial. The interval between the plotted graph values is of twenty data points for the first experimental trial and ten data points for the second experimental trial. The gap between the extreme values of the experimental data curves and those of the corresponding fitted curves is due to dielectric absorption, a form of switching inertia common to all bulk crystal dielectrics.

Fig. 8
Fig. 8

Plot of the curve-fitted intensities corresponding to the relaxation transients when the electric circuit was opened after having the BaTiO3 crystal under a constant (a) −400 V/mm during the first experimental trial and (b) +400 V/mm during the second experimental trial. The interval between the plotted graph values is of ten data points for each case.

Fig. 9
Fig. 9

Same as Fig. 8 but for a constant (a) −200 V/mm during the first experimental trial and (b) +200 V/mm during the second experimental trial. The interval between the plotted graph values is often data points for each case.

Fig. 10
Fig. 10

Pictures of BaTiO3 crystal’s surface taken with the CCD camera during the first experimental trial; presented in chronological order are the crystal’s images at (a) +600 V/mm, (b) −600 V/mm, and (c) the first few seconds after the electrical circuit was opened.

Fig. 11
Fig. 11

Same as Fig. 10 but for the second experimental trial with images at (a) +600 V/mm, (b) −600 V/mm, and (c) the first few seconds after the electrical circuit was opened.

Fig. 12
Fig. 12

Images (in negative) of the two polarized light distributions on the screen taken with the digital camera during the first experimental trial. Presented in chronological order are the pair of light spots at (a) +600 V/mm, (b) −600 V/mm, and (c) the first few seconds after the electrical circuit was opened.

Fig. 13
Fig. 13

Same as Fig. 12 but for the second experimental trial with the pair of light spots at (a) +600 V/mm, (b) −600 V/mm, (c) first few seconds after the electrical circuit was opened.

Fig. 14
Fig. 14

Magnified picture of the discontinuous intensity regions in Fig. 8(b). This steplike behavior in the intensity patterns is considered by the authors to be an optical analog of the ferroelectric Barkhausen effect.

Tables (2)

Tables Icon

Table 1 Magnitudes of the Time Constants for the Three Types of Transients and the Deduced Values of the Bulk Electrical Conductivity of Tetragonal BaTiO3: Experimental Trial 1

Tables Icon

Table 2 Magnitudes of the Time Constants for the Three Types of Transients and the Deduced Values of the Bulk Electrical Conductivity of Tetragonal BaTiO3: Experimental Trial 2

Equations (39)

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V C ( t ) + i ( t ) R = V ( t ) ,
i ( t ) - V C ( t ) R C - V C ( t ) R a = d Q ( t ) d t ,
Q ( t ) = C V C ( t ) ,
d V C d t + 1 C ( 1 R + 1 R C + 1 R a ) V C = 1 C R V .
V C ( t ) = V C ( t 0 ) exp [ - ( t - t o ) τ ] + 1 R C t 0 t V ( t ) exp [ - ( t - t ) τ ] d t
τ = C 1 / R + 1 / R C + 1 / R a .
V C ( t ) = τ R C V { 1 - exp [ - ( t - t o ) τ ] } .
τ τ e = R C ,
V C ( t ) V { 1 - exp [ - ( t - t o ) τ e ] } ,
V C ( t ) = - τ R C V { 1 - 2 exp [ - ( t - t o ) τ ] } ,
V C ( t ) - V { 1 - 2 exp [ - ( t - t o ) τ s ] } ,
V C ( t ) = - V exp [ - ( t - t o ) τ ] ,
τ = C 1 / R C + 1 / R a
τ τ r = R C C ,
V C ( t ) - V exp [ - ( t - t o ) τ r ] ,
τ r = ρ s ɛ x ɛ 0 .
A y 0 = A z 0 = A 0 .
A y = A 0 exp ( i ϕ y ) ,
A z = A 0 exp ( i ϕ z ) ,
ϕ y = 2 π λ ( n y - 1 ) l x ,
ϕ z = 2 π λ ( n z - 1 ) l x ,
1 n y 2 = 1 n o 2 + R 12 E 1 2 ,
1 n z 2 = 1 n e 2 + R 13 E 1 2 .
n y n o - n o 3 2 R 12 E 1 2 ,
n z n e - n e 3 2 R 13 E 1 2 .
A y = A y cos ( θ ) - A z sin ( θ ) ,
A z = A y sin ( θ ) + A z cos ( θ ) .
I y = I 0 [ 1 - sin ( 2 θ ) cos ( Δ ϕ ) ] ,
I z = I 0 [ 1 + sin ( 2 θ ) cos ( Δ ϕ ) ] .
I 0 = A 0 2 ,
Δ ϕ = 2 π λ ( n z - n y ) l x
Δ ϕ 0 = 2 π λ ( n e - n o ) l x 0 ,
I y 0 = I 0 [ 1 - sin ( 2 θ ) cos ( Δ ϕ 0 ) ] ,
I z 0 = I 0 [ 1 + sin ( 2 θ ) cos ( Δ ϕ 0 ) ] ,
l x = l x 0 ( 1 + s x ) ,
l x l x 0 .
E 1 ( t ) = V C ( t ) l x 0 .
I y r = I y I y 0 = 1 - sin ( 2 θ ) cos ( Δ ϕ ) 1 - sin ( 2 θ ) cos ( Δ ϕ 0 ) ,
I z r = I z I z 0 = 1 + sin ( 2 θ ) cos ( Δ ϕ ) 1 + sin ( 2 θ ) cos ( Δ ϕ 0 ) .

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