Abstract

We report a method for measuring the off-diagonal coefficients of the quadratic electro-optic (Kerr) tensor by using polarized light transmission. The method relies on designing an experimental configuration in which the linear electro-optic (Pockels) effect does not contribute to the data. Our method can be used to obtain off-diagonal Kerr coefficients for all but two of the 20 crystal point groups for which the Pockels effect and the Kerr effect coexist. Our theoretical model includes effects from transmission, multiple reflections, and electrostriction but neglects absorption in the crystal. To verify the method, we used it to measure the R12 and R13 Kerr coefficients for a (100)-type single crystal of ferroelectric barium titanate (BaTiO3) at room temperature (23.5°). To our knowledge, this is the first time this method has been used and the first time these coefficients have been measured for the unclamped crystal in the tetragonal state. The mean values obtained with this method are R12=-3.5±0.3×10-17 m2/V2 and R13=-8.0±0.7×10-17 m2/V2.

© 2005 Optical Society of America

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References

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  1. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, San Diego, 2003).
  2. S. V. Popov, Y. U. Svirko, N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, Bristol, UK, 1995).
  3. A. F. Devonshire, “Theory of barium titanate—part I,” Philos. Mag. 40, 1040–1055 (1949).
  4. A. F. Devonshire, “Theory of barium titanate—part II,” Philos. Mag. 42, 1065–1079 (1951).
  5. A. F. Devonshire, “Theory of ferroelectrics,” Adv. Phys. 3, 85–130 (1954).
    [CrossRef]
  6. A. D. Franklin, “Ferroelectricity of barium titanate single crystals,” Prog. Dielectr. 4, 171–215 (1959).
  7. W. J. Merz, “Ferroelectricity,” Prog. Dielectr. 6, 101–149 (1961).
  8. E. T. Jaynes, Ferroelectricity (Princeton U. Press, Princeton, N.J., 1953).
  9. H. D. Megaw, Ferroelectricity in Crystals (Methuen, London, 1957).
  10. W. Känzig, “Ferroelectrics and antiferroelectrics,” in Vol. 4 of Solid State Physics (Academic, New York, 1957), pp. 1–197.
  11. F. Jona, G. Shirane, Ferroelectric Crystals (Pergamon, New York, 1962; reprint, Dover, New York, 1993).
  12. J. C. Burfoot, Ferroelectrics—An Introduction to the Physical Principles (Van Nostrand, London, 1967).
  13. J. Grindlay, An Introduction to the Phenomenological Theory of Ferroelectricity (Pergamon, Oxford, UK, 1970).
  14. T. Mitsui, I. Tatsuzaki, E. Nakamura, An Introduction to the Physics of Ferroelectrics (Gordon & Breach, New York, 1976).
  15. M. E. Lines, A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Clarendon, Oxford, UK, 1977).
  16. J. C. Burfoot, G. W. Taylor, Polar Dielectrics and Their Applications (Macmillan, London, 1979).
  17. V. M. Fridkin, Photoferroelectrics (Springer-Verlag, New York, 1979).
  18. B. A. Strukov, A. P. Levanyuk, Ferroelectric Phenomena in Crystals (Springer-Verlag, New York, 1998).
  19. D. Mayerhofer, “Transition to the ferroelectric state in barium titanate,” Phys. Rev. 112, 413–423 (1958).
    [CrossRef]
  20. W. Haas, R. Johannes, P. Cholet, “Light beam deflection using the Kerr effect in single crystal prisms of BaTiO3,” Appl. Opt. 3, 988–989 (1964).
    [CrossRef]
  21. V. É. Perfilova, A. S. Sonin, “The electro-optic properties of single crystals of barium titanate,” Sov. Phys. Solid State 8, 82–84 (1966).
  22. A. S. Sonin, V. É. Perfilova, “Electro-optical properties of barium titanate in the paraelectric phase,” Sov. Phys. Crystallogr. 14, 419–420 (1969).
  23. F.-S. Chen, “Modulators for optical communications,” Proc. IEEE 58, 1440–1457 (1970).
    [CrossRef]
  24. K. H. Hellwege, Landolt-Börnstein, New Series III, Vol. 2 (Springer-Verlag, Berlin, 1969).
  25. K. H. Hellwege, Landolt-Börnstein, New Series III, Vol. 16 (Springer-Verlag, Berlin, 1981).
  26. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 2003).
  27. M. J. Weber, Handbook of Optical Materials (CRC Press, Boca Raton, Fla., 2003).
  28. R. L. Sutherland, Handbook of Nonlinear Optics, 2nd ed. (Marcel Dekker, New York, 2003).
  29. J. F. Nye, Physical Properties of Crystals (Oxford U. Press, New York, 2001).
  30. A. R. Johnston, J. M. Weingart, “Determination of the low-frequency linear electro-optic effect in tetragonal BaTiO3,” J. Opt. Soc. Am. 55, 828–834 (1965).
    [CrossRef]
  31. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987).
  32. M. E. Drougard, D. R. Young, “Domain clamping effect in barium titanate single crystals,” Phys. Rev. 94, 1561–1564 (1954).
    [CrossRef]
  33. 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).
  34. E. Burcsu, “Investigations of large strain actuation in barium titanate,” Ph.D. thesis (California Institute of Technology, Pasadena, Calif., 2001), http://etd.caltech.edu/etd/available/etd-10232001-192042/ .
  35. M.T.I. Corporation, www.mticrystal.com .
  36. I. P. Kaminow, An Introduction to Electro-optic Devices (Academic, New York, 1974).
  37. A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, New York, 1997).
  38. R. D. Guenther, Modern Optics (Wiley, New York, 1990).
  39. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
  40. K. Iizuka, Elements of Photonics (Wiley, New York, 2002).
  41. E. Hecht, Optics, 4th ed. (Pearson Addison Wesley, New York, 2001).
  42. M. V. Klein, T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986).
  43. G. Fowles, Introduction to Modern Optics, 2nd ed. (Dover, New York, 1989).
  44. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 2002).
  45. C. C. Davis, Lasers and Electro-Optics (Cambridge U. Press, Cambridge, UK, 1996).
  46. M. V. Klassen-Neklyudova, Mechanical Twinning of Crystals (Consultants Bureau, New York, 1964).
  47. M. Melnichuk, L. T. Wood, “Time-resolved optical transients in tetragonal BaTiO3,” J. Opt. Soc. Am. A (to be published).

1970 (1)

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

1969 (1)

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

1966 (1)

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

1965 (1)

1964 (1)

1961 (1)

W. J. Merz, “Ferroelectricity,” Prog. Dielectr. 6, 101–149 (1961).

1959 (1)

A. D. Franklin, “Ferroelectricity of barium titanate single crystals,” Prog. Dielectr. 4, 171–215 (1959).

1958 (1)

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

1954 (2)

A. F. Devonshire, “Theory of ferroelectrics,” Adv. Phys. 3, 85–130 (1954).
[CrossRef]

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

1951 (1)

A. F. Devonshire, “Theory of barium titanate—part II,” Philos. Mag. 42, 1065–1079 (1951).

1949 (1)

A. F. Devonshire, “Theory of barium titanate—part I,” Philos. Mag. 40, 1040–1055 (1949).

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987).

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).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 2002).

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, San Diego, 2003).

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).

E. Burcsu, “Investigations of large strain actuation in barium titanate,” Ph.D. thesis (California Institute of Technology, Pasadena, Calif., 2001), http://etd.caltech.edu/etd/available/etd-10232001-192042/ .

Burfoot, J. C.

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

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

Chen, F.-S.

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

Cholet, P.

Davis, C. C.

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

Devonshire, A. F.

A. F. Devonshire, “Theory of ferroelectrics,” Adv. Phys. 3, 85–130 (1954).
[CrossRef]

A. F. Devonshire, “Theory of barium titanate—part II,” Philos. Mag. 42, 1065–1079 (1951).

A. F. Devonshire, “Theory of barium titanate—part I,” Philos. Mag. 40, 1040–1055 (1949).

Drougard, M. E.

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

Fowles, G.

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

Franklin, A. D.

A. D. Franklin, “Ferroelectricity of barium titanate single crystals,” Prog. Dielectr. 4, 171–215 (1959).

Fridkin, V. M.

V. M. Fridkin, Photoferroelectrics (Springer-Verlag, New York, 1979).

Furtak, T. E.

M. V. Klein, T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986).

Glass, A. M.

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

Grindlay, J.

J. Grindlay, An Introduction to the Phenomenological Theory of Ferroelectricity (Pergamon, Oxford, UK, 1970).

Guenther, R. D.

R. D. Guenther, Modern Optics (Wiley, New York, 1990).

Haas, W.

Hecht, E.

E. Hecht, Optics, 4th ed. (Pearson Addison Wesley, New York, 2001).

Hellwege, K. H.

K. H. Hellwege, Landolt-Börnstein, New Series III, Vol. 16 (Springer-Verlag, Berlin, 1981).

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

Iizuka, K.

K. Iizuka, Elements of Photonics (Wiley, New York, 2002).

Jaynes, E. T.

E. T. Jaynes, Ferroelectricity (Princeton U. Press, Princeton, N.J., 1953).

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 Electro-optic Devices (Academic, New York, 1974).

Känzig, W.

W. Känzig, “Ferroelectrics and antiferroelectrics,” in Vol. 4 of Solid State Physics (Academic, New York, 1957), pp. 1–197.

Klassen-Neklyudova, M. V.

M. V. Klassen-Neklyudova, Mechanical Twinning of Crystals (Consultants Bureau, New York, 1964).

Klein, M. V.

M. V. Klein, T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986).

Levanyuk, A. P.

B. A. Strukov, A. P. Levanyuk, Ferroelectric Phenomena in Crystals (Springer-Verlag, New York, 1998).

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]

Megaw, H. D.

H. D. Megaw, Ferroelectricity in Crystals (Methuen, London, 1957).

Melnichuk, M.

M. Melnichuk, L. T. Wood, “Time-resolved optical transients in tetragonal BaTiO3,” J. Opt. Soc. Am. A (to be published).

Merz, W. J.

W. J. Merz, “Ferroelectricity,” Prog. Dielectr. 6, 101–149 (1961).

Mitsui, T.

T. Mitsui, I. Tatsuzaki, E. Nakamura, An Introduction to the Physics of Ferroelectrics (Gordon & Breach, New York, 1976).

Nakamura, E.

T. Mitsui, I. Tatsuzaki, E. Nakamura, An Introduction to the Physics of Ferroelectrics (Gordon & Breach, New York, 1976).

Nye, J. F.

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

Perfilova, V. É.

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

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

Popov, S. V.

S. V. Popov, Y. U. Svirko, N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, Bristol, UK, 1995).

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).

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).

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, “Electro-optical properties of barium titanate in the paraelectric phase,” Sov. Phys. Crystallogr. 14, 419–420 (1969).

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

Strukov, B. A.

B. A. Strukov, A. P. Levanyuk, Ferroelectric Phenomena in Crystals (Springer-Verlag, New York, 1998).

Sutherland, R. L.

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

Svirko, Y. U.

S. V. Popov, Y. U. Svirko, N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, Bristol, UK, 1995).

Tatsuzaki, I.

T. Mitsui, I. Tatsuzaki, E. Nakamura, An Introduction to the Physics of Ferroelectrics (Gordon & Breach, New York, 1976).

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, New York, 1991).

Weber, M. J.

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

Weingart, J. M.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 2002).

Wood, L. T.

M. Melnichuk, L. T. Wood, “Time-resolved optical transients in tetragonal BaTiO3,” J. Opt. Soc. Am. A (to be published).

Yariv, A.

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

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 2003).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 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]

Zheludev, N. I.

S. V. Popov, Y. U. Svirko, N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, Bristol, UK, 1995).

Adv. Phys. (1)

A. F. Devonshire, “Theory of ferroelectrics,” Adv. Phys. 3, 85–130 (1954).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Philos. Mag. (2)

A. F. Devonshire, “Theory of barium titanate—part I,” Philos. Mag. 40, 1040–1055 (1949).

A. F. Devonshire, “Theory of barium titanate—part II,” Philos. Mag. 42, 1065–1079 (1951).

Phys. Rev. (2)

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

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

Proc. IEEE (1)

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

Prog. Dielectr. (2)

A. D. Franklin, “Ferroelectricity of barium titanate single crystals,” Prog. Dielectr. 4, 171–215 (1959).

W. J. Merz, “Ferroelectricity,” Prog. Dielectr. 6, 101–149 (1961).

Sov. Phys. Crystallogr. (1)

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

Sov. Phys. Solid State (1)

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

Other (35)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987).

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, San Diego, 2003).

S. V. Popov, Y. U. Svirko, N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, Bristol, UK, 1995).

E. T. Jaynes, Ferroelectricity (Princeton U. Press, Princeton, N.J., 1953).

H. D. Megaw, Ferroelectricity in Crystals (Methuen, London, 1957).

W. Känzig, “Ferroelectrics and antiferroelectrics,” in Vol. 4 of Solid State Physics (Academic, New York, 1957), pp. 1–197.

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

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

J. Grindlay, An Introduction to the Phenomenological Theory of Ferroelectricity (Pergamon, Oxford, UK, 1970).

T. Mitsui, I. Tatsuzaki, E. Nakamura, An Introduction to the Physics of Ferroelectrics (Gordon & Breach, New York, 1976).

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

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

V. M. Fridkin, Photoferroelectrics (Springer-Verlag, New York, 1979).

B. A. Strukov, A. P. Levanyuk, Ferroelectric Phenomena in Crystals (Springer-Verlag, New York, 1998).

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).

E. Burcsu, “Investigations of large strain actuation in barium titanate,” Ph.D. thesis (California Institute of Technology, Pasadena, Calif., 2001), http://etd.caltech.edu/etd/available/etd-10232001-192042/ .

M.T.I. Corporation, www.mticrystal.com .

I. P. Kaminow, An Introduction to Electro-optic Devices (Academic, New York, 1974).

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

R. D. Guenther, Modern Optics (Wiley, New York, 1990).

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).

K. Iizuka, Elements of Photonics (Wiley, New York, 2002).

E. Hecht, Optics, 4th ed. (Pearson Addison Wesley, New York, 2001).

M. V. Klein, T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986).

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

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 2002).

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

M. V. Klassen-Neklyudova, Mechanical Twinning of Crystals (Consultants Bureau, New York, 1964).

M. Melnichuk, L. T. Wood, “Time-resolved optical transients in tetragonal BaTiO3,” J. Opt. Soc. Am. A (to be published).

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

K. H. Hellwege, Landolt-Börnstein, New Series III, Vol. 16 (Springer-Verlag, Berlin, 1981).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 2003).

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

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

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

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Figures (5)

Fig. 1
Fig. 1

Greatly exaggerated schematic of the refraction index ellipses in the xz plane and their corresponding rotation angles for the case with zero, positive, or negative applied electric field. The electric field is parallel to the x axis; the y axis points upward out of the paper. The Kerr effect is not considered. The ellipses associated with the nonzero electric fields and the one corresponding to a zero electric field intersect the original axes in the same points (for individual products rijEj=0, i, j=1, 2, 3); for this experimental configuration the refraction indexes read by the probing light at normal incidence on the BaTiO3 sample do not change because of the Pockels effect when the electric field is applied in either the +x or the -x direction.

Fig. 2
Fig. 2

Simple schematic of our optical amplitude modulation system.

Fig. 3
Fig. 3

Schematic of the experimental setup; the y axis points upward out of the paper. S, screen; R, ruler; DC, digital camera; L1, L2, L3, lenses; BS1, BS2, BS3, beam splitters; D1, D2, D3, light intensity detector; GW, gold wire; PS, power supply; WP, Wollaston prism; C, computer; CCD, camera; IL, incandescent lamp; PO, 45° linear polarizer.

Fig. 4
Fig. 4

Plot of Iy, Iz, and Im versus time for the first experimental trial. The applied electric field (E1) across the BaTiO3 sample was switched in a steplike fashion approximately every 50 s for 500 s. The values of the electric voltage taken in chronological order are 0, +400, -400, 0, +600, -600, 0, +200, -200, 0 V.

Fig. 5
Fig. 5

Plot of Iy, Iz, and Im versus time for the second experimental trial. The applied electric field (E1) across the BaTiO3 sample was switched in a steplike fashion approximately every 50 s for 500 s. The values of the electric voltage taken in chronological order are 0, -400, +400, 0, -600, +600, -600, 0, +200, 0 V. This time the -400 V voltage drop on the sample was kept on for only ∼20 s.

Tables (2)

Tables Icon

Table 1 Orthogonally Polarized Intensities Iyr, Izr and Off-Diagonal Kerr Coefficients R12, R13 for Externally Applied Electric Fields E1, First Experimental Trial

Tables Icon

Table 2 Orthogonally Polarized Intensities Iyr, Izr and Off-Diagonal Kerr Coefficients R12, R13 for Externally Applied Electric Fields E1, Second Experimental Trial

Equations (39)

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

x2n12+y2n22+z2n32=1.
E=E1xˆ+E2yˆ+E3zˆ,
x2n12+y2n22+z2n32+2yzn42+2xzn52+2xyn62=1
x2n12+y2n22+z2n32=1.
tan(2ω4)=2r4jEj(1/n22)-(1/n32),
tan(2ω5)=2r5jEj(1/n12)-(1/n32),
tan(2ω6)=2r6jEj(1/n12)-(1/n22),
(11)1;(22)2;(33)3;(23), (32)4;(13), (31)5;(12), (21)6.
1ni2=1ni2+rijEj+Ri(kl)EkEl,
1n12=1n12+r1jEj+R1(kl)EkEl,
1n22=1n22+r2jEj+R2(kl)EkEl,
1n32=1n32+r3jEj+R3(kl)EkEl.
1/n121/n221/n321/n421/n521/n62=1/no21/no21/ne2000+00r1300r1300r330r510r5100000E1E2E3+R11R12R13000R12R11R13000R13R13R33000000R44000000R44000000R66×E12E22E32E2E3E1E3E1E2.
tan(2ϖ5)=2r51E1(1/no2)-(1/ne2).
Ay0=Az0=A0.
Ay1=tyAy0,
Az1=tzAz0,
ty=(1-ry2)exp(-iφy)1-ry2 exp(-2iφy)=[(1-ry2)2 cos(φy)]-i[(1-ry4)sin(φy)](1+ry4)-2ry2 cos(2φy),
tz=(1-rz2)exp(-iφz)1-rz2 exp(-2iφz)=[(1-rz2)2 cos(φz)]-i[(1-rz4)sin(φz)](1+rz4)-2rz2 cos(2φz).
ry=ny-1ny+1,
rz=nz-1nz+1.
φy=(2π/λ)nylx,
φz=(2π/λ)nzlx,
Ay=Ay1 cos(θ)-Az1 sin(θ),
Az=Az1 cos(θ)+Ay1 sin(θ).
Iy=A02Ty cos2(θ)+Tz sin2(θ)-12Tyz sin(2θ),
Iz=A02Tz cos2(θ)+Ty sin2(θ)+12Tyz sin(2θ),
Ty=|ty|2=(1-ry2)2(1+ry4)-2ry2 cos(2φy),
Tz=|tz|2=(1-rz2)2(1+rz4)-2rz2 cos(2φz),
Tyz=tytz*+ty*tz=2(1-ry2)(1-rz2)[(1+ry2rz2)cos(Δφ)-(ry2+rz2)cos(φy+φz)][(1+ry4)-2ry2 cos(2φy)][(1+rz4)-2rz2 cos(2φz)],
Δφ=φz-φy.
Ty=1(2π)2 02π02πTy(φy)dφydφz=1-ry21+ry2,
Tz=1(2π)2 02π02πTz(φz)dφydφz=1-rz21+rz2,
Tyz=1(2π)2 02π02πTyz(φy, φz)dφydφz=2(1+ry2rz2)cos(Δφ)(1+ry2)(1+rz2).
Iy=A02Tycos2(θ)+Tzsin2(θ)-12Tyzsin(2θ),
Iz=A02Tzcos2(θ)+Tysin2(θ)+12Tyzsin(2θ).
lx=lx0(1+sx),
Iyr=IyIy0=Tycos2(θ)+Tzsin2(θ)-(1/2)Tyzsin(2θ)Ty0 cos2(θ)+Tz0 sin2(θ)-(1/2)T(yz)0 sin(2θ),
Izr=IzIz0=Tzcos2(θ)+Tysin2(θ)+(1/2)Tyzsin(2θ)Tz0 cos2(θ)+Ty0 sin2(θ)+(1/2)T(yz)0 sin(2θ),

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