Abstract

We present the formalism for the calculation of all second- and third-order nonlinear susceptibility coefficients based on the Landau–Devonshire free-energy expansion for cubic symmetry in the high-temperature paraelectric phase and the Landau–Khalatnikov dynamical equations. Second-order phase transition and single-frequency input waves are considered. Detailed results are given for all nonvanishing tensor elements of the second- and third-order nonlinear optical effects in the paraelectric and the tetragonal and rhombohedral ferroelectric phases.

© 2002 Optical Society of America

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  1. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1986).
  2. M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Clarendon, Oxford, UK, 1977).
  3. Y. Ishibashi and H. Orihara, “A phenomenological theory of nonlinear dielectric response,” Ferroelectrics 156, 185–188 (1994).
  4. J. Osman, Y. Ishibashi, S.-C. Lim, and D. R. Tilley, “Nonlinear optic coefficients in the ferroelectric phase,” J. Korean Phys. Soc. 32, S446–S449 (1998).
  5. C. Haas, “Phase transitions in ferroelectric and antiferroelectric crytals,” Phys. Rev. 140, A863–A868 (1965).
  6. J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).
  7. J. Grindlay, An Introduction to the Phenomenological Theory of Ferroelectricity (Pergamon, New York, 1970).
  8. A. F. Devonshire, “Theory of barium titanate (Part 1),” Philos. Mag. 40, 1040–1063 (1949).
  9. K. Fujita and Y. Ishibashi, “Roles of the higher order aniso-tropic terms in successive structural phase transitions: The method of determination of phenomenological parameters,” Jpn. J. Appl. Phys., 36, 254–259 (1997).
  10. Y. Ishibashi and M. Iwata, “Morphotropic phase boundary in solid solution systems of perovskite-type oxide ferroelectrics,” Jpn. J. Appl. Phys. 37, L985–L987 (1998).
  11. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, Cambridge, UK 1990).
  12. H. Orihara and Y. Ishibashi, “A phenomenological theory of nonlinear dielectric response II. Miller’s rule and nonlinear response in nonferroelectrics,” J. Phys. Soc. Jpn. 66, 242–246 (1997).
  13. S. V. Popov, Yu. P. Svirko, and N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, London, 1995).
  14. Y. G. Wang, W. L. Zhong, and P. L. Zhang, “Size effects onthe Curie temperature of ferroelectric particles,” Solid State Commun. 92, 519–523 (1994).
  15. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  16. D. L. Mills, Nonlinear Optics (Springer-Verlag, Berlin, 1991).
  17. Y. Ishibashi and M. Iwata, “A theory of morphotropic phase boundary in solid-solution systems of perovskite-type oxide ferroelectrics,” Jpn. J. Appl. Phys. 38, 800–804 (1999).
  18. M. Iwata and Y. Ishibashi, “Theory of morphotropic phase boundary in solid solution systems of perovskite-type oxide ferroelectrics: engineered domain configurations,” Jpn. J. Appl. Phys. 39, 5156–5163 (2000).
  19. L. Gag, J. Osman, and D. R. Tilley, “Effective-medium theory of dielectric-constant anomalies in ferroelectric composites,” Ferroelectrics 255, 59–72 (2001).
  20. E. Fatuzzo and W. J. Merz, Ferroelectricity (North-Holland, Amsterdam, 1967).

2001 (1)

L. Gag, J. Osman, and D. R. Tilley, “Effective-medium theory of dielectric-constant anomalies in ferroelectric composites,” Ferroelectrics 255, 59–72 (2001).

2000 (1)

M. Iwata and Y. Ishibashi, “Theory of morphotropic phase boundary in solid solution systems of perovskite-type oxide ferroelectrics: engineered domain configurations,” Jpn. J. Appl. Phys. 39, 5156–5163 (2000).

1999 (1)

Y. Ishibashi and M. Iwata, “A theory of morphotropic phase boundary in solid-solution systems of perovskite-type oxide ferroelectrics,” Jpn. J. Appl. Phys. 38, 800–804 (1999).

1998 (3)

J. Osman, Y. Ishibashi, S.-C. Lim, and D. R. Tilley, “Nonlinear optic coefficients in the ferroelectric phase,” J. Korean Phys. Soc. 32, S446–S449 (1998).

J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).

Y. Ishibashi and M. Iwata, “Morphotropic phase boundary in solid solution systems of perovskite-type oxide ferroelectrics,” Jpn. J. Appl. Phys. 37, L985–L987 (1998).

1997 (2)

H. Orihara and Y. Ishibashi, “A phenomenological theory of nonlinear dielectric response II. Miller’s rule and nonlinear response in nonferroelectrics,” J. Phys. Soc. Jpn. 66, 242–246 (1997).

K. Fujita and Y. Ishibashi, “Roles of the higher order aniso-tropic terms in successive structural phase transitions: The method of determination of phenomenological parameters,” Jpn. J. Appl. Phys., 36, 254–259 (1997).

1994 (2)

Y. Ishibashi and H. Orihara, “A phenomenological theory of nonlinear dielectric response,” Ferroelectrics 156, 185–188 (1994).

Y. G. Wang, W. L. Zhong, and P. L. Zhang, “Size effects onthe Curie temperature of ferroelectric particles,” Solid State Commun. 92, 519–523 (1994).

1965 (1)

C. Haas, “Phase transitions in ferroelectric and antiferroelectric crytals,” Phys. Rev. 140, A863–A868 (1965).

1949 (1)

A. F. Devonshire, “Theory of barium titanate (Part 1),” Philos. Mag. 40, 1040–1063 (1949).

Devonshire, A. F.

A. F. Devonshire, “Theory of barium titanate (Part 1),” Philos. Mag. 40, 1040–1063 (1949).

Fujita, K.

K. Fujita and Y. Ishibashi, “Roles of the higher order aniso-tropic terms in successive structural phase transitions: The method of determination of phenomenological parameters,” Jpn. J. Appl. Phys., 36, 254–259 (1997).

Gag, L.

L. Gag, J. Osman, and D. R. Tilley, “Effective-medium theory of dielectric-constant anomalies in ferroelectric composites,” Ferroelectrics 255, 59–72 (2001).

Haas, C.

C. Haas, “Phase transitions in ferroelectric and antiferroelectric crytals,” Phys. Rev. 140, A863–A868 (1965).

Ishibashi, Y.

M. Iwata and Y. Ishibashi, “Theory of morphotropic phase boundary in solid solution systems of perovskite-type oxide ferroelectrics: engineered domain configurations,” Jpn. J. Appl. Phys. 39, 5156–5163 (2000).

Y. Ishibashi and M. Iwata, “A theory of morphotropic phase boundary in solid-solution systems of perovskite-type oxide ferroelectrics,” Jpn. J. Appl. Phys. 38, 800–804 (1999).

Y. Ishibashi and M. Iwata, “Morphotropic phase boundary in solid solution systems of perovskite-type oxide ferroelectrics,” Jpn. J. Appl. Phys. 37, L985–L987 (1998).

J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).

J. Osman, Y. Ishibashi, S.-C. Lim, and D. R. Tilley, “Nonlinear optic coefficients in the ferroelectric phase,” J. Korean Phys. Soc. 32, S446–S449 (1998).

K. Fujita and Y. Ishibashi, “Roles of the higher order aniso-tropic terms in successive structural phase transitions: The method of determination of phenomenological parameters,” Jpn. J. Appl. Phys., 36, 254–259 (1997).

H. Orihara and Y. Ishibashi, “A phenomenological theory of nonlinear dielectric response II. Miller’s rule and nonlinear response in nonferroelectrics,” J. Phys. Soc. Jpn. 66, 242–246 (1997).

Y. Ishibashi and H. Orihara, “A phenomenological theory of nonlinear dielectric response,” Ferroelectrics 156, 185–188 (1994).

Iwata, M.

M. Iwata and Y. Ishibashi, “Theory of morphotropic phase boundary in solid solution systems of perovskite-type oxide ferroelectrics: engineered domain configurations,” Jpn. J. Appl. Phys. 39, 5156–5163 (2000).

Y. Ishibashi and M. Iwata, “A theory of morphotropic phase boundary in solid-solution systems of perovskite-type oxide ferroelectrics,” Jpn. J. Appl. Phys. 38, 800–804 (1999).

Y. Ishibashi and M. Iwata, “Morphotropic phase boundary in solid solution systems of perovskite-type oxide ferroelectrics,” Jpn. J. Appl. Phys. 37, L985–L987 (1998).

Lim, S.-C.

J. Osman, Y. Ishibashi, S.-C. Lim, and D. R. Tilley, “Nonlinear optic coefficients in the ferroelectric phase,” J. Korean Phys. Soc. 32, S446–S449 (1998).

Orihara, H.

H. Orihara and Y. Ishibashi, “A phenomenological theory of nonlinear dielectric response II. Miller’s rule and nonlinear response in nonferroelectrics,” J. Phys. Soc. Jpn. 66, 242–246 (1997).

Y. Ishibashi and H. Orihara, “A phenomenological theory of nonlinear dielectric response,” Ferroelectrics 156, 185–188 (1994).

Osman, J.

L. Gag, J. Osman, and D. R. Tilley, “Effective-medium theory of dielectric-constant anomalies in ferroelectric composites,” Ferroelectrics 255, 59–72 (2001).

J. Osman, Y. Ishibashi, S.-C. Lim, and D. R. Tilley, “Nonlinear optic coefficients in the ferroelectric phase,” J. Korean Phys. Soc. 32, S446–S449 (1998).

J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).

Tilley, D. R.

L. Gag, J. Osman, and D. R. Tilley, “Effective-medium theory of dielectric-constant anomalies in ferroelectric composites,” Ferroelectrics 255, 59–72 (2001).

J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).

J. Osman, Y. Ishibashi, S.-C. Lim, and D. R. Tilley, “Nonlinear optic coefficients in the ferroelectric phase,” J. Korean Phys. Soc. 32, S446–S449 (1998).

Wang, Y. G.

Y. G. Wang, W. L. Zhong, and P. L. Zhang, “Size effects onthe Curie temperature of ferroelectric particles,” Solid State Commun. 92, 519–523 (1994).

Zhang, P. L.

Y. G. Wang, W. L. Zhong, and P. L. Zhang, “Size effects onthe Curie temperature of ferroelectric particles,” Solid State Commun. 92, 519–523 (1994).

Zhong, W. L.

Y. G. Wang, W. L. Zhong, and P. L. Zhang, “Size effects onthe Curie temperature of ferroelectric particles,” Solid State Commun. 92, 519–523 (1994).

Ferroelectrics (2)

Y. Ishibashi and H. Orihara, “A phenomenological theory of nonlinear dielectric response,” Ferroelectrics 156, 185–188 (1994).

L. Gag, J. Osman, and D. R. Tilley, “Effective-medium theory of dielectric-constant anomalies in ferroelectric composites,” Ferroelectrics 255, 59–72 (2001).

J. Korean Phys. Soc. (1)

J. Osman, Y. Ishibashi, S.-C. Lim, and D. R. Tilley, “Nonlinear optic coefficients in the ferroelectric phase,” J. Korean Phys. Soc. 32, S446–S449 (1998).

J. Phys. Soc. Jpn. (1)

H. Orihara and Y. Ishibashi, “A phenomenological theory of nonlinear dielectric response II. Miller’s rule and nonlinear response in nonferroelectrics,” J. Phys. Soc. Jpn. 66, 242–246 (1997).

Jpn. J. Appl. Phys. (5)

Y. Ishibashi and M. Iwata, “A theory of morphotropic phase boundary in solid-solution systems of perovskite-type oxide ferroelectrics,” Jpn. J. Appl. Phys. 38, 800–804 (1999).

M. Iwata and Y. Ishibashi, “Theory of morphotropic phase boundary in solid solution systems of perovskite-type oxide ferroelectrics: engineered domain configurations,” Jpn. J. Appl. Phys. 39, 5156–5163 (2000).

J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).

K. Fujita and Y. Ishibashi, “Roles of the higher order aniso-tropic terms in successive structural phase transitions: The method of determination of phenomenological parameters,” Jpn. J. Appl. Phys., 36, 254–259 (1997).

Y. Ishibashi and M. Iwata, “Morphotropic phase boundary in solid solution systems of perovskite-type oxide ferroelectrics,” Jpn. J. Appl. Phys. 37, L985–L987 (1998).

Philos. Mag. (1)

A. F. Devonshire, “Theory of barium titanate (Part 1),” Philos. Mag. 40, 1040–1063 (1949).

Phys. Rev. (1)

C. Haas, “Phase transitions in ferroelectric and antiferroelectric crytals,” Phys. Rev. 140, A863–A868 (1965).

Solid State Commun. (1)

Y. G. Wang, W. L. Zhong, and P. L. Zhang, “Size effects onthe Curie temperature of ferroelectric particles,” Solid State Commun. 92, 519–523 (1994).

Other (8)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

D. L. Mills, Nonlinear Optics (Springer-Verlag, Berlin, 1991).

S. V. Popov, Yu. P. Svirko, and N. I. Zheludev, Susceptibility Tensors for Nonlinear Optics (Institute of Physics, London, 1995).

E. Fatuzzo and W. J. Merz, Ferroelectricity (North-Holland, Amsterdam, 1967).

C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1986).

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

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, Cambridge, UK 1990).

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

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