Abstract

We present a method of determining the distribution of sizes of ferroelectric 180° domains in BaTiO3, using second-harmonic scattering. We find that the domains are rods with approximately square cross sections that extend from the -c to the +c face of the crystal, with widths ranging from 2 to 150 µm.

© 1997 Optical Society of America

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References

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  1. M. DiDomenico and S. H. Wemple, J. Appl. Phys. 40, 720 (1969).
    [CrossRef]
  2. R. C. Miller, Phys. Rev. A 134, 1313 (1964).
    [CrossRef]
  3. M. Horowitz, A. Bekker, and B. Fischer, Appl. Phys. Lett. 62, 2619 (1993).
    [CrossRef]
  4. F. Micheron and G. Bismuth, Appl. Phys. Lett. 20, 79 (1972).
    [CrossRef]
  5. R. S. Cudney, J. Fousek, M. Zgonik, P. Günter, M. H. Garrett, and D. Rytz, Phys. Rev. Lett. 72, 3883 (1994).
    [CrossRef] [PubMed]
  6. R. S. Cudney, P. Bernasconi, J. Fousek, M. Zgonik, and P. Günter, in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper CWA5.
  7. Y. Qiao, S. Orlov, D. Psaltis, and R. R. Neurgaonkar, Opt. Lett. 18, 1004 (1993).
    [CrossRef] [PubMed]
  8. A. Kewitsch, M. Segev, A. Yariv, and R. Neurgaonkar, Opt. Lett. 18, 1262 (1993).
    [CrossRef] [PubMed]
  9. G. Dolino, Phys. Rev. B 6, 4025 (1972).
    [CrossRef]
  10. H. Vogt, H. Happ, and H. G. Häfele, Phys. Status Solidi A 1, 439 (1970).
    [CrossRef]
  11. R. Hellwarth and P. Christensen, Appl. Opt. 14, 247 (1975).
    [CrossRef] [PubMed]
  12. Y. Uesu, S. Kurimura, and Y. Yamamoto, Ferroelectrics 169, 249 (1995).
    [CrossRef]
  13. P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
    [CrossRef]
  14. V. Grubsky, S. MacCormack, and J. Feinberg, Opt. Lett. 21, 6 (1996).
    [CrossRef] [PubMed]

1996 (1)

1995 (1)

Y. Uesu, S. Kurimura, and Y. Yamamoto, Ferroelectrics 169, 249 (1995).
[CrossRef]

1994 (1)

R. S. Cudney, J. Fousek, M. Zgonik, P. Günter, M. H. Garrett, and D. Rytz, Phys. Rev. Lett. 72, 3883 (1994).
[CrossRef] [PubMed]

1993 (3)

1975 (1)

1972 (2)

F. Micheron and G. Bismuth, Appl. Phys. Lett. 20, 79 (1972).
[CrossRef]

G. Dolino, Phys. Rev. B 6, 4025 (1972).
[CrossRef]

1970 (1)

H. Vogt, H. Happ, and H. G. Häfele, Phys. Status Solidi A 1, 439 (1970).
[CrossRef]

1969 (1)

M. DiDomenico and S. H. Wemple, J. Appl. Phys. 40, 720 (1969).
[CrossRef]

1964 (1)

R. C. Miller, Phys. Rev. A 134, 1313 (1964).
[CrossRef]

1962 (1)

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Bekker, A.

M. Horowitz, A. Bekker, and B. Fischer, Appl. Phys. Lett. 62, 2619 (1993).
[CrossRef]

Bernasconi, P.

R. S. Cudney, P. Bernasconi, J. Fousek, M. Zgonik, and P. Günter, in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper CWA5.

Bismuth, G.

F. Micheron and G. Bismuth, Appl. Phys. Lett. 20, 79 (1972).
[CrossRef]

Christensen, P.

Cudney, R. S.

R. S. Cudney, J. Fousek, M. Zgonik, P. Günter, M. H. Garrett, and D. Rytz, Phys. Rev. Lett. 72, 3883 (1994).
[CrossRef] [PubMed]

R. S. Cudney, P. Bernasconi, J. Fousek, M. Zgonik, and P. Günter, in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper CWA5.

DiDomenico, M.

M. DiDomenico and S. H. Wemple, J. Appl. Phys. 40, 720 (1969).
[CrossRef]

Dolino, G.

G. Dolino, Phys. Rev. B 6, 4025 (1972).
[CrossRef]

Feinberg, J.

Fischer, B.

M. Horowitz, A. Bekker, and B. Fischer, Appl. Phys. Lett. 62, 2619 (1993).
[CrossRef]

Fousek, J.

R. S. Cudney, J. Fousek, M. Zgonik, P. Günter, M. H. Garrett, and D. Rytz, Phys. Rev. Lett. 72, 3883 (1994).
[CrossRef] [PubMed]

R. S. Cudney, P. Bernasconi, J. Fousek, M. Zgonik, and P. Günter, in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper CWA5.

Garrett, M. H.

R. S. Cudney, J. Fousek, M. Zgonik, P. Günter, M. H. Garrett, and D. Rytz, Phys. Rev. Lett. 72, 3883 (1994).
[CrossRef] [PubMed]

Grubsky, V.

Günter, P.

R. S. Cudney, J. Fousek, M. Zgonik, P. Günter, M. H. Garrett, and D. Rytz, Phys. Rev. Lett. 72, 3883 (1994).
[CrossRef] [PubMed]

R. S. Cudney, P. Bernasconi, J. Fousek, M. Zgonik, and P. Günter, in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper CWA5.

Häfele, H. G.

H. Vogt, H. Happ, and H. G. Häfele, Phys. Status Solidi A 1, 439 (1970).
[CrossRef]

Happ, H.

H. Vogt, H. Happ, and H. G. Häfele, Phys. Status Solidi A 1, 439 (1970).
[CrossRef]

Hellwarth, R.

Horowitz, M.

M. Horowitz, A. Bekker, and B. Fischer, Appl. Phys. Lett. 62, 2619 (1993).
[CrossRef]

Kewitsch, A.

Kurimura, S.

Y. Uesu, S. Kurimura, and Y. Yamamoto, Ferroelectrics 169, 249 (1995).
[CrossRef]

MacCormack, S.

Maker, P. D.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Micheron, F.

F. Micheron and G. Bismuth, Appl. Phys. Lett. 20, 79 (1972).
[CrossRef]

Miller, R. C.

R. C. Miller, Phys. Rev. A 134, 1313 (1964).
[CrossRef]

Neurgaonkar, R.

Neurgaonkar, R. R.

Nisenoff, M.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Orlov, S.

Psaltis, D.

Qiao, Y.

Rytz, D.

R. S. Cudney, J. Fousek, M. Zgonik, P. Günter, M. H. Garrett, and D. Rytz, Phys. Rev. Lett. 72, 3883 (1994).
[CrossRef] [PubMed]

Savage, C. M.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Segev, M.

Terhune, R. W.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Uesu, Y.

Y. Uesu, S. Kurimura, and Y. Yamamoto, Ferroelectrics 169, 249 (1995).
[CrossRef]

Vogt, H.

H. Vogt, H. Happ, and H. G. Häfele, Phys. Status Solidi A 1, 439 (1970).
[CrossRef]

Wemple, S. H.

M. DiDomenico and S. H. Wemple, J. Appl. Phys. 40, 720 (1969).
[CrossRef]

Yamamoto, Y.

Y. Uesu, S. Kurimura, and Y. Yamamoto, Ferroelectrics 169, 249 (1995).
[CrossRef]

Yariv, A.

Zgonik, M.

R. S. Cudney, J. Fousek, M. Zgonik, P. Günter, M. H. Garrett, and D. Rytz, Phys. Rev. Lett. 72, 3883 (1994).
[CrossRef] [PubMed]

R. S. Cudney, P. Bernasconi, J. Fousek, M. Zgonik, and P. Günter, in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper CWA5.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

M. Horowitz, A. Bekker, and B. Fischer, Appl. Phys. Lett. 62, 2619 (1993).
[CrossRef]

F. Micheron and G. Bismuth, Appl. Phys. Lett. 20, 79 (1972).
[CrossRef]

Ferroelectrics (1)

Y. Uesu, S. Kurimura, and Y. Yamamoto, Ferroelectrics 169, 249 (1995).
[CrossRef]

J. Appl. Phys. (1)

M. DiDomenico and S. H. Wemple, J. Appl. Phys. 40, 720 (1969).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

R. C. Miller, Phys. Rev. A 134, 1313 (1964).
[CrossRef]

Phys. Rev. B (1)

G. Dolino, Phys. Rev. B 6, 4025 (1972).
[CrossRef]

Phys. Rev. Lett. (2)

R. S. Cudney, J. Fousek, M. Zgonik, P. Günter, M. H. Garrett, and D. Rytz, Phys. Rev. Lett. 72, 3883 (1994).
[CrossRef] [PubMed]

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Phys. Status Solidi A (1)

H. Vogt, H. Happ, and H. G. Häfele, Phys. Status Solidi A 1, 439 (1970).
[CrossRef]

Other (1)

R. S. Cudney, P. Bernasconi, J. Fousek, M. Zgonik, and P. Günter, in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper CWA5.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: f=100 mm, pulse intensity 3 MW/cm2, crystal dimensions 2.45 mm×5.1 mm×4.8 mm.

Fig. 2
Fig. 2

Far-field second-harmonic scattering patterns: a) single-domain crystal, b) same sample depoled by 40%.

Fig. 3
Fig. 3

Second-harmonic intensity and theoretical best fit versus scattering angle. The same scale is used for both curves. Parameters used in the theoretical fit: n2ω=2.414, nω=2.350. A least-squares fit was performed with the Levenberg–Marquardt algorithm.

Fig. 4
Fig. 4

Number of domains versus domain width.

Equations (11)

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

2ik2ω·Ei2ω,q=-ω2c2χijk2rEjωEkω×expiq·r,
Ei2ω,q=AiV2ηr-1expiq·rdr,
Ai=iωncχijk2EjωEkω,
ηr=1in+domains0in-domains.
I2ωbulkq=A2Lx2Ly2Lz2 sinc2qxLx2π×sinc2qyLy2πsinc2qzLz2π,
qy=2ωcsin θy,
Ei2ω,q=AiLz sincqzLz2π2j=1Naj2×sincqxaj2πsincqyaj2πexpiϕj-LxLy sincqxLx2πsincqyLy2π,
I2ωtotalq=I2ωbulkq+I2ωdomainsq,
I2ωdomainsq=4A2Lz2 sinc2qzLz2π×igaiai4sinc2qxai2πsinc2qyai2π.
ΔVV=ΔQ2PSA,
igaiai2=ΔQ2PS.

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