Abstract

The development of a spatial subharmonic, i.e., of a light wave propagating at the bisector of two pump waves, with orthogonal polarizations incident upon a BaTiO3 crystal in a plane normal to the optical axis is observed and studied. Parametric amplification of a seed wave meeting the phase-matching condition in the presence of two pump waves is shown to be the main reason for subharmonic generation in this crystal.

© 1991 Optical Society of America

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  1. S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).
    [CrossRef]
  2. K. Ringhofer, L. Solymar, Appl. Phys. Lett. 53, 1939 (1988)
    [CrossRef]
  3. K. Ringhofer, L. Solymar, Appl. Phys. B 48, 395 (1989).
    [CrossRef]
  4. L. B. Au, K. Ringhofer, L. Solymar, presented at the OSA Topical Meeting on Photorefractive Materials, Effects, and Devices II, Aussois, France, 1990.
  5. A. Novikov, S. Odoulov, Ukrainian Phys. J. 35, 1657 (1987).
  6. O. P. Nestiorkin, Opt. Commun. 81, 315 (1991).
    [CrossRef]
  7. A. Blenowski, B. Sturman, J. Otten, K. Ringhofer, in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991).
  8. D. C. Jones, L. Solymar, Appl. Phys. B 50, 355 (1990).
    [CrossRef]
  9. D. L. Webb, L. Solymar, Opt. Commun. 74, 386 (1990).
    [CrossRef]
  10. D. L. Webb, I. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).
    [CrossRef]
  11. S. Lyuksyutov, M. Vasnetsov, L. Solymar, Opt. Commun. 80, 385 (1991).
    [CrossRef]
  12. R. Rupp, F. Drees, Appl. Phys. B 39, 223 (1986).
    [CrossRef]
  13. D. Temple, C. Warde, J. Opt. Soc. Am. B 3, 337 (1986).
    [CrossRef]
  14. M. Ewbank, P. Yeh, J. Feinberg, Opt. Commun. 59, 423 (1986).
    [CrossRef]
  15. S. Odoulov, B. Sturman, L. Holtmann, E. Kraetzig, Appl. Phys. B 52, 317 (1991).
    [CrossRef]
  16. N. Kukhtarev, E. Kratzig, H. C. Kulich, R. A. Rupp, J. Albers, Appl. Phys. B 35, 17 (1984).
    [CrossRef]
  17. D. J. Webb, K. H. Ringhofer, L. Solymar, Electron. Lett. 27, 889 (1991).
    [CrossRef]
  18. D. R. Erbschloe, L. Solymar, Appl. Phys. Lett. 53, 1135 (1988).
    [CrossRef]
  19. D. L. Staebler, J. J. Amodei, J. Appl. Phys. 43, 1042 (1972).
    [CrossRef]

1991 (4)

O. P. Nestiorkin, Opt. Commun. 81, 315 (1991).
[CrossRef]

S. Lyuksyutov, M. Vasnetsov, L. Solymar, Opt. Commun. 80, 385 (1991).
[CrossRef]

S. Odoulov, B. Sturman, L. Holtmann, E. Kraetzig, Appl. Phys. B 52, 317 (1991).
[CrossRef]

D. J. Webb, K. H. Ringhofer, L. Solymar, Electron. Lett. 27, 889 (1991).
[CrossRef]

1990 (3)

D. C. Jones, L. Solymar, Appl. Phys. B 50, 355 (1990).
[CrossRef]

D. L. Webb, L. Solymar, Opt. Commun. 74, 386 (1990).
[CrossRef]

D. L. Webb, I. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).
[CrossRef]

1989 (1)

K. Ringhofer, L. Solymar, Appl. Phys. B 48, 395 (1989).
[CrossRef]

1988 (3)

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).
[CrossRef]

K. Ringhofer, L. Solymar, Appl. Phys. Lett. 53, 1939 (1988)
[CrossRef]

D. R. Erbschloe, L. Solymar, Appl. Phys. Lett. 53, 1135 (1988).
[CrossRef]

1987 (1)

A. Novikov, S. Odoulov, Ukrainian Phys. J. 35, 1657 (1987).

1986 (3)

D. Temple, C. Warde, J. Opt. Soc. Am. B 3, 337 (1986).
[CrossRef]

R. Rupp, F. Drees, Appl. Phys. B 39, 223 (1986).
[CrossRef]

M. Ewbank, P. Yeh, J. Feinberg, Opt. Commun. 59, 423 (1986).
[CrossRef]

1984 (1)

N. Kukhtarev, E. Kratzig, H. C. Kulich, R. A. Rupp, J. Albers, Appl. Phys. B 35, 17 (1984).
[CrossRef]

1972 (1)

D. L. Staebler, J. J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Albers, J.

N. Kukhtarev, E. Kratzig, H. C. Kulich, R. A. Rupp, J. Albers, Appl. Phys. B 35, 17 (1984).
[CrossRef]

Amodei, J. J.

D. L. Staebler, J. J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Au, I. B.

D. L. Webb, I. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).
[CrossRef]

Au, L. B.

L. B. Au, K. Ringhofer, L. Solymar, presented at the OSA Topical Meeting on Photorefractive Materials, Effects, and Devices II, Aussois, France, 1990.

Blenowski, A.

A. Blenowski, B. Sturman, J. Otten, K. Ringhofer, in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991).

Drees, F.

R. Rupp, F. Drees, Appl. Phys. B 39, 223 (1986).
[CrossRef]

Ducollet, H.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).
[CrossRef]

Erbschloe, D. R.

D. R. Erbschloe, L. Solymar, Appl. Phys. Lett. 53, 1135 (1988).
[CrossRef]

Ewbank, M.

M. Ewbank, P. Yeh, J. Feinberg, Opt. Commun. 59, 423 (1986).
[CrossRef]

Feinberg, J.

M. Ewbank, P. Yeh, J. Feinberg, Opt. Commun. 59, 423 (1986).
[CrossRef]

Herriau, J. P.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).
[CrossRef]

Holtmann, L.

S. Odoulov, B. Sturman, L. Holtmann, E. Kraetzig, Appl. Phys. B 52, 317 (1991).
[CrossRef]

Huignard, J. P.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).
[CrossRef]

Imbert, B.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).
[CrossRef]

Jones, D. C.

D. L. Webb, I. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).
[CrossRef]

D. C. Jones, L. Solymar, Appl. Phys. B 50, 355 (1990).
[CrossRef]

Kraetzig, E.

S. Odoulov, B. Sturman, L. Holtmann, E. Kraetzig, Appl. Phys. B 52, 317 (1991).
[CrossRef]

Kratzig, E.

N. Kukhtarev, E. Kratzig, H. C. Kulich, R. A. Rupp, J. Albers, Appl. Phys. B 35, 17 (1984).
[CrossRef]

Kukhtarev, N.

N. Kukhtarev, E. Kratzig, H. C. Kulich, R. A. Rupp, J. Albers, Appl. Phys. B 35, 17 (1984).
[CrossRef]

Kulich, H. C.

N. Kukhtarev, E. Kratzig, H. C. Kulich, R. A. Rupp, J. Albers, Appl. Phys. B 35, 17 (1984).
[CrossRef]

Lyuksyutov, S.

S. Lyuksyutov, M. Vasnetsov, L. Solymar, Opt. Commun. 80, 385 (1991).
[CrossRef]

Mallick, S.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).
[CrossRef]

Nestiorkin, O. P.

O. P. Nestiorkin, Opt. Commun. 81, 315 (1991).
[CrossRef]

Novikov, A.

A. Novikov, S. Odoulov, Ukrainian Phys. J. 35, 1657 (1987).

Odoulov, S.

S. Odoulov, B. Sturman, L. Holtmann, E. Kraetzig, Appl. Phys. B 52, 317 (1991).
[CrossRef]

A. Novikov, S. Odoulov, Ukrainian Phys. J. 35, 1657 (1987).

Otten, J.

A. Blenowski, B. Sturman, J. Otten, K. Ringhofer, in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991).

Ringhofer, K.

K. Ringhofer, L. Solymar, Appl. Phys. B 48, 395 (1989).
[CrossRef]

K. Ringhofer, L. Solymar, Appl. Phys. Lett. 53, 1939 (1988)
[CrossRef]

A. Blenowski, B. Sturman, J. Otten, K. Ringhofer, in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991).

L. B. Au, K. Ringhofer, L. Solymar, presented at the OSA Topical Meeting on Photorefractive Materials, Effects, and Devices II, Aussois, France, 1990.

Ringhofer, K. H.

D. J. Webb, K. H. Ringhofer, L. Solymar, Electron. Lett. 27, 889 (1991).
[CrossRef]

Rupp, R.

R. Rupp, F. Drees, Appl. Phys. B 39, 223 (1986).
[CrossRef]

Rupp, R. A.

N. Kukhtarev, E. Kratzig, H. C. Kulich, R. A. Rupp, J. Albers, Appl. Phys. B 35, 17 (1984).
[CrossRef]

Solymar, L.

D. J. Webb, K. H. Ringhofer, L. Solymar, Electron. Lett. 27, 889 (1991).
[CrossRef]

S. Lyuksyutov, M. Vasnetsov, L. Solymar, Opt. Commun. 80, 385 (1991).
[CrossRef]

D. C. Jones, L. Solymar, Appl. Phys. B 50, 355 (1990).
[CrossRef]

D. L. Webb, I. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).
[CrossRef]

D. L. Webb, L. Solymar, Opt. Commun. 74, 386 (1990).
[CrossRef]

K. Ringhofer, L. Solymar, Appl. Phys. B 48, 395 (1989).
[CrossRef]

D. R. Erbschloe, L. Solymar, Appl. Phys. Lett. 53, 1135 (1988).
[CrossRef]

K. Ringhofer, L. Solymar, Appl. Phys. Lett. 53, 1939 (1988)
[CrossRef]

L. B. Au, K. Ringhofer, L. Solymar, presented at the OSA Topical Meeting on Photorefractive Materials, Effects, and Devices II, Aussois, France, 1990.

Staebler, D. L.

D. L. Staebler, J. J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Sturman, B.

S. Odoulov, B. Sturman, L. Holtmann, E. Kraetzig, Appl. Phys. B 52, 317 (1991).
[CrossRef]

A. Blenowski, B. Sturman, J. Otten, K. Ringhofer, in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991).

Temple, D.

Vasnetsov, M.

S. Lyuksyutov, M. Vasnetsov, L. Solymar, Opt. Commun. 80, 385 (1991).
[CrossRef]

Warde, C.

Webb, D. J.

D. J. Webb, K. H. Ringhofer, L. Solymar, Electron. Lett. 27, 889 (1991).
[CrossRef]

Webb, D. L.

D. L. Webb, I. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).
[CrossRef]

D. L. Webb, L. Solymar, Opt. Commun. 74, 386 (1990).
[CrossRef]

Yeh, P.

M. Ewbank, P. Yeh, J. Feinberg, Opt. Commun. 59, 423 (1986).
[CrossRef]

Appl. Phys. B (5)

K. Ringhofer, L. Solymar, Appl. Phys. B 48, 395 (1989).
[CrossRef]

D. C. Jones, L. Solymar, Appl. Phys. B 50, 355 (1990).
[CrossRef]

R. Rupp, F. Drees, Appl. Phys. B 39, 223 (1986).
[CrossRef]

S. Odoulov, B. Sturman, L. Holtmann, E. Kraetzig, Appl. Phys. B 52, 317 (1991).
[CrossRef]

N. Kukhtarev, E. Kratzig, H. C. Kulich, R. A. Rupp, J. Albers, Appl. Phys. B 35, 17 (1984).
[CrossRef]

Appl. Phys. Lett. (3)

D. R. Erbschloe, L. Solymar, Appl. Phys. Lett. 53, 1135 (1988).
[CrossRef]

D. L. Webb, I. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).
[CrossRef]

K. Ringhofer, L. Solymar, Appl. Phys. Lett. 53, 1939 (1988)
[CrossRef]

Electron. Lett. (1)

D. J. Webb, K. H. Ringhofer, L. Solymar, Electron. Lett. 27, 889 (1991).
[CrossRef]

J. Appl. Phys. (2)

D. L. Staebler, J. J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).
[CrossRef]

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

Opt. Commun. (4)

S. Lyuksyutov, M. Vasnetsov, L. Solymar, Opt. Commun. 80, 385 (1991).
[CrossRef]

M. Ewbank, P. Yeh, J. Feinberg, Opt. Commun. 59, 423 (1986).
[CrossRef]

D. L. Webb, L. Solymar, Opt. Commun. 74, 386 (1990).
[CrossRef]

O. P. Nestiorkin, Opt. Commun. 81, 315 (1991).
[CrossRef]

Ukrainian Phys. J. (1)

A. Novikov, S. Odoulov, Ukrainian Phys. J. 35, 1657 (1987).

Other (2)

A. Blenowski, B. Sturman, J. Otten, K. Ringhofer, in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991).

L. B. Au, K. Ringhofer, L. Solymar, presented at the OSA Topical Meeting on Photorefractive Materials, Effects, and Devices II, Aussois, France, 1990.

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Figures (5)

Fig. 1
Fig. 1

Wave-vector diagram for nonlinear mixing of copropagating orthogonally polarized eigenwaves of the crystal.

Fig. 2
Fig. 2

Far-field patterns of output intensity for (a) exact subharmonic phase matching (θ = 23°) and slightly above critical angle, (b) θ = 25°, (c) θ = 27°. There is no external seed beam.

Fig. 3
Fig. 3

Apex angle of the cone of scattered waves 0s as a function of pump intersection angle θ. The solid curve represents the dependence calculated from Eq. (5).

Fig. 4
Fig. 4

Temporal dependence of intensity for the signal beam (seed beam) transmitted through the sample in the direction of the first subharmonic.

Fig. 5
Fig. 5

Gain factor Γ versus pump intensity ratio r. The solid curve is the dependence calculated from Eq. (7).

Equations (9)

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k p o + k p e - 2 k sh = 0 ,
θ = sin - 1 [ n o ( n o - n e ) ] 1 / 2 = 23 ° ,
k s o = 2 k p e - k sh ,
k p e + k p o = k s 1 e + K s 2 e .
4 sin 2 θ s = [ ( n o 2 - sin 2 θ ) 1 / 2 + ( n e 2 - sin 2 θ ) 1 / 2 ] 2 - 4 n e 2 .
d A p o / d x = - f ( A sh ) 2 ( A p e ) * , d A sh / d x = - f A p o A p e ( A sh ) * , d A p e / d x = f A s o A sh ( A p e ) * , d A s o / d x = f ( A p e ) 2 ( A sh ) * .
A sh ( x ) 2 = A sh ( 0 ) 2 sin ( ϕ / 2 ) exp [ ± 2 f x ( A p o A p e 2 ) 1 / 2 ] ,
ϕ = 2 ϕ sh - ϕ p o - ϕ p e .
Γ = ( 1 / x ) ln [ I sh ( ) / I sh ( 0 ) ] ,

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