Abstract

Frequency shifts and dynamic instabilities in photorefractive cat self-pumped phase conjugators and bridge mutually pumped phase conjugators are studied by use of a two-dimensional model. Intrinsic electric fields inside the crystals induce the frequency shifts and dynamic instabilities observed in these experiments. In cat mirrors, for small values of the electric field the phase-conjugate reflectivity and the frequency shift are constant. With a further increase in the electric field the reflectivity and the frequency shift become periodic through Hopf bifurcation. For a large value of the electric field both the reflectivity and the frequency shift fluctuate chaotically. In bridge mirrors, for small values of the electric field the phase-conjugate reflectivity is stable, and no frequency shift exists. With a further increase in the electric field the reflectivity and the frequency shift become periodically oscillating in time. For a large value of the electric field both the reflectivity and the frequency shift fluctuate chaotically. The phase-conjugate outputs of the two beams oscillate in an almost synchronous manner.

© 1999 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  28. A nonuniform internal electric field E0 that result from nonuniform intensity distributions throughout the crystal volume will give similar qualitative results.
  29. For E0 taken along the other direction the phase conjugator shows similar qualitative output behavior.
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    [CrossRef]

1997 (3)

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 55, 3092 (1997).
[CrossRef]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 56, 936 (1997).
[CrossRef]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, J. Opt. Soc. Am. B 14, 852 (1997).
[CrossRef]

1995 (2)

A. A. Zozulya, M. Saffman, and D. Z. Anderson, J. Opt. Soc. Am. B 12, 225 (1995).
[CrossRef]

A. A. Zozulya, G. Montemezzani, and D. Z. Anderson, Phys. Rev. A 52, 4167 (1995).
[CrossRef] [PubMed]

1994 (1)

1992 (1)

T. Rauch, C. Denz, and T. Tschudi, Opt. Commun. 88, 160 (1992).
[CrossRef]

1990 (3)

1988 (1)

1987 (2)

D. J. Gauthier, P. Narum, and R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[CrossRef] [PubMed]

S. Weiss, S. Sternklar, and B. Fischer, Opt. Lett. 12, 114 (1987).
[CrossRef] [PubMed]

1986 (3)

1985 (4)

P. Gunter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

J. F. Lam, Appl. Phys. Lett. 46, 909 (1985).
[CrossRef]

T. Y. Chang and R. W. Hellwarth, Opt. Lett. 10, 408 (1985).
[CrossRef] [PubMed]

M. D. Ewbank and P. Yeh, Opt. Lett. 10, 496 (1985).
[CrossRef] [PubMed]

1984 (3)

1983 (1)

1982 (1)

Albers, J.

P. Gunter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

Anderson, D. Z.

A. A. Zozulya, M. Saffman, and D. Z. Anderson, J. Opt. Soc. Am. B 12, 225 (1995).
[CrossRef]

A. A. Zozulya, G. Montemezzani, and D. Z. Anderson, Phys. Rev. A 52, 4167 (1995).
[CrossRef] [PubMed]

Bacher, G. D.

Boyd, R. W.

D. J. Gauthier, P. Narum, and R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[CrossRef] [PubMed]

Chang, T. Y.

Dai, J. H.

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, J. Opt. Soc. Am. B 14, 852 (1997).
[CrossRef]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 55, 3092 (1997).
[CrossRef]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 56, 936 (1997).
[CrossRef]

Denz, C.

T. Rauch, C. Denz, and T. Tschudi, Opt. Commun. 88, 160 (1992).
[CrossRef]

Eason, R. W.

Ewbank, M. D.

Feinberg, J.

Fischer, B.

Fisher, R. A.

Gauthier, D. J.

D. J. Gauthier, P. Narum, and R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[CrossRef] [PubMed]

Gower, M. C.

M. C. Gower, Opt. Lett. 11, 458 (1986).
[CrossRef] [PubMed]

A. M. C. Smout, R. W. Eason, and M. C. Gower, Opt. Commun. 59, 77 (1986).
[CrossRef]

Gunter, P.

P. Gunter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

Hellwarth, R. W.

Hussain, G.

James, S. W.

Jeffrey, P. M.

Kobesky, L.

A. K. Majumdar and L. Kobesky, Opt. Commun. 75, 339 (1990).
[CrossRef]

Lam, J. F.

J. F. Lam, Appl. Phys. Lett. 46, 909 (1985).
[CrossRef]

MacDonald, K. R.

K. R. MacDonald and J. Feinberg, J. Opt. Soc. Am. A 1, 1213(A) (1984).

K. R. MacDonald and J. Feinberg, J. Opt. Soc. Am. 73, 548 (1983).
[CrossRef]

Majumdar, A. K.

A. K. Majumdar and L. Kobesky, Opt. Commun. 75, 339 (1990).
[CrossRef]

Montemezzani, G.

A. A. Zozulya, G. Montemezzani, and D. Z. Anderson, Phys. Rev. A 52, 4167 (1995).
[CrossRef] [PubMed]

Moore, T. R.

Narum, P.

D. J. Gauthier, P. Narum, and R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[CrossRef] [PubMed]

Nowak, A. V.

Ramsey, J.

Rauch, T.

T. Rauch, C. Denz, and T. Tschudi, Opt. Commun. 88, 160 (1992).
[CrossRef]

Saffman, M.

A. A. Zozulya, M. Saffman, and D. Z. Anderson, J. Opt. Soc. Am. B 12, 225 (1995).
[CrossRef]

Smout, A. M. C.

A. M. C. Smout, R. W. Eason, and M. C. Gower, Opt. Commun. 59, 77 (1986).
[CrossRef]

Sternklar, S.

Tschudi, T.

T. Rauch, C. Denz, and T. Tschudi, Opt. Commun. 88, 160 (1992).
[CrossRef]

Voit, E.

P. Gunter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

Wang, D.

Wang, P. Y.

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, J. Opt. Soc. Am. B 14, 852 (1997).
[CrossRef]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 55, 3092 (1997).
[CrossRef]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 56, 936 (1997).
[CrossRef]

Weiss, S.

Whitten, W.

Wu, X.

Xie, P.

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 55, 3092 (1997).
[CrossRef]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, J. Opt. Soc. Am. B 14, 852 (1997).
[CrossRef]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 56, 936 (1997).
[CrossRef]

Ye, P.

Yeh, P.

Zha, M. Z.

P. Gunter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

Zhang, H. J.

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 56, 936 (1997).
[CrossRef]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, J. Opt. Soc. Am. B 14, 852 (1997).
[CrossRef]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 55, 3092 (1997).
[CrossRef]

Zhang, Z.

Zozulya, A. A.

A. A. Zozulya, M. Saffman, and D. Z. Anderson, J. Opt. Soc. Am. B 12, 225 (1995).
[CrossRef]

A. A. Zozulya, G. Montemezzani, and D. Z. Anderson, Phys. Rev. A 52, 4167 (1995).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. F. Lam, Appl. Phys. Lett. 46, 909 (1985).
[CrossRef]

J. Opt. Soc. Am. (1)

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

K. R. MacDonald and J. Feinberg, J. Opt. Soc. Am. A 1, 1213(A) (1984).

J. Opt. Soc. Am. B (6)

Opt. Commun. (4)

P. Gunter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

A. M. C. Smout, R. W. Eason, and M. C. Gower, Opt. Commun. 59, 77 (1986).
[CrossRef]

A. K. Majumdar and L. Kobesky, Opt. Commun. 75, 339 (1990).
[CrossRef]

T. Rauch, C. Denz, and T. Tschudi, Opt. Commun. 88, 160 (1992).
[CrossRef]

Opt. Lett. (8)

Phys. Rev. A (3)

A. A. Zozulya, G. Montemezzani, and D. Z. Anderson, Phys. Rev. A 52, 4167 (1995).
[CrossRef] [PubMed]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 55, 3092 (1997).
[CrossRef]

P. Xie, J. H. Dai, P. Y. Wang, and H. J. Zhang, Phys. Rev. A 56, 936 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

D. J. Gauthier, P. Narum, and R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[CrossRef] [PubMed]

Other (5)

M. Segev, D. Engin, A. Yariv, and G. C. Valley, Opt. Lett. 18, 1828 (1993); D. Engin, M. Segev, S. Orlov, A. Yariv, and G. C. Valley, J. Opt. Soc. Am. B 11, 1708 (1994).
[CrossRef] [PubMed]

H. Lin, J. L. Radloff, and J. Dai, Opt. Commun. 105, 347 (1994); J. Dai and H. Lin, Opt. Commun. 113, 335 (1994).
[CrossRef]

See, for details, J. Feinberg and K. R. MacDonald, in Photorefractive Materials and Their Application, P. Gunter and J. P. Huignard, eds. (Springer-Verlag 1989), pp. 151–203.

A nonuniform internal electric field E0 that result from nonuniform intensity distributions throughout the crystal volume will give similar qualitative results.

For E0 taken along the other direction the phase conjugator shows similar qualitative output behavior.

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Figures (15)

Fig. 1
Fig. 1

Schematic diagram of a cat self-pumped phase conjugator in a BaTiO3 crystal.

Fig. 2
Fig. 2

Stable output angular intensity distribution of the forward beam. E0=0.

Fig. 3
Fig. 3

Temporal evolution of the output phase-conjugate reflectivity R. E0=0.

Fig. 4
Fig. 4

Temporal evolution of (a) the phase-conjugate reflectivity, (b) the output phase, and (c) the frequency shift. E0=20 V/mm.

Fig. 5
Fig. 5

Stable frequency shift versus electric field.

Fig. 6
Fig. 6

Temporal evolution of (a) the phase-conjugate reflectivity and (b) the frequency shift. E0=30 V/mm.

Fig. 7
Fig. 7

Temporal evolution of (a) the phase-conjugate reflectivity and (b) the frequency shift. E0=50 V/mm.

Fig. 8
Fig. 8

Temporal evolution of (a) the phase-conjugate reflectivity and (b) the frequency shift. E0=60 V/mm.

Fig. 9
Fig. 9

Temporal evolution of (a) the phase-conjugate reflectivity and (b) the frequency shift. E0=68 V/mm.

Fig. 10
Fig. 10

Temporal evolution of (a) the phase-conjugate reflectivity and (b) the frequency shift. E0=150 V/mm.

Fig. 11
Fig. 11

Schematic diagram of a mutually pumped phase conjugator in a BaTiO3 crystal.

Fig. 12
Fig. 12

Temporal evolution of the output phase-conjugate reflectivity R1=θ|fB(θ, 0, t)|2/θ|fF(θ, 0, t)|2. E0=0.

Fig. 13
Fig. 13

Temporal evolution of the output phases φB(θ=0, z=0, t) for 1, E0=0;2, E0=5 V/mm;3, E0=10 V/mm; 3 and 4, E0=14 V/mm.

Fig. 14
Fig. 14

Temporal evolution of the output phase-conjugate reflectivities (a) R1=θ|fB(θ, 0, t)|2/θ|fF(θ, 0, t)|2 and (b) R2=θ|fF(θ, L, t)|2/θ|fB(θ, L, t)|2. (c) Frequency shift between the output phase-conjugate beam and its corresponding input beam (forward beam). E0=40 V/mm.

Fig. 15
Fig. 15

Temporal evolution of (a) the output phase-conjugate reflectivity R1 and (b) the frequency shift between the conjugate beam and its corresponding input beam (forward beam). E0=62 V/mm.

Tables (1)

Tables Icon

Table 1 Parameters of Nominally Undoped BaTiO3

Equations (8)

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fF(θ, z, t)z=1cos θθ[Q(θ, θ, z, t)fF(θ, z, t)]-αL2fF(θ, z, t),
fB*(θ, z, t)z=1cos θθ[Q(θ, θ, z, t)fB*(θ, z, t)]+αL2fB*(θ, z, t),
τ(θ, θ) Q(θ, θ, z, t)t+Q(θ, θ, z, t)
=γ (θ, θ)I0(z, t)[fF(θ, z, t)fF*(θ, z, t)
+fB*(θ, z, t)fB(θ, z, t)],
γ (θ, θ)=-iωno32creff(θ, θ)ESC(θ, θ)cos(θ-θ),
ESC(θ, θ)=Eq(Ed-iE0)E0+i(Eq+Ed),
τ(θ, θ)=τ 1+Ed/EM1+Ed/Eq,

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