Abstract

We present a simple method for suppressing fluctuation of the space-charge field in a photorefractive wave-mixing system. The method can be applicable to any type of such a system, such as two-wave mixing and four-wave mixing. In this method an external illuminating intensity, which is incoherent with the interacting beams, is turned on or off according to the sign of the deviation of the photorefractive output from a set value. The set value can be chosen from a wide range.

© 2001 Optical Society of America

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References

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  1. A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
    [CrossRef]
  2. N. V. Kukhatarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. Steady state,” Ferroelectrics 22, 949–964 (1979).
    [CrossRef]
  3. See, for example, P. Günter and J. P. Huignard, eds., Photorefractive Materials and Their Applications, Vols. 61 and 62 of Topics in Applied Physics (Springer–Verlag, 1988, 1989), Vols. 1 and 2.
  4. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  5. P. Xie, I. A. Taj, and T. Mishima, “Origin of temporal fluctuation in the photorefractive effect,” J. Opt. Soc. Am. B (to be published).
  6. H. Risken, The Fokker–Planck Equation: Method of Solution and Application (Springer–Verlag, Berlin, 1984).
  7. D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
    [CrossRef] [PubMed]
  8. P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effect for Bi12SiO20 and BaTiO3 with shallow traps,” J. Opt. Soc. Am. B 8, 1053–1063 (1991).
    [CrossRef]

1991 (1)

1990 (1)

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef] [PubMed]

1979 (1)

N. V. Kukhatarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. Steady state,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

1966 (1)

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Ballman, A. A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Boyd, G. D.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Feinberg, J.

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef] [PubMed]

Kukhatarev, N. V.

N. V. Kukhatarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. Steady state,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Levinstein, J. J.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Mahgerefteh, D.

P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effect for Bi12SiO20 and BaTiO3 with shallow traps,” J. Opt. Soc. Am. B 8, 1053–1063 (1991).
[CrossRef]

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef] [PubMed]

Markov, V. B.

N. V. Kukhatarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. Steady state,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Nassau, K.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Odulov, S. G.

N. V. Kukhatarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. Steady state,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Smith, R. G.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Soskin, M. S.

N. V. Kukhatarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. Steady state,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Tayebati, P.

Vinetskii, V. L.

N. V. Kukhatarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. Steady state,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

Appl. Phys. Lett. (1)

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, and K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhatarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. Steady state,” Ferroelectrics 22, 949–964 (1979).
[CrossRef]

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

Phys. Rev. Lett. (1)

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[CrossRef] [PubMed]

Other (4)

See, for example, P. Günter and J. P. Huignard, eds., Photorefractive Materials and Their Applications, Vols. 61 and 62 of Topics in Applied Physics (Springer–Verlag, 1988, 1989), Vols. 1 and 2.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

P. Xie, I. A. Taj, and T. Mishima, “Origin of temporal fluctuation in the photorefractive effect,” J. Opt. Soc. Am. B (to be published).

H. Risken, The Fokker–Planck Equation: Method of Solution and Application (Springer–Verlag, Berlin, 1984).

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Figures (5)

Fig. 1
Fig. 1

Temporal evolution of the space-charge field with the suppression described by Eqs. (10) for t<15 s and without suppression for t15 s. E10=83.5×102 V/m. For comparison, we use the same realization for Langevin noise in Figs. 1 and Fig. 2.

Fig. 2
Fig. 2

Temporal evolution of the space-charge field with suppression described by Eqs. (11) for t<15 s and without suppression for t15 s. (a) E10=83.5×102 V/m, (b) E10=100×102 V/m, (c) E10=46×102 V/m.

Fig. 3
Fig. 3

Temporal evolution of the output signal intensity I2(t) with suppression for t<150τ0 and without suppression for t150τ0. (a) I20=4.48, (b) I20=8.48. For comparison, we use the same realizations for Langevin noise in (a) and (b).

Fig. 4
Fig. 4

Temporal evolution of the output phase-conjugate intensity I3(0, t) with suppression for t<125τ0 and without suppression for t125τ0. (a) I30=58, (b) I30=75. For comparison, we use the same realization for Langevin noise in Figs. 4 and 5.

Fig. 5
Fig. 5

Temporal evolution of the output phase-conjugate intensity I3(0, t) with suppression for t<125τ0 and without suppression for t125τ0. I30=75.

Tables (1)

Tables Icon

Table 1 Parameter Values Used in the Calculation

Equations (31)

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Nit=(sI+β)(ND-Ni)-γDnNi,
(Ni-n)t+1qJ=0,
J=qμnE+μkBTn,
E=(q/)(Ni-n-NA),
m=I1/I0,
Ni(t, z)=N0(t)+Re[N1(t)exp(-ikz)],
n0t=(sI0+β)(ND-n0-NA)-γDn0(n0+NA),
N0=n0+NA,
N1t=1ED+EμD×EDsI0(ND-N0)m-ED(sI0+β+γDn0)+γDqN0n0kN1,
E1i(q/k)N1,
Δf(t)=0,Δf(t)Δf(t)=Dδ(t-t),
I0(t)=I0+Iinc(t),
m(t)=I1I0+Iinc(t),
Iinc(t)=Ic+α1[|E1(t)|-E10],|E1(t)|E10,
Iinc(t)=Ic+α2[|E1(t)|-E10],|E1(t)|>E10,
Iinc(t)=Imax,Ic+α2[|E1(t)|-E10]Imax.
Iinc(t)=0,|E1(t)|E10,
Iinc(t)=Imax,|E1(t)|>E10.
A1z=-QA2,
A2*z=QA1*,
τ Qt+Q=γI0+Iinc(t)A1A2*,
γ=γ0[1+Δf(t)],
τ=τ0,Iinc(t)=0,
τ=τ0/x,Iinc(t)=Imax,
Iinc(t)=0,I2(t)I20,
Iinc(t)=Imax,I2(t)>I20,
A1z=QA4,
A2*z=QA3*,
A3z=-QA2,
A4*z=-QA1*,
τ Qt+Q=γI0+Iinc(t)(A1A4*+A2*A3),

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