Abstract

Image amplification and beam fanning in a photorefractive medium are described by the multivariable Langevin equations when the random volume scattering is included owing to the inhomogeneities and/or defects distributed throughout the medium. The effects of the random volume scattering on the image amplification and the beam fanning are studied analytically in the undepleted-pump approximation and numerically, and they are compared with the surface scattering.

[Optical Society of America ]

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References

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  1. J. F. Heanue , M. C. Bashaw , and L. Hesselink , Volume holographic storage and retrieval of digital data , Science SCIEAS 265 , 749 ( 1994
    [CrossRef] [PubMed]
  2. J. H. Hong , A. E. Chiou , and P. Yeh , Image amplification by two-wave mixing in photorefractive crystals , Appl. Opt. APOPAI 29 , 3026 ( 1990
    [CrossRef] [PubMed]
  3. P. Xie , J. H. Dai , P. Y. Wang , and H. J. Zhang , Spatial fidelity of image amplification in photorefractive crystals , Appl. Opt. APOPAI 35 , 7102 ( 1996
    [CrossRef] [PubMed]
  4. M. Segev , D. Engin , A. Yariv , and G. C. Valley , Temporal evolution of fanning in photorefractive materials , Opt. Lett. OPLEDP 18 , 956 ( 1993
    [CrossRef] [PubMed]
  5. R. L. Honeycutt , Stochastic Runge Kutta algorithms. I. White noise , Phys. Rev. A PLRAAN 45 , 600 ( 1992
    [CrossRef] [PubMed]
  6. P. Xie , J. H. Dai , P. Y. Wang , and H. J. Zhang , Self-pumped phase conjugation in photorefractive crystals: reflectivity and spatial fidelity , Phys. Rev. A PLRAAN 55 , 3092 ( 1997
    [CrossRef]

Honeycutt, R. L

R. L. Honeycutt , Stochastic Runge Kutta algorithms. I. White noise , Phys. Rev. A PLRAAN 45 , 600 ( 1992
[CrossRef] [PubMed]

Other (6)

J. F. Heanue , M. C. Bashaw , and L. Hesselink , Volume holographic storage and retrieval of digital data , Science SCIEAS 265 , 749 ( 1994
[CrossRef] [PubMed]

J. H. Hong , A. E. Chiou , and P. Yeh , Image amplification by two-wave mixing in photorefractive crystals , Appl. Opt. APOPAI 29 , 3026 ( 1990
[CrossRef] [PubMed]

P. Xie , J. H. Dai , P. Y. Wang , and H. J. Zhang , Spatial fidelity of image amplification in photorefractive crystals , Appl. Opt. APOPAI 35 , 7102 ( 1996
[CrossRef] [PubMed]

M. Segev , D. Engin , A. Yariv , and G. C. Valley , Temporal evolution of fanning in photorefractive materials , Opt. Lett. OPLEDP 18 , 956 ( 1993
[CrossRef] [PubMed]

R. L. Honeycutt , Stochastic Runge Kutta algorithms. I. White noise , Phys. Rev. A PLRAAN 45 , 600 ( 1992
[CrossRef] [PubMed]

P. Xie , J. H. Dai , P. Y. Wang , and H. J. Zhang , Self-pumped phase conjugation in photorefractive crystals: reflectivity and spatial fidelity , Phys. Rev. A PLRAAN 55 , 3092 ( 1997
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Spatial-intensity distributions of the amplified image beam for γL=4: (a) γ=1 and L=4, (b) γ=10 and L=0.4; q=10-9/mm.

Fig. 2
Fig. 2

Spatial-intensity distributions of the amplified image beam in a BaTiO3 crystal of L=5 mm with (a) q=0, (b) q=10-9, and (c) q=10-8, in units of mm-1.

Fig. 3
Fig. 3

(a) Spatial fidelity of the image amplification versus the volume-scattering strength q; (b) [A(x, L)-G×A(x, 0)]2dx versus q. The solid line is the fit curve.

Fig. 4
Fig. 4

Solid curves represent {exp[2γ(-α, θ)L/cos θ]}/2γ(-α, θ)/cos θ versus θ, and dashed curves represent exp[2γ(-α, θ)L/cos θ] versus θ: (a) L=0.5 mm, (b) L=1.2 mm.

Fig. 5
Fig. 5

Angular-intensity distributions of the fanning beam in a BaTiO3:Ce crystal of L=0.8 mm for (a) volume scattering and (b) surface scattering. The input angle of the input wave is α=15°, and the c axis makes an angle of 45° with respect to the direction of the pump wave.

Fig. 6
Fig. 6

Numerical simulation of the beam path in a BaTiO3 crystal with the angle between the crystal c axis and the propagating direction of the input beam being 35°. q=4×10-9/mm.

Equations (20)

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Ep(x, z, t)Ap(z)exp[i(k sin αx+k cos αz-ωt)]+c.c.,
Es(x, z, t)=As(x, z) exp[i(kz-ωt)]+c.c.,
As(x, z)=θfs(θ, z)×exp[ik sin θx+i(k cos θ-k)z],
dAp(z)dz=-1cos θθγ(-α, θ)I0(z) fs(θ, z)f0*(θ, z)Ap(z)-αL2 Ap(z),
dfs(θ, z)dz=1cos θ γ(-α, θ)I0(z) Ap(z)Ap*(z)fs(θ, z)-θγ(θ, θ)I0(z) fs(θ, z)fs*(θ, z)fs(θ, z)-αL2 fs(θ, z)+σ(θ, z)I0(z).
σP(θ, z)=0,
σP(θ, z)σP(θ, z)=2qδPPδθθδ(z-z),
dXidz=hi({X}, z)+j[gij({X}, z)Γj(z)],
dXdz=γX+Γ(z),
P(X, z)z=-γ X (XP)+D 2X2 P.
P(X, z|X, z)=-γ2πD{1-exp[2γ(z-z)]}×expγ(X-exp[γ(z-z)]X)22D{1-exp[2γ(z-z)]}.
W(X, L)=γ2πD exp(2γL)× exp-γ2D exp(2γL) [X-C exp(γL)]2,
X=C exp(γL),
(X-X)2=Dγ exp(2γL)=qI0(0)2γ exp(2γL)qr2γ [C exp(γL)]2,
(X-X)2=[(1±εr)C exp(γL)-C exp(γL)]2εr[C exp(γL)]2.
X2=qIP(0)2γ exp(2γL),
X2=εIP(0) exp(2γL).
FI=As(x, 0)As(x, L)dx|As(x, 0)|2dx|As(x, L)|2dx,
exp[2γ(-α, θ)L/cos θ]2γ(-α, θ)/cos θ.
exp[2γ(-α,θ)L/cos θ]2γ(-α,θ)/cos θ,

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