Abstract

A new restoration method for a distorted image transmitted through a single step-index multimode fiber is presented. The transmission of the reference beam along with the image enables one to compensate on a real-time basis for the distortion caused by the fiber modal phase dispersion. At the receiver end the interference between the Fourier-transformed image and the reference beam creates gratings in a photorefractive crystal. It is theoretically shown that, owing to the spatial segregation characteristic of the Fourier-transformed mode distribution of the step-index fiber, the phase conjugation of the transmitted image through four-wave mixing obtained from the crystal reconstructs the original image.

© 1990 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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1985 (1)

B. Fischer, S. Sternklar, Appl. Phys. Lett. 46, 113 (1985).
[CrossRef]

1982 (1)

1980 (1)

K. Kitayama, S. Seikai, N. Uchida, IEEE J. Quantum Electron. QE-16356 (1980).
[CrossRef]

1976 (4)

1967 (1)

Dunning, G. J.

Fischer, B.

B. Fischer, S. Sternklar, Appl. Phys. Lett. 46, 113 (1985).
[CrossRef]

Gover, A.

Ikeda, M.

Ikegami, T.

Keck, D. B.

Kitayama, K.

K. Kitayama, S. Seikai, N. Uchida, IEEE J. Quantum Electron. QE-16356 (1980).
[CrossRef]

Lee, C. P.

Lind, R. C.

Lohmann, A. W.

Olshansky, R.

Paris, D. P.

Seikai, S.

K. Kitayama, S. Seikai, N. Uchida, IEEE J. Quantum Electron. QE-16356 (1980).
[CrossRef]

Sternklar, S.

B. Fischer, S. Sternklar, Appl. Phys. Lett. 46, 113 (1985).
[CrossRef]

Sugimura, A.

Tateda, M.

M. Tateda, Ph.D. dissertation (University of Tokyo, Tokyo, 1981), p. 20.

Uchida, N.

K. Kitayama, S. Seikai, N. Uchida, IEEE J. Quantum Electron. QE-16356 (1980).
[CrossRef]

Werlich, H. W.

Yariv, A.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

A. Yariv, Appl. Phys. Lett. 28, 88 (1976).
[CrossRef]

B. Fischer, S. Sternklar, Appl. Phys. Lett. 46, 113 (1985).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Kitayama, S. Seikai, N. Uchida, IEEE J. Quantum Electron. QE-16356 (1980).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Other (1)

M. Tateda, Ph.D. dissertation (University of Tokyo, Tokyo, 1981), p. 20.

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Figures (2)

Fig. 1
Fig. 1

Block diagram of the restoration method.

Fig. 2
Fig. 2

Schematic for the optical implementation of this restoration method. Lenses L3, L4, L5, and L6 perform the Fourier transformation. BS's, beam splitters; PBS, polarization beam splitter.

Equations (17)

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i x ( r , θ ) = A m x m x ( r , θ ) ,
i y ( r , θ ) = A m y m y ( r , θ ) ,
A m x = i x ( r , θ ) m x ( r , θ ) r d r d θ ,
A m y = i y ( r , θ ) m y I r , θ ) r d r d θ ,
u x ( r , θ ) = A m x m x ( r , θ ) exp ( i β m L ) ,
u y ( r , θ ) = A m y m y ( r , θ ) exp ( i β m L ) ,
U x ( r f , θ f ) ( u x ) = A m x E m ( r f , θ f ) exp ( i β m L ) ,
U y ( r j , θ f ) ( u y ) = A m y E m ( r f , θ f ) exp ( i β m L ) ,
E ν μ ( r f , θ f ) ( ν μ ) 2 π j u ( cos μ θ sin μ θ ) 1 κ + k f 1 ( κ k f ) 1 / 2 × sin ( κ k f ) a ( κ k f ) a ,
κ = ( k 2 n 1 2 β m 2 ) 1 / 2 = ( 2 ) 1 / 2 m a ,
k f = k r f f ,
U ( r f , θ f ) U x ( r f , θ f ) U y * ( r f , θ f ) U p ( r f , θ f ) .
A m x = 1 ,
U ( r f , θ f ) A m y * | E m ( r f , θ f ) | 2 + m n A m y * E m * E n .
T m = E m ( r f , θ f ) | E m ( r f , θ f ) | 2 .
[ U ( r f , θ f ) T m ] A m n υ * m n ( r , θ ) = i y * ( r , θ ) .
U p ( r f , θ f ) E m ( r f , θ f ) | E m ( r f , θ f ) | 2 .

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