Abstract

We demonstrate experimentally that the effects of nonreciprocal elements or media that would otherwise spoil phase conjugation can be neutralized by using a tandem combination of a modal- and polarization-scrambling fiber and a phase-conjugate mirror. A theoretical model to explain the experimental results is presented.

© 1987 Optical Society of America

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References

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  1. A. Yariv, “Operator algebra for propagation problems involving phase conjugation,” submitted to Opt. Lett.
  2. J. Feinberg, Opt. Lett. 7, 486 (1982).
    [CrossRef] [PubMed]
  3. A. Yariv, Y. Tomita, K. Kyuma, Opt. Lett. 11, 809 (1986).
    [CrossRef] [PubMed]
  4. K. Kyuma, A. Yariv, S-K. Kwong, Appl. Phys. Lett. 49, 617 (1986).
    [CrossRef]

1986 (2)

A. Yariv, Y. Tomita, K. Kyuma, Opt. Lett. 11, 809 (1986).
[CrossRef] [PubMed]

K. Kyuma, A. Yariv, S-K. Kwong, Appl. Phys. Lett. 49, 617 (1986).
[CrossRef]

1982 (1)

Feinberg, J.

Kwong, S-K.

K. Kyuma, A. Yariv, S-K. Kwong, Appl. Phys. Lett. 49, 617 (1986).
[CrossRef]

Kyuma, K.

A. Yariv, Y. Tomita, K. Kyuma, Opt. Lett. 11, 809 (1986).
[CrossRef] [PubMed]

K. Kyuma, A. Yariv, S-K. Kwong, Appl. Phys. Lett. 49, 617 (1986).
[CrossRef]

Tomita, Y.

Yariv, A.

A. Yariv, Y. Tomita, K. Kyuma, Opt. Lett. 11, 809 (1986).
[CrossRef] [PubMed]

K. Kyuma, A. Yariv, S-K. Kwong, Appl. Phys. Lett. 49, 617 (1986).
[CrossRef]

A. Yariv, “Operator algebra for propagation problems involving phase conjugation,” submitted to Opt. Lett.

Appl. Phys. Lett. (1)

K. Kyuma, A. Yariv, S-K. Kwong, Appl. Phys. Lett. 49, 617 (1986).
[CrossRef]

Opt. Lett. (2)

Other (1)

A. Yariv, “Operator algebra for propagation problems involving phase conjugation,” submitted to Opt. Lett.

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic diagram of a wave that propagates through an element A, is phase conjugated, and returns to the initial plane. (b) A method to undo the nonreciprocal effect. PCM, phase-conjugate mirror; P, polarizer; F, Faraday rotator.

Fig. 2
Fig. 2

The experimental arrangement used to demonstrate polarization recovery with a nonreciprocal medium. P1, P2, are x polarizers; BS, beam splitter; PBS, polarizing beam splitter; L1, L2, lenses; D1, D2, photodetectors; F, variable Faraday rotator.

Fig. 3
Fig. 3

Experimental results: open circles, degree of polarization; closed circles, power of phase-conjugate beam. The solid curve is from the theoretical model.

Equations (12)

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| E x E y | 4 = [ cos θ sin θ sin θ cos θ ] × ϕ * { [ cos θ sin θ sin θ cos θ ] [ E x E y ] 1 } = [ cos 2 θ sin 2 θ sin 2 θ cos 2 θ ] [ E x * E y * ] 1 ,
| E x E y | 4 = [ cos α 2 i sin α 2 i sin α 2 cos α 2 ] × ϕ * { [ cos α 2 i sin α 2 i sin α 2 cos α 2 ] [ E x E y ] 1 } = [ 1 0 0 1 ] [ E x * E y * ] 1 ,
E ( 1 ) = n = 1 N ( a R n ( 1 ) E R n + a L n ( 1 ) E L n ) = [ a R 1 ( 1 ) a R N ( 1 ) a L 1 ( 1 ) a L N ( 1 ) ] ,
E ( 4 ) = M F P ϕ * [ PFME ( 1 ) ] ,
M = [ M RR M RL M LR M LL ] , M = [ M RR M RL M LR M LL ]
F = ( e i θ I 0 0 e i θ I ) , F = ( e i θ I 0 0 e i θ I )
P = 1 2 [ I I I I ] = P
E ( 4 ) = 1 2 { M RR M RR * e i 2 θ + M RR M LR * + M RL M RR * + M RL M LR * e 2 i θ M LR M RR * e 21 θ + M LR M LR * + M LL M RR * + M LL M LR * e 2 i θ × M RR M RL * e i 2 θ + M RR M LL * + M RL M RL * + M RL M LL * e 2 i θ M LR M RL * e 21 θ + M LR M LL * + M LL M RL * + M LL M LL * e 2 i θ } ( E ( 1 ) ) * .
M RR M RR * ~ M RL M LR * ~ M LR M RL * ~ M LL M LL * ~ ½ I
M RR M LR ~ M RL M RR * ~ M LR M RR * ~ M LR M LR * ~ M LL M RR * ~ M LL M LR * ~ M RR M RL * ~ M RR M LL * ~ M RL M RL * ~ M RL M LL * ~ M LR M LL * ~ M LL M RL * = 0 .
E ( 4 ) = ¼ ( e 2 i θ + e 2 i θ ) I ( E ( 1 ) ) * , E ( 4 ) = ½ cos 2 θ ( E ( 1 ) ) * .
| E ( out ) | 2 = ¼ | E ( in ) | 2 i = 1 N cos 2 ( 2 θ i ) .

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