Abstract

So-called polarization-insensitive optical phase conjugation with four-wave mixing in a dispersion-shifted fiber by the use of two orthogonally polarized pumps is analyzed theoretically. An inherent polarization dependence as a result of polarization-dependent cross talk, asymmetrical depletion of the two pumps and input signal, and polarization-sensitive phase conjugation is identified.

© 1996 Optical Society of America

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References

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  1. A. Yariv, D. Fekete, D. PepperOpt. Lett. 4, 52 (1979).
    [CrossRef] [PubMed]
  2. W. Pieper, C. Kurtzke, R. Schnabel, D. Breuer, R. Ludwig, K. Petermann, H. WeberElectron. Lett. 30, 724 (1994).
    [CrossRef]
  3. A. Gnauck, R. Jopson, R. DerosierIEEE Photon. Technol. Lett. 7, 582 (1995).
    [CrossRef]
  4. R. Jopson, R. TenchElectron. Lett. 29, 2216 (1993).
    [CrossRef]
  5. A. Gnauck, R. Jopson, P. Iannone, R. DerosierElectron. Lett. 30, 727 (1994).
    [CrossRef]
  6. K. InoueJ. Lightwave Technol. 12, 1916 (1994).
    [CrossRef]
  7. Y. ShenThe Principles of Nonlinear Optics (Wiley, New York, 1984).
  8. X. Zhang, B. F. Jørgensen“Analysis of optical phase-conjugation using four-wave mixing in a dispersion-shifted fiber,”Opto-electronics (to be published).

1995

A. Gnauck, R. Jopson, R. DerosierIEEE Photon. Technol. Lett. 7, 582 (1995).
[CrossRef]

1994

A. Gnauck, R. Jopson, P. Iannone, R. DerosierElectron. Lett. 30, 727 (1994).
[CrossRef]

K. InoueJ. Lightwave Technol. 12, 1916 (1994).
[CrossRef]

W. Pieper, C. Kurtzke, R. Schnabel, D. Breuer, R. Ludwig, K. Petermann, H. WeberElectron. Lett. 30, 724 (1994).
[CrossRef]

1993

R. Jopson, R. TenchElectron. Lett. 29, 2216 (1993).
[CrossRef]

1979

Breuer, D.

W. Pieper, C. Kurtzke, R. Schnabel, D. Breuer, R. Ludwig, K. Petermann, H. WeberElectron. Lett. 30, 724 (1994).
[CrossRef]

Derosier, R.

A. Gnauck, R. Jopson, R. DerosierIEEE Photon. Technol. Lett. 7, 582 (1995).
[CrossRef]

A. Gnauck, R. Jopson, P. Iannone, R. DerosierElectron. Lett. 30, 727 (1994).
[CrossRef]

Fekete, D.

Gnauck, A.

A. Gnauck, R. Jopson, R. DerosierIEEE Photon. Technol. Lett. 7, 582 (1995).
[CrossRef]

A. Gnauck, R. Jopson, P. Iannone, R. DerosierElectron. Lett. 30, 727 (1994).
[CrossRef]

Iannone, P.

A. Gnauck, R. Jopson, P. Iannone, R. DerosierElectron. Lett. 30, 727 (1994).
[CrossRef]

Inoue, K.

K. InoueJ. Lightwave Technol. 12, 1916 (1994).
[CrossRef]

Jopson, R.

A. Gnauck, R. Jopson, R. DerosierIEEE Photon. Technol. Lett. 7, 582 (1995).
[CrossRef]

A. Gnauck, R. Jopson, P. Iannone, R. DerosierElectron. Lett. 30, 727 (1994).
[CrossRef]

R. Jopson, R. TenchElectron. Lett. 29, 2216 (1993).
[CrossRef]

Jørgensen, B. F.

X. Zhang, B. F. Jørgensen“Analysis of optical phase-conjugation using four-wave mixing in a dispersion-shifted fiber,”Opto-electronics (to be published).

Kurtzke, C.

W. Pieper, C. Kurtzke, R. Schnabel, D. Breuer, R. Ludwig, K. Petermann, H. WeberElectron. Lett. 30, 724 (1994).
[CrossRef]

Ludwig, R.

W. Pieper, C. Kurtzke, R. Schnabel, D. Breuer, R. Ludwig, K. Petermann, H. WeberElectron. Lett. 30, 724 (1994).
[CrossRef]

Pepper, D.

Petermann, K.

W. Pieper, C. Kurtzke, R. Schnabel, D. Breuer, R. Ludwig, K. Petermann, H. WeberElectron. Lett. 30, 724 (1994).
[CrossRef]

Pieper, W.

W. Pieper, C. Kurtzke, R. Schnabel, D. Breuer, R. Ludwig, K. Petermann, H. WeberElectron. Lett. 30, 724 (1994).
[CrossRef]

Schnabel, R.

W. Pieper, C. Kurtzke, R. Schnabel, D. Breuer, R. Ludwig, K. Petermann, H. WeberElectron. Lett. 30, 724 (1994).
[CrossRef]

Shen, Y.

Y. ShenThe Principles of Nonlinear Optics (Wiley, New York, 1984).

Tench, R.

R. Jopson, R. TenchElectron. Lett. 29, 2216 (1993).
[CrossRef]

Weber, H.

W. Pieper, C. Kurtzke, R. Schnabel, D. Breuer, R. Ludwig, K. Petermann, H. WeberElectron. Lett. 30, 724 (1994).
[CrossRef]

Yariv, A.

Zhang, X.

X. Zhang, B. F. Jørgensen“Analysis of optical phase-conjugation using four-wave mixing in a dispersion-shifted fiber,”Opto-electronics (to be published).

Electron. Lett.

R. Jopson, R. TenchElectron. Lett. 29, 2216 (1993).
[CrossRef]

A. Gnauck, R. Jopson, P. Iannone, R. DerosierElectron. Lett. 30, 727 (1994).
[CrossRef]

W. Pieper, C. Kurtzke, R. Schnabel, D. Breuer, R. Ludwig, K. Petermann, H. WeberElectron. Lett. 30, 724 (1994).
[CrossRef]

IEEE Photon. Technol. Lett.

A. Gnauck, R. Jopson, R. DerosierIEEE Photon. Technol. Lett. 7, 582 (1995).
[CrossRef]

J. Lightwave Technol.

K. InoueJ. Lightwave Technol. 12, 1916 (1994).
[CrossRef]

Opt. Lett.

Other

Y. ShenThe Principles of Nonlinear Optics (Wiley, New York, 1984).

X. Zhang, B. F. Jørgensen“Analysis of optical phase-conjugation using four-wave mixing in a dispersion-shifted fiber,”Opto-electronics (to be published).

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Figures (3)

Fig. 1
Fig. 1

Schematic configuration of so-called polarization-insensitive optical phase conjugation by the use of two orthogonally polarized pumps.

Fig. 2
Fig. 2

Conversion efficiency versus conversion fiber length for a linearly polarized input signal oriented at π/4 with respect to the x direction. Pump frequency separation Ωp/2π = 126 GHz. Dashed curves, PC contribution; solid curves, PC + CT + PS contribution.

Fig. 3
Fig. 3

Conversion efficiency versus polarization angle of the input signal with respect to the x direction: (a) Ωp/2π = 126 GHz, (b) Ωp/2π = 252 GHz. The other parameters are as in Fig. 2.

Equations (5)

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E ( x , y , z , t ) = A P , x ( z ) exp ( i Ω P / 2 t ) x + A P , y ( z ) × exp ( i Ω P / 2 t ) y + [ A S , x ( z ) x + A S , y ( z ) y ] × exp ( i Ω S t ) + A F , x ( z ) exp [ i ( Ω P + Ω S ) t ] x + A F , y ( z ) exp [ i ( Ω P + Ω S ) t ] y + [ A C , x ( z ) x + A C , y ( z ) y ] exp ( i Ω C t ) ,
B P , n = [ | A P , n | 2 + 2 | A S , n | 2 + 2 | A F , n | 2 + 2 | A C , n | 2 + 2 3 ( | A P , m | 2 + | A S , m | 2 + | A F , m | 2 + | A C , m | 2 ) ] A P , n + 2 A P , n * A S , n A F , n exp i ( 2 β P , n + β S + β F , n ) z ] + A P , m * A S , n A C , m * exp i [ ( β P , n β P , m + β S + β C ) z ] + A P , m A F , n A C , m * exp i [ ( β P , n + β P , m + β F , n β C ) z ] + A P , m A F , m * A C , n exp i [ ( β P , n + β P , m β F , m + β C ) z ] + A P , m * A S , m A C , n exp i [ ( β P , n β P , m + β S + β F , n ) z ] ,
B S , n = [ 2 | A P , n | 2 + | A S , n | 2 + 2 | A F , n | 2 + 2 | A C , n | 2 + 2 3 ( | A P , m | 2 + | A S , m | 2 + | A F , m | 2 + | A C , m | 2 ) ] A S , n + A P , n 2 A F , n * exp i [ ( 2 β P , n β S β F , n ) z ] + A P , n A P , m A C , m * exp i [ ( β P , n + β P , m β C β S ) z ] ,
B F , n = [ 2 | A P , n | 2 + 2 | A S , n | 2 + | A F , n | 2 + 2 | A C , n | 2 + 2 3 ( | A P , m | 2 + | A S , m | 2 + | A F , m | 2 + | A C , m | 2 ) ] A F , n + A P , n 2 A S , n * exp i [ ( 2 β P , n β S β F , n ) z ] + A P , n A P , m * A C , m exp i [ ( β P , n β P , m β F , n + β C ) z ] + A F , m * A C , n A C , m exp i [ ( β F , n β F , m + 2 β C ) z ] ,
B C , n = [ | A C , n | 2 + 2 | A P , n | 2 + 2 | A S , n | 2 + 2 | A F , n | 2 + 2 3 ( | A P , m | 2 + | A F , m | 2 + | A C , m | 2 + | A S , m | 2 ) ] A C , n + A P , n A P , m A S , m * exp i [ ( β P , n + β P , m β S β C ) ] + A P , n A P , m * A F , m exp i [ ( β P , n β P , m + β F , m β C ) ] + A F , n A F , m A C , m * exp i [ ( β F , n + β F , m 2 β C ) ] + A S , n A S , m * A C , m .

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