Abstract

Phase-sensitive amplification (PSA) has the potential to improve significantly the performance of optical communication systems. PSA is known to occur in χ (2) devices, and in a fiber interferometer, which is an example of a χ (3) device. In this report some four-wave mixing processes are described, which produce PSA directly in fibers.

© 2004 Optical Society of America

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References

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  1. R. Loudon, �??Theory of noise accumulation in linear optical-amplifier chains,�?? IEEE J. Quantum Electron. 21, 766�??773 (1985).
    [CrossRef]
  2. H. P. Yuen, �??Reduction of quantum fluctuation and suppression of the Gordon�??Haus effect with phase-sensitive linear amplifiers,�?? Opt. Lett. 17, 73�??75 (1992).
    [CrossRef] [PubMed]
  3. Y. Mu and C. M. Savage, �??Parametric amplifiers in phase-noise-limited optical communications,�?? J. Opt. Soc. Am. B 9, 65�??70 (1992)
    [CrossRef]
  4. R. D. Li, P. Kumar, W. L. Kath and J. N. Kutz, �??Combating dispersion with parametric amplifers,�?? IEEE Photon. Technol. Lett. 5, 669�??672 (1993).
    [CrossRef]
  5. W. Imajuku and A. Takada, �??Reduction of fiber-nonlinearity-enhanced amplifier noise by means of phase-sensitive amplifiers,�?? Opt. Lett. 22, 31�??33 (1997)
    [CrossRef] [PubMed]
  6. R. Loudon, The Quantum Theory of Light, 3rd Ed. (Oxford University Press, Oxford, 2000)
  7. H. P. Yuen and J. H. Shapiro, �??Generation and detection of two-photon coherent states in degenerate four-wave mixing,�?? Opt. Lett. 4, 334�??336 (1979).
    [CrossRef] [PubMed]
  8. B. Yurke, �??Use of cavities in squeezed-state-generation,�?? Phys. Rev. A 29, 408�??410 (1984).
    [CrossRef]
  9. P. Kumar and J. H. Shapiro, �??Squeezed-state generation via forward degenerate four-wave mixing,�?? Phys. Rev. A 30, 1568�??1571 (1984).
    [CrossRef]
  10. M. D. Levenson, R. M. Shelby, A. Aspect, M. Reid and D. F.Walls, �??Generation and detection of squeezed states of light by nondegenerate four-wave mixing in an optical fiber,�?? Phys. Rev. A 32, 1550�??1562 (1985).
    [CrossRef] [PubMed]
  11. M. J. Potasek and B. Yurke, �??Squeezed light generation in a medium governed by the nonlinear Schrödinger equation,�?? Phys. Rev. A 35, 3974�??3977 (1987).
    [CrossRef] [PubMed]
  12. T. A. B. Kennedy and S. Wabnitz, �??Quantum propagation: Squeezing via modulational polarization instabilities in a birefringent nonlinear medium,�?? Phys. Rev. A 38, 563�??566 (1988).
    [CrossRef] [PubMed]
  13. M. Shirasaki and H. A. Haus, �??Squeezing of pulses in a nonlinear interferometer,�?? J. Opt. Soc. Am. B 7, 30�??34 (1990).
    [CrossRef]
  14. M. E. Marhic and C. H. Hsia, �??Optical amplification in a nonlinear interferometer,�?? Electron. Lett. 27, 210�??211 (1991).
    [CrossRef]
  15. P. Narum and R. W. Boyd, �??Nonfrequency-shifted phase conjugation by Brillouin-enhanced four-wave mixing,�?? IEEE J. Quantum Electron. 23, 1211�??1216 (1987).
    [CrossRef]
  16. C. J. McKinstrie, S. Radic and A. R. Chraplyvy, �??Parametric amplifiers driven by two pump waves,�?? IEEE J. Sel. Top. Quantum Electron. 8, 538�??547 and 956 (2002), and references therein.
    [CrossRef]
  17. C. J. McKinstrie, S. Radic and C. Xie, �??Parametric instabilities driven by orthogonal pump waves in birefringent fibers,�?? Opt. Express 11, 2619�??2633 (2003) and references therein.
    [CrossRef] [PubMed]
  18. C. J. McKinstrie, H. Kogelnik, R. M. Jopson, S. Radic and A. V. Kanaev, �??Four-wave mixing in fibers with random birefringence,�?? Opt. Express 12, 2033�??2055 (2004) and refrences therein.
    [CrossRef] [PubMed]

Electron. Lett. (1)

M. E. Marhic and C. H. Hsia, �??Optical amplification in a nonlinear interferometer,�?? Electron. Lett. 27, 210�??211 (1991).
[CrossRef]

IEEE J. Quantum Electron. (2)

P. Narum and R. W. Boyd, �??Nonfrequency-shifted phase conjugation by Brillouin-enhanced four-wave mixing,�?? IEEE J. Quantum Electron. 23, 1211�??1216 (1987).
[CrossRef]

R. Loudon, �??Theory of noise accumulation in linear optical-amplifier chains,�?? IEEE J. Quantum Electron. 21, 766�??773 (1985).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C. J. McKinstrie, S. Radic and A. R. Chraplyvy, �??Parametric amplifiers driven by two pump waves,�?? IEEE J. Sel. Top. Quantum Electron. 8, 538�??547 and 956 (2002), and references therein.
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. D. Li, P. Kumar, W. L. Kath and J. N. Kutz, �??Combating dispersion with parametric amplifers,�?? IEEE Photon. Technol. Lett. 5, 669�??672 (1993).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (5)

B. Yurke, �??Use of cavities in squeezed-state-generation,�?? Phys. Rev. A 29, 408�??410 (1984).
[CrossRef]

P. Kumar and J. H. Shapiro, �??Squeezed-state generation via forward degenerate four-wave mixing,�?? Phys. Rev. A 30, 1568�??1571 (1984).
[CrossRef]

M. D. Levenson, R. M. Shelby, A. Aspect, M. Reid and D. F.Walls, �??Generation and detection of squeezed states of light by nondegenerate four-wave mixing in an optical fiber,�?? Phys. Rev. A 32, 1550�??1562 (1985).
[CrossRef] [PubMed]

M. J. Potasek and B. Yurke, �??Squeezed light generation in a medium governed by the nonlinear Schrödinger equation,�?? Phys. Rev. A 35, 3974�??3977 (1987).
[CrossRef] [PubMed]

T. A. B. Kennedy and S. Wabnitz, �??Quantum propagation: Squeezing via modulational polarization instabilities in a birefringent nonlinear medium,�?? Phys. Rev. A 38, 563�??566 (1988).
[CrossRef] [PubMed]

Other (1)

R. Loudon, The Quantum Theory of Light, 3rd Ed. (Oxford University Press, Oxford, 2000)

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Figures (4)

Fig. 1.
Fig. 1.

Polarization diagram for degenerate scalar FWM.

Fig. 2.
Fig. 2.

Polarization diagram for degenerate vector FWM.

Fig. 3.
Fig. 3.

Polarization diagrams for cascaded scalar BS and PC. During BS pump 3 is on and pump 5 is off, whereas during PC pump 3 is off and pump 5 is on.

Fig. 4.
Fig. 4.

Polarization diagrams for cascaded vector BS and PC. During BS pump 3 is on and pump 5 is off, whereas during PC pump 3 is off and pump 5 is on.

Equations (40)

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d z A 1 = i 2 γ ¯ A 2 A 1 * exp ( iβz ) ,
d z A 2 = i γ ¯ A 1 2 exp ( iβz ) ,
A 1 ( z ) = B 1 ( z ) exp ( iβz 2 ) .
( d z ) B 1 = B 1 * ,
B 1 ( z ) = μ ( z ) B 1 ( 0 ) + ν ( z ) B 1 ( 0 ) * ,
μ ( z ) = cosh ( κz ) + i ( δ κ ) sinh ( κz ) ,
ν ( z ) = i ( γ κ ) sinh ( κz )
d z A 1 = i γ ¯ ( A 1 2 + 2 A 2 2 + 2 A 3 2 ) A 1 + i γ ¯ A 2 2 A 3 * exp ( iβz ) ,
d z A 2 = i γ ¯ ( 2 A 1 2 + A 2 2 + 2 A 3 2 ) A 2 + i 2 γ ¯ A 3 A 1 A 2 * exp ( iβz ) ,
d z A 3 = i γ ¯ ( 2 A 1 2 + 2 A 2 2 + A 3 2 ) A 3 + i γ ¯ A 1 * A 2 2 exp ( iβz ) ,
A 3 ( z ) = A 3 ( 0 ) exp [ i γ ¯ ( 2 P 1 + P 3 ) z ] ,
A 1 ( z ) = A 1 ( 0 ) exp [ i γ ¯ ( P 1 + 2 P 3 ) z ] .
A 2 ( z ) = B 2 ( z ) exp [ iβz 2 + i 3 γ ¯ ( P 3 + P 1 ) z 2 ] .
( d z ) B 2 = B 2 * ,
d z A 1 = i γ ¯ ( A 1 2 + 2 A 2 2 + ε A 3 2 + ε A 4 2 ) A 1 + i γ ¯ ε A 2 A 3 A 4 * exp ( iβz ) ,
d z A 2 = i γ ¯ ( 2 A 1 2 + A 2 2 + ε A 3 2 + ε A 4 2 ) A 2 + i γ ¯ ε A 3 * A 4 A 1 exp ( iβz ) ,
d z A 3 = i γ ¯ ( ε A 1 2 + ε A 2 2 + A 3 2 + 2 A 4 2 ) A 3 + i γ ¯ ε A 4 A 1 A 2 * exp ( iβz ) ,
d z A 4 = i γ ¯ ( ε A 1 2 + ε A 2 2 + 2 A 3 2 + A 4 2 ) A 4 + i γ ¯ ε A 1 * A 2 A 3 exp ( iβz ) ,
A 4 ( z ) = A 4 ( 0 ) exp [ i γ ¯ ( ε P 1 + P 4 ) z ] ,
A 1 ( z ) = A 1 ( 0 ) exp [ i γ ¯ ( P 1 + ε P 4 ) z ] .
A 2 ( z ) = B 2 ( z ) exp [ iβz 2 + i γ ¯ 3 P 1 z 2 + i γ ¯ ( ε 1 2 ) P 4 z ] ,
A 3 ( z ) = B 3 ( z ) exp [ iβz 2 + i γ ¯ ( ε 1 2 ) P 1 z + i γ ¯ 3 P 4 z 2 ] .
( d z ) B 2 = B 3 * ,
( d z + ) B 3 * = i γ * B 2 ,
B 2 ( z ) = μ ( z ) B 2 ( 0 ) + ν ( z ) B 3 * ( 0 ) ,
B 3 * ( z ) = ν * ( z ) B 2 ( 0 ) + μ * ( z ) B 3 * ( 0 ) ,
A 1 ( z ) = A 1 ( 0 ) exp [ i γ ¯ ( P 1 + ε P 3 ) z ] ,
A 3 ( z ) = A 3 ( 0 ) exp [ i γ ¯ ( ε P 1 + P 3 ) z ] .
A 2 ( z ) = B 2 ( z ) exp [ iβz 2 + i γ ¯ 3 P 1 z 2 + i γ ¯ ( ε + 1 2 ) P 3 z ] ,
A 4 ( z ) = B 4 ( z ) exp [ iβz 2 + i γ ¯ ( ε + 1 2 ) P 1 z + i γ ¯ 3 P 3 z 2 ] .
( d z ) B 2 = B 4 ,
( d z + ) B 4 = i γ * B 2 ,
B 2 ( z ) = μ ¯ ( z ) B 2 ( 0 ) + ν ¯ ( z ) B 4 ( 0 ) ,
B 4 ( z ) = ν ¯ * ( z ) B 2 ( 0 ) + μ ¯ * ( z ) B 4 ( 0 ) ,
μ ¯ ( z ) = cos ( kz ) + i ( δ k ) sin ( kz ) ,
ν ¯ ( z ) = i ( γ k ) sin ( kz )
( d z ) B 2 = B 4 * ,
( d z + ) B 4 * = i γ * B 2 ,
B 2 ( z ) = μ ( z z ) B 2 ( z ) + ν ( z z ) B 4 * ( z ) ,
B 4 * ( z ) = ν * ( z z ) B 2 ( z ) + μ * ( z z ) B 4 * ( z ) ,

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