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]
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    [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]
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    [Crossref] [PubMed]
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    [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]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [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]

2004 (1)

2003 (1)

2002 (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]

1997 (1)

1993 (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]

1992 (2)

1991 (1)

M. E. Marhic and C. H. Hsia, “Optical amplification in a nonlinear interferometer,” Electron. Lett. 27, 210–211 (1991).
[Crossref]

1990 (1)

1988 (1)

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]

1987 (2)

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]

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]

1985 (2)

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]

R. Loudon, “Theory of noise accumulation in linear optical-amplifier chains,” IEEE J. Quantum Electron. 21, 766–773 (1985).
[Crossref]

1984 (2)

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]

1979 (1)

Aspect, A.

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]

Boyd, R. W.

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]

Chraplyvy, A. R.

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]

Haus, H. A.

Hsia, C. H.

M. E. Marhic and C. H. Hsia, “Optical amplification in a nonlinear interferometer,” Electron. Lett. 27, 210–211 (1991).
[Crossref]

Imajuku, W.

Jopson, R. M.

Kanaev, A. V.

Kath, W. L.

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]

Kennedy, T. A. B.

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]

Kogelnik, H.

Kumar, P.

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]

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

Kutz, J. N.

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]

Levenson, M. D.

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]

Li, R. D.

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]

Loudon, R.

R. Loudon, “Theory of noise accumulation in linear optical-amplifier chains,” IEEE J. Quantum Electron. 21, 766–773 (1985).
[Crossref]

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

Marhic, M. E.

M. E. Marhic and C. H. Hsia, “Optical amplification in a nonlinear interferometer,” Electron. Lett. 27, 210–211 (1991).
[Crossref]

McKinstrie, C. J.

Mu, Y.

Narum, P.

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]

Potasek, M. J.

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]

Radic, S.

Reid, M.

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]

Savage, C. M.

Shapiro, J. H.

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

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]

Shelby, R. M.

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]

Shirasaki, M.

Takada, A.

Wabnitz, S.

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]

Walls, D. F.

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]

Xie, C.

Yuen, H. P.

Yurke, B.

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]

B. Yurke, “Use of cavities in squeezed-state-generation,” Phys. Rev. A 29, 408–410 (1984).
[Crossref]

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)

Equations on this page are rendered with MathJax. Learn more.

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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