Abstract

We theoretically and numerically explain the power saturation and the additional phase noise brought by the fiber optical parametric amplifier (FOPA). An equation to calculate an approximation to the saturated signal output power is presented. We also propose a scheme for alleviating the phase noise brought by the FOPA at the saturated state. In simulation, by controlling the decisive factor dispersion difference term Δk of the FOPA, amplitude-noise and additional phase noise reduction of quadrature phase shift keying (QPSK) based on the saturated FOPA is studied, which can provide promising performance to deal with PSK signals.

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References

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  1. M. Matsumoto, “Fiber-based all-optical signal regeneration,” IEEE J. Sel. Top. Quantum Electron.18(2), 738–752 (2012).
    [CrossRef]
  2. M. Gao, J. Kurumida, and S. Namiki, “Wide range operation of regenerative optical parametric wavelength converter using ASE-degraded 43-Gb/s RZ-DPSK signals,” Opt. Express19(23), 23258–23270 (2011).
    [CrossRef] [PubMed]
  3. G. K. P. Lei, C. Shu, and H. K. Tsang, “Amplitude noise reduction, pulse format conversion, and wavelength multicast of PSK signal in a fiber optical parametric amplifier,” National Fiber Optics Engineers Conference (NFOEC), JW2A.79, Mar. 2012.
  4. C. S. Brès, A. O. J. Wiberg, J. Coles, and S. Radic, “160-Gb/s optical time division multiplexing and multicasting in parametric amplifiers,” Opt. Express16(21), 16609–16615 (2008).
    [PubMed]
  5. P. O. Hedekvist and P. A. Anderson, “Noise characteristics of fiber-based optical phase conjugators,” J. Lightwave Technol.17(1), 74–79 (1999).
    [CrossRef]
  6. P. Kylemark, P. O. Hedekvist, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Noise characteristics of fiber optical parametric amplifiers,” J. Lightwave Technol.22(2), 409–416 (2004).
    [CrossRef]
  7. S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy, “All-optical regeneration in one- and two-pump parametric amplifiers using highly nonlinear optical fiber,” IEEE Photon. Technol. Lett.15(7), 957–959 (2003).
    [CrossRef]
  8. M. Matsumoto, “Phase noise generation in an amplitude limiter using saturation of a fiber-optic parametric amplifier,” Opt. Lett.33(15), 1638–1640 (2008).
    [CrossRef] [PubMed]
  9. P. Kylemark, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Semi-analytic saturation theory of fiber optical parametric amplifiers,” J. Lightwave Technol.24(9), 3471–3479 (2006).
    [CrossRef]
  10. S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An optical parametric amplified fiber switch for optical signal processing and regeneration,” J. Sel. Top. Quantum Electron.14(3), 674–680 (2008).
    [CrossRef]
  11. M. Sköld, J. Yang, H. Sunnerud, M. Karlsson, S. Oda, and P. A. Andrekson, “Constellation diagram analysis of DPSK signal regeneration in a saturated parametric amplifier,” Opt. Express16(9), 5974–5982 (2008).
    [CrossRef] [PubMed]
  12. G. Agrawal, Nonlinear Fiber Optics, 4th ed.(Aademic Press, 2007) Chap. 10.
  13. G. Cappellini and S. Trillo, “Third-order three-wave mixing in singlemode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B8(4), 824–838 (1991).
    [CrossRef]
  14. R. Elschner and K. Petermann, “Impact of pump-induced nonlinear phase noise on parametric amplification and wavelength conversion of phase modulated signals,” in Proc. Eur. Conf. Opt. Commun. (ECOC), Sep. 2009, Paper.

2012

M. Matsumoto, “Fiber-based all-optical signal regeneration,” IEEE J. Sel. Top. Quantum Electron.18(2), 738–752 (2012).
[CrossRef]

2011

2008

2006

2004

2003

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy, “All-optical regeneration in one- and two-pump parametric amplifiers using highly nonlinear optical fiber,” IEEE Photon. Technol. Lett.15(7), 957–959 (2003).
[CrossRef]

1999

1991

Anderson, P. A.

Andrekson, P. A.

Brès, C. S.

Cappellini, G.

Centanni, J. C.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy, “All-optical regeneration in one- and two-pump parametric amplifiers using highly nonlinear optical fiber,” IEEE Photon. Technol. Lett.15(7), 957–959 (2003).
[CrossRef]

Chraplyvy, A. R.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy, “All-optical regeneration in one- and two-pump parametric amplifiers using highly nonlinear optical fiber,” IEEE Photon. Technol. Lett.15(7), 957–959 (2003).
[CrossRef]

Coles, J.

Futami, F.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An optical parametric amplified fiber switch for optical signal processing and regeneration,” J. Sel. Top. Quantum Electron.14(3), 674–680 (2008).
[CrossRef]

Gao, M.

Hedekvist, P. O.

Huettl, B.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An optical parametric amplified fiber switch for optical signal processing and regeneration,” J. Sel. Top. Quantum Electron.14(3), 674–680 (2008).
[CrossRef]

Jopson, R. M.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy, “All-optical regeneration in one- and two-pump parametric amplifiers using highly nonlinear optical fiber,” IEEE Photon. Technol. Lett.15(7), 957–959 (2003).
[CrossRef]

Karlsson, M.

Kurumida, J.

Kylemark, P.

Ludwig, R.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An optical parametric amplified fiber switch for optical signal processing and regeneration,” J. Sel. Top. Quantum Electron.14(3), 674–680 (2008).
[CrossRef]

Matsumoto, M.

McKinstrie, C. J.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy, “All-optical regeneration in one- and two-pump parametric amplifiers using highly nonlinear optical fiber,” IEEE Photon. Technol. Lett.15(7), 957–959 (2003).
[CrossRef]

Namiki, S.

Oda, S.

Okabe, R.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An optical parametric amplified fiber switch for optical signal processing and regeneration,” J. Sel. Top. Quantum Electron.14(3), 674–680 (2008).
[CrossRef]

Radic, S.

C. S. Brès, A. O. J. Wiberg, J. Coles, and S. Radic, “160-Gb/s optical time division multiplexing and multicasting in parametric amplifiers,” Opt. Express16(21), 16609–16615 (2008).
[PubMed]

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy, “All-optical regeneration in one- and two-pump parametric amplifiers using highly nonlinear optical fiber,” IEEE Photon. Technol. Lett.15(7), 957–959 (2003).
[CrossRef]

Schmidt-Langhorst, C.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An optical parametric amplified fiber switch for optical signal processing and regeneration,” J. Sel. Top. Quantum Electron.14(3), 674–680 (2008).
[CrossRef]

Schubert, C.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An optical parametric amplified fiber switch for optical signal processing and regeneration,” J. Sel. Top. Quantum Electron.14(3), 674–680 (2008).
[CrossRef]

Sköld, M.

Sunnerud, H.

Trillo, S.

Watanabe, S.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An optical parametric amplified fiber switch for optical signal processing and regeneration,” J. Sel. Top. Quantum Electron.14(3), 674–680 (2008).
[CrossRef]

Weber, H.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An optical parametric amplified fiber switch for optical signal processing and regeneration,” J. Sel. Top. Quantum Electron.14(3), 674–680 (2008).
[CrossRef]

Wiberg, A. O. J.

Yang, J.

IEEE J. Sel. Top. Quantum Electron.

M. Matsumoto, “Fiber-based all-optical signal regeneration,” IEEE J. Sel. Top. Quantum Electron.18(2), 738–752 (2012).
[CrossRef]

IEEE Photon. Technol. Lett.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy, “All-optical regeneration in one- and two-pump parametric amplifiers using highly nonlinear optical fiber,” IEEE Photon. Technol. Lett.15(7), 957–959 (2003).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

J. Sel. Top. Quantum Electron.

S. Watanabe, F. Futami, R. Okabe, R. Ludwig, C. Schmidt-Langhorst, B. Huettl, C. Schubert, and H. Weber, “An optical parametric amplified fiber switch for optical signal processing and regeneration,” J. Sel. Top. Quantum Electron.14(3), 674–680 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Other

R. Elschner and K. Petermann, “Impact of pump-induced nonlinear phase noise on parametric amplification and wavelength conversion of phase modulated signals,” in Proc. Eur. Conf. Opt. Commun. (ECOC), Sep. 2009, Paper.

G. K. P. Lei, C. Shu, and H. K. Tsang, “Amplitude noise reduction, pulse format conversion, and wavelength multicast of PSK signal in a fiber optical parametric amplifier,” National Fiber Optics Engineers Conference (NFOEC), JW2A.79, Mar. 2012.

G. Agrawal, Nonlinear Fiber Optics, 4th ed.(Aademic Press, 2007) Chap. 10.

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Figures (10)

Fig. 1
Fig. 1

The additional phase noise introduced by the saturated FOPA working as an amplitude limiter.

Fig. 2
Fig. 2

Evolution of signal power in the fiber for different input powers. The dashed, full, and dot lines are corresponding to the input signal power 0.35mW, 0.17mW and 0.05mW, respectively.

Fig. 3
Fig. 3

The Saturation Behavior in the FOPA.

Fig. 4
Fig. 4

(a) The power evolution of the signals with input power 0.35 mW (red solid line) and input power 0.05 mW (green dashed line). (b) Illustration of the concided part and uncoincide part of the two signals by moving the dashed line along the length axis.

Fig. 5
Fig. 5

Transmission relations of input signal power and output power (full line)/output nonlinear phase shift (dashed line).

Fig. 6
Fig. 6

Transmission relations of input signal power and output power (full line)/output nonlinear phase shift (dashed line).

Fig. 7
Fig. 7

The relation between input signal SNR and output phase noise before (blue)/after (red) the optimization.

Fig. 8
Fig. 8

FOPA configuration for numerical simulation.

Fig. 9
Fig. 9

Constellations of the signal (SNR 20dB) before (a), after (b) (c) the FOPA, (c) is the optimized result.

Fig. 10
Fig. 10

Constellations of the signal (SNR 15dB) before (a), after (b) (c) the FOPA, (c) is the optimized result.

Equations (23)

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d E 0 dz =iγ[ | E 0 | 2 +2( | E 1 | 2 + | E 2 | 2 ) ] E 0 +2iγ E 1 E 2 E 0 * exp(iΔkz),
d E 1 dz =iγ[ | E 1 | 2 +2( | E 0 | 2 + | E 2 | 2 ) ] E 1 +iγ E 2 * E 0 * E 0 exp(iΔkz),
d E 2 dz =iγ[ | E 2 | 2 +2( | E 1 | 2 + | E 0 | 2 ) ] E 2 +iγ E 1 * E 0 * E 0 exp(iΔkz).
dη dξ =4η a 1 a 2 sinϕ,
d a 1 dξ =η a 2 sinϕ,
d a 2 dξ =η a 1 sinϕ,
d ϕ 0 dξ =η+2( a 1 2 + a 2 2 )+2 a 1 a 2 cosϕ,
d ϕ 1 dξ = a 1 2 +2(η+ a 2 2 )+ a 2 a 1 ηcosϕ,
d ϕ 2 dξ = a 2 2 +2(η+ a 1 2 )+ a 1 a 2 ηcosϕ,
dϕ dξ =κ+2η( a 1 2 + a 2 2 )+[( a 1 a 2 + a 2 a 1 )η4 a 1 a 2 ]cosϕ.
η(ξ)= (bc)a sn 2 [± (( 7 /2 )ξ+δ)/g](ac)b (bc) sn 2 [± (( 7 /2 )ξ+δ)/g](ac) , where g= 2 [(ac)(bd)] 1/2 , δ= η(0) b d η [f( η )] 1/2 .
a= 1 7 { (κ3)+ [ (κ3) 2 14H] 1/2 }1,
b=κ+1 [ (κ+1) 2 +2H] 1/2 1,
c= 1 7 { (κ3) [ (κ3) 2 14H] 1/2 } 1 7 (2κ+1),
d=κ+1+ [ (κ+1) 2 +2H] 1/2 2κ+1.
P signal (L)= A 1 2 (L)= 1 2 (1c)P 4+κ 7 P= 4 7 P+ Δk 7γ ,
d ϕ 1 dz =γ[ | E 1 | 2 +2( | E 0 | 2 + | E 2 | 2 )+ | E 2 | | E 1 | | E 0 | 2 cosϕ] =γ[ A 1 2 +2( A 0 2 + A 2 2 )+ A 2 A 1 A 0 2 cosϕ].
d ϕ 1 dz =γ[2P A 1 2 + A 2 A 1 A 0 2 cosϕ].
Δ ϕ 1 = d ϕ red d ϕ green =γ L phaseR (2P+2ΔP A 1 2 + A 2 A 1 A 0 2 cosϕ)dz γ L phaseG (2P A 1 2 + A 2 A 1 A 0 2 cosϕ)dz .
Δ ϕ 1 γ L phaseR (2ΔP A 1 2 + A 0 2 )dz .
Δ ϕ 1 =γ L phaseR (2P+2ΔP A 1 2 + A 2 A 1 A 0 2 cosϕ)dz γ L phaseG (2P A 1 2 + A 2 A 1 A 0 2 cosϕ)dz <γ( A 0 2 (L) A 1 2 (L)) L phaseR .
Δ ϕ 1 < 1 7 (3κ+5)γP L phaseR .
4<κ< 5 3 .

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