Abstract

We show for the first time, to the best of our knowledge, that, in a coherent communication system that employs a phase-shift-keying signal and Raman amplification, besides the pump relative intensity noise (RIN) transfer to the amplitude, the signal’s phase will also be affected by pump RIN through the pump–signal cross-phase modulation. Although the average pump power induced linear phase change can be compensated for by the phase-correction algorithm, a relative phase noise (RPN) parameter has been found to characterize pump RIN induced stochastic phase noise. This extra phase noise brings non-negligible system impairments in terms of the Q-factor penalty. The calculation shows that copumping leads to much more stringent requirements to pump RIN, and relatively larger fiber dispersion helps to suppress the RPN induced impairment. A higher-order phase-shift keying (PSK) signal is less tolerant to noise than a lower-order PSK.

© 2013 Optical Society of America

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References

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  1. X. Zhou, L. E. Nelson, R. Isaac, P. Magil, B. Zhu, and D. W. Peckham, in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OM2A.2.
  2. C. R. S. Fludger, V. Handerek, and R. J. Mears, J. Lightwave Technol. 19, 1140 (2001).
    [CrossRef]
  3. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  4. S. Zhang, P. Y. Kam, J. Chen, and C. Yu, Opt. Express 18, 12088 (2010).
    [CrossRef]

2010 (1)

2001 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Chen, J.

Fludger, C. R. S.

Handerek, V.

Isaac, R.

X. Zhou, L. E. Nelson, R. Isaac, P. Magil, B. Zhu, and D. W. Peckham, in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OM2A.2.

Kam, P. Y.

Magil, P.

X. Zhou, L. E. Nelson, R. Isaac, P. Magil, B. Zhu, and D. W. Peckham, in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OM2A.2.

Mears, R. J.

Nelson, L. E.

X. Zhou, L. E. Nelson, R. Isaac, P. Magil, B. Zhu, and D. W. Peckham, in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OM2A.2.

Peckham, D. W.

X. Zhou, L. E. Nelson, R. Isaac, P. Magil, B. Zhu, and D. W. Peckham, in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OM2A.2.

Yu, C.

Zhang, S.

Zhou, X.

X. Zhou, L. E. Nelson, R. Isaac, P. Magil, B. Zhu, and D. W. Peckham, in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OM2A.2.

Zhu, B.

X. Zhou, L. E. Nelson, R. Isaac, P. Magil, B. Zhu, and D. W. Peckham, in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OM2A.2.

J. Lightwave Technol. (1)

Opt. Express (1)

Other (2)

X. Zhou, L. E. Nelson, R. Isaac, P. Magil, B. Zhu, and D. W. Peckham, in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OM2A.2.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (2)

Fig. 1.
Fig. 1.

Estimated Q penalty of QPSK signal versus pump RIN on the copumping and counterpumping configuration. The walk-off parameters in the copumping configuration are 2, 4, and 6ps/m, respectively, and in the counterpumping configuration is 9800ps/m. The bit rate is 100Gb/s, the linewidth of the signal laser and the LO is 300 kHz, and γs=20dB.

Fig. 2.
Fig. 2.

Estimated Q penalty versus pump RIN for different order PSK signal. The walk-off parameter is 2ps/m for all, the bit rate is 100Gb/s, the linewidth of the signal laser and the LO is 300 kHz, and γb=15dB.

Equations (21)

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±Ap±z+αp2Ap±=iγp|Ap±|2Ap±,
AszdAsT+αs2As=iγs(2fR)|Ap±|2As+gs2|Ap±|2As,
As(z,T)=As(0,T+zd)exp(αs2z)·exp{[iγs(2fR)+gs2]Ψ±(z,T)}.
Ψ+(z,T)=0z|Ap+(0,T+zdzd)|2exp(αpz)dz,
Ψ(z,T)=0z|Ap(L,T+zdzd)|2exp[αp(Lz)]dz.
A=As(0,T+zd)exp(αs2z)exp[gs2Ψ±(z,T)],
θ=γs(2fR)Ψ±(z,T).
|Ap+(z,T)|2=Pp+(z,T)=Pp0exp(αz)[1+msin(2πfT+φ0)],
|Ap(z,T)|2=Pp(z,T)=Pp0exp[α(Lz)][1+msin(2πfT+φ0)],
Ψ+(z,T)=Pp01eαpzαp+mPp0M(z)cos(2πfT+2πfzd+φ0)αp2+(2πfd)2+mPp0N(z)sin(2πfT+2πfzd+φ0)αp2+(2πfd)2,
Ψ(z,T)=Pp0eαpLeαpz1αp+mPp0eαpLM(z)cos[2πfT+2πfzd+φ0]αp2+(2πfd)2+mPp0eαpLN(z)sin[2πfT+2πfzd+φ0]αp2+(2πfd)2,
M(z)=eαpz[αpsin(2πfdz)+2πfdcos(2πfdz)]2πfd,
N(z)=eαpz[2πfdsin(2πfdz)αpcos(2πfdz)]+αp,
M(z)=eαpz[αpsin(2πfdz)+2πfdcos(2πfdz)]2πfd,
N(z)=eαpz[2πfdsin(2πfdz)+αpcos(2πfdz)]αp.
RINs(f)co=δP2P2=RINp(f)M2(z)+N2(z)[αp2+(2πfd)2]2gs2Pp02,
RINs(f)counter=δP2P2=RINp(f)M2(z)+N2(z)[αp2+(2πfd)2]2gs2Pp02e2αpL.
RPNs(f)co=RINp(f)M2(z)+N2(z)[αp2+(2πfd)2]2αp2(1eαpz)2,
RPNs(f)counter=RINp(f)M2(z)+N2(z)[αp2+(2πfd)2]2αp2(eαpz1)2.
Pb(e)=ππPb(e|Δθ)p(Δθ)dΔθ,
σΔθ22L2+3L+16Lσp2+12L(σn2+σRPN2).

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