## Reduction of nonlinear phase noise using optical phase conjugation in quasi-linear optical transmission systems

Optics Express, Vol. 15, Issue 5, pp. 2166-2177 (2007)

http://dx.doi.org/10.1364/OE.15.002166

Acrobat PDF (144 KB)

### Abstract

An analytical expression for the variance of nonlinear phase noise for a quasi-linear system using the midpoint optical phase conjugation (OPC) is obtained. It is shown that the the system with OPC and dispersion inversion (DI) can exactly cancel the nonlinear phase noise up to the first order in nonlinear coefficient if the amplifier and the end point of the system are equidistant from the OPC. It is found that the nonlinear phase noise variance of the midpoint phase-conjugated optical transmission system with DI is smaller than that of the system without DI.

© 2007 Optical Society of America

## 1. Introduction

1. J.P. Gordon and L.F. Mollenauer, “Phase noise in photonic communication systems using linear amplifiers,” Opt.Lett. **15**, 1351–1353 (1990). [CrossRef] [PubMed]

2. A. Mecozzi, “Limits to long-haul coherent transmission set by the Kerr nonlinearity and noise of the in-line amplifiers,” J. Lightwave Technol. **12**, 1993–2000 (1994). [CrossRef]

16. X. Zhu, S. Kumar, and X. Li, “Comparison between DPSK and OOK modulation schemes in nonlinear optical transmission systems,” App. Opt. **45**, 6812–6822 (2006). [CrossRef]

11. S.L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, “Optical phase conjugation for ultra long haul phase- shift-keyed transmission,” IEEE J. of Lightwave Technol. **24**, 54–64 (2006). [CrossRef]

14. C.J. McKinstrie, S. Radic, and C. Xie, “Reduction of soliton phase jitter by in-line phase conjugation,” Opt. Lett. **28**, 1519–1521 (2003). [CrossRef] [PubMed]

15. D. Boivin, G. -K. Chang, J. R. Barry, and M. Hanna, “Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion,” J. Opt. Soc. Am. B **23**, 2019–2023 (2006). [CrossRef]

*L*/2 and 2

_{tot}*L*/3, respectively. This is consistent with previously published results obtained [14

_{tot}14. C.J. McKinstrie, S. Radic, and C. Xie, “Reduction of soliton phase jitter by in-line phase conjugation,” Opt. Lett. **28**, 1519–1521 (2003). [CrossRef] [PubMed]

15. D. Boivin, G. -K. Chang, J. R. Barry, and M. Hanna, “Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion,” J. Opt. Soc. Am. B **23**, 2019–2023 (2006). [CrossRef]

9. K. P. Ho, “Mid-Span Compensation of Nonlinear Phase Noise,” Optics Comm. **245**, 391–398 (2005). [CrossRef]

17. A.G. Striegler and B. Schmauss, “Compensation of intrachannel effects in symmetric dispersion-managed transmission systems,” J. of Lightwave Technol. **22**, 1877–1882 (2004). [CrossRef]

19. A. Chowdhury and R.J. Essiambre, “Optical phase conjugation and psuedo linear transmission,” Opt.Lett. **29**,
1105–1107 (2004). [CrossRef] [PubMed]

20. P. Minzioni, F. Alberti, and A. Schiffini, “Experimental demonstration of nonlinearity and dispersion compensation in an embedded link by optical phase conjugation,” IEEE Photon. Technol. Lett. **16**, 813–815 (2004). [CrossRef]

21. P. Kaewplung, T. Angkaew, and K. Kikuchi, “Simultaneous suppression of third order dispersion and side band instability in single channel optical fiber transmission by midway optical phase conjugation employing higher order dispersion management,” J. Lightwave Technol. **21**, 1465–1473 (2003). [CrossRef]

22. H. Wei and D.V. Plant, “Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation,” Opt. Express **12**, 1938–1958 (2004). [CrossRef] [PubMed]

23. H. Wei and D.V. Plant, “Intra-channel nonlinearity compensation with scaled translational symmetry,” Opt. Express , **12**, 4282–4296 (2004). [CrossRef] [PubMed]

24. X. Tang and Z. Wu, “Reduction of intrachannel nonlinearity using optical phase conjugation,” IEEE Photon. Technol. Lett. **17**, 1863–1865 (2005). [CrossRef]

25. R. Holzlohner, V.S. Grigoryan, C.R. Menyuk, and W.L. Kath, “Accurate calculation of eye diagrams and bit error
rates in optical transmission systems using linearization,” J. Lightwave Technol. **20**, 389–400 (2002). [CrossRef]

28. A. Vanucci, P. Serena, and A. Bononi, “The RP method: a new tool for the iterative solution of the nonlinear Schrodinger equation,” J. Lightwave Technol. **20**, 1102–1112 (2002). [CrossRef]

25. R. Holzlohner, V.S. Grigoryan, C.R. Menyuk, and W.L. Kath, “Accurate calculation of eye diagrams and bit error
rates in optical transmission systems using linearization,” J. Lightwave Technol. **20**, 389–400 (2002). [CrossRef]

26. I. Gabitov and S. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. **21**, 327–329 (1996). [CrossRef]

27. E.E. Narimanov and P. Mitra, “The channel capacity of a fiber optics communication system: perturbation theory,” J. Lightwave Technol. **20**, 530–537 (2002). [CrossRef]

29. S. Kumar and D. Yang, “Second order theory for self-phase modulation and cross-phase modulation in optical fibers,” J. Lightwave Technol. **23**, 2073 (2005). [CrossRef]

## 2. Nonlinear phase noise

_{2}(

*z*) is the dispersion profile, γ is the nonlinear coefficient,

*w*(

*z*)=∫

^{z}

_{0}α(

*s*)

*ds*, α(

*z*) is the fiber loss/amplifier gain profile. The field can be expanded into a series

*u*denotes the jth-order correction. The zeroth order field

_{j}*u*

_{0}corresponds to the solution of the linear part of Eq. (1). Without loss of generality, let us consider an amplifier located at

*z*=0−. The total field after the amplifier can be written as

*x*(

*t*,0) ≡

*x*

_{0}(

*t*) is the input signal field and

*n*(

*t*,0) ≡

*n*

_{0}(

*t*) is the noise field due to the amplifier. We assume that the noise field

*n*

_{0}(

*t*) is much smaller than the signal filed

*x*

_{0}(

*t*).Consider a dispersion compensated fiber system

**H**of length

*L*and accumulative dispersion profile

_{opc}*S*(

*z*)=∫

^{z}

_{0}β

_{2}(

*x*)

*dx*with

*S*(

*L*)=0. The system

_{opc}**H**consists of several amplifiers and dispersion managed fibers as shown in Fig. 1. Let

*L*be the amplifier spacing. Following the first order perturbation theory [26

26. I. Gabitov and S. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. **21**, 327–329 (1996). [CrossRef]

29. S. Kumar and D. Yang, “Second order theory for self-phase modulation and cross-phase modulation in optical fibers,” J. Lightwave Technol. **23**, 2073 (2005). [CrossRef]

**H**up to the first order in γ can be written as

*u*

_{0}(

*t*,

*z*) is the zeroth order solution,

*u*(

*t*,0)=

*u*

_{0}(

*t*,0) and

*u*(

_{j}*t*,0)=0,

*j*>0 and

*m*٭(

*t*) is the linear impulse response of the fiber,

**U**

^{H}

_{in}and

**U**

^{H}

_{out}are vectors corresponding to

*u*(

*t*,0) and

*u*(

*t*,

*L*), respectively,

_{opc}**V**(

*S*(

*z*),

**U**

^{H}

_{in}) is a vector corresponding to |

*u*

_{0}(

*t*,

*z*)|

^{2}

*u*

_{0}(

*t*,

*z*) and

**M**(

*S*) is a matrix corresponding to the kernel

*m*(

*t*,

*z*). For simplicity, let us assume that the input signal field

*x*

_{0}(

*t*) is real. The zeroth order field can be decomposed into signal field and noise field as

**H**is defined as

*X*(

*t*)=

*X*(

_{r}*t*)+

*iX*(

_{i}*t*),

*X*=

*Y*,

*n*

_{0}. In the above approximation, the second and higher order terms in γ are ignored. To understand the evolution of nonlinear phase noise, let us consider a part of integrand of Eq. (5):

*n*(

*t*) and we ignore them. Therefore, ASE-induced nonlinear phase noise originates mainly from the second and third terms in Eq. (12). Using Eqs. (9), (5) and (11), the ASE-induced nonlinear phase shift corresponding to the second term in Eq. (12) is given by

**H**excluding the first, fourth and fifth terms of Eq. (12) is given by

**H**passes through an OPC. The output of OPC is simply the complex-conjugate of its input UH out and is given by

**G**as shown in Fig. 1. Therefore, the signal input

**G**is

**G**can be written as

**G**and

**H**, respectively.

### 2.1. System without dispersion inversion

*L*=

_{opc}*L*/2. The corresponding accumulated dispersion profile is shown in Fig. 2(a).Using Eq. (23) in Eq. (22) and retaining only the terms that are first order in

_{tot}*γ*, we obtain

**G**(corresponding the second term in Eq. (12)) as

*n*in Eq.(25) indicates that the contribution to the phase noise originating from

_{0r}*n*is eliminated using the OPC. Since n0r and

_{0r}*n*are statistically independent and convolution with

_{0i}*m*and

_{r}*m*does not change this property, it follows that the OPC provides a partial reduction of the variance of nonlinear phase noise. A similar analysis for the nonlinear phase noise originating from the third term in Eq. (12) also shows the partial reduction.

_{i}### 2.2. System with dispersion inversion

*G*is identical to system

*H*except for the sign of

*S*(

*z*)[21

21. P. Kaewplung, T. Angkaew, and K. Kikuchi, “Simultaneous suppression of third order dispersion and side band instability in single channel optical fiber transmission by midway optical phase conjugation employing higher order dispersion management,” J. Lightwave Technol. **21**, 1465–1473 (2003). [CrossRef]

24. X. Tang and Z. Wu, “Reduction of intrachannel nonlinearity using optical phase conjugation,” IEEE Photon. Technol. Lett. **17**, 1863–1865 (2005). [CrossRef]

*G*up to the first order in

*γ*is

*z*=0 can be exactly cancelled up to the first order in

*γ*if the dispersion profile after the OPC is inverted as shown in Fig. 2(b). For a system without dispersion inversion (DI), the nonlinear phase noise due to the in-phase noise component n0r of an amplifier at

*z*=0 can be eliminated using OPC (Eq. (25)) whereas for a system with DI, nonlinear phase noise due to both

*n*and

_{0r}*n*are eliminated. The nonlinear phase noise due to an amplifier located at

_{0i}*z*=

*nL*,

*z*<

*L*becomes zero at (

_{opc}*N*−

_{a}*n*)

*L*and it builds up from (

*N*−

_{a}*n*)

*L*to the end of the system. Refs. [21

21. P. Kaewplung, T. Angkaew, and K. Kikuchi, “Simultaneous suppression of third order dispersion and side band instability in single channel optical fiber transmission by midway optical phase conjugation employing higher order dispersion management,” J. Lightwave Technol. **21**, 1465–1473 (2003). [CrossRef]

24. X. Tang and Z. Wu, “Reduction of intrachannel nonlinearity using optical phase conjugation,” IEEE Photon. Technol. Lett. **17**, 1863–1865 (2005). [CrossRef]

30. I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R.S. Vodhanel, and C.-C. Wang, “Demonstration of negative dispersion fibers for DWDM metropolitan area networks,” IEEE J. Sel. Top. Quantum Electron. **7**, 439–460 (2001). [CrossRef]

**H**or

**G**could be represented by several spans of a dispersion managed fiber consisting of two equal segments with the dispersion of the first segment being anomalous whereas that of the second segment is equal in magnitude but opposite in sign, as shown in Fig.1. From the above derivation, we see that the noise source and the end point of the system should be equidistant from the OPC to cancel the nonlinear phase noise. However, the above condition is not fulfilled for all the amplifiers and clearly, the noise added by the amplifiers located after the OPC can not be compensated and therefore, only partial compensation of nonlinear phase noise is achieved.

### 3. Variance of nonlinear phase noise

10. S. Kumar, “Effect of dispersion on nonlinear phase noise in optical transmission systems,” Opt.Lett. **30**, 3278–3280 (2005). [CrossRef]

1. J.P. Gordon and L.F. Mollenauer, “Phase noise in photonic communication systems using linear amplifiers,” Opt.Lett. **15**, 1351–1353 (1990). [CrossRef] [PubMed]

1. J.P. Gordon and L.F. Mollenauer, “Phase noise in photonic communication systems using linear amplifiers,” Opt.Lett. **15**, 1351–1353 (1990). [CrossRef] [PubMed]

10. S. Kumar, “Effect of dispersion on nonlinear phase noise in optical transmission systems,” Opt.Lett. **30**, 3278–3280 (2005). [CrossRef]

10. S. Kumar, “Effect of dispersion on nonlinear phase noise in optical transmission systems,” Opt.Lett. **30**, 3278–3280 (2005). [CrossRef]

*L*be the amplifier spacing.Consider an amplifier located at

*mL*,

*m*<=

*Na*/2. Let the signal field at

*mL*be

*T*

_{0}is the half-width at 1/e- intensity point,

*T*=√π

_{eff}*T*

_{0}and

*E*is the pulse energy. Following the first order perturbation approach [33

33. A. Mecozzi, C.B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. **12**, 392–394 (2000). [CrossRef]

**30**, 3278–3280 (2005). [CrossRef]

*G*, we find that the signal field at the output of

*G*is

*mL*changes the signal energy by δ

*E*which is translated into phase fluctuations by the self-phase modulation (SPM).Therefore, change in nonlinear phase due to the noise added by the amplifier at

*mL*up to the first order in

*γ*is

*h*

_{r}(

*t*)=Re[

*h*(

*t*)]. For the standard configuration without midpoint OPC, the corresponding nonlinear phase change is given by [10

**30**, 3278–3280 (2005). [CrossRef]

*mL*(

*m*<

*N*

_{a}/2) to the end of the transmission line

*N*

_{a}*L*while for the system with midpoint OPC, it builds up only from (

*N*−

_{a}*m*)

*L*to

*N*. The amplifier noise added after the OPC is not compensated. Therefore, we have

_{a}L**30**, 3278–3280 (2005). [CrossRef]

**30**, 3278–3280 (2005). [CrossRef]

*γ*. If we include the small higher order correction [10

**30**, 3278–3280 (2005). [CrossRef]

#### 3.1. Optimal location of OPC

**H**and

**G**of Fig. 1a are identical except that the transmission distances in each of these systems are unequal. Let

*rN*be the length of the system

_{a}L**H**where

*N*− 1 is the total number of amplifiers in a combined system (

_{a}**H**and

**G**),

*L*be the amplifier spacing and

*rN*is an integer.

_{a}*mL*(

*m*<=

*rN*) is given by

_{a}*f*(

*r*,

*t*) is given by Eq. (34). When

*m*>

*rN*, the nonlinear phase change is (

_{a}*N*−

_{a}*m*)

*γh*(

_{r}*t*)δ

*E*/

*T*. Therefore, the variance of the peak nonlinear phase noise due to all the amplifiers can be written as

_{eff}*r*which gives

14. C.J. McKinstrie, S. Radic, and C. Xie, “Reduction of soliton phase jitter by in-line phase conjugation,” Opt. Lett. **28**, 1519–1521 (2003). [CrossRef] [PubMed]

15. D. Boivin, G. -K. Chang, J. R. Barry, and M. Hanna, “Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion,” J. Opt. Soc. Am. B **23**, 2019–2023 (2006). [CrossRef]

9. K. P. Ho, “Mid-Span Compensation of Nonlinear Phase Noise,” Optics Comm. **245**, 391–398 (2005). [CrossRef]

#### 4. Numerical simulations

^{−1}km

^{−1}, bit rate=40 Gb/s, wavelength=1.55 μm, fiber lossα =0.2 dB/km, spacing between amplifiers=80 km,

*n*=3, launched peak power=3 mW and computational bandwidth=2.4 THz. The dispersion management is achieved by using a 40 Km long anomalous dispersion fiber followed by a normal dispersion fiber of the same length and same absolute dispersion. Pre- /post-compensation fibers are not used. Total transmission distance=800 Km. A Gaussian pulse with full width half-maximum (FWHM) of 12.5 ps is launched to the fiber link. White Gaussian noise with a power spectral density per polarization as given by

_{sp}*β*

_{2}|) of the first or the second fiber segment within an amplifier spacing. The discrepancy between analytical and numerical results are due to the following reasons: (i) ignoring the third order terms in

*γ*in Eq.(43) and (ii) ignoring the second order perturbation term in

*γ*for the optical field in Eq. (32).

8. K.-P. Ho and H.-C. Wang, “Comparison of nonlinear phase noise and intrachannel four wave mixing for RZ-DPSK signals in dispersive transmission systems,” IEEE Photon. Technol. Lett. **17**, 1426–1428 (2005). [CrossRef]

13. K.-P. Ho and H.-C. Wang, “Effect of dispersion on nonlinear phase noise,” Opt. Lett. **31**, 2109–2111 (2006). [CrossRef] [PubMed]

*n*=0 and obtain the variances σ

_{sp}^{2}

_{10}for a bit ZERO and σ

^{2}

_{11}for a bit ONE at the end of the link. Next we turn on the amplifier noise and obtain the variance σ

^{2}

_{2j},

*j*=0, 1. The variance of linear and ASE-induced nonlinear phase noise (which includes SPM, IXPM and IFWM) is given by σ

^{2}

_{j}=σ

^{2}

_{2j}−σ

^{2}

_{1j}and is plotted in Fig. 4 for a bit ZER0. The results for bit ONE is very similar since the noise statistics for a bit ZERO and a bit ONE are the same.Comparing Figs. 3 and 4 for a system without OPC, we see that the variance has increased only a little due to ASE-IXPM interaction while according to Ref. [8

8. K.-P. Ho and H.-C. Wang, “Comparison of nonlinear phase noise and intrachannel four wave mixing for RZ-DPSK signals in dispersive transmission systems,” IEEE Photon. Technol. Lett. **17**, 1426–1428 (2005). [CrossRef]

8. K.-P. Ho and H.-C. Wang, “Comparison of nonlinear phase noise and intrachannel four wave mixing for RZ-DPSK signals in dispersive transmission systems,” IEEE Photon. Technol. Lett. **17**, 1426–1428 (2005). [CrossRef]

*β*

_{2}=-10 ps

^{2}/km, a given bit interacts with at most three or four neighboring bits on both sides while in Ref. [8

**17**, 1426–1428 (2005). [CrossRef]

## 5. Conclusions

## References and links

1. | J.P. Gordon and L.F. Mollenauer, “Phase noise in photonic communication systems using linear amplifiers,” Opt.Lett. |

2. | A. Mecozzi, “Limits to long-haul coherent transmission set by the Kerr nonlinearity and noise of the in-line amplifiers,” J. Lightwave Technol. |

3. | C. McKinstrie, C. Xie, and T. Lakoba, ”Efficient modeling of phase jitter in dispersion-managed soliton systems,” Opt. Lett. |

4. | A.G. Green, P.P. Mitra, and L.G.L. Wegener, “Effect of chromatic dispersion on nonlinear phase noise” Opt.Lett. |

5. | C.J. McKinstrie and C. Xie, “Phase jitter in single-channel soliton systems with constant dispersion,” IEEE J. Sel. Top. Quantum Electron. |

6. | H. Kim and A.H. Gnauck, “Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise,” IEEE Photon. Technol. Lett. |

7. | M. Hanna, D. Boivin, P.-A. Lacourt, and J.-P. Goedgebuer, “Calculation of optical phase jitter in dispersion-managed systems by the use of the moment method,” J. Opt. Soc. Am. B |

8. | K.-P. Ho and H.-C. Wang, “Comparison of nonlinear phase noise and intrachannel four wave mixing for RZ-DPSK signals in dispersive transmission systems,” IEEE Photon. Technol. Lett. |

9. | K. P. Ho, “Mid-Span Compensation of Nonlinear Phase Noise,” Optics Comm. |

10. | S. Kumar, “Effect of dispersion on nonlinear phase noise in optical transmission systems,” Opt.Lett. |

11. | S.L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P.M. Krummrich, W. Sohler, G.-D. Khoe, and H. de Waardt, “Optical phase conjugation for ultra long haul phase- shift-keyed transmission,” IEEE J. of Lightwave Technol. |

12. | F. Zhang, C.-A. Bunge, and K. Petermann, “Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems,” Opt. Lett. |

13. | K.-P. Ho and H.-C. Wang, “Effect of dispersion on nonlinear phase noise,” Opt. Lett. |

14. | C.J. McKinstrie, S. Radic, and C. Xie, “Reduction of soliton phase jitter by in-line phase conjugation,” Opt. Lett. |

15. | D. Boivin, G. -K. Chang, J. R. Barry, and M. Hanna, “Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion,” J. Opt. Soc. Am. B |

16. | X. Zhu, S. Kumar, and X. Li, “Comparison between DPSK and OOK modulation schemes in nonlinear optical transmission systems,” App. Opt. |

17. | A.G. Striegler and B. Schmauss, “Compensation of intrachannel effects in symmetric dispersion-managed transmission systems,” J. of Lightwave Technol. |

18. | G.P. Agrawal, “Fiber-optic communication systems,” (John Wiley and Sons, New York,1995). |

19. | A. Chowdhury and R.J. Essiambre, “Optical phase conjugation and psuedo linear transmission,” Opt.Lett. |

20. | P. Minzioni, F. Alberti, and A. Schiffini, “Experimental demonstration of nonlinearity and dispersion compensation in an embedded link by optical phase conjugation,” IEEE Photon. Technol. Lett. |

21. | P. Kaewplung, T. Angkaew, and K. Kikuchi, “Simultaneous suppression of third order dispersion and side band instability in single channel optical fiber transmission by midway optical phase conjugation employing higher order dispersion management,” J. Lightwave Technol. |

22. | H. Wei and D.V. Plant, “Simultaneous nonlinearity suppression and wide-band dispersion compensation using optical phase conjugation,” Opt. Express |

23. | H. Wei and D.V. Plant, “Intra-channel nonlinearity compensation with scaled translational symmetry,” Opt. Express , |

24. | X. Tang and Z. Wu, “Reduction of intrachannel nonlinearity using optical phase conjugation,” IEEE Photon. Technol. Lett. |

25. | R. Holzlohner, V.S. Grigoryan, C.R. Menyuk, and W.L. Kath, “Accurate calculation of eye diagrams and bit error
rates in optical transmission systems using linearization,” J. Lightwave Technol. |

26. | I. Gabitov and S. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. |

27. | E.E. Narimanov and P. Mitra, “The channel capacity of a fiber optics communication system: perturbation theory,” J. Lightwave Technol. |

28. | A. Vanucci, P. Serena, and A. Bononi, “The RP method: a new tool for the iterative solution of the nonlinear Schrodinger equation,” J. Lightwave Technol. |

29. | S. Kumar and D. Yang, “Second order theory for self-phase modulation and cross-phase modulation in optical fibers,” J. Lightwave Technol. |

30. | I. Tomkos, D. Chowdhury, J. Conradi, J. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, R.S. Vodhanel, and C.-C. Wang, “Demonstration of negative dispersion fibers for DWDM metropolitan area networks,” IEEE J. Sel. Top. Quantum Electron. |

31. | V. Bhagavatula, G. Berkey, D. Chowdhury, A. Evans, and M. Li, “Novel fibers for dispersion-managed high-bitrate systems,” Optical Fiber Conference, TuD2, 21–22, 1998. |

32. | S. Kumar and A.F. Evans, “Collision-induced impairments in in dispersion managed fiber systems” in ”Massive WDM and TDM solitons systems,” A. Hasegawa, Ed. (Kluwer Academic, Dordrecht, 2000), pp. 351–364. |

33. | A. Mecozzi, C.B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(190.3270) Nonlinear optics : Kerr effect

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.5040) Nonlinear optics : Phase conjugation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: August 28, 2006

Revised Manuscript: November 2, 2006

Manuscript Accepted: February 21, 2007

Published: March 5, 2007

**Citation**

Shiva Kumar and Ling Liu, "Reduction of nonlinear phase noise using optical phase conjugation
in quasi-linear optical transmission systems," Opt. Express **15**, 2166-2177 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-2166

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### References

- J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communication systems using linear amplifiers," Opt.Lett. 15, 1351-1353 (1990). [CrossRef] [PubMed]
- A. Mecozzi, "Limits to long-haul coherent transmission set by the Kerr nonlinearity and noise of the in-line amplifiers," J. Lightwave Technol. 12, 1993-2000 (1994). [CrossRef]
- C. McKinstrie, C. Xie, and T. Lakoba, "Efficient modeling of phase jitter in dispersion-managed soliton systems," Opt. Lett. 27, 1887-1889 (2002). [CrossRef]
- A. G. Green, P. P. Mitra, and L. G. L. Wegener, "Effect of chromatic dispersion on nonlinear phase noise" Opt. Lett. 28, 2455-2457 (2003). [CrossRef] [PubMed]
- C. J. McKinstrie and C. Xie, "Phase jitter in single-channel soliton systems with constant dispersion," IEEE J. Sel. Top. Quantum Electron. 8, 616-625 (2002). [CrossRef]
- H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003). [CrossRef]
- M. Hanna, D. Boivin, P.-A. Lacourt, and J.-P. Goedgebuer, "Calculation of optical phase jitter in dispersionmanaged systems by the use of the moment method," J. Opt. Soc. Am. B 21, 24-28 (2004). [CrossRef]
- K.-P. Ho and H.-C. Wang, "Comparison of nonlinear phase noise and intrachannel four wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426-1428 (2005). [CrossRef]
- K.-P. Ho, "Mid-Span Compensation of Nonlinear Phase Noise," Optics Comm. 245, 391-398 (2005). [CrossRef]
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