## Analysis of Nonlinear Phase Noise in Coherent Fiber-Optic Systems Based on Phase Shift Keying

Journal of Lightwave Technology, Vol. 27, Issue 21, pp. 4722-4733 (2009)

Acrobat PDF (339 KB)

### Abstract

Analytical expressions for the phase variance in a nonlinear fiber optic system based on phase-shift keying are developed. The Gauss-Hermite functions are used as the orthogonal basis to represent the noise field. Number of degrees of freedom (DOF) to accurately model the phase variance is estimated. The amplifier noise excites higher order Gauss-Hermite noise modes and the nonlinear mixing of a signal pulse and higher order Gauss-Hermite noise mode leads to new noise fields which enhance the nonlinear phase noise. The higher order noise modes propagate linearly and enhance the linear phase noise if the matched filter is not used at the receiver. Analytical expression for the optimum launch power is developed taking into account the linear and nonlinear phase noise.

© 2009 IEEE

**Citation**

Shiva Kumar, "Analysis of Nonlinear Phase Noise in Coherent Fiber-Optic Systems Based on Phase Shift Keying," J. Lightwave Technol. **27**, 4722-4733 (2009)

http://www.opticsinfobase.org/jlt/abstract.cfm?URI=jlt-27-21-4722

Sort: Year | Journal | Reset

### References

- J. P. Gordon, L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. 15, 1351-1353 (1990).
- H. Kim, 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).
- P. J. Winzer, R.-J. Essiambre, "Advanced modulation formats for high capacity optical transport networks," J. Lightw. Technol. 24, 4711-4728 (2006).
- S. L. Jansen, D. van den Borne, B. Spinnler, S. Calabro, H. Suche, P. M. Krummrich, W. Sohler, G.-D. Khoe, H. de Waardt, "Optical phase conjugation for ultra long haul phase- shift-keyed transmission," IEEE J. Lightw. Technol. 24, 54-64 (2006).
- A. Mecozzi, "Limits to the long haul coherent transmission set by the Kerr nonlinearity and noise of in-line amplifiers," J. Lightw. Technol. 12, 1993-2000 (1994).
- K.-P. Ho, "Probability density of nonlinear phase noise," J. Opt. Soc. Amer. B 20, 1875-1879 (2003).
- K.-P. Ho, "Asymptotic probability density of nonlinear phase noise," Opt. Lett. 28, 1350-1352 (2003).
- Mecozzi, "Probability density functions of the nonlinear phase noise," Opt. Lett. 29, 673-675 (2004).
- A. G. Green, P. P. Mitra, L. G. L. Wegener, "Effect of chromatic dispersion on nonlinear phase noise," Opt. Lett. 28, 2455-2457 (2003).
- S. Kumar, "Effect of dispersion on nonlinear phase noise in optical transmission systems," Opt. Lett. 30, 3278-3280 (2005).
- C. J. McKinstrie, C. Xie, T. Lakoba, "Efficient modeling of phase jitter in dispersion-managed soliton systems," Opt. Lett. 27, 1887-1889 (2002).
- C. J. McKinstrie, C. Xie, "Phase jitter in single-channel soliton systems with constant dispersion," IEEE J. Sel. Top. Quant. Electron. 8, 616-625 (2002).
- M. Hanna, D. Boivin, P.-A. Lacourt, J.-P. Goedgebuer, "Calculation of optical phase jitter in dispersion-managed systems by the use of the moment method," J. Opt. Soc. Amer. B 21, 24-28 (2004).
- K.-P. Ho, 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).
- K.-P. Ho, H.-C. Wang, "Effect of dispersion on nonlinear phase noise," Opt. Lett. 31, 2109-2111 (2006).
- F. Zhang, C.-A. Bunge, K. Petermann, "Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems," Opt. Lett. 31, 1038-1040 (2006).
- P. Serena, A. Orlandini, A. Bononi, "Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightw. Technol. 24, 2026-2037 (2006).
- X. Zhu, S. Kumar, X. Li, "Comparison between DPSK and OOK modulation schemes in nonlinear optical transmission systems," Appl. Opt. 45, 6812-6822 (2006).
- A. Demir, "Nonlinear phase noise in optical fiber communication systems," J. Lightw. Technol. 25, 2002-2032 (2007).
- B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, 2007) pp. 95-97.
- A. E. Siegman, "Hermite-gaussian functions of complex argument as optical-beam eigenfunctions," J. Opt. Soc. Amer. 63, 1093-1094 (1973).
- P. Lazaridis, G. Debarge, P. Gallion, "Exact solutions for linear propagation of chirped pulses using a chirped Gauss-Hermite orthogonal basis," Opt. Lett. 22, 685-687 (1997).
- S. K. Turitsyn, V. K. Mezentsev, "Dynamics of self-similar dispersion managed soliton presented in the basis of chirped Gauss-Hermite functions," JETP Lett. 67, 616-621 (1998).
- T. I. Lakoba, D. J. Kaup, "Hermite-Gaussian expansion for pulse propagation in strongly dispersion managed fibers," Phys. Rev. E 58, 6728-6741 (1998).
- G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
- A. Mecozzi, C. B. Clausen, M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).
- R.-J. Essiambre, G. Raybon, B. Mikkelsen, Optical Fiber Telecommunications IV B (Academic, 2002) pp. 232-304.
- S. Kumar, D. Yang, "Second order theory for self-phase modulation and cross-phase modulation in optical fibers," J. Lightw. Technol. 23, 2073-2080 (2005).
- J. G. Proakis, Digital Communications (McGraw-Hill, 2001) pp. 268.
- J. Li, E. Spiller, G. Biondini, "Noise-induced perturbations of dispersion managed solitons," Phys. Rev. A 75, 053818-1-053818-13 (2007).
- C. Sulem, P. L. Sulem, The Nonlinear Schrodinger Equation (Springer-Verlag, 1999).
- S. Kumar, A. Hasegawa, "Quasi-soliton propagation in dispersion-managed optical fibers," Opt. Lett. 22, 372-374 (1997).

## Cited By |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.