## Numerical simulation of nonlinear pulse propagation in optical fibers with randomly varying birefringence |

JOSA B, Vol. 30, Issue 9, pp. 2443-2451 (2013)

http://dx.doi.org/10.1364/JOSAB.30.002443

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### Abstract

This paper is concerned with the evolution of nonlinear pulses driven by random polarization mode dispersion (PMD). The evolution of the slowly varying envelopes is governed by the stochastic Manakov equation, which has been derived as the limit of the Manakov PMD equation. The aim in this work is to investigate the effect of the PMD on Manakov’s solitons and soliton wave-train propagation. I also study the statistical property of the differential group delay (DGD), and, using Monte Carlo simulations, I compute its probability density function. For linear pulses with zero group-velocity dispersion, I propose an algorithm, based on importance sampling, to estimate the outage probability, i.e., the probability that the value of the DGD exceeds an acceptance level.

© 2013 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(000.4430) General : Numerical approximation and analysis

(060.2430) Fiber optics and optical communications : Fibers, single-mode

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(260.1440) Physical optics : Birefringence

(270.5530) Quantum optics : Pulse propagation and temporal solitons

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 18, 2013

Revised Manuscript: July 15, 2013

Manuscript Accepted: July 20, 2013

Published: August 23, 2013

**Citation**

Maxime Gazeau, "Numerical simulation of nonlinear pulse propagation in optical fibers with randomly varying birefringence," J. Opt. Soc. Am. B **30**, 2443-2451 (2013)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-9-2443

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### References

- G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
- C. R. Menyuk and A. Galtarossa, eds., Polarization Mode Dispersion (Springer, 2005) [Originally published in Opt. Fiber Commun. Rep. 1, 312–344 (2004)].
- J. Garnier, J. Fatome, and G. L. Meur, “Statistical analysis of pulse propagation driven by polarization-mode dispersion,” J. Opt. Soc. Am. B 19, 1968–1977 (2002). [CrossRef]
- D. Marcuse, P. K. A. Wai, and C. R. Menyuk, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997). [CrossRef]
- C. R. Menyuk and B. S. Marks, “Interaction of polarization mode dispersion and nonlinearity in optical fiber transmission systems,” J. Lightwave Technol. 24, 2806–2826 (2006). [CrossRef]
- S. Wabnitz and K. Turitsyn, “Mitigation of nonlinear and PMD impairments by bit-synchronous polarization scrambling,” J. Lightwave Technol. 30, 2494–2501 (2012). [CrossRef]
- A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171–172 (1973). [CrossRef]
- C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: equal propagation amplitudes,” Opt. Lett. 12, 614–616 (1987). [CrossRef]
- C. R. Menyuk, “Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes,” J. Opt. Soc. Am. B 5, 392–402 (1988). [CrossRef]
- L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, “Resistance of solitons to the effects of polarization dispersion in optical fibers,” Opt. Lett. 14, 1219–1221 (1989). [CrossRef]
- P. K. A. Wai, C. R. Menyuk, and H. H. Chen, “Stability of solitons in randomly varying birefringent fibers,” Opt. Lett. 16, 1231–1233 (1991). [CrossRef]
- Y. Chung, V. V. Lebedev, and S. S. Vergeles, “Interaction of solitons through radiation in optical fibers with randomly varying birefringence,” Opt. Lett. 29, 1245–1247 (2004). [CrossRef]
- V. Chernyak, M. Chertkov, I. Gabitov, I. Kolokolov, and V. Lebedev, “PMD-induced fluctuations of bit-error rate in optical fiber systems,” J. Lightwave Technol. 22, 1155–1168 (2004). [CrossRef]
- T. Ueda and W. L. Kath, “Stochastic simulation of pulses in nonlinear-optical fibers with random birefringence,” J. Opt. Soc. Am. B 11, 818–825 (1994). [CrossRef]
- A. de Bouard and M. Gazeau, “A diffusion approximation theorem for a nonlinear PDE with application to random birefringent optical fibers,” Ann. Appl. Probab. 22, 2460–2504 (2012). [CrossRef]
- M. Gazeau, “Analyse de modèles mathématiques pour la propagation de la lumière dans les fibers optiques en présence de biréfringence aléatoire,” Thèse de Doctorat (Ecole Polytechnique, 2012).
- P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996). [CrossRef]
- M. Gazeau, “Strong order of convergence of a semi-discrete scheme for the stochastic Manakov equation,” preprint (2013), available at http://hal.archives-ouvertes.fr/hal-00850617.
- A. Hasegawa, “Effect of polarization mode dispersion in optical soliton transmission in fibers,” Physica D 188, 241–246 (2004). [CrossRef]
- J. Yang, “Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics,” Phys. Rev. E 59, 2393–2405 (1999). [CrossRef]
- J. Yang, “Suppression of Manakov soliton interference in optical fibers,” Phys. Rev. E 65, 036606 (2002). [CrossRef]
- R. Radhakrishnan, M. Lakshmanan, and J. Hietarinta, “Inelastic collision and switching of coupled bright solitons in optical fibers,” Phys. Rev. E 56, 2213–2216 (1997). [CrossRef]
- J. Yang, Nonlinear Waves in Integrable and Non-integrable Systems (Society for Industrial and Applied Mathematics, 2010).
- A. Kebaier, “Statistical Romberg extrapolation: a new variance reduction method and applications to option pricing,” Ann. Appl. Probab. 15, 2681–2705 (2005). [CrossRef]
- M. B. Giles, “Multilevel Monte Carlo path simulation,” Oper. Res. 56, 607–617 (2008). [CrossRef]
- K. A. Cliffe, M. B. Giles, R. Scheichl, and A. L. Teckentrup, “Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients,” Comput. Vis. Sci. 14, 3–15 (2011). [CrossRef]
- J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000). [CrossRef]
- G. J. Foschini, L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Probability densities of second-order polarization mode dispersion including polarization dependent chromatic fiber dispersion,” IEEE Photon. Technol. Lett. 12, 293–295 (2000). [CrossRef]
- J. Garnier and R. Marty, “Effective pulse dynamics in optical fibers with polarization mode dispersion,” Wave Motion 43, 544–560 (2006). [CrossRef]
- N. J. Newton, “Variance reduction for simulated diffusions,” SIAM J. Appl. Math. 54, 1780–1805 (1994). [CrossRef]
- E. Fournie, J. Lebuchoux, and N. Touzi, “Small noise expansion and importance sampling,” Asymptot. Anal. 14, 361–376 (1997).
- J.-P. Fouque and T. A. Tullie, “Variance reduction for Monte Carlo simulation in a stochastic volatility environment,” Quant. Finance 2, 24–30 (2002). [CrossRef]

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