American Institute of Mathematical Sciences

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October  2011, 4(5): 1069-1078. doi: 10.3934/dcdss.2011.4.1069

Interaction length of DM solitons in the presence of third order dispersion with loss and amplification

Francisco J. Diaz-Otero 1, and  Pedro Chamorro-Posada 2,

1. 

Departamento de Teoría de la Señal y Comunicaciones, Universidad de Vigo, ETSI Telecomunicación, Campus Universitario s/n, 36310 Vigo, Spain
2. 

Departamento de Teoría de la Señal y Comunicaciones e Ingeniería Telemática, Universidad de Valladolid, ETSI Telecomunicación, Campus Miguel Delibes s/n, 47011 Valladolid, Spain

Received  September 2009 Revised  January 2010 Published  December 2010

We present an analysis of the interaction properties of time-division multiplexed dispersion-managed solitons in the strong management regime. The study is based on an ordinary differential equations model, obtained by means of the variational method, which takes into account third order dispersion, loss and periodic amplification. The validity of the model is assessed by comparing the variational results with direct simulations of the underlying partial differential equations, finding excellent agreement. We first study the conditions for stable single soliton pulse propagation as the amplifier position is varied in the dispersion map. Interactions between adjacent pulses are then investigated for both lossless and lossy systems and the effect of third-order dispersion is addressed. We find that the increase found in the interaction distance can be explained by an asymmetric effective shift of the average dispersion of each of the soliton pulses induced in the interaction process.
Keywords: Optical Fiber Communication., Third Order Dispersion, Dispersion Management, Variational Approximation, Optical solitons.
Mathematics Subject Classification: Primary: 35A15, 35Q51; Secondary: 37K4.
Citation: Francisco J. Diaz-Otero, Pedro Chamorro-Posada. Interaction length of DM solitons in the presence of third order dispersion with loss and amplification. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1069-1078. doi: 10.3934/dcdss.2011.4.1069
References:
[1]

G. P. Agrawal, "Nonlinear Fiber Optics,", 3rd edition, (2001).   Google Scholar

[2]

D. Anderson, Variational approach to nonlinear pulse propagation in optical fibers,, Phys. Rev. A, 27 (1983).  doi: 10.1103/PhysRevA.27.3135.  Google Scholar

[3]

M. K. Chin and X. Y. Tang, Quasi-stable soliton transmission in dispersion managed fiber links with lumped amplifiers,, IEEE Photon. Technol. Lett., 9 (1997), 538.  doi: 10.1109/68.559414.  Google Scholar

[4]

F. J. Diaz-Otero and P. Chamorro-Posada, Interchannel soliton collisions in periodic dispersion maps in the presence of third order dispersion,, J. Nonlin. Math. Phys., 15 Supp. 3 (2008), 137.  doi: 10.2991/jnmp.2008.15.s3.14.  Google Scholar

[5]

I. Gabitov, E. G. Shapiro and S. K. Turitsyn, Optical pulse dynamics in fiber links with dispersion compensation,, Opt. Commun., 134 (1997), 317.  doi: 10.1016/S0030-4018(96)00574-3.  Google Scholar

[6]

K. Hizanidis, B. Malomed, H. Nistazakis and D. Frantzeskakis, Stabilizing soliton transmission by third-order dispersion in dispersion-compensated fibre links,, Pure Appl. Opt., 7 (1998).  doi: 10.1088/0963-9659/7/4/003.  Google Scholar

[7]

T. Inoue, H. Sugahara, A. Maruta and Y. Kodama, Interactions between dispersion managed solitons in optical-time-division-multiplexed systems,, IEEE Photon. Technol. Lett., 12 (2000), 299.  doi: 10.1109/68.826920.  Google Scholar

[8]

D. J. Kaup, B. A. Malomed and J. Yang, Collision-induced pulse timing jitter in a wavelength-division-multiplexing system with strong dispersion management,, J. Opt. Soc. Am. B, 16 (1999), 1628.  doi: 10.1364/JOSAB.16.001628.  Google Scholar

[9]

T. Lakoba and G. Agrawal, Effects of third-order dispersion on dispersion-managed solitons,, J. Opt. Soc. Am. B, 16 (1999), 1332.  doi: 10.1364/JOSAB.16.001332.  Google Scholar

[10]

T. I. Lakoba, J. Yang, D. J. Kaup and B. A. Malomed, Conditions of stationary pulse propagation in the strong dispersion management regime,, Opt. Commun., 149 (1998), 366.  doi: 10.1016/S0030-4018(98)00015-7.  Google Scholar

[11]

B. A. Malomed, D. F. Parker and N. F. Smyth, Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber,, Phys. Rev. E, 48 (1993), 1418.  doi: 10.1103/PhysRevE.48.1418.  Google Scholar

[12]

M. Matsumoto, Analysis of interaction between stretched pulses propagating in dispersion-managed fibers,, Photon. Technol. Lett., 10 Supp. 3 (1998), 373.  doi: 10.1109/68.661414.  Google Scholar

[13]

L. F. Mollenauer and J. P. Gordon, "Solitons in Optical Fibers: Fundamentals and Applications,", Elsevier/Academic Press, (2006).   Google Scholar

[14]

S. Mookherjea and A. Yariv, Hamiltonian dynamics of breathers with third-order dispersion,, J. Opt. Soc. Am. B, 18 (2001), 1150.  doi: 10.1364/JOSAB.18.001150.  Google Scholar

[15]

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama and A. Hasegawa, Interaction between guiding centre solitons in a periodically compensated optical transmission line,, Electron. Lett., 33 (1997), 1063.  doi: 10.1049/el:19970715.  Google Scholar

[16]

L. J. Richardson, J. H. B. Nijhof and W. Forysiak, An interpretation of the energy variations of dispersion managed solitons in terms of effective average dispersion,, Opt. Commun., 189 (2001), 63.  doi: 10.1016/S0030-4018(01)01004-5.  Google Scholar

[17]

N. J. Smith, N. J. Doran, F. M. Knox and W. Forysiak, Energy-scaling characteristics of solitons in strongly dispersion-managed fibers,, Opt. Lett., 21 (1996), 1981.  doi: 10.1364/OL.21.001981.  Google Scholar

[18]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow and I. Bennion, Enhanced power solitons in optical fibers with periodic dispersion management,, Electron. Lett., 32 (1996), 54.  doi: 10.1049/el:19960062.  Google Scholar

[19]

H. Sugahara, H. Kato, T. Inoue, A. Maruta and Y. Kodama, Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,, J. Lightwave Technol., 17 (1999).  doi: 10.1109/50.788560.  Google Scholar

[20]

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga and S. Akiba, Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,, Electron. Lett., 31 (1995), 2027.  doi: 10.1049/el:19951387.  Google Scholar

[21]

M. Wald, B. A. Malomed and F. Lederer, Interactions of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines,, Opt. Lett., 26 (2001), 965.  doi: 10.1364/OL.26.000965.  Google Scholar

[22]

M. Wald, B. A. Malomed and F. Lederer, Interaction of moderately dispersion-managed solitons,, Opt. Commun., 172 (1999), 31.  doi: 10.1016/S0030-4018(99)00621-5.  Google Scholar

[23]

T. S. Yang and W. L. Kath, Analysis of enhanced-power solitons in dispersion-managed optical fibers,, Opt. Lett., 22 (1997), 985.  doi: 10.1364/OL.22.000985.  Google Scholar

[24]

T. Yu, E. A. Golovchenko, A. N. Pilipetskii and C. R. Menyuk, Dispersion-managed soliton interactions in optical fibers,, Opt. Lett., 22 (1997), 793.  doi: 10.1364/OL.22.000793.  Google Scholar

[25]

T. Yu, R.-M. Mu, V. S. Grigoryan and C. R. Menyuk, Energy enhancement of dispersion-managed solitons in optical fiber transmission systems with lumped amplifiers,, IEEE Photon. Technol. Lett., 11 (1999), 75.  doi: 10.1109/68.736397.  Google Scholar

show all references

References:
[1]

G. P. Agrawal, "Nonlinear Fiber Optics,", 3rd edition, (2001).   Google Scholar

[2]

D. Anderson, Variational approach to nonlinear pulse propagation in optical fibers,, Phys. Rev. A, 27 (1983).  doi: 10.1103/PhysRevA.27.3135.  Google Scholar

[3]

M. K. Chin and X. Y. Tang, Quasi-stable soliton transmission in dispersion managed fiber links with lumped amplifiers,, IEEE Photon. Technol. Lett., 9 (1997), 538.  doi: 10.1109/68.559414.  Google Scholar

[4]

F. J. Diaz-Otero and P. Chamorro-Posada, Interchannel soliton collisions in periodic dispersion maps in the presence of third order dispersion,, J. Nonlin. Math. Phys., 15 Supp. 3 (2008), 137.  doi: 10.2991/jnmp.2008.15.s3.14.  Google Scholar

[5]

I. Gabitov, E. G. Shapiro and S. K. Turitsyn, Optical pulse dynamics in fiber links with dispersion compensation,, Opt. Commun., 134 (1997), 317.  doi: 10.1016/S0030-4018(96)00574-3.  Google Scholar

[6]

K. Hizanidis, B. Malomed, H. Nistazakis and D. Frantzeskakis, Stabilizing soliton transmission by third-order dispersion in dispersion-compensated fibre links,, Pure Appl. Opt., 7 (1998).  doi: 10.1088/0963-9659/7/4/003.  Google Scholar

[7]

T. Inoue, H. Sugahara, A. Maruta and Y. Kodama, Interactions between dispersion managed solitons in optical-time-division-multiplexed systems,, IEEE Photon. Technol. Lett., 12 (2000), 299.  doi: 10.1109/68.826920.  Google Scholar

[8]

D. J. Kaup, B. A. Malomed and J. Yang, Collision-induced pulse timing jitter in a wavelength-division-multiplexing system with strong dispersion management,, J. Opt. Soc. Am. B, 16 (1999), 1628.  doi: 10.1364/JOSAB.16.001628.  Google Scholar

[9]

T. Lakoba and G. Agrawal, Effects of third-order dispersion on dispersion-managed solitons,, J. Opt. Soc. Am. B, 16 (1999), 1332.  doi: 10.1364/JOSAB.16.001332.  Google Scholar

[10]

T. I. Lakoba, J. Yang, D. J. Kaup and B. A. Malomed, Conditions of stationary pulse propagation in the strong dispersion management regime,, Opt. Commun., 149 (1998), 366.  doi: 10.1016/S0030-4018(98)00015-7.  Google Scholar

[11]

B. A. Malomed, D. F. Parker and N. F. Smyth, Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber,, Phys. Rev. E, 48 (1993), 1418.  doi: 10.1103/PhysRevE.48.1418.  Google Scholar

[12]

M. Matsumoto, Analysis of interaction between stretched pulses propagating in dispersion-managed fibers,, Photon. Technol. Lett., 10 Supp. 3 (1998), 373.  doi: 10.1109/68.661414.  Google Scholar

[13]

L. F. Mollenauer and J. P. Gordon, "Solitons in Optical Fibers: Fundamentals and Applications,", Elsevier/Academic Press, (2006).   Google Scholar

[14]

S. Mookherjea and A. Yariv, Hamiltonian dynamics of breathers with third-order dispersion,, J. Opt. Soc. Am. B, 18 (2001), 1150.  doi: 10.1364/JOSAB.18.001150.  Google Scholar

[15]

T. Okamawari, Y. Ueda, A. Maruta, Y. Kodama and A. Hasegawa, Interaction between guiding centre solitons in a periodically compensated optical transmission line,, Electron. Lett., 33 (1997), 1063.  doi: 10.1049/el:19970715.  Google Scholar

[16]

L. J. Richardson, J. H. B. Nijhof and W. Forysiak, An interpretation of the energy variations of dispersion managed solitons in terms of effective average dispersion,, Opt. Commun., 189 (2001), 63.  doi: 10.1016/S0030-4018(01)01004-5.  Google Scholar

[17]

N. J. Smith, N. J. Doran, F. M. Knox and W. Forysiak, Energy-scaling characteristics of solitons in strongly dispersion-managed fibers,, Opt. Lett., 21 (1996), 1981.  doi: 10.1364/OL.21.001981.  Google Scholar

[18]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow and I. Bennion, Enhanced power solitons in optical fibers with periodic dispersion management,, Electron. Lett., 32 (1996), 54.  doi: 10.1049/el:19960062.  Google Scholar

[19]

H. Sugahara, H. Kato, T. Inoue, A. Maruta and Y. Kodama, Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,, J. Lightwave Technol., 17 (1999).  doi: 10.1109/50.788560.  Google Scholar

[20]

M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga and S. Akiba, Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission,, Electron. Lett., 31 (1995), 2027.  doi: 10.1049/el:19951387.  Google Scholar

[21]

M. Wald, B. A. Malomed and F. Lederer, Interactions of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines,, Opt. Lett., 26 (2001), 965.  doi: 10.1364/OL.26.000965.  Google Scholar

[22]

M. Wald, B. A. Malomed and F. Lederer, Interaction of moderately dispersion-managed solitons,, Opt. Commun., 172 (1999), 31.  doi: 10.1016/S0030-4018(99)00621-5.  Google Scholar

[23]

T. S. Yang and W. L. Kath, Analysis of enhanced-power solitons in dispersion-managed optical fibers,, Opt. Lett., 22 (1997), 985.  doi: 10.1364/OL.22.000985.  Google Scholar

[24]

T. Yu, E. A. Golovchenko, A. N. Pilipetskii and C. R. Menyuk, Dispersion-managed soliton interactions in optical fibers,, Opt. Lett., 22 (1997), 793.  doi: 10.1364/OL.22.000793.  Google Scholar

[25]

T. Yu, R.-M. Mu, V. S. Grigoryan and C. R. Menyuk, Energy enhancement of dispersion-managed solitons in optical fiber transmission systems with lumped amplifiers,, IEEE Photon. Technol. Lett., 11 (1999), 75.  doi: 10.1109/68.736397.  Google Scholar

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