Abstract

We address the problem of characterization of light pulses that propagate in long-haul high-bit-rate optical communication systems under strongly perturbed conditions. We show that the conventional technique for characterization of the phase and intensity profile of such pulses becomes qualitatively inconsistent when the pulse’s profile is asymmetrically distorted with respect to its center of mass. We resolve these inconsistencies by partially reformulating the conventional technique by means of appropriate pulse parameters, which we call upgraded parameters, that allow a fair characterization of the intensity and phase of all types of light pulses, including those that are asymmetrically distorted. We illustrate the effectiveness of the upgraded parameters by applying them to a meticulous characterization of light pulses in a dispersion-managed optical fiber system in which third-order dispersion is acting as a strong perturbation.

© 2009 Optical Society of America

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  28. J. Posth, T. Schafer, E. Laedke, and K. Spatschek, “Fast optimization procedures for third-order dispersion for dispersion management,” Opt. Commun. 219, 241-249 (2003).
    [CrossRef]
  29. A. H. Liang, H. Toda, and A. Hasegawa, “High speed soliton transmission in dense periodic fibers,” Opt. Lett. 24, 799-801 (1999).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2007 (1)

2006 (2)

M. Funabashi, Z. Zhu, Z. Pan, B. Xian, L. Paraschis, D. L. Harris, and S. J. B. Yoo, “Cascadability of optical 3R regeneration for NRZ format investigated in recirculating loop transmission over field fibers,” IEEE Photon. Technol. Lett. 18, 2081-083 (2006).
[CrossRef]

A. Labruyere and P. Tchofo Dinda, “Analytical design of nonlinear optical loop mirrors for fiber-optic communication systems,” Opt. Commun. 266, 676-680 (2006).
[CrossRef]

2004 (5)

Z. Shumin, L. Fuyun, X. Wencheng, Y. Shiping, W. Jian, and D. Xiaoyi, “Enhanced compression of high-order solitons in dispersion decreasing fibers due to the combined effects of negative third-order dispersion and raman self-scattering,” Opt. Commun. 237, 1-8 (2004).
[CrossRef]

J. Fatome, S. Pitois, P. Tchofo Dinda, G. Millot, E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin, “Effectiveness of fiber lines with symmetric dispersion swing for 160 Gb/s terrestrial transmission systems,” IEEE Photon. Technol. Lett. 16, 2365-2367 (2004).
[CrossRef]

S. Wielandy, P. S. Westbrook, M. Fishteyn, P. Reyes, W. Shairer, H. Rohde, and G. Lehmann, “Demonstration of automatic dispersion control for 160 Gbit/s transmission over 275 km of deployed fibre,” Electron. Lett. 40, 690-691 (2004).
[CrossRef]

A. Gray, Z. Huang, Y. W. A. Lee, I. Y. Khrushchevand, and I. Bennion, “Experimental observation of autosoliton propagation in a dispersion-managed system guided by nonlinear optical loop mirrors,” Opt. Lett. 29, 926-928 (2004).
[CrossRef] [PubMed]

K. Nakkeeran, Y. C. Kwan, P. K. A. Wai, A. Labruyere, P. Tchofo Dinda, and A. B. Moubissi, “Analytical design of densely dispersion-managed optical fiber transmission systems with Gaussian and raised cosine return-to-zero ansatze,” J. Opt. Soc. Am. B 21, 1901-1907 (2004).
[CrossRef]

2003 (9)

F. Matera, V. Eramo, A. Schiffini, M. Guglielmucci, and M. Settembre, “Numerical investigation on design of wide geographical optical-transport networks based on N×40-Gb/s transmission,” J. Lightwave Technol. 21, 456-465 (2003).
[CrossRef]

J. Fatome, S. Pitois, P. Tchofo Dinda, and G. Millot, “Experimental demonstration of 160-GHz densely dispersion-managed soliton transmission in a single channel over 896 km of commercial fibres,” Opt. Express 11, 1553-1558 (2003).
[CrossRef] [PubMed]

S. Boscolo, S. K. Turitsyn, and K. J. Blow, “All optical passive 2R regeneration for N×40 Gbit/s WDM transmission using NOLM and novel filtering technique,” Opt. Commun. 217, 227-232 (2003).
[CrossRef]

J. C. Simon, L. Bramerie, F. Ginovart, V. Roncin, M. Gay, S. Feve, E. Le Cren, and M. L. Chares, “All-optical regeneration techniques,” Ann. Telecommun. 58, 1708-1724 (2003).

H. Masuda, H. Kawakami, S. Kuwahara, A. Hirano, K. Sato, and Y. Miyamoto, “1.28 Tbit/s(32×43 Gbit/s) field trial over 528 km(6×88 km) DSF using L-band remotely-pumped EDFA/distributed Raman hybrid inline amplifiers,” Electron. Lett. 39, 1668-1670 (2003).
[CrossRef]

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

S. Bigo, Y. Frignac, J. C. Antona, and G. Charlet, “Design of multiterabit/s terrestrial transmission systems facilitated by simple analytical tools,” Ann. Telecommun. 58, 1757-1784 (2003).

P. Tchofo Dinda, A. Labruyere, K. Nakkeeran, J. Fatome, A. B. Moubissi, S. Pitois, and G. Millot, “On the designing of densely dispersion-managed optical fiber systems for ultra-fast optical communication,” Ann. Telecommun. 58, 1785-1808 (2003).

J. Posth, T. Schafer, E. Laedke, and K. Spatschek, “Fast optimization procedures for third-order dispersion for dispersion management,” Opt. Commun. 219, 241-249 (2003).
[CrossRef]

2002 (1)

2001 (3)

P. Tchofo Dinda, A. B. Moubissi, and K. Nakkeeran, “Collective variable theory for optical solitons in fibers,” Phys. Rev. E 64, 016608 (2001).
[CrossRef]

P. Tchofo Dinda, K. Nakkeeran, and A. B. Moubissi, “Optimized Hermite-Gaussian ansatz functions for dispersion-managed solitons,” Opt. Commun. 187, 427-433 (2001).
[CrossRef]

L. J. Richardson, W. Forysiak, and N. J. Doran, “Trans-oceanic 160-Gbit/s single-channel transmission using short-period dispersion management,” IEEE Photon. Technol. Lett. 13, 209-211 (2001).
[CrossRef]

2000 (1)

A. Maruta, Y. Yamamoto, S. Okamoto, A. Suziki, T. Morita, A. Agata, and A. Hasegawa, “Effectiveness of densely dispersion managed solitons in ultrahigh speed transmission,” Electron. Lett. 36, 1947-1949 (2000).
[CrossRef]

1999 (4)

1997 (1)

1995 (2)

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol. 1, 187-217 (1995).
[CrossRef]

J. G. Caputo, N. Flytzanis, and M. P. Sorensen, “Ring laser configuration studied by collective coordinates,” J. Opt. Soc. Am. B 12, 139-145 (1995).
[CrossRef]

1988 (1)

R. Boesch, P. Stancioff, and C. R. Willis, “Hamiltonian equations for multiple-collective-variable theories of nonlinear klein-gordon equations: a projection-operator approach,” Phys. Rev. B 38, 6713-6735 (1988).
[CrossRef]

Aceves, A. B.

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol. 1, 187-217 (1995).
[CrossRef]

Ackaert, A.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Agata, A.

A. Maruta, Y. Yamamoto, S. Okamoto, A. Suziki, T. Morita, A. Agata, and A. Hasegawa, “Effectiveness of densely dispersion managed solitons in ultrahigh speed transmission,” Electron. Lett. 36, 1947-1949 (2000).
[CrossRef]

Agrawal, G. P.

Antona, J. C.

S. Bigo, Y. Frignac, J. C. Antona, and G. Charlet, “Design of multiterabit/s terrestrial transmission systems facilitated by simple analytical tools,” Ann. Telecommun. 58, 1757-1784 (2003).

Bennion, I.

Berg, T.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Bigo, S.

S. Bigo, Y. Frignac, J. C. Antona, and G. Charlet, “Design of multiterabit/s terrestrial transmission systems facilitated by simple analytical tools,” Ann. Telecommun. 58, 1757-1784 (2003).

Blow, K. J.

S. Boscolo, S. K. Turitsyn, and K. J. Blow, “All optical passive 2R regeneration for N×40 Gbit/s WDM transmission using NOLM and novel filtering technique,” Opt. Commun. 217, 227-232 (2003).
[CrossRef]

Boesch, R.

R. Boesch, P. Stancioff, and C. R. Willis, “Hamiltonian equations for multiple-collective-variable theories of nonlinear klein-gordon equations: a projection-operator approach,” Phys. Rev. B 38, 6713-6735 (1988).
[CrossRef]

Boscolo, S.

S. Boscolo, S. K. Turitsyn, and K. J. Blow, “All optical passive 2R regeneration for N×40 Gbit/s WDM transmission using NOLM and novel filtering technique,” Opt. Commun. 217, 227-232 (2003).
[CrossRef]

Bramerie, L.

J. C. Simon, L. Bramerie, F. Ginovart, V. Roncin, M. Gay, S. Feve, E. Le Cren, and M. L. Chares, “All-optical regeneration techniques,” Ann. Telecommun. 58, 1708-1724 (2003).

Caputo, J. G.

Chares, M. L.

J. C. Simon, L. Bramerie, F. Ginovart, V. Roncin, M. Gay, S. Feve, E. Le Cren, and M. L. Chares, “All-optical regeneration techniques,” Ann. Telecommun. 58, 1708-1724 (2003).

Charlet, G.

S. Bigo, Y. Frignac, J. C. Antona, and G. Charlet, “Design of multiterabit/s terrestrial transmission systems facilitated by simple analytical tools,” Ann. Telecommun. 58, 1757-1784 (2003).

Chen, D. Z.

Cuenot, B.

J. Fatome, S. Pitois, P. Tchofo Dinda, G. Millot, E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin, “Effectiveness of fiber lines with symmetric dispersion swing for 160 Gb/s terrestrial transmission systems,” IEEE Photon. Technol. Lett. 16, 2365-2367 (2004).
[CrossRef]

Debarge, G.

Demeester, P.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Dinda, P. Tchofo

A. Labruyere and P. Tchofo Dinda, “Analytical design of nonlinear optical loop mirrors for fiber-optic communication systems,” Opt. Commun. 266, 676-680 (2006).
[CrossRef]

K. Nakkeeran, Y. C. Kwan, P. K. A. Wai, A. Labruyere, P. Tchofo Dinda, and A. B. Moubissi, “Analytical design of densely dispersion-managed optical fiber transmission systems with Gaussian and raised cosine return-to-zero ansatze,” J. Opt. Soc. Am. B 21, 1901-1907 (2004).
[CrossRef]

J. Fatome, S. Pitois, P. Tchofo Dinda, G. Millot, E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin, “Effectiveness of fiber lines with symmetric dispersion swing for 160 Gb/s terrestrial transmission systems,” IEEE Photon. Technol. Lett. 16, 2365-2367 (2004).
[CrossRef]

J. Fatome, S. Pitois, P. Tchofo Dinda, and G. Millot, “Experimental demonstration of 160-GHz densely dispersion-managed soliton transmission in a single channel over 896 km of commercial fibres,” Opt. Express 11, 1553-1558 (2003).
[CrossRef] [PubMed]

P. Tchofo Dinda, A. Labruyere, K. Nakkeeran, J. Fatome, A. B. Moubissi, S. Pitois, and G. Millot, “On the designing of densely dispersion-managed optical fiber systems for ultra-fast optical communication,” Ann. Telecommun. 58, 1785-1808 (2003).

P. Tchofo Dinda, K. Nakkeeran, and A. Labruyere, “Suppression of soliton self-frequency shift by up-shifted filtering,” Opt. Lett. 27, 382-384 (2002).
[CrossRef]

P. Tchofo Dinda, A. B. Moubissi, and K. Nakkeeran, “Collective variable theory for optical solitons in fibers,” Phys. Rev. E 64, 016608 (2001).
[CrossRef]

P. Tchofo Dinda, K. Nakkeeran, and A. B. Moubissi, “Optimized Hermite-Gaussian ansatz functions for dispersion-managed solitons,” Opt. Commun. 187, 427-433 (2001).
[CrossRef]

Doran, N. J.

L. J. Richardson, W. Forysiak, and N. J. Doran, “Trans-oceanic 160-Gbit/s single-channel transmission using short-period dispersion management,” IEEE Photon. Technol. Lett. 13, 209-211 (2001).
[CrossRef]

Eramo, V.

Erasme, D.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Fatome, J.

J. Fatome, S. Pitois, P. Tchofo Dinda, G. Millot, E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin, “Effectiveness of fiber lines with symmetric dispersion swing for 160 Gb/s terrestrial transmission systems,” IEEE Photon. Technol. Lett. 16, 2365-2367 (2004).
[CrossRef]

P. Tchofo Dinda, A. Labruyere, K. Nakkeeran, J. Fatome, A. B. Moubissi, S. Pitois, and G. Millot, “On the designing of densely dispersion-managed optical fiber systems for ultra-fast optical communication,” Ann. Telecommun. 58, 1785-1808 (2003).

J. Fatome, S. Pitois, P. Tchofo Dinda, and G. Millot, “Experimental demonstration of 160-GHz densely dispersion-managed soliton transmission in a single channel over 896 km of commercial fibres,” Opt. Express 11, 1553-1558 (2003).
[CrossRef] [PubMed]

Fedoruk, M. P.

Feve, S.

J. C. Simon, L. Bramerie, F. Ginovart, V. Roncin, M. Gay, S. Feve, E. Le Cren, and M. L. Chares, “All-optical regeneration techniques,” Ann. Telecommun. 58, 1708-1724 (2003).

Fevrier, H.

Fishteyn, M.

S. Wielandy, P. S. Westbrook, M. Fishteyn, P. Reyes, W. Shairer, H. Rohde, and G. Lehmann, “Demonstration of automatic dispersion control for 160 Gbit/s transmission over 275 km of deployed fibre,” Electron. Lett. 40, 690-691 (2004).
[CrossRef]

Flytzanis, N.

Forysiak, W.

L. J. Richardson, W. Forysiak, and N. J. Doran, “Trans-oceanic 160-Gbit/s single-channel transmission using short-period dispersion management,” IEEE Photon. Technol. Lett. 13, 209-211 (2001).
[CrossRef]

Frignac, Y.

S. Bigo, Y. Frignac, J. C. Antona, and G. Charlet, “Design of multiterabit/s terrestrial transmission systems facilitated by simple analytical tools,” Ann. Telecommun. 58, 1757-1784 (2003).

Funabashi, M.

M. Funabashi, Z. Zhu, Z. Pan, B. Xian, L. Paraschis, D. L. Harris, and S. J. B. Yoo, “Cascadability of optical 3R regeneration for NRZ format investigated in recirculating loop transmission over field fibers,” IEEE Photon. Technol. Lett. 18, 2081-083 (2006).
[CrossRef]

Fuyun, L.

Z. Shumin, L. Fuyun, X. Wencheng, Y. Shiping, W. Jian, and D. Xiaoyi, “Enhanced compression of high-order solitons in dispersion decreasing fibers due to the combined effects of negative third-order dispersion and raman self-scattering,” Opt. Commun. 237, 1-8 (2004).
[CrossRef]

Gallion, P.

Gay, M.

J. C. Simon, L. Bramerie, F. Ginovart, V. Roncin, M. Gay, S. Feve, E. Le Cren, and M. L. Chares, “All-optical regeneration techniques,” Ann. Telecommun. 58, 1708-1724 (2003).

Ginovart, F.

J. C. Simon, L. Bramerie, F. Ginovart, V. Roncin, M. Gay, S. Feve, E. Le Cren, and M. L. Chares, “All-optical regeneration techniques,” Ann. Telecommun. 58, 1708-1724 (2003).

Gornakova, A.

Gosselin, S.

J. Fatome, S. Pitois, P. Tchofo Dinda, G. Millot, E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin, “Effectiveness of fiber lines with symmetric dispersion swing for 160 Gb/s terrestrial transmission systems,” IEEE Photon. Technol. Lett. 16, 2365-2367 (2004).
[CrossRef]

Gray, A.

Grosso, G.

Guglielmucci, M.

Harris, D. L.

M. Funabashi, Z. Zhu, Z. Pan, B. Xian, L. Paraschis, D. L. Harris, and S. J. B. Yoo, “Cascadability of optical 3R regeneration for NRZ format investigated in recirculating loop transmission over field fibers,” IEEE Photon. Technol. Lett. 18, 2081-083 (2006).
[CrossRef]

Hasegawa, A.

A. Maruta, Y. Yamamoto, S. Okamoto, A. Suziki, T. Morita, A. Agata, and A. Hasegawa, “Effectiveness of densely dispersion managed solitons in ultrahigh speed transmission,” Electron. Lett. 36, 1947-1949 (2000).
[CrossRef]

A. H. Liang, H. Toda, and A. Hasegawa, “High speed soliton transmission in dense periodic fibers,” Opt. Lett. 24, 799-801 (1999).
[CrossRef]

A. Hasegawa and Y. Kodama, Solitons in Optical Communication (Oxford U. Press, 1995).

Hirano, A.

H. Masuda, H. Kawakami, S. Kuwahara, A. Hirano, K. Sato, and Y. Miyamoto, “1.28 Tbit/s(32×43 Gbit/s) field trial over 528 km(6×88 km) DSF using L-band remotely-pumped EDFA/distributed Raman hybrid inline amplifiers,” Electron. Lett. 39, 1668-1670 (2003).
[CrossRef]

Huang, Z.

Jian, W.

Z. Shumin, L. Fuyun, X. Wencheng, Y. Shiping, W. Jian, and D. Xiaoyi, “Enhanced compression of high-order solitons in dispersion decreasing fibers due to the combined effects of negative third-order dispersion and raman self-scattering,” Opt. Commun. 237, 1-8 (2004).
[CrossRef]

Kawakami, H.

H. Masuda, H. Kawakami, S. Kuwahara, A. Hirano, K. Sato, and Y. Miyamoto, “1.28 Tbit/s(32×43 Gbit/s) field trial over 528 km(6×88 km) DSF using L-band remotely-pumped EDFA/distributed Raman hybrid inline amplifiers,” Electron. Lett. 39, 1668-1670 (2003).
[CrossRef]

Khrushchevand, I. Y.

Kodama, Y.

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol. 1, 187-217 (1995).
[CrossRef]

A. Hasegawa and Y. Kodama, Solitons in Optical Communication (Oxford U. Press, 1995).

Kuwahara, S.

H. Masuda, H. Kawakami, S. Kuwahara, A. Hirano, K. Sato, and Y. Miyamoto, “1.28 Tbit/s(32×43 Gbit/s) field trial over 528 km(6×88 km) DSF using L-band remotely-pumped EDFA/distributed Raman hybrid inline amplifiers,” Electron. Lett. 39, 1668-1670 (2003).
[CrossRef]

Kwan, Y. C.

Labruyere, A.

A. Labruyere and P. Tchofo Dinda, “Analytical design of nonlinear optical loop mirrors for fiber-optic communication systems,” Opt. Commun. 266, 676-680 (2006).
[CrossRef]

K. Nakkeeran, Y. C. Kwan, P. K. A. Wai, A. Labruyere, P. Tchofo Dinda, and A. B. Moubissi, “Analytical design of densely dispersion-managed optical fiber transmission systems with Gaussian and raised cosine return-to-zero ansatze,” J. Opt. Soc. Am. B 21, 1901-1907 (2004).
[CrossRef]

P. Tchofo Dinda, A. Labruyere, K. Nakkeeran, J. Fatome, A. B. Moubissi, S. Pitois, and G. Millot, “On the designing of densely dispersion-managed optical fiber systems for ultra-fast optical communication,” Ann. Telecommun. 58, 1785-1808 (2003).

P. Tchofo Dinda, K. Nakkeeran, and A. Labruyere, “Suppression of soliton self-frequency shift by up-shifted filtering,” Opt. Lett. 27, 382-384 (2002).
[CrossRef]

Laedke, E.

J. Posth, T. Schafer, E. Laedke, and K. Spatschek, “Fast optimization procedures for third-order dispersion for dispersion management,” Opt. Commun. 219, 241-249 (2003).
[CrossRef]

Lagasse, P.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Lakoba, T. I.

Lazardis, P.

Le Cren, E.

J. C. Simon, L. Bramerie, F. Ginovart, V. Roncin, M. Gay, S. Feve, E. Le Cren, and M. L. Chares, “All-optical regeneration techniques,” Ann. Telecommun. 58, 1708-1724 (2003).

Le Rouzic, E.

J. Fatome, S. Pitois, P. Tchofo Dinda, G. Millot, E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin, “Effectiveness of fiber lines with symmetric dispersion swing for 160 Gb/s terrestrial transmission systems,” IEEE Photon. Technol. Lett. 16, 2365-2367 (2004).
[CrossRef]

Lee, Y. W. A.

Lehmann, G.

S. Wielandy, P. S. Westbrook, M. Fishteyn, P. Reyes, W. Shairer, H. Rohde, and G. Lehmann, “Demonstration of automatic dispersion control for 160 Gbit/s transmission over 275 km of deployed fibre,” Electron. Lett. 40, 690-691 (2004).
[CrossRef]

Liang, A. H.

Mamyshev, P.

Maruta, A.

A. Maruta, Y. Yamamoto, S. Okamoto, A. Suziki, T. Morita, A. Agata, and A. Hasegawa, “Effectiveness of densely dispersion managed solitons in ultrahigh speed transmission,” Electron. Lett. 36, 1947-1949 (2000).
[CrossRef]

Masuda, H.

H. Masuda, H. Kawakami, S. Kuwahara, A. Hirano, K. Sato, and Y. Miyamoto, “1.28 Tbit/s(32×43 Gbit/s) field trial over 528 km(6×88 km) DSF using L-band remotely-pumped EDFA/distributed Raman hybrid inline amplifiers,” Electron. Lett. 39, 1668-1670 (2003).
[CrossRef]

Matera, F.

Mezentsev, V. K.

S. K. Turitsyn, T. Schafer, K. H. Spatschek, and V. K. Mezentsev, “Path-averaged chirped optical solitons in dispersion-managed fiber communication lines,” Opt. Commun. 163, 122-158 (1999).
[CrossRef]

Millot, G.

J. Fatome, S. Pitois, P. Tchofo Dinda, G. Millot, E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin, “Effectiveness of fiber lines with symmetric dispersion swing for 160 Gb/s terrestrial transmission systems,” IEEE Photon. Technol. Lett. 16, 2365-2367 (2004).
[CrossRef]

J. Fatome, S. Pitois, P. Tchofo Dinda, and G. Millot, “Experimental demonstration of 160-GHz densely dispersion-managed soliton transmission in a single channel over 896 km of commercial fibres,” Opt. Express 11, 1553-1558 (2003).
[CrossRef] [PubMed]

P. Tchofo Dinda, A. Labruyere, K. Nakkeeran, J. Fatome, A. B. Moubissi, S. Pitois, and G. Millot, “On the designing of densely dispersion-managed optical fiber systems for ultra-fast optical communication,” Ann. Telecommun. 58, 1785-1808 (2003).

Minot, Ch.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Miyamoto, Y.

H. Masuda, H. Kawakami, S. Kuwahara, A. Hirano, K. Sato, and Y. Miyamoto, “1.28 Tbit/s(32×43 Gbit/s) field trial over 528 km(6×88 km) DSF using L-band remotely-pumped EDFA/distributed Raman hybrid inline amplifiers,” Electron. Lett. 39, 1668-1670 (2003).
[CrossRef]

Morita, T.

A. Maruta, Y. Yamamoto, S. Okamoto, A. Suziki, T. Morita, A. Agata, and A. Hasegawa, “Effectiveness of densely dispersion managed solitons in ultrahigh speed transmission,” Electron. Lett. 36, 1947-1949 (2000).
[CrossRef]

Moubissi, A. B.

K. Nakkeeran, Y. C. Kwan, P. K. A. Wai, A. Labruyere, P. Tchofo Dinda, and A. B. Moubissi, “Analytical design of densely dispersion-managed optical fiber transmission systems with Gaussian and raised cosine return-to-zero ansatze,” J. Opt. Soc. Am. B 21, 1901-1907 (2004).
[CrossRef]

P. Tchofo Dinda, A. Labruyere, K. Nakkeeran, J. Fatome, A. B. Moubissi, S. Pitois, and G. Millot, “On the designing of densely dispersion-managed optical fiber systems for ultra-fast optical communication,” Ann. Telecommun. 58, 1785-1808 (2003).

P. Tchofo Dinda, A. B. Moubissi, and K. Nakkeeran, “Collective variable theory for optical solitons in fibers,” Phys. Rev. E 64, 016608 (2001).
[CrossRef]

P. Tchofo Dinda, K. Nakkeeran, and A. B. Moubissi, “Optimized Hermite-Gaussian ansatz functions for dispersion-managed solitons,” Opt. Commun. 187, 427-433 (2001).
[CrossRef]

Nakkeeran, K.

K. Nakkeeran, Y. C. Kwan, P. K. A. Wai, A. Labruyere, P. Tchofo Dinda, and A. B. Moubissi, “Analytical design of densely dispersion-managed optical fiber transmission systems with Gaussian and raised cosine return-to-zero ansatze,” J. Opt. Soc. Am. B 21, 1901-1907 (2004).
[CrossRef]

P. Tchofo Dinda, A. Labruyere, K. Nakkeeran, J. Fatome, A. B. Moubissi, S. Pitois, and G. Millot, “On the designing of densely dispersion-managed optical fiber systems for ultra-fast optical communication,” Ann. Telecommun. 58, 1785-1808 (2003).

P. Tchofo Dinda, K. Nakkeeran, and A. Labruyere, “Suppression of soliton self-frequency shift by up-shifted filtering,” Opt. Lett. 27, 382-384 (2002).
[CrossRef]

P. Tchofo Dinda, A. B. Moubissi, and K. Nakkeeran, “Collective variable theory for optical solitons in fibers,” Phys. Rev. E 64, 016608 (2001).
[CrossRef]

P. Tchofo Dinda, K. Nakkeeran, and A. B. Moubissi, “Optimized Hermite-Gaussian ansatz functions for dispersion-managed solitons,” Opt. Commun. 187, 427-433 (2001).
[CrossRef]

Okamoto, S.

A. Maruta, Y. Yamamoto, S. Okamoto, A. Suziki, T. Morita, A. Agata, and A. Hasegawa, “Effectiveness of densely dispersion managed solitons in ultrahigh speed transmission,” Electron. Lett. 36, 1947-1949 (2000).
[CrossRef]

Omahony, M.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Pan, Z.

M. Funabashi, Z. Zhu, Z. Pan, B. Xian, L. Paraschis, D. L. Harris, and S. J. B. Yoo, “Cascadability of optical 3R regeneration for NRZ format investigated in recirculating loop transmission over field fibers,” IEEE Photon. Technol. Lett. 18, 2081-083 (2006).
[CrossRef]

Paraschis, L.

M. Funabashi, Z. Zhu, Z. Pan, B. Xian, L. Paraschis, D. L. Harris, and S. J. B. Yoo, “Cascadability of optical 3R regeneration for NRZ format investigated in recirculating loop transmission over field fibers,” IEEE Photon. Technol. Lett. 18, 2081-083 (2006).
[CrossRef]

Patzak, E.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Penticost, S.

Perrier, P.

Pincemin, E.

J. Fatome, S. Pitois, P. Tchofo Dinda, G. Millot, E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin, “Effectiveness of fiber lines with symmetric dispersion swing for 160 Gb/s terrestrial transmission systems,” IEEE Photon. Technol. Lett. 16, 2365-2367 (2004).
[CrossRef]

Pitois, S.

J. Fatome, S. Pitois, P. Tchofo Dinda, G. Millot, E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin, “Effectiveness of fiber lines with symmetric dispersion swing for 160 Gb/s terrestrial transmission systems,” IEEE Photon. Technol. Lett. 16, 2365-2367 (2004).
[CrossRef]

P. Tchofo Dinda, A. Labruyere, K. Nakkeeran, J. Fatome, A. B. Moubissi, S. Pitois, and G. Millot, “On the designing of densely dispersion-managed optical fiber systems for ultra-fast optical communication,” Ann. Telecommun. 58, 1785-1808 (2003).

J. Fatome, S. Pitois, P. Tchofo Dinda, and G. Millot, “Experimental demonstration of 160-GHz densely dispersion-managed soliton transmission in a single channel over 896 km of commercial fibres,” Opt. Express 11, 1553-1558 (2003).
[CrossRef] [PubMed]

Politi, Ch.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Posth, J.

J. Posth, T. Schafer, E. Laedke, and K. Spatschek, “Fast optimization procedures for third-order dispersion for dispersion management,” Opt. Commun. 219, 241-249 (2003).
[CrossRef]

Puc, A.

Rao, S.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Reyes, P.

S. Wielandy, P. S. Westbrook, M. Fishteyn, P. Reyes, W. Shairer, H. Rohde, and G. Lehmann, “Demonstration of automatic dispersion control for 160 Gbit/s transmission over 275 km of deployed fibre,” Electron. Lett. 40, 690-691 (2004).
[CrossRef]

Richardson, L. J.

L. J. Richardson, W. Forysiak, and N. J. Doran, “Trans-oceanic 160-Gbit/s single-channel transmission using short-period dispersion management,” IEEE Photon. Technol. Lett. 13, 209-211 (2001).
[CrossRef]

Rohde, H.

S. Wielandy, P. S. Westbrook, M. Fishteyn, P. Reyes, W. Shairer, H. Rohde, and G. Lehmann, “Demonstration of automatic dispersion control for 160 Gbit/s transmission over 275 km of deployed fibre,” Electron. Lett. 40, 690-691 (2004).
[CrossRef]

Roncin, V.

J. C. Simon, L. Bramerie, F. Ginovart, V. Roncin, M. Gay, S. Feve, E. Le Cren, and M. L. Chares, “All-optical regeneration techniques,” Ann. Telecommun. 58, 1708-1724 (2003).

Sanitair, J.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Sato, K.

H. Masuda, H. Kawakami, S. Kuwahara, A. Hirano, K. Sato, and Y. Miyamoto, “1.28 Tbit/s(32×43 Gbit/s) field trial over 528 km(6×88 km) DSF using L-band remotely-pumped EDFA/distributed Raman hybrid inline amplifiers,” Electron. Lett. 39, 1668-1670 (2003).
[CrossRef]

Schafer, T.

J. Posth, T. Schafer, E. Laedke, and K. Spatschek, “Fast optimization procedures for third-order dispersion for dispersion management,” Opt. Commun. 219, 241-249 (2003).
[CrossRef]

S. K. Turitsyn, T. Schafer, K. H. Spatschek, and V. K. Mezentsev, “Path-averaged chirped optical solitons in dispersion-managed fiber communication lines,” Opt. Commun. 163, 122-158 (1999).
[CrossRef]

Schiffini, A.

Settembre, M.

Shairer, W.

S. Wielandy, P. S. Westbrook, M. Fishteyn, P. Reyes, W. Shairer, H. Rohde, and G. Lehmann, “Demonstration of automatic dispersion control for 160 Gbit/s transmission over 275 km of deployed fibre,” Electron. Lett. 40, 690-691 (2004).
[CrossRef]

Shiping, Y.

Z. Shumin, L. Fuyun, X. Wencheng, Y. Shiping, W. Jian, and D. Xiaoyi, “Enhanced compression of high-order solitons in dispersion decreasing fibers due to the combined effects of negative third-order dispersion and raman self-scattering,” Opt. Commun. 237, 1-8 (2004).
[CrossRef]

Shumin, Z.

Z. Shumin, L. Fuyun, X. Wencheng, Y. Shiping, W. Jian, and D. Xiaoyi, “Enhanced compression of high-order solitons in dispersion decreasing fibers due to the combined effects of negative third-order dispersion and raman self-scattering,” Opt. Commun. 237, 1-8 (2004).
[CrossRef]

Simon, J. C.

J. C. Simon, L. Bramerie, F. Ginovart, V. Roncin, M. Gay, S. Feve, E. Le Cren, and M. L. Chares, “All-optical regeneration techniques,” Ann. Telecommun. 58, 1708-1724 (2003).

Sorensen, M. P.

Spatschek, K.

J. Posth, T. Schafer, E. Laedke, and K. Spatschek, “Fast optimization procedures for third-order dispersion for dispersion management,” Opt. Commun. 219, 241-249 (2003).
[CrossRef]

Spatschek, K. H.

S. K. Turitsyn, T. Schafer, K. H. Spatschek, and V. K. Mezentsev, “Path-averaged chirped optical solitons in dispersion-managed fiber communication lines,” Opt. Commun. 163, 122-158 (1999).
[CrossRef]

Stancioff, P.

R. Boesch, P. Stancioff, and C. R. Willis, “Hamiltonian equations for multiple-collective-variable theories of nonlinear klein-gordon equations: a projection-operator approach,” Phys. Rev. B 38, 6713-6735 (1988).
[CrossRef]

Suziki, A.

A. Maruta, Y. Yamamoto, S. Okamoto, A. Suziki, T. Morita, A. Agata, and A. Hasegawa, “Effectiveness of densely dispersion managed solitons in ultrahigh speed transmission,” Electron. Lett. 36, 1947-1949 (2000).
[CrossRef]

Toda, H.

Tromborg, B.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Turitsyn, S. K.

S. Boscolo, S. K. Turitsyn, and K. J. Blow, “All optical passive 2R regeneration for N×40 Gbit/s WDM transmission using NOLM and novel filtering technique,” Opt. Commun. 217, 227-232 (2003).
[CrossRef]

S. K. Turitsyn, M. P. Fedoruk, and A. Gornakova, “Reduced-power optical solitons in fiber lines with short-scale dispersion management,” Opt. Lett. 24, 869-871 (1999).
[CrossRef]

S. K. Turitsyn, T. Schafer, K. H. Spatschek, and V. K. Mezentsev, “Path-averaged chirped optical solitons in dispersion-managed fiber communication lines,” Opt. Commun. 163, 122-158 (1999).
[CrossRef]

Vogel, P.

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

Wabnitz, S.

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol. 1, 187-217 (1995).
[CrossRef]

V. E. Zakharov and S. Wabnitz, Optical Solitons: Theoretical Challenges and Industrial Perspectives (Springer-Verlag, 1998).

Wai, P. K. A.

Wellbrock, G.

Wencheng, X.

Z. Shumin, L. Fuyun, X. Wencheng, Y. Shiping, W. Jian, and D. Xiaoyi, “Enhanced compression of high-order solitons in dispersion decreasing fibers due to the combined effects of negative third-order dispersion and raman self-scattering,” Opt. Commun. 237, 1-8 (2004).
[CrossRef]

Westbrook, P. S.

S. Wielandy, P. S. Westbrook, M. Fishteyn, P. Reyes, W. Shairer, H. Rohde, and G. Lehmann, “Demonstration of automatic dispersion control for 160 Gbit/s transmission over 275 km of deployed fibre,” Electron. Lett. 40, 690-691 (2004).
[CrossRef]

Wielandy, S.

S. Wielandy, P. S. Westbrook, M. Fishteyn, P. Reyes, W. Shairer, H. Rohde, and G. Lehmann, “Demonstration of automatic dispersion control for 160 Gbit/s transmission over 275 km of deployed fibre,” Electron. Lett. 40, 690-691 (2004).
[CrossRef]

Willis, C. R.

R. Boesch, P. Stancioff, and C. R. Willis, “Hamiltonian equations for multiple-collective-variable theories of nonlinear klein-gordon equations: a projection-operator approach,” Phys. Rev. B 38, 6713-6735 (1988).
[CrossRef]

Xia, T. J.

Xian, B.

M. Funabashi, Z. Zhu, Z. Pan, B. Xian, L. Paraschis, D. L. Harris, and S. J. B. Yoo, “Cascadability of optical 3R regeneration for NRZ format investigated in recirculating loop transmission over field fibers,” IEEE Photon. Technol. Lett. 18, 2081-083 (2006).
[CrossRef]

Xiaoyi, D.

Z. Shumin, L. Fuyun, X. Wencheng, Y. Shiping, W. Jian, and D. Xiaoyi, “Enhanced compression of high-order solitons in dispersion decreasing fibers due to the combined effects of negative third-order dispersion and raman self-scattering,” Opt. Commun. 237, 1-8 (2004).
[CrossRef]

Yamamoto, Y.

A. Maruta, Y. Yamamoto, S. Okamoto, A. Suziki, T. Morita, A. Agata, and A. Hasegawa, “Effectiveness of densely dispersion managed solitons in ultrahigh speed transmission,” Electron. Lett. 36, 1947-1949 (2000).
[CrossRef]

Yoo, S. J. B.

M. Funabashi, Z. Zhu, Z. Pan, B. Xian, L. Paraschis, D. L. Harris, and S. J. B. Yoo, “Cascadability of optical 3R regeneration for NRZ format investigated in recirculating loop transmission over field fibers,” IEEE Photon. Technol. Lett. 18, 2081-083 (2006).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov and S. Wabnitz, Optical Solitons: Theoretical Challenges and Industrial Perspectives (Springer-Verlag, 1998).

Zhu, Z.

M. Funabashi, Z. Zhu, Z. Pan, B. Xian, L. Paraschis, D. L. Harris, and S. J. B. Yoo, “Cascadability of optical 3R regeneration for NRZ format investigated in recirculating loop transmission over field fibers,” IEEE Photon. Technol. Lett. 18, 2081-083 (2006).
[CrossRef]

Ann. Telecommun. (4)

S. Bigo, Y. Frignac, J. C. Antona, and G. Charlet, “Design of multiterabit/s terrestrial transmission systems facilitated by simple analytical tools,” Ann. Telecommun. 58, 1757-1784 (2003).

P. Tchofo Dinda, A. Labruyere, K. Nakkeeran, J. Fatome, A. B. Moubissi, S. Pitois, and G. Millot, “On the designing of densely dispersion-managed optical fiber systems for ultra-fast optical communication,” Ann. Telecommun. 58, 1785-1808 (2003).

A. Ackaert, P. Demeester, P. Lagasse, Ch. Politi, M. Omahony, T. Berg, B. Tromborg, J. Sanitair, E. Patzak, S. Rao, P. Vogel, Ch. Minot, and D. Erasme, “European 1st-programme ROADMAP for optical communications,” Ann. Telecommun. 58, 1550-1585 (2003).

J. C. Simon, L. Bramerie, F. Ginovart, V. Roncin, M. Gay, S. Feve, E. Le Cren, and M. L. Chares, “All-optical regeneration techniques,” Ann. Telecommun. 58, 1708-1724 (2003).

Electron. Lett. (3)

H. Masuda, H. Kawakami, S. Kuwahara, A. Hirano, K. Sato, and Y. Miyamoto, “1.28 Tbit/s(32×43 Gbit/s) field trial over 528 km(6×88 km) DSF using L-band remotely-pumped EDFA/distributed Raman hybrid inline amplifiers,” Electron. Lett. 39, 1668-1670 (2003).
[CrossRef]

S. Wielandy, P. S. Westbrook, M. Fishteyn, P. Reyes, W. Shairer, H. Rohde, and G. Lehmann, “Demonstration of automatic dispersion control for 160 Gbit/s transmission over 275 km of deployed fibre,” Electron. Lett. 40, 690-691 (2004).
[CrossRef]

A. Maruta, Y. Yamamoto, S. Okamoto, A. Suziki, T. Morita, A. Agata, and A. Hasegawa, “Effectiveness of densely dispersion managed solitons in ultrahigh speed transmission,” Electron. Lett. 36, 1947-1949 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

J. Fatome, S. Pitois, P. Tchofo Dinda, G. Millot, E. Le Rouzic, B. Cuenot, E. Pincemin, and S. Gosselin, “Effectiveness of fiber lines with symmetric dispersion swing for 160 Gb/s terrestrial transmission systems,” IEEE Photon. Technol. Lett. 16, 2365-2367 (2004).
[CrossRef]

L. J. Richardson, W. Forysiak, and N. J. Doran, “Trans-oceanic 160-Gbit/s single-channel transmission using short-period dispersion management,” IEEE Photon. Technol. Lett. 13, 209-211 (2001).
[CrossRef]

M. Funabashi, Z. Zhu, Z. Pan, B. Xian, L. Paraschis, D. L. Harris, and S. J. B. Yoo, “Cascadability of optical 3R regeneration for NRZ format investigated in recirculating loop transmission over field fibers,” IEEE Photon. Technol. Lett. 18, 2081-083 (2006).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (3)

Opt. Commun. (6)

Z. Shumin, L. Fuyun, X. Wencheng, Y. Shiping, W. Jian, and D. Xiaoyi, “Enhanced compression of high-order solitons in dispersion decreasing fibers due to the combined effects of negative third-order dispersion and raman self-scattering,” Opt. Commun. 237, 1-8 (2004).
[CrossRef]

S. Boscolo, S. K. Turitsyn, and K. J. Blow, “All optical passive 2R regeneration for N×40 Gbit/s WDM transmission using NOLM and novel filtering technique,” Opt. Commun. 217, 227-232 (2003).
[CrossRef]

A. Labruyere and P. Tchofo Dinda, “Analytical design of nonlinear optical loop mirrors for fiber-optic communication systems,” Opt. Commun. 266, 676-680 (2006).
[CrossRef]

S. K. Turitsyn, T. Schafer, K. H. Spatschek, and V. K. Mezentsev, “Path-averaged chirped optical solitons in dispersion-managed fiber communication lines,” Opt. Commun. 163, 122-158 (1999).
[CrossRef]

P. Tchofo Dinda, K. Nakkeeran, and A. B. Moubissi, “Optimized Hermite-Gaussian ansatz functions for dispersion-managed solitons,” Opt. Commun. 187, 427-433 (2001).
[CrossRef]

J. Posth, T. Schafer, E. Laedke, and K. Spatschek, “Fast optimization procedures for third-order dispersion for dispersion management,” Opt. Commun. 219, 241-249 (2003).
[CrossRef]

Opt. Express (1)

Opt. Fiber Technol. (1)

S. Wabnitz, Y. Kodama, and A. B. Aceves, “Control of optical soliton interactions,” Opt. Fiber Technol. 1, 187-217 (1995).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. B (1)

R. Boesch, P. Stancioff, and C. R. Willis, “Hamiltonian equations for multiple-collective-variable theories of nonlinear klein-gordon equations: a projection-operator approach,” Phys. Rev. B 38, 6713-6735 (1988).
[CrossRef]

Phys. Rev. E (1)

P. Tchofo Dinda, A. B. Moubissi, and K. Nakkeeran, “Collective variable theory for optical solitons in fibers,” Phys. Rev. E 64, 016608 (2001).
[CrossRef]

Other (3)

A. Hasegawa and Y. Kodama, Solitons in Optical Communication (Oxford U. Press, 1995).

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

V. E. Zakharov and S. Wabnitz, Optical Solitons: Theoretical Challenges and Industrial Perspectives (Springer-Verlag, 1998).

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Figures (6)

Fig. 1
Fig. 1

Schematic representation of the dispersion map of the dense DM fiber system.

Fig. 2
Fig. 2

Thin solid curves show the ansatz profile reconstructed from the CCs obtained by solving the VEs [Eqs. (8)]. The dotted curves show the exact pulse profile obtained by numerically solving the NLSE with TOD. The thick solid curves show the ansatz profile reconstructed from the CCs obtained from the RFM procedure.

Fig. 3
Fig. 3

Evolution of the temporal pulse parameters for the pulse propagation in the fiber system. The thin (thick) dashed curves in (a)–(e) show the conventional CCs obtained from the VE [Eq. (8) (RFM)], in the presence of TOD. The thin (thick) solid curves show their upgraded versions, obtained from the data given by the thin (thick) dashed curves. In (b) and (c) the thin (thick) circles correspond to X ̃ 1 cm and X ̃ 2 cm , respectively, obtained from the VE (RFM). The thin (thick) solid curves correspond to X ̃ 1 pp and X ̃ 2 pp , obtained from the VE (RFM). In all the figures the crosses show the conventional CCs for an ideal system without TOD.

Fig. 4
Fig. 4

Evolution of the spectral pulse parameters obtained from Eqs. (6) and the CCs in Figs. 3, in the presence of TOD. The thin (thick) dashed curves in (a)–(e) show the conventional CCs obtained from the results of the VE (RFM) procedure, in the presence of TOD. The thin (thick) solid curves show their upgraded versions, obtained from the data given by the thin (thick) dashed curves. In (a) and (b) the thin (thick) circles correspond to Y ̃ 1 cm and Y ̃ 2 cm , respectively, obtained from the VE (RFM) procedure. The thin (thick) solid curves correspond to Y ̃ 1 pp and Y ̃ 2 pp , obtained from the VE (RFM) procedure.

Fig. 5
Fig. 5

Plots showing the ratio between upgraded and conventional CCs, obtained from Eqs. (12, 13, 15, 19, 16, 20).

Fig. 6
Fig. 6

Evolution of the RFE obtained from the procedure of minimization of the RFE, for the same initial conditions as in Fig. 3, in the presence of TOD. The solid (dashed) curves show results obtained with the upgraded (conventional) ansatz.

Tables (2)

Tables Icon

Table 1 Pulse Parameters Obtained from the Conventional CCs, With X 7 = 0

Tables Icon

Table 2 Pulse Parameters Obtained from the Upgraded CCs, with X 7 0

Equations (59)

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ψ z + i β 2 ( z ) 2 2 ψ t 2 + β 3 ( z ) 6 3 ψ t 3 i γ ( z ) ψ 2 ψ = α ( z ) 2 ψ ,
ψ ( z , t ) = f ( X 1 , X 2 , , X N , t ) + q ( z , t ) ,
f CA = X 1 exp [ ( t X 2 ) 2 X 3 2 + i 1 2 X 4 ( t X 2 ) 2 i X 5 ( t X 2 ) + i X 6 ] .
f UA = X 1 [ 1 + X 7 ( t X 2 ) X 3 ] exp [ ( t X 2 ) 2 X 3 2 + i X 4 2 ( t X 2 ) 2 i X 5 ( t X 2 ) + i X 6 ] ,
f ̂ UA = Y 1 [ 1 + Y 7 ( w Y 2 ) Y 3 ] exp [ ( w Y 2 ) 2 Y 3 2 + i Y 4 2 ( w Y 2 ) 2 + i Y 5 ( w Y 2 ) + i Y 6 ] ,
Y 1 = X 1 X 3 2 π 2 i X 4 X 3 2 ,
Y 2 = X 5 ,
Y 3 = 4 + X 4 2 X 3 4 X 3 ,
Y 4 = X 4 X 3 4 4 + X 4 2 X 3 4 ,
Y 5 = X 2 ,
Y 6 = X 2 X 5 + X 6 + φ + π ,
Y 7 = X 7 ( X 4 X 3 2 2 i ) 4 + X 4 2 X 3 4 = X 7 X 4 X 3 2 4 + X 4 2 X 3 4 + i 2 X 7 4 + X 4 2 X 3 4 = Y 7 r + i Y 7 i .
Y 1 exp ( i φ ) = X 1 X 3 2 π 4 + X 4 2 X 3 4 2 + i X 4 X 3 2 .
X ̇ 1 = Δ X 1 + β 3 X 1 [ 3 X 3 4 X 4 2 ( X 7 2 8 ) + 12 X 7 2 + 32 ] 48 X 7 X 3 3 ,
X ̇ 2 = Δ X 2 + β 3 ( 3 X 3 4 X 7 2 X 4 2 + 12 X 7 2 12 X 3 4 X 4 2 + 16 ) 24 X 3 2 X 7 2 ,
X ̇ 3 = Δ X 3 + β 3 ( 3 X 3 4 X 4 2 4 ) 6 X 7 X 3 2 ,
X ̇ 4 = Δ X 4 + X 7 2 16 M X 3 4 [ 1024 β 2 ( 3 X 7 2 4 ) 2 γ X 1 2 X 3 2 ( 9 X 7 6 + 144 X 7 4 528 X 7 2 + 1024 ) ] + β 3 2 X 7 M X 3 4 [ X 3 5 X 4 3 ( 3 X 7 4 8 X 7 2 + 16 ) + 4 X 3 X 4 ( 3 X 7 4 + 8 X 7 2 + 16 ) 32 X 5 X 7 ( 3 X 7 2 4 ) ] ,
X ̇ 5 = Δ X 5 + 8 β 2 X 7 ( 16 3 X 7 4 ) X 3 3 M + 2 γ X 1 2 X 7 ( 9 X 7 6 + 18 X 7 4 + 128 ) 4 X 3 M + β 3 24 X 3 3 X 7 2 M [ 3 X 4 3 X 3 5 ( 3 X 7 8 48 X 7 6 96 X 7 4 + 256 X 7 2 256 ) + 4 X 4 X 3 ( 9 X 7 8 480 X 7 4 + 256 ) + 192 X 5 X 7 ( 3 X 7 4 16 ) ] ,
X ̇ 6 = Δ X 6 + 6 β 2 X 7 4 ( 3 X 7 2 4 ) X 3 2 M + 3 2 γ X 1 2 X 7 2 ( 45 X 7 6 + 408 X 7 4 624 X 7 2 + 512 ) 128 M + β 3 24 M X 3 2 X 7 2 [ 6 X 4 3 X 3 5 X 7 3 ( 15 X 7 4 24 X 7 2 + 16 ) + 3 X 5 X 4 2 X 3 4 ( 9 X 7 8 192 X 7 4 + 256 X 7 2 256 ) 24 X 3 X 4 X 7 3 ( 3 X 7 4 24 X 7 2 + 16 ) 4 X 5 ( 81 X 7 8 288 X 7 6 256 ) ] ,
X ̇ 7 = β 3 48 X 3 3 X 7 2 [ 3 X 4 2 X 3 4 ( X 7 4 16 ) 4 ( 3 X 7 4 + 16 X 7 2 + 16 ) ] ,
Δ X 1 = β 2 2 X 1 X 4 β 3 2 X 1 X 4 X 5 ,
Δ X 2 = β 2 X 5 + β 3 8 ( 4 X 3 2 + X 3 2 X 4 2 + 4 X 5 2 ) ,
Δ X 3 = β 2 X 3 X 4 + β 3 X 3 X 4 X 5 ,
Δ X 4 = β 2 ( X 4 2 4 X 3 4 ) + β 3 X 5 ( 4 X 3 4 X 4 2 ) 2 γ X 1 2 X 3 2 ,
Δ X 5 = 0 ,
Δ X 6 = β 2 ( 1 X 3 2 X 5 2 2 ) + β 3 ( X 3 2 X 4 2 X 5 8 X 5 2 X 3 2 + X 5 3 3 ) + 5 2 γ 8 X 1 2 .
ψ ( 0 , t ) = f CA [ 1 + X 7 ( 0 ) ( t X 2 ( 0 ) ) X 3 ( 0 ) ] = f CA + ϕ ,
X ̃ 1 pp = max ( F ) .
X ̃ 1 pp = X 1 2 ( 1 + 1 + 2 X 7 2 ) exp [ ( 1 1 + 2 X 7 2 ) 2 2 X 7 2 ] ,
X ̃ 2 pp = X 2 + X 3 2 X 7 ( 1 + 2 X 7 2 1 ) .
X ̃ 2 cm = + ( t F 2 ) d t + F 2 d t .
X ̃ 2 cm = X 2 + 2 X 3 X 7 4 + X 7 2 .
X ̃ 1 cm f UA ( t = X ̃ 2 cm ) = X 1 ( 1 + 2 X 7 2 4 + X 7 2 ) exp [ ( 2 X 7 2 4 + X 7 2 ) ] .
X ̃ 3 = 2 L 1 N 1 X ̃ 2 2 , N 1 = + F 2 d t , L 1 = + ( t 2 F 2 ) d t ,
X ̃ 4 = i 2 + ( t X 2 ) ( F F t * F * F t ) d t + ( t X 2 ) 2 F 2 d t .
X ̃ 3 = X 3 16 + 3 X 7 4 ( 4 + X 7 2 ) 2 ,
X ̃ 4 = X 4 8 X 7 X 5 X 3 ( 4 + 3 X 7 2 ) .
Y ̃ 1 pp = max ( F ̂ ) ,
F ̂ w ( Y ̃ 2 pp ) = 0 ,
Y ̃ 2 cm = + ( w F ̂ 2 ) d w + F ̂ 2 d w = X 5 ,
Y ̃ 3 = 2 L 1 w N 1 w Y ̃ 2 cm 2 , N 1 w = + F ̂ 2 d w , L 1 w = + ( w 2 F ̂ 2 ) d w ,
Y ̃ 4 = i 2 + ( w Y 2 ) ( F ̂ F ̂ w * F ̂ * F ̂ w ) d w + ( w Y 2 ) 2 F ̂ 2 d w ,
Y ̃ 5 = X ̃ 2 .
Y ̃ 1 pp = { Y ̃ 1 pp 1 = Y 1 [ ( 1 + Y 7 r Y 3 ( Y ̃ 2 pp 1 Y 2 ) ) 2 + Y 7 i 2 Y 3 2 ( Y ̃ 2 pp 1 Y 2 ) 2 ] exp ( ( Y ̃ 2 pp 1 Y 2 ) 2 Y 3 2 ) Y ̃ 1 pp 2 = Y 1 [ ( 1 + Y 7 r Y 3 ( Y ̃ 2 pp 2 Y 2 ) ) 2 + Y 7 i 2 Y 3 2 ( Y ̃ 2 pp 2 Y 2 ) 2 ] exp ( ( Y ̃ 2 pp 2 Y 2 ) 2 Y 3 2 ) Y ̃ 1 pp 3 = Y 1 [ ( 1 + Y 7 r Y 3 ( Y ̃ 2 pp 3 X 5 ) ) 2 + Y 7 i 2 Y 3 2 ( Y ̃ 2 pp 3 X 5 ) 2 ] exp ( ( Y ̃ 2 pp 3 X 5 ) 2 Y 3 2 ) } ,
Y ̃ 2 pp = { Y ̃ 2 pp 1 = Y 2 + ρ 6 2 ( 3 ζ ξ 2 ) 9 ( ρ ξ ) Y ̃ 2 pp 2 = Y 2 ρ 12 + 3 ζ ξ 2 9 ( ρ ξ ) + i 3 ( ρ 2 + 12 ζ 4 ξ 2 ) 12 ρ Y ̃ 2 pp 3 = Y 2 ρ 12 + 3 ζ ξ 2 9 ( ρ ξ ) i 3 ( ρ 2 + 12 ζ 4 ξ 2 ) 12 ρ } ,
Y ̃ 2 cm = Y 2 + 2 Y 3 Y 7 r 4 + Y ̃ 7 2 ,
Y ̃ 3 = Y 3 16 ( Y 7 i 2 + 1 ) + 3 Y 7 4 ( 4 + Y 7 2 ) 2 ,
Y ̃ 4 = 4 Y 7 r ( Y 7 i + 2 Y 5 Y 3 ) + Y 4 Y 3 2 ( 4 + 3 Y 7 r 2 3 Y 7 i 2 ) Y 3 2 ( 4 + 3 Y 7 2 ) ,
δ = Y 7 r Y 3 3 2 X 7 2 ,
ζ = Y 3 2 ( 2 X 7 2 ) 2 X 7 2 ,
ξ = 2 Y 7 r Y 3 X 7 2 ,
μ = 4 ζ 3 ζ 2 ξ 2 18 ξ ζ δ + 27 δ 2 + 4 δ ξ 3 ,
σ = 4 ( 9 ξ ζ 27 δ 2 ξ 3 ) ,
ρ = ( σ + 12 3 μ ) 1 3 .
e q 2 d t = ψ f UA ( X 1 , X 2 , , X 7 , t ) 2 d t .
C j = d e d X j 0 .
C j = e X j = R [ q f UA * X j ] d t = 0 ( j = 1 , 2 , , 7 ) ,
e ( X 1 ( z ) , X 2 ( z ) , , X 7 ( z ) ) E ( z ) < ϵ 1 ,
E ( z ) ψ ( z , t ) 2 d t ,

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