Abstract

We present a useful analytical method for designing grating-compensated dispersion-managed (DM) soliton systems for any desired input pulse widths and energies. The pulse-width and chirp evolution equations derived from the variational method are solved exactly to obtain the explicit analytical expressions for the length of the dispersion map and the grating dispersion. We also extend our analytical method to design grating-compensated DM soliton systems with loss and gain. We show that our analytically designed DM soliton systems also apply even if the chirped fiber gratings have group-delay ripples. The results obtained from our analytical method are in good agreement with those obtained from full numerical simulations. Finally a 160-Gbits/s transmission system is simulated with all the important higher-order effects to show the effectiveness of our analytical design.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  26. A. B. Moubissi, K. Nakkeeran, P. Tchofo Dinda, and S. Wabnitz, “Average dispersion decreasing densely dispersion-managed fiber transmission systems,” IEEE Photon. Technol. Lett. 14, 1279–1281 (2002).
    [CrossRef]
  27. H. Chotard, Y. Painchaud, A. Mailloux, M. Morin, F. Trépanier, and M. Guy, “Group delay ripple of cascaded Bragg grating gain flattening filters,” IEEE Photon. Technol. Lett. 14, 1130–1132 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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  30. P. T. Dinda, K. Nakkeeran, and A. Labruyére, “Suppression of soliton self-frequency shift by upshifted filtering,” Opt. Lett. 27, 382–384 (2002).
    [CrossRef]
  31. S. K. Turitsyn and V. K. Mezentsev, “Chirped solitons with strong confinement in transmission links with in-line fiber Bragg gratings,” Opt. Lett. 23, 600–602 (1998).
    [CrossRef]

2003 (5)

P. Li, J. Shuisheng, Y. Fengping, N. Tigang, and W. Zhi, “Long-haul WDM system through conventional single mode optical fiber with dispersion compensation by chirped fiber Bragg grating,” Opt. Commun. 222, 169–178 (2003).
[CrossRef]

K. Nakkeeran, Y. H. C. Kwan, and P. K. A. Wai, “Method to find the stationary solution parameters of chirped fiber grating compensated dispersion-managed fiber systems,” Opt. Commun. 215, 315–321 (2003).
[CrossRef]

K. Nakkeeran, A. B. Moubissi, and P. Tchofo Dinda, “Analytical design of dispersion-managed fiber system with map strength 1.65,” Phys. Lett. A 308, 417–425 (2003).
[CrossRef]

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]

M. Ibsen and R. Feced, “Fiber Bragg gratings for puredispersion-slope compensation,” Opt. Lett. 28, 980–982 (2003).
[CrossRef] [PubMed]

2002 (4)

P. T. Dinda, K. Nakkeeran, and A. Labruyére, “Suppression of soliton self-frequency shift by upshifted filtering,” Opt. Lett. 27, 382–384 (2002).
[CrossRef]

E. Poutrina and G. P. Agrawal, “Design rules for dispersion-managed soliton systems,” Opt. Commun. 206, 193–200 (2002).
[CrossRef]

A. B. Moubissi, K. Nakkeeran, P. Tchofo Dinda, and S. Wabnitz, “Average dispersion decreasing densely dispersion-managed fiber transmission systems,” IEEE Photon. Technol. Lett. 14, 1279–1281 (2002).
[CrossRef]

H. Chotard, Y. Painchaud, A. Mailloux, M. Morin, F. Trépanier, and M. Guy, “Group delay ripple of cascaded Bragg grating gain flattening filters,” IEEE Photon. Technol. Lett. 14, 1130–1132 (2002).
[CrossRef]

2001 (4)

A. Sahara, T. Komukai, E. Yamada, and M. Nakazawa, “40 Gbits/s return-to-zero transmission over 500 km of standard fibre using chirped fibre Bragg gratings with small group delay ripples,” Electron. Lett. 37, 8–9 (2001).
[CrossRef]

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

Y. H. C. Kwan, P. K. A. Wai, and H. Y. Tam, “Effect of group-delay ripples on dispersion-managed soliton communication systems with chirped fiber gratings,” Opt. Lett. 26, 959–961 (2001).
[CrossRef]

K. Nakkeeran, A. B. Moubissi, P. Tchofo Dinda, and S. Wabnitz, “Analytical method for designing dispersion-managed fiber systems,” Opt. Lett. 26, 1544–1546 (2001).
[CrossRef]

2000 (3)

L. J. Richardson, W. Forysiak, and N. J. Doran, “Dispersion-managed soliton propagation in short-period dispersion maps,” Opt. Lett. 25, 1010–1012 (2000).
[CrossRef]

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

A. H. Gnauck, J. M. Wiesenfeld, L. D. Garrett, M. Eiselt, F. Forghieri, L. Arcangeli, B. Agogliata, V. Gusmeroli, and D. Scarano, “16×20 Gb/s, 400-km WDM transmission over NZDSF using a slope-compensating fiber-grating module,” IEEE Photon. Technol. Lett. 12, 437–439 (2000).
[CrossRef]

1999 (4)

1998 (3)

1997 (3)

1996 (1)

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

1979 (1)

A. Bondeson, M. Lisak, and D. Anderson, “Soliton perturbations—variational principle for the soliton parameters,” Phys. Scr. 20, 479–485 (1979).
[CrossRef]

Agogliata, B.

A. H. Gnauck, J. M. Wiesenfeld, L. D. Garrett, M. Eiselt, F. Forghieri, L. Arcangeli, B. Agogliata, V. Gusmeroli, and D. Scarano, “16×20 Gb/s, 400-km WDM transmission over NZDSF using a slope-compensating fiber-grating module,” IEEE Photon. Technol. Lett. 12, 437–439 (2000).
[CrossRef]

Agrawal, G. P.

E. Poutrina and G. P. Agrawal, “Design rules for dispersion-managed soliton systems,” Opt. Commun. 206, 193–200 (2002).
[CrossRef]

Anderson, D.

A. Bondeson, M. Lisak, and D. Anderson, “Soliton perturbations—variational principle for the soliton parameters,” Phys. Scr. 20, 479–485 (1979).
[CrossRef]

Arcangeli, L.

A. H. Gnauck, J. M. Wiesenfeld, L. D. Garrett, M. Eiselt, F. Forghieri, L. Arcangeli, B. Agogliata, V. Gusmeroli, and D. Scarano, “16×20 Gb/s, 400-km WDM transmission over NZDSF using a slope-compensating fiber-grating module,” IEEE Photon. Technol. Lett. 12, 437–439 (2000).
[CrossRef]

Atieh, A. K.

Bennion, I.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Berntson, A.

Blow, K. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Bondeson, A.

A. Bondeson, M. Lisak, and D. Anderson, “Soliton perturbations—variational principle for the soliton parameters,” Phys. Scr. 20, 479–485 (1979).
[CrossRef]

Chotard, H.

H. Chotard, Y. Painchaud, A. Mailloux, M. Morin, F. Trépanier, and M. Guy, “Group delay ripple of cascaded Bragg grating gain flattening filters,” IEEE Photon. Technol. Lett. 14, 1130–1132 (2002).
[CrossRef]

Chrostowski, J.

Dinda, P. T.

P. T. Dinda, K. Nakkeeran, and A. Labruyére, “Suppression of soliton self-frequency shift by upshifted filtering,” Opt. Lett. 27, 382–384 (2002).
[CrossRef]

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

Dinda, P. Tchofo

K. Nakkeeran, A. B. Moubissi, and P. Tchofo Dinda, “Analytical design of dispersion-managed fiber system with map strength 1.65,” Phys. Lett. A 308, 417–425 (2003).
[CrossRef]

A. B. Moubissi, K. Nakkeeran, P. Tchofo Dinda, and S. Wabnitz, “Average dispersion decreasing densely dispersion-managed fiber transmission systems,” IEEE Photon. Technol. Lett. 14, 1279–1281 (2002).
[CrossRef]

K. Nakkeeran, A. B. Moubissi, P. Tchofo Dinda, and S. Wabnitz, “Analytical method for designing dispersion-managed fiber systems,” Opt. Lett. 26, 1544–1546 (2001).
[CrossRef]

Doran, N. J.

L. J. Richardson, W. Forysiak, and N. J. Doran, “Dispersion-managed soliton propagation in short-period dispersion maps,” Opt. Lett. 25, 1010–1012 (2000).
[CrossRef]

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

A. Berntson, N. J. Doran, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900–902 (1998).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Eiselt, M.

A. H. Gnauck, J. M. Wiesenfeld, L. D. Garrett, M. Eiselt, F. Forghieri, L. Arcangeli, B. Agogliata, V. Gusmeroli, and D. Scarano, “16×20 Gb/s, 400-km WDM transmission over NZDSF using a slope-compensating fiber-grating module,” IEEE Photon. Technol. Lett. 12, 437–439 (2000).
[CrossRef]

Eramo, V.

Feced, R.

Fedoruk, M. P.

Fengping, Y.

P. Li, J. Shuisheng, Y. Fengping, N. Tigang, and W. Zhi, “Long-haul WDM system through conventional single mode optical fiber with dispersion compensation by chirped fiber Bragg grating,” Opt. Commun. 222, 169–178 (2003).
[CrossRef]

Forghieri, F.

A. H. Gnauck, J. M. Wiesenfeld, L. D. Garrett, M. Eiselt, F. Forghieri, L. Arcangeli, B. Agogliata, V. Gusmeroli, and D. Scarano, “16×20 Gb/s, 400-km WDM transmission over NZDSF using a slope-compensating fiber-grating module,” IEEE Photon. Technol. Lett. 12, 437–439 (2000).
[CrossRef]

Forysiak, W.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

L. J. Richardson, W. Forysiak, and N. J. Doran, “Dispersion-managed soliton propagation in short-period dispersion maps,” Opt. Lett. 25, 1010–1012 (2000).
[CrossRef]

Galko, P.

Garrett, L. D.

A. H. Gnauck, J. M. Wiesenfeld, L. D. Garrett, M. Eiselt, F. Forghieri, L. Arcangeli, B. Agogliata, V. Gusmeroli, and D. Scarano, “16×20 Gb/s, 400-km WDM transmission over NZDSF using a slope-compensating fiber-grating module,” IEEE Photon. Technol. Lett. 12, 437–439 (2000).
[CrossRef]

Gnauck, A. H.

A. H. Gnauck, J. M. Wiesenfeld, L. D. Garrett, M. Eiselt, F. Forghieri, L. Arcangeli, B. Agogliata, V. Gusmeroli, and D. Scarano, “16×20 Gb/s, 400-km WDM transmission over NZDSF using a slope-compensating fiber-grating module,” IEEE Photon. Technol. Lett. 12, 437–439 (2000).
[CrossRef]

Golovchenko, E. A.

Gornakova, A.

Guglielmucci, M.

Gusmeroli, V.

A. H. Gnauck, J. M. Wiesenfeld, L. D. Garrett, M. Eiselt, F. Forghieri, L. Arcangeli, B. Agogliata, V. Gusmeroli, and D. Scarano, “16×20 Gb/s, 400-km WDM transmission over NZDSF using a slope-compensating fiber-grating module,” IEEE Photon. Technol. Lett. 12, 437–439 (2000).
[CrossRef]

Guy, M.

H. Chotard, Y. Painchaud, A. Mailloux, M. Morin, F. Trépanier, and M. Guy, “Group delay ripple of cascaded Bragg grating gain flattening filters,” IEEE Photon. Technol. Lett. 14, 1130–1132 (2002).
[CrossRef]

Hasegawa, A.

Ibsen, M.

Imai, T.

E. Yamada, T. Imai, T. Komukai, and M. Nakazawa, “10 Gbits/s soliton transmission over 2900 km using 1.3 μm singlemode fibres and dispersion compensation using chirped fibre Bragg gratings,” Electron. Lett. 35, 728–729 (1999).
[CrossRef]

Knox, F. M.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Komukai, T.

A. Sahara, T. Komukai, E. Yamada, and M. Nakazawa, “40 Gbits/s return-to-zero transmission over 500 km of standard fibre using chirped fibre Bragg gratings with small group delay ripples,” Electron. Lett. 37, 8–9 (2001).
[CrossRef]

E. Yamada, T. Imai, T. Komukai, and M. Nakazawa, “10 Gbits/s soliton transmission over 2900 km using 1.3 μm singlemode fibres and dispersion compensation using chirped fibre Bragg gratings,” Electron. Lett. 35, 728–729 (1999).
[CrossRef]

Kumar, S.

Kutz, J. N.

J. N. Kutz and P. K. A. Wai, “Ideal amplifier spacing for reduction of Gordon-Haus jitters in dispersion-managed soliton communications,” Electron. Lett. 34, 522–523 (1998).
[CrossRef]

Kwan, Y. H. C.

K. Nakkeeran, Y. H. C. Kwan, and P. K. A. Wai, “Method to find the stationary solution parameters of chirped fiber grating compensated dispersion-managed fiber systems,” Opt. Commun. 215, 315–321 (2003).
[CrossRef]

Y. H. C. Kwan, P. K. A. Wai, and H. Y. Tam, “Effect of group-delay ripples on dispersion-managed soliton communication systems with chirped fiber gratings,” Opt. Lett. 26, 959–961 (2001).
[CrossRef]

Labruyére, A.

Li, P.

P. Li, J. Shuisheng, Y. Fengping, N. Tigang, and W. Zhi, “Long-haul WDM system through conventional single mode optical fiber with dispersion compensation by chirped fiber Bragg grating,” Opt. Commun. 222, 169–178 (2003).
[CrossRef]

Liang, A. H.

Lisak, M.

A. Bondeson, M. Lisak, and D. Anderson, “Soliton perturbations—variational principle for the soliton parameters,” Phys. Scr. 20, 479–485 (1979).
[CrossRef]

Mailloux, A.

H. Chotard, Y. Painchaud, A. Mailloux, M. Morin, F. Trépanier, and M. Guy, “Group delay ripple of cascaded Bragg grating gain flattening filters,” IEEE Photon. Technol. Lett. 14, 1130–1132 (2002).
[CrossRef]

Matera, F.

Menyuk, C. R.

Mezentsev, V. K.

S. K. Turitsyn and V. K. Mezentsev, “Chirped solitons with strong confinement in transmission links with in-line fiber Bragg gratings,” Opt. Lett. 23, 600–602 (1998).
[CrossRef]

V. K. Mezentsev and S. K. Turitsyn, “Solitons with Gaussian tails in dispersion-managed communication systems using gratings,” Phys. Lett. A 237, 37–42 (1997).
[CrossRef]

Morin, M.

H. Chotard, Y. Painchaud, A. Mailloux, M. Morin, F. Trépanier, and M. Guy, “Group delay ripple of cascaded Bragg grating gain flattening filters,” IEEE Photon. Technol. Lett. 14, 1130–1132 (2002).
[CrossRef]

Moubissi, A. B.

K. Nakkeeran, A. B. Moubissi, and P. Tchofo Dinda, “Analytical design of dispersion-managed fiber system with map strength 1.65,” Phys. Lett. A 308, 417–425 (2003).
[CrossRef]

A. B. Moubissi, K. Nakkeeran, P. Tchofo Dinda, and S. Wabnitz, “Average dispersion decreasing densely dispersion-managed fiber transmission systems,” IEEE Photon. Technol. Lett. 14, 1279–1281 (2002).
[CrossRef]

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

K. Nakkeeran, A. B. Moubissi, P. Tchofo Dinda, and S. Wabnitz, “Analytical method for designing dispersion-managed fiber systems,” Opt. Lett. 26, 1544–1546 (2001).
[CrossRef]

Myslinkski, P.

Nakazawa, M.

A. Sahara, T. Komukai, E. Yamada, and M. Nakazawa, “40 Gbits/s return-to-zero transmission over 500 km of standard fibre using chirped fibre Bragg gratings with small group delay ripples,” Electron. Lett. 37, 8–9 (2001).
[CrossRef]

E. Yamada, T. Imai, T. Komukai, and M. Nakazawa, “10 Gbits/s soliton transmission over 2900 km using 1.3 μm singlemode fibres and dispersion compensation using chirped fibre Bragg gratings,” Electron. Lett. 35, 728–729 (1999).
[CrossRef]

Nakkeeran, K.

K. Nakkeeran, Y. H. C. Kwan, and P. K. A. Wai, “Method to find the stationary solution parameters of chirped fiber grating compensated dispersion-managed fiber systems,” Opt. Commun. 215, 315–321 (2003).
[CrossRef]

K. Nakkeeran, A. B. Moubissi, and P. Tchofo Dinda, “Analytical design of dispersion-managed fiber system with map strength 1.65,” Phys. Lett. A 308, 417–425 (2003).
[CrossRef]

A. B. Moubissi, K. Nakkeeran, P. Tchofo Dinda, and S. Wabnitz, “Average dispersion decreasing densely dispersion-managed fiber transmission systems,” IEEE Photon. Technol. Lett. 14, 1279–1281 (2002).
[CrossRef]

P. T. Dinda, K. Nakkeeran, and A. Labruyére, “Suppression of soliton self-frequency shift by upshifted filtering,” Opt. Lett. 27, 382–384 (2002).
[CrossRef]

K. Nakkeeran, A. B. Moubissi, P. Tchofo Dinda, and S. Wabnitz, “Analytical method for designing dispersion-managed fiber systems,” Opt. Lett. 26, 1544–1546 (2001).
[CrossRef]

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

Nijhof, J. H. B.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

A. Berntson, N. J. Doran, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900–902 (1998).
[CrossRef]

Painchaud, Y.

H. Chotard, Y. Painchaud, A. Mailloux, M. Morin, F. Trépanier, and M. Guy, “Group delay ripple of cascaded Bragg grating gain flattening filters,” IEEE Photon. Technol. Lett. 14, 1130–1132 (2002).
[CrossRef]

Pilipetskii, A. N.

Poutrina, E.

E. Poutrina and G. P. Agrawal, “Design rules for dispersion-managed soliton systems,” Opt. Commun. 206, 193–200 (2002).
[CrossRef]

Richardson, L. J.

Sahara, A.

A. Sahara, T. Komukai, E. Yamada, and M. Nakazawa, “40 Gbits/s return-to-zero transmission over 500 km of standard fibre using chirped fibre Bragg gratings with small group delay ripples,” Electron. Lett. 37, 8–9 (2001).
[CrossRef]

Scarano, D.

A. H. Gnauck, J. M. Wiesenfeld, L. D. Garrett, M. Eiselt, F. Forghieri, L. Arcangeli, B. Agogliata, V. Gusmeroli, and D. Scarano, “16×20 Gb/s, 400-km WDM transmission over NZDSF using a slope-compensating fiber-grating module,” IEEE Photon. Technol. Lett. 12, 437–439 (2000).
[CrossRef]

Schiffini, A.

Settembre, M.

Shuisheng, J.

P. Li, J. Shuisheng, Y. Fengping, N. Tigang, and W. Zhi, “Long-haul WDM system through conventional single mode optical fiber with dispersion compensation by chirped fiber Bragg grating,” Opt. Commun. 222, 169–178 (2003).
[CrossRef]

Smith, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

Tam, H. Y.

Tigang, N.

P. Li, J. Shuisheng, Y. Fengping, N. Tigang, and W. Zhi, “Long-haul WDM system through conventional single mode optical fiber with dispersion compensation by chirped fiber Bragg grating,” Opt. Commun. 222, 169–178 (2003).
[CrossRef]

Toda, H.

Trépanier, F.

H. Chotard, Y. Painchaud, A. Mailloux, M. Morin, F. Trépanier, and M. Guy, “Group delay ripple of cascaded Bragg grating gain flattening filters,” IEEE Photon. Technol. Lett. 14, 1130–1132 (2002).
[CrossRef]

Turitsyn, S. K.

Wabnitz, S.

A. B. Moubissi, K. Nakkeeran, P. Tchofo Dinda, and S. Wabnitz, “Average dispersion decreasing densely dispersion-managed fiber transmission systems,” IEEE Photon. Technol. Lett. 14, 1279–1281 (2002).
[CrossRef]

K. Nakkeeran, A. B. Moubissi, P. Tchofo Dinda, and S. Wabnitz, “Analytical method for designing dispersion-managed fiber systems,” Opt. Lett. 26, 1544–1546 (2001).
[CrossRef]

Wai, P. K. A.

K. Nakkeeran, Y. H. C. Kwan, and P. K. A. Wai, “Method to find the stationary solution parameters of chirped fiber grating compensated dispersion-managed fiber systems,” Opt. Commun. 215, 315–321 (2003).
[CrossRef]

Y. H. C. Kwan, P. K. A. Wai, and H. Y. Tam, “Effect of group-delay ripples on dispersion-managed soliton communication systems with chirped fiber gratings,” Opt. Lett. 26, 959–961 (2001).
[CrossRef]

J. N. Kutz and P. K. A. Wai, “Ideal amplifier spacing for reduction of Gordon-Haus jitters in dispersion-managed soliton communications,” Electron. Lett. 34, 522–523 (1998).
[CrossRef]

Wiesenfeld, J. M.

A. H. Gnauck, J. M. Wiesenfeld, L. D. Garrett, M. Eiselt, F. Forghieri, L. Arcangeli, B. Agogliata, V. Gusmeroli, and D. Scarano, “16×20 Gb/s, 400-km WDM transmission over NZDSF using a slope-compensating fiber-grating module,” IEEE Photon. Technol. Lett. 12, 437–439 (2000).
[CrossRef]

Yamada, E.

A. Sahara, T. Komukai, E. Yamada, and M. Nakazawa, “40 Gbits/s return-to-zero transmission over 500 km of standard fibre using chirped fibre Bragg gratings with small group delay ripples,” Electron. Lett. 37, 8–9 (2001).
[CrossRef]

E. Yamada, T. Imai, T. Komukai, and M. Nakazawa, “10 Gbits/s soliton transmission over 2900 km using 1.3 μm singlemode fibres and dispersion compensation using chirped fibre Bragg gratings,” Electron. Lett. 35, 728–729 (1999).
[CrossRef]

Yu, T.

Zhi, W.

P. Li, J. Shuisheng, Y. Fengping, N. Tigang, and W. Zhi, “Long-haul WDM system through conventional single mode optical fiber with dispersion compensation by chirped fiber Bragg grating,” Opt. Commun. 222, 169–178 (2003).
[CrossRef]

Electron. Lett. (4)

E. Yamada, T. Imai, T. Komukai, and M. Nakazawa, “10 Gbits/s soliton transmission over 2900 km using 1.3 μm singlemode fibres and dispersion compensation using chirped fibre Bragg gratings,” Electron. Lett. 35, 728–729 (1999).
[CrossRef]

A. Sahara, T. Komukai, E. Yamada, and M. Nakazawa, “40 Gbits/s return-to-zero transmission over 500 km of standard fibre using chirped fibre Bragg gratings with small group delay ripples,” Electron. Lett. 37, 8–9 (2001).
[CrossRef]

J. N. Kutz and P. K. A. Wai, “Ideal amplifier spacing for reduction of Gordon-Haus jitters in dispersion-managed soliton communications,” Electron. Lett. 34, 522–523 (1998).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54–55 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

A. H. Gnauck, J. M. Wiesenfeld, L. D. Garrett, M. Eiselt, F. Forghieri, L. Arcangeli, B. Agogliata, V. Gusmeroli, and D. Scarano, “16×20 Gb/s, 400-km WDM transmission over NZDSF using a slope-compensating fiber-grating module,” IEEE Photon. Technol. Lett. 12, 437–439 (2000).
[CrossRef]

A. B. Moubissi, K. Nakkeeran, P. Tchofo Dinda, and S. Wabnitz, “Average dispersion decreasing densely dispersion-managed fiber transmission systems,” IEEE Photon. Technol. Lett. 14, 1279–1281 (2002).
[CrossRef]

H. Chotard, Y. Painchaud, A. Mailloux, M. Morin, F. Trépanier, and M. Guy, “Group delay ripple of cascaded Bragg grating gain flattening filters,” IEEE Photon. Technol. Lett. 14, 1130–1132 (2002).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Commun. (3)

E. Poutrina and G. P. Agrawal, “Design rules for dispersion-managed soliton systems,” Opt. Commun. 206, 193–200 (2002).
[CrossRef]

K. Nakkeeran, Y. H. C. Kwan, and P. K. A. Wai, “Method to find the stationary solution parameters of chirped fiber grating compensated dispersion-managed fiber systems,” Opt. Commun. 215, 315–321 (2003).
[CrossRef]

P. Li, J. Shuisheng, Y. Fengping, N. Tigang, and W. Zhi, “Long-haul WDM system through conventional single mode optical fiber with dispersion compensation by chirped fiber Bragg grating,” Opt. Commun. 222, 169–178 (2003).
[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

S. K. Turitsyn and V. K. Mezentsev, “Chirped solitons with strong confinement in transmission links with in-line fiber Bragg gratings,” Opt. Lett. 23, 600–602 (1998).
[CrossRef]

A. Berntson, N. J. Doran, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900–902 (1998).
[CrossRef]

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

L. J. Richardson, W. Forysiak, and N. J. Doran, “Dispersion-managed soliton propagation in short-period dispersion maps,” Opt. Lett. 25, 1010–1012 (2000).
[CrossRef]

Y. H. C. Kwan, P. K. A. Wai, and H. Y. Tam, “Effect of group-delay ripples on dispersion-managed soliton communication systems with chirped fiber gratings,” Opt. Lett. 26, 959–961 (2001).
[CrossRef]

K. Nakkeeran, A. B. Moubissi, P. Tchofo Dinda, and S. Wabnitz, “Analytical method for designing dispersion-managed fiber systems,” Opt. Lett. 26, 1544–1546 (2001).
[CrossRef]

P. T. Dinda, K. Nakkeeran, and A. Labruyére, “Suppression of soliton self-frequency shift by upshifted filtering,” Opt. Lett. 27, 382–384 (2002).
[CrossRef]

M. Ibsen and R. Feced, “Fiber Bragg gratings for puredispersion-slope compensation,” Opt. Lett. 28, 980–982 (2003).
[CrossRef] [PubMed]

Phys. Lett. A (2)

V. K. Mezentsev and S. K. Turitsyn, “Solitons with Gaussian tails in dispersion-managed communication systems using gratings,” Phys. Lett. A 237, 37–42 (1997).
[CrossRef]

K. Nakkeeran, A. B. Moubissi, and P. Tchofo Dinda, “Analytical design of dispersion-managed fiber system with map strength 1.65,” Phys. Lett. A 308, 417–425 (2003).
[CrossRef]

Phys. Rev. E (1)

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

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[CrossRef]

Other (3)

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

S. G. Evangelides, N. S. Bergano, and C. R. Davidson, “Intersymbol interference induced by delay ripple in fiber Bragg gratings,” in Optical Fiber Communication Conference, Vol. 4 of 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 5–7.

C. Scheerer, C. Glingener, G. Fischer, M. Bohn, and W. Rosenkranz, “System impact of ripples in grating group delay,” in 1999 International Conference on Transparent Optical Networks (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 33–36.

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Figures (17)

Fig. 1
Fig. 1

Temporal pulse profile of solitons in grating-compensated DM soliton systems with GDR.

Fig. 2
Fig. 2

Maximum FWHMs used in the design of lossless CFG-compensated DM soliton systems for a map strength of 1.65 (solid line) and 3 (dashed line).

Fig. 3
Fig. 3

Grating dispersion (g) and map length (L) obtained by the analytical method for designing lossless CFG-compensated DM soliton systems for a map strength of 1.65 (solid line) and 3 (dashed line).

Fig. 4
Fig. 4

FWHM of the DM solitons obtained from the numerical averaging method at the middle of the fibers versus pulse energy E0 for lossless DM soliton systems.

Fig. 5
Fig. 5

Schematic of grating-compensated DM soliton systems with the dispersion map length equal to the amplifier spacing.

Fig. 6
Fig. 6

Grating dispersion (g) obtained by the analytical method for the design of lossy CFG-compensated DM soliton systems with the amplifier spacing equal to the map length for S=1.65 (solid line) and 3 (dashed line).

Fig. 7
Fig. 7

FWHM of the solitons at the beginning of the dispersion maps versus pulse energy Ein for lossy DM soliton systems. Map strength of (a) 1.65 and (b) 3. Solid and dashed curves represent the results obtained in the designed DM soliton systems without and with GDR in the gratings, respectively.

Fig. 8
Fig. 8

Schematic of grating-compensated DM soliton systems with the dispersion map length shorter than the amplifier spacing. The grating dispersion g¯ is i=14gi/4 and the fiber length L is i=14(Li1+Li2)/4.

Fig. 9
Fig. 9

Maximum FWHMs used in the design of lossy CFG-compensated DM soliton systems for a map strength of 1 (dotted line, lower), 1.65 (solid line), and 3 (dashed line).

Fig. 10
Fig. 10

FWHM of the solitons at the beginning of the dispersion maps versus pulse energy Ein for lossy DM soliton systems. Solid (lower), dotted, and dashed lines represent the results for map strengths of 1, 1.65, and 3, respectively.

Fig. 11
Fig. 11

FWHM of the DM solitons obtained from the numerical averaging method at the beginning of the dispersion maps versus pulse energy Ein for lossy DM soliton systems. Crosses and circles are data points for the designed DM soliton system without and with GDR in the gratings, respectively. The ripple amplitude and period of the GDR are 5 ps and 0.064 nm.

Fig. 12
Fig. 12

Effect of GDR in the gratings for lossy DM soliton systems. (a) FWHM of the DM solitons versus ripple amplitude for a constant ripple period of 0.064 nm. (b) FWHM of the DM solitons versus ripple period for a constant ripple amplitude of 5 ps. The pulse energy is 0.13 pJ.

Fig. 13
Fig. 13

Effect of ripple period and amplitude of the gratings on the ratio of the energy in the central peak (Ec) to total energy (E) for lossy DM soliton systems. (a) Energy ratio versus ripple period for a constant ripple period of 0.064 nm. (b) Energy ratio versus ripple amplitude for a constant ripple amplitude of 5 ps. The pulse energy is 0.13 pJ.

Fig. 14
Fig. 14

Effect of GDR in the gratings for lossy DM soliton systems. (a) Percentage of energy difference for a constant ripple period of 0.064 nm. (b) Percentage of energy difference for a constant ripple amplitude of 5 ps. The FWHM of the DM solitons is 5 ps.

Fig. 15
Fig. 15

Evolution of a Gaussian ansatz in the analytically designed CFG-compensated DM soliton system with GDR. The ripple amplitude and period are 5 ps and 0.064 nm, respectively. The pulse shapes are taken just after every five amplifiers.

Fig. 16
Fig. 16

Slow dynamics of the pulse width of the Gaussian ansatz propagating in the analytically designed DM soliton system with a ripple amplitude of 5 ps and a period of 0.064 nm in CFGs.

Fig. 17
Fig. 17

(a) Intensity (solid curve) and timing (dashed curve) Q factors versus propagation distance. The dotted line shows the value of Q=6. (b) Eye diagram of a particular random sequence after 7400 km.

Tables (3)

Tables Icon

Table 1 Fiber Lengths of the Dispersion Mapsa

Tables Icon

Table 2 Grating Dispersions of the Dispersion Mapsa

Tables Icon

Table 3 Average Values of Map Length and Grating Dispersiona

Equations (25)

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i ψz-β(z)2 2ψt2+γ|ψ|2ψ=0,
F(ω)=expigω22,
q(z, t)=x1 exp-(t-x2)2x32+ix4(t-x2)22+x5(t-x2)+x6,
dx3dz=-βx3x4,
dx4dz=βx42-4x34-2γE0x33,
x3out2=x3in2H,
x4out=1H x4in-gx4in2+4x3in4,
H=g2x4in2+4x3in4-2gx4in+1,
d2x3dz2=4β2x33+2βγE0x32.
12 dx3dz2=-2β2x32-2βγE0x3+c.
c=2β2x3min2+2βγE0x3min.
x4in=-1βx3max -4β2x3max2-22βγE0x3max+2c1/2.
g=2x3max4x4in4+x3max4x4in2.
L=2G-γβE0 ln(4cx3min-22γβE0)cc,
G=[cA+γβE0 ln(22cA+4cx3max-22γβE0)]/(2cc),
A=2cx3max2-22βγE0x3max-4β2.
S=|Lβ-g|τ02,
x3max=R|Lβ-g|S1/2,
x3max=(1.65)1/2τ0=(1.65×2 ln 2)1/2x3min.
x3max<(1.65×2 ln 2)1/2x3min[x3max>(1.65×2 ln 2)1/2x3min].
Ea1=1(Lin1/2) 0Lin1/2Ein1 exp(-αz)dz,
Ein1βa1=Ea1βa1
Ea2=1(Lin2/2) 0Lin2/2Ein2 exp(-αz)dz.
L=1m i=1m(Li1+Li2),
g¯=1m i=1mgi,

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