Abstract

We show that third-order dispersion, filtering, and amplification in a fiber Bragg grating dispersion-managed soliton system can lead to the formation of bound multisoliton solutions. We have found that these solutions appear due to the presence of nonsymmetrical terms in the transfer function of chirped gratings. We present an analytical approximation for the time delay of a chirped grating in the vicinity of the central frequency that takes into account higher-order dispersion terms. We also study the tolerance of these newly found multisoliton solutions to the presence of third-order dispersion in the fiber link and to random variations in the gratings parameters due to manufacture or variations in the operating conditions.

© 2001 Optical Society of America

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References

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  1. N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997).
    [Crossref]
  2. J. P. Gordon and L. F. Mollenauer, “Scheme for the characterization of dispersion-managed solitons,” Opt. Lett. 24, 223–225 (1999).
    [Crossref]
  3. D. S. Govan, W. Forysiak, and N. J. Doran, “Long-distance 40-Gbits soliton transmission over standard fiber by use of dispersion management,” Opt. Lett. 23, 1523–1525 (1998).
    [Crossref]
  4. M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical fiber transmission line,” Electron. Lett. 31, 216–217 (1995).
    [Crossref]
  5. C. Paré and P. A. Bélanger, “Antisymmetric soliton in a dispersion-managed system,” Opt. Commun. 168, 103–109 (1999).
    [Crossref]
  6. J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “Dispersion-managed solitons in the normal dispersion regime: A physical interpretation,” Opt. Lett. 23, 1674–1676 (1998).
    [Crossref]
  7. G. M. Carter, J. M. Jacob, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, “Timing-jitter reduction for a dispersion-managed soliton system: Experimental evidence,” Opt. Lett. 22, 513–515 (1997).
    [Crossref] [PubMed]
  8. T. I. Lakoba and R. S. Tasgal, “Novel mechanism of suppression of radiation by dispersion-managed solitons in randomly birefringent fibers,” Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CMF6, p. 31.
  9. S. Kumar and A. Hasegawa, “Quasi-soliton propagation in dispersion-managed optical fibers,” Opt. Lett. 22, 372–374 (1997).
    [Crossref] [PubMed]
  10. Y. Kodama, S. Kumar, and A. Maruta, “Chirped nonlinear pulse propagation in a dispersion-compensated system,” Opt. Lett. 22, 1689–1671 (1997).
    [Crossref]
  11. S. K. Turytsin and V. M. Mezentsev, “Chirped solitons with strong confinement in transmission links with in-line fiber Bragg gratings,” Opt. Lett. 23, 600–602 (1998).
    [Crossref]
  12. J. D. Ania-Castañón, P. Garcı́a-Fernández, and J. M. Soto-Crespo, “Stable multisoliton pulses in dispersion management with fiber Bragg gratings,” Opt. Lett. 25, 159–161 (2000).
    [Crossref]
  13. Y. Chen and H. A. Haus, “Dispersion-managed solitons in the net positive dispersion regime,” J. Opt. Soc. Am. B 16, 24–30 (1999).
    [Crossref]
  14. K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” IEEE J. Lightwave Technol. 15, 1263–1276 (1997).
    [Crossref]
  15. S. H. Yun, D. J. Richardson, and B. Y. Kim, “Interrogation of fiber grating sensor arrays with a wavelength-swept fiber laser,” Opt. Lett. 23, 843–845 (1998).
    [Crossref]
  16. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  17. F. Oullette, “Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides,” Opt. Lett. 12, 847–849 (1987).
    [Crossref]
  18. V. V. Afanasjev and N. N. Akhmediev, “Soliton interaction in nonequilibrium dynamical systems,” Phys. Rev. E 53, 6471–6475 (1996).
    [Crossref]
  19. N. N. Akmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
    [Crossref]
  20. J. M. Soto-Crespo and N. N. Akhmediev, “Multisoliton regime of pulse generation by lasers passively mode locked with a slow saturable absorber,” J. Opt. Soc. Am. B 16, 674–677 (1999).
    [Crossref]
  21. T. I. Lakoba and G. P. Agrawal, “Effects of third-order dispersion on dispersion-managed solitons,” J. Opt. Soc. Am. B 16, 1332–1343 (1999).
    [Crossref]
  22. A. Hasegawa, Y. Kodama, and Y. Kodama, Solitons in Optical Communications, Vol. 7 of Oxford Series in Optical and Imaging Science (Clarendon, Oxford, 1995).
  23. R. Kashyap and M. de Lacerda Rocha, “On the group delay characteristics of chirped fiber Bragg gratings,” Opt. Commun. 153, 19–22 (1998).
    [Crossref]
  24. R. Kashyap, Fiber Bragg Gratings, Optics and Photonics Series (Academic, San Diego, Calif., 1999).
  25. K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, “Influence of nonideal chirped fiber Bragg grating characteristics on dispersion cancellation,” IEEE Photon. Technol. Lett. 10, 1476–1478 (1998).
    [Crossref]
  26. E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

2000 (1)

1999 (5)

1998 (6)

1997 (6)

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” IEEE J. Lightwave Technol. 15, 1263–1276 (1997).
[Crossref]

G. M. Carter, J. M. Jacob, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, “Timing-jitter reduction for a dispersion-managed soliton system: Experimental evidence,” Opt. Lett. 22, 513–515 (1997).
[Crossref] [PubMed]

S. Kumar and A. Hasegawa, “Quasi-soliton propagation in dispersion-managed optical fibers,” Opt. Lett. 22, 372–374 (1997).
[Crossref] [PubMed]

Y. Kodama, S. Kumar, and A. Maruta, “Chirped nonlinear pulse propagation in a dispersion-compensated system,” Opt. Lett. 22, 1689–1671 (1997).
[Crossref]

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997).
[Crossref]

N. N. Akmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
[Crossref]

1996 (1)

V. V. Afanasjev and N. N. Akhmediev, “Soliton interaction in nonequilibrium dynamical systems,” Phys. Rev. E 53, 6471–6475 (1996).
[Crossref]

1995 (1)

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical fiber transmission line,” Electron. Lett. 31, 216–217 (1995).
[Crossref]

1987 (1)

Afanasjev, V. V.

V. V. Afanasjev and N. N. Akhmediev, “Soliton interaction in nonequilibrium dynamical systems,” Phys. Rev. E 53, 6471–6475 (1996).
[Crossref]

Agrawal, G. P.

Akhmediev, N. N.

Akmediev, N. N.

N. N. Akmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
[Crossref]

Ania-Castañón, J. D.

Ankiewicz, A.

N. N. Akmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
[Crossref]

Bélanger, P. A.

C. Paré and P. A. Bélanger, “Antisymmetric soliton in a dispersion-managed system,” Opt. Commun. 168, 103–109 (1999).
[Crossref]

Carter, G. M.

Chen, Y.

de Lacerda Rocha, M.

R. Kashyap and M. de Lacerda Rocha, “On the group delay characteristics of chirped fiber Bragg gratings,” Opt. Commun. 153, 19–22 (1998).
[Crossref]

Doran, N. J.

Durkin, M.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, “Influence of nonideal chirped fiber Bragg grating characteristics on dispersion cancellation,” IEEE Photon. Technol. Lett. 10, 1476–1478 (1998).
[Crossref]

Ennser, K.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, “Influence of nonideal chirped fiber Bragg grating characteristics on dispersion cancellation,” IEEE Photon. Technol. Lett. 10, 1476–1478 (1998).
[Crossref]

Forysiak, W.

Garci´a-Fernández, P.

Golovchenko, E. A.

Gordon, J. P.

Govan, D. S.

Hasegawa, A.

S. Kumar and A. Hasegawa, “Quasi-soliton propagation in dispersion-managed optical fibers,” Opt. Lett. 22, 372–374 (1997).
[Crossref] [PubMed]

A. Hasegawa, Y. Kodama, and Y. Kodama, Solitons in Optical Communications, Vol. 7 of Oxford Series in Optical and Imaging Science (Clarendon, Oxford, 1995).

Haus, H. A.

Hill, K. O.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” IEEE J. Lightwave Technol. 15, 1263–1276 (1997).
[Crossref]

Iannone, E.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

Ibsen, M.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, “Influence of nonideal chirped fiber Bragg grating characteristics on dispersion cancellation,” IEEE Photon. Technol. Lett. 10, 1476–1478 (1998).
[Crossref]

Jacob, J. M.

Kashyap, R.

R. Kashyap and M. de Lacerda Rocha, “On the group delay characteristics of chirped fiber Bragg gratings,” Opt. Commun. 153, 19–22 (1998).
[Crossref]

R. Kashyap, Fiber Bragg Gratings, Optics and Photonics Series (Academic, San Diego, Calif., 1999).

Kim, B. Y.

Knox, F. M.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997).
[Crossref]

Kodama, Y.

Y. Kodama, S. Kumar, and A. Maruta, “Chirped nonlinear pulse propagation in a dispersion-compensated system,” Opt. Lett. 22, 1689–1671 (1997).
[Crossref]

A. Hasegawa, Y. Kodama, and Y. Kodama, Solitons in Optical Communications, Vol. 7 of Oxford Series in Optical and Imaging Science (Clarendon, Oxford, 1995).

A. Hasegawa, Y. Kodama, and Y. Kodama, Solitons in Optical Communications, Vol. 7 of Oxford Series in Optical and Imaging Science (Clarendon, Oxford, 1995).

Kubota, H.

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical fiber transmission line,” Electron. Lett. 31, 216–217 (1995).
[Crossref]

Kumar, S.

Lakoba, T. I.

T. I. Lakoba and G. P. Agrawal, “Effects of third-order dispersion on dispersion-managed solitons,” J. Opt. Soc. Am. B 16, 1332–1343 (1999).
[Crossref]

T. I. Lakoba and R. S. Tasgal, “Novel mechanism of suppression of radiation by dispersion-managed solitons in randomly birefringent fibers,” Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CMF6, p. 31.

Laming, R. I.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, “Influence of nonideal chirped fiber Bragg grating characteristics on dispersion cancellation,” IEEE Photon. Technol. Lett. 10, 1476–1478 (1998).
[Crossref]

Maruta, A.

Matera, F.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

Mecozzi, A.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

Meltz, G.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” IEEE J. Lightwave Technol. 15, 1263–1276 (1997).
[Crossref]

Menyuk, C. R.

Mezentsev, V. M.

Mollenauer, L. F.

Nakazawa, M.

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical fiber transmission line,” Electron. Lett. 31, 216–217 (1995).
[Crossref]

Nijhof, J. H. B.

Oullette, F.

Paré, C.

C. Paré and P. A. Bélanger, “Antisymmetric soliton in a dispersion-managed system,” Opt. Commun. 168, 103–109 (1999).
[Crossref]

Pilipetskii, A. N.

Richardson, D. J.

Settembre, M.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

Smith, N. J.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997).
[Crossref]

Soto-Crespo, J. M.

Tasgal, R. S.

T. I. Lakoba and R. S. Tasgal, “Novel mechanism of suppression of radiation by dispersion-managed solitons in randomly birefringent fibers,” Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CMF6, p. 31.

Turytsin, S. K.

Yun, S. H.

Zervas, M. N.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, “Influence of nonideal chirped fiber Bragg grating characteristics on dispersion cancellation,” IEEE Photon. Technol. Lett. 10, 1476–1478 (1998).
[Crossref]

Electron. Lett. (1)

M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical fiber transmission line,” Electron. Lett. 31, 216–217 (1995).
[Crossref]

IEEE J. Lightwave Technol. (1)

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” IEEE J. Lightwave Technol. 15, 1263–1276 (1997).
[Crossref]

IEEE Photon. Technol. Lett. (1)

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, and R. I. Laming, “Influence of nonideal chirped fiber Bragg grating characteristics on dispersion cancellation,” IEEE Photon. Technol. Lett. 10, 1476–1478 (1998).
[Crossref]

J. Lightwave Technol. (1)

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808–1822 (1997).
[Crossref]

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

Opt. Commun. (2)

R. Kashyap and M. de Lacerda Rocha, “On the group delay characteristics of chirped fiber Bragg gratings,” Opt. Commun. 153, 19–22 (1998).
[Crossref]

C. Paré and P. A. Bélanger, “Antisymmetric soliton in a dispersion-managed system,” Opt. Commun. 168, 103–109 (1999).
[Crossref]

Opt. Lett. (10)

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “Dispersion-managed solitons in the normal dispersion regime: A physical interpretation,” Opt. Lett. 23, 1674–1676 (1998).
[Crossref]

G. M. Carter, J. M. Jacob, C. R. Menyuk, E. A. Golovchenko, and A. N. Pilipetskii, “Timing-jitter reduction for a dispersion-managed soliton system: Experimental evidence,” Opt. Lett. 22, 513–515 (1997).
[Crossref] [PubMed]

S. Kumar and A. Hasegawa, “Quasi-soliton propagation in dispersion-managed optical fibers,” Opt. Lett. 22, 372–374 (1997).
[Crossref] [PubMed]

Y. Kodama, S. Kumar, and A. Maruta, “Chirped nonlinear pulse propagation in a dispersion-compensated system,” Opt. Lett. 22, 1689–1671 (1997).
[Crossref]

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

J. D. Ania-Castañón, P. Garcı́a-Fernández, and J. M. Soto-Crespo, “Stable multisoliton pulses in dispersion management with fiber Bragg gratings,” Opt. Lett. 25, 159–161 (2000).
[Crossref]

F. Oullette, “Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides,” Opt. Lett. 12, 847–849 (1987).
[Crossref]

J. P. Gordon and L. F. Mollenauer, “Scheme for the characterization of dispersion-managed solitons,” Opt. Lett. 24, 223–225 (1999).
[Crossref]

D. S. Govan, W. Forysiak, and N. J. Doran, “Long-distance 40-Gbits soliton transmission over standard fiber by use of dispersion management,” Opt. Lett. 23, 1523–1525 (1998).
[Crossref]

S. H. Yun, D. J. Richardson, and B. Y. Kim, “Interrogation of fiber grating sensor arrays with a wavelength-swept fiber laser,” Opt. Lett. 23, 843–845 (1998).
[Crossref]

Phys. Rev. E (1)

V. V. Afanasjev and N. N. Akhmediev, “Soliton interaction in nonequilibrium dynamical systems,” Phys. Rev. E 53, 6471–6475 (1996).
[Crossref]

Phys. Rev. Lett. (1)

N. N. Akmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).
[Crossref]

Other (5)

A. Hasegawa, Y. Kodama, and Y. Kodama, Solitons in Optical Communications, Vol. 7 of Oxford Series in Optical and Imaging Science (Clarendon, Oxford, 1995).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

T. I. Lakoba and R. S. Tasgal, “Novel mechanism of suppression of radiation by dispersion-managed solitons in randomly birefringent fibers,” Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CMF6, p. 31.

R. Kashyap, Fiber Bragg Gratings, Optics and Photonics Series (Academic, San Diego, Calif., 1999).

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

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Figures (10)

Fig. 1
Fig. 1

Reflectivity (dashed curve) and time delay (solid curve) corresponding to one of the chirped FBGs used for periodic dispersion compensation.

Fig. 2
Fig. 2

Evolution of a pulse pair with initial zero phase difference over a distance of 60 Mm.

Fig. 3
Fig. 3

Evolution of a pulse pair over a single period.

Fig. 4
Fig. 4

Evolution of the signal frequency during propagation.

Fig. 5
Fig. 5

Time delay of a FBG under the approximation of period variation for the ripples (thin curve), and numerically obtained from the coupled mode equations (thick curve). The simulated time delay is vertically displaced for comparison.

Fig. 6
Fig. 6

Evolution in the interaction plane of a pulse pair, initially identical and in phase, with β3=-0.063 ps3/km (continuous curve) and β3=0.063 ps3/km (dotted curve). The common origin of both trajectories is marked in the figure with a black dot. The open square signals the situation for the β3<0 case at 60 Mm, while the open circle shows the situation for the case β3>0 at 36.4 Mm, just before the collapse of the signal. ρ and θ are, respectively, the time distance and the phase difference between peaks.

Fig. 7
Fig. 7

Evolution of a soliton pair in the interaction plane through 60 Mm with a random variation of the grating length of up to 5%. The black dot represents the origin, while the open circle represents the situation at a distance of 60 Mm.

Fig. 8
Fig. 8

Same as Fig. 7, but with a random variation of the grating coupling constant κ of up to 5%.

Fig. 9
Fig. 9

Same as Fig. 7, but with a random variation of the grating chirp parameter F of up to 5%.

Fig. 10
Fig. 10

Evolution in the interaction plane of a pulse pair through 60 Mm for the case β3=0.063 ps3/km-1 with a random variation of 1% for L and F and of 1.5% for κ. The origin is represented with a black dot, ρ0 and θ0 are the coordinates of the bound state.

Tables (2)

Tables Icon

Table 1 Parameters of the Simulation

Tables Icon

Table 2 Robustness Against Grating Parameter Variationsa

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

i Ez=-i2ΓE+12β2 2ET2-i6β3 3ET3-γ|E|2E,
E(0, T)
=P1/2k=0n-1 exp-(1+iC)(T+kτ0)22T02+iΦk,
dRdz+iδR=-iκ(z)S exp-iFzl2,
dSdz-iδS=iκ(z)R expiFzl2,
τ±(ω)=a1ω+a2+b sin2πΩFp0(ωΩF)ω,
θ+(ω)=τ+(ω)dω=c+a2ω+a12ω2+b(p0ΩF)1/2C¯2ω-ΩF(p0ΩF)1/2sinπΩF2p0-b(p0ΩF)1/2S¯2ω-ΩF(p0ΩF)1/2cosπΩF2p0,
θ-(ω)=τ-(ω)dω=c+a2ω+a12ω2-b(p0ΩF)1/2C¯2ω+ΩF(p0ΩF)1/2sinπΩF2p0+b(p0ΩF)1/2S¯2ω+ΩF(p0ΩF)1/2cosπΩF2p0,
S¯(x)=π21/20x sin t2dt,C¯(x)=π21/20x cos t2dt.
θ+(ω)θ0+a2ω+12 a1-2πbp0ω2-2πb3p0ΩFω3,
θ-(ω)θ0+a2ω+12 a1-2πbp0ω2+2πb3p0ΩFω3,
θ0=c+b (p0ΩF)1/22 cosπΩF2p0S¯ΩFp01/2-sinπΩF2p0C¯ΩFp01/2.
C3(ω)±=2πb3p0ΩFω3.
C3(ω)±=β3±6Lgω3,
β3±=4πbp0ΩFLg

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