Abstract

We propose a high-repetition-rate soliton-train source based on adiabatic compression of a dual-frequency optical signal in nonuniform fiber Bragg gratings. As the signal propagates through the grating, it is reshaped into a train of Bragg solitons whose repetition rate is predetermined by the frequency of initial sinusoidal modulation. We develop an approximate analytical model to predict the width of compressed soliton-like pulses and to provide conditions for adiabatic compression. We demonstrate numerically the formation of a 40-GHz train of 2.6-ps pulses and find that the numerical results are in good agreement with the predictions of our analytical model. The scheme relies on the dispersion provided by the grating, which can be up to six orders of magnitude larger than of fiber and makes it possible to reduce the fiber length significantly.

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  1. J. J. Veselka and S. K. Korotky, "Pulse generation for soliton systems using lithium niobate modulators," IEEE J. Sel. Top. Quantum Electron. 2, 300-310 (1996).
    [CrossRef]
  2. A. Hasegawa, "Generation of a train of soliton pulses by induced modulational instability in optical fibers," Opt. Lett. 9, 288-290 (1984).
    [CrossRef] [PubMed]
  3. K. Tai, A. Tomita, J. L. Jewell and A. Hasegawa, "Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability," Appl. Phys. Lett. 49, 236-238 (1986).
    [CrossRef]
  4. E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov and S. V. Chernikov, "Generation of a train of fundamental solitons at a high repetition rate in optical fibers," Opt. Lett. 14, 1008-1010 (1989).
    [CrossRef] [PubMed]
  5. V. A. Bogatyrev, M. M. Bubnov, E. M. Dianov, A. S. Kurkov, P. V. Mamyshev, A. M. Prokhorov, S. D. Rumyantsev, V. A. Semenov, S. L. Semenov, A. A. Sysoliatin, S. V. Chernikov, A. N. Guryanov, G. G. Devyatykh and S. I. Miroshnichenko, "A single-mode fiber with chromatic dispersion varying along the length," J. Lightwave Technol. 9, 561-566 (1991).
    [CrossRef]
  6. P. V. Mamyshev, S. V. Chernikov and E. M. Dianov, "Generation of fundamental soliton trains for high-bit- rate optical fiber communication lines," IEEE J. Quantum Electron. 27, 2347-2355 (1991).
    [CrossRef]
  7. S.V. Chernikov, D.J. Richardson, R.I. Laming, E.M. Dianov and D.N. Payne, "70 Gbit/s fiber based source of fundamental solitons at 1550nm," Electron. Lett. 28, 1210-1212 (1992).
    [CrossRef]
  8. M. Romagnoli, S. Trillo and S. Wabnitz, "Soliton switching in nonlinear couplers," Optical and Quantum Electon. 24, S1237-S1267 (1992).
    [CrossRef]
  9. S. V. Chernikov, J. R. Taylor and R. Kashyap, "Comblike dispersion-profiled fiber for soliton pulse train generation," Opt. Lett. 19, 539-541 (1994).
    [CrossRef] [PubMed]
  10. E. A. Swanson and S. R. Chinn, "23-GHz and 123-GHz soliton pulse generation using two cw lasers and standard single-mode fiber," IEEE Photon. Technol. Lett. 6, 796-799 (1994).
    [CrossRef]
  11. N. Akhmediev and A. Ankiewicz, "Generation of a train of solitons with arbitrary phase difference between neighboring solitons," Opt. Lett. 19, 545-547 (1994).
    [CrossRef] [PubMed]
  12. B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhozi, Z. Brodzeli and F. Ouellette, "Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission," Electron. Lett. 32, 1610-1611 (1996).
    [CrossRef]
  13. N. M. Litchinitser, B. J. Eggleton and D. B. Patterson, "Fiber Bragg gratings for dispersion compensation in transmission: Theoretical model and design criterion for nearly ideal pulse compression," J. Lightwave Technol. 15, 1303-1313 (1997).
    [CrossRef]
  14. G. Lenz and B. J. Eggleton, "Adiabatic Bragg soliton compression in nonuniform grating structures," J. Opt. Soc. Am. B, in press.
  15. A. Asseh, H. Storoy, B. E. Sahlgren, S. Sandgren and R. A. H. Stubbe, "A writing technique for long fiber Bragg gratings with complex reflectivity profiles," J. Lightwave Technol. 15, 1419-1423 (1997).
    [CrossRef]
  16. L. Dong, M. J. Cole, M. Durkin, M. Ibsen and R. I. Laming, "40Gbit/s 1.55um transmission over 109km of non-dispersion-shifted fiber with long continuously chirped fiber gratings," in 1996 Opt. Fiber Commun. Conf. (OFC96), postdeadline paper PD6.
  17. R. E. Slusher, B. J. Eggleton, C. M. de Sterke and T. A. Strasser, "Nonlinear pulse reflections from chirped fiber gratings," Opt. Express 3, (1998). http://epubs.osa.org/oearchive/source/6996.htm
    [CrossRef] [PubMed]
  18. C. M. de Sterke and J. E. Sipe, in Progress in Optics XXXIII, ed. by E. Wolf (North-Holand, Amsterdam, 1994), pp. 203-260.
  19. A. B. Aceves and S. Wabnitz, "Self-induced transparency solitons in nonlinear refractive periodic media," Phys. Lett. A 141, 37-42 (1989).
    [CrossRef]
  20. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug and J. E. Sipe, "Bragg grating solitons," Phys. Rev. Lett. 76, 1627-1630 (1996).
    [CrossRef] [PubMed]
  21. D. Taverner, N. G. R. Broderick, D. T. Richardson , R. I. Laming and M. Ibsen, "Nonlinear self-switching and multiple gap-soliton formation in a fiber Bragg grating," Opt. Lett. 23, 328-330 (1998).
    [CrossRef]
  22. B. J. Eggleton, C. M. de Sterke and R. E. Slusher, "Bragg solitons in the nonlinear Schrödinger limit: theory and experiment," submitted to J. Opt. Soc. Am. B (1998).
  23. C. M. de Sterke and J. E. Sipe, "Coupled modes and the nonlinear Schrödinger equation," Phys. Rev. A 42, 550-555 (1990).
    [CrossRef]
  24. C. M. de Sterke and B. J. Eggleton, "Bragg solitons and the nonlinear Schrödinger equation," Phys. Rev. E., in press.
  25. B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser and R. E. Slusher, "Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings," Opt. Commun. 149, 267-271 (1998).
    [CrossRef]
  26. G. P. Agrawal, Nonlinear Fiber Optics, (Academic, New York, 1995).
  27. J. P. Gordon, "Interaction forces among solitons in optical fibers," Opt. Lett. 8, 596-598 (1983).
    [CrossRef] [PubMed]
  28. M. Asobe, "Nonlinear optical properties of chalcogenide glass fibers and their application to all-optical switching," Opt. Fiber Technol. 3, 142-148 (1997).
    [CrossRef]

Other (28)

J. J. Veselka and S. K. Korotky, "Pulse generation for soliton systems using lithium niobate modulators," IEEE J. Sel. Top. Quantum Electron. 2, 300-310 (1996).
[CrossRef]

A. Hasegawa, "Generation of a train of soliton pulses by induced modulational instability in optical fibers," Opt. Lett. 9, 288-290 (1984).
[CrossRef] [PubMed]

K. Tai, A. Tomita, J. L. Jewell and A. Hasegawa, "Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability," Appl. Phys. Lett. 49, 236-238 (1986).
[CrossRef]

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov and S. V. Chernikov, "Generation of a train of fundamental solitons at a high repetition rate in optical fibers," Opt. Lett. 14, 1008-1010 (1989).
[CrossRef] [PubMed]

V. A. Bogatyrev, M. M. Bubnov, E. M. Dianov, A. S. Kurkov, P. V. Mamyshev, A. M. Prokhorov, S. D. Rumyantsev, V. A. Semenov, S. L. Semenov, A. A. Sysoliatin, S. V. Chernikov, A. N. Guryanov, G. G. Devyatykh and S. I. Miroshnichenko, "A single-mode fiber with chromatic dispersion varying along the length," J. Lightwave Technol. 9, 561-566 (1991).
[CrossRef]

P. V. Mamyshev, S. V. Chernikov and E. M. Dianov, "Generation of fundamental soliton trains for high-bit- rate optical fiber communication lines," IEEE J. Quantum Electron. 27, 2347-2355 (1991).
[CrossRef]

S.V. Chernikov, D.J. Richardson, R.I. Laming, E.M. Dianov and D.N. Payne, "70 Gbit/s fiber based source of fundamental solitons at 1550nm," Electron. Lett. 28, 1210-1212 (1992).
[CrossRef]

M. Romagnoli, S. Trillo and S. Wabnitz, "Soliton switching in nonlinear couplers," Optical and Quantum Electon. 24, S1237-S1267 (1992).
[CrossRef]

S. V. Chernikov, J. R. Taylor and R. Kashyap, "Comblike dispersion-profiled fiber for soliton pulse train generation," Opt. Lett. 19, 539-541 (1994).
[CrossRef] [PubMed]

E. A. Swanson and S. R. Chinn, "23-GHz and 123-GHz soliton pulse generation using two cw lasers and standard single-mode fiber," IEEE Photon. Technol. Lett. 6, 796-799 (1994).
[CrossRef]

N. Akhmediev and A. Ankiewicz, "Generation of a train of solitons with arbitrary phase difference between neighboring solitons," Opt. Lett. 19, 545-547 (1994).
[CrossRef] [PubMed]

B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhozi, Z. Brodzeli and F. Ouellette, "Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission," Electron. Lett. 32, 1610-1611 (1996).
[CrossRef]

N. M. Litchinitser, B. J. Eggleton and D. B. Patterson, "Fiber Bragg gratings for dispersion compensation in transmission: Theoretical model and design criterion for nearly ideal pulse compression," J. Lightwave Technol. 15, 1303-1313 (1997).
[CrossRef]

G. Lenz and B. J. Eggleton, "Adiabatic Bragg soliton compression in nonuniform grating structures," J. Opt. Soc. Am. B, in press.

A. Asseh, H. Storoy, B. E. Sahlgren, S. Sandgren and R. A. H. Stubbe, "A writing technique for long fiber Bragg gratings with complex reflectivity profiles," J. Lightwave Technol. 15, 1419-1423 (1997).
[CrossRef]

L. Dong, M. J. Cole, M. Durkin, M. Ibsen and R. I. Laming, "40Gbit/s 1.55um transmission over 109km of non-dispersion-shifted fiber with long continuously chirped fiber gratings," in 1996 Opt. Fiber Commun. Conf. (OFC96), postdeadline paper PD6.

R. E. Slusher, B. J. Eggleton, C. M. de Sterke and T. A. Strasser, "Nonlinear pulse reflections from chirped fiber gratings," Opt. Express 3, (1998). http://epubs.osa.org/oearchive/source/6996.htm
[CrossRef] [PubMed]

C. M. de Sterke and J. E. Sipe, in Progress in Optics XXXIII, ed. by E. Wolf (North-Holand, Amsterdam, 1994), pp. 203-260.

A. B. Aceves and S. Wabnitz, "Self-induced transparency solitons in nonlinear refractive periodic media," Phys. Lett. A 141, 37-42 (1989).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug and J. E. Sipe, "Bragg grating solitons," Phys. Rev. Lett. 76, 1627-1630 (1996).
[CrossRef] [PubMed]

D. Taverner, N. G. R. Broderick, D. T. Richardson , R. I. Laming and M. Ibsen, "Nonlinear self-switching and multiple gap-soliton formation in a fiber Bragg grating," Opt. Lett. 23, 328-330 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke and R. E. Slusher, "Bragg solitons in the nonlinear Schrödinger limit: theory and experiment," submitted to J. Opt. Soc. Am. B (1998).

C. M. de Sterke and J. E. Sipe, "Coupled modes and the nonlinear Schrödinger equation," Phys. Rev. A 42, 550-555 (1990).
[CrossRef]

C. M. de Sterke and B. J. Eggleton, "Bragg solitons and the nonlinear Schrödinger equation," Phys. Rev. E., in press.

B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser and R. E. Slusher, "Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings," Opt. Commun. 149, 267-271 (1998).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, (Academic, New York, 1995).

J. P. Gordon, "Interaction forces among solitons in optical fibers," Opt. Lett. 8, 596-598 (1983).
[CrossRef] [PubMed]

M. Asobe, "Nonlinear optical properties of chalcogenide glass fibers and their application to all-optical switching," Opt. Fiber Technol. 3, 142-148 (1997).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Generation of a high-repetition-rate soliton train based on adiabatic compression in a nonuniform fiber Bragg grating. The stop-band width varies along the grating because of changes in the index modulation depth.

Fig. 2.
Fig. 2.

Axial variations of κ(z) (black line) and |β2eff(z)| (red line) inside the grating.

Fig. 3.
Fig. 3.

Input sinusoidal signal (upper plot), and soliton train generated at the grating output (lower plot).

Fig. 4.
Fig. 4.

Input dual-frequency signal spectrum (upper plot) and output spectrum of the soliton train (lower plot).

Equations (19)

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i E + z + i 1 V E + t + κ E + Γ s E + 2 E + + 2 Γ × E 2 E + = 0 ,
i E z + i 1 V E t + κ E + + Γ s E 2 E + 2 Γ × E + 2 E = 0 .
i A z 1 2 β 2 2 A t 2 + Γ A 2 A = 0 .
β 2 = 1 V 2 1 γ 2 v 3 δ , Γ = Γ 0 3 v 2 2 v ,
N 2 = L D L NL = Γ I in T 2 β 2 = E S Γ 2 σ eff T | β 2 = 1 ,
E S π n 2 σ eff λ T ( z ) β 2 eff ( z ) = 1 ,
β 2 eff = 2 V 2 ( 3 v 2 ) γ 2 v 2 δ .
T ( L ) = T ( 0 ) β 2 eff ( L ) β 2 eff ( 0 ) .
ξ = 1 T 2 ( 0 ) 0 z β 2 ( z ) d z , F = T ( 0 ) Γ ( z ) β 2 ( z ) A ( z ) ,
i F ξ + 1 2 2 F τ 2 + F 2 F = i g ( ξ ) F ,
g ( ξ ) = 1 2 Γ Γ ξ 1 2 β 2 β 2 ξ = 1 2 β 2 eff β 2 eff ξ .
G eff ( ξ ) = exp ( 2 0 ξ g ( ξ ) ) .
G eff ( z ) = β 2 ( 0 ) β 2 ( z ) Γ ( z ) Γ ( 0 ) = β 2 eff ( 0 ) β 2 eff ( z ) .
T ( L ) = T ( 0 ) G eff ( L ) ,
g L D 1 .
L D 2 L ln ( β 2 eff ( 0 ) β 2 eff ( z ) ) 1 .
A ( t , 0 ) = A 0 sin ( π t T S ) ,
κ ( z ) = κ 0 ( 1 C z ) ,
β 2 eff ( z ) = 2 κ 2 ( z ) δ V 2 [ 2 δ 2 + κ 2 ( z ) ] [ δ 2 κ 2 ( z ) ] .

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